Hydro Max

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HydromaxWindows Version 13

User Manual

© Formation Design Systems Pty Ltd 1984 - 2007

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License and CopyrightHydromax Program© 1985-2007 Formation Design Systems.

Hydromax is copyrighted and all rights are reserved. The license for use is granted to the purchaser by Formation Design Systems as a single user license and does not permit the program to be used on more than one machine at one time. Copying of the program toother media is permitted for back-up purposes as long as all copies remain in the

possession of the purchaser.

Hydromax User Manual© 2007 Formation Design Systems.All rights reserved. No part of this publication may be reproduced, transmitted,transcribed, stored in a retrieval system, or translated into any language in any form or

by any means, without the written permission of Formation Design Systems. FormationDesign Systems reserves the right to revise this publication from time to time and to

make changes to the contents without obligation to notify any person or organization ofsuch changes.

DISCLAIMER OF WARRANTY Neither Formation Design Systems, nor the author of this program and documentationare liable or responsible to the purchaser or user for loss or damage caused, or alleged to

be caused, directly or indirectly by the software and its attendant documentation,including (but not limited to) interruption on service, loss of business, or anticipatory

profits. No Formation Design Systems’ distributor, agent, or employee is authorized tomake any modification, extension, or addition to this warranty.

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Contents

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ContentsLicense and Copyright.... ...................................................................................................... iii Contents.. .............................................................................................................................. v

About this Manual .. .............................................................................................................. 1 Chapter 1 Introduction.. ........................................................................................................ 3 Chapter 2 Quickstart.. ........................................................................................................... 7

Upright Hydrostatics Quickstart .. ............................................................................ 8 Large Angle Stability Quickstart .. ........................................................................... 9 Equilibrium Condition Quickstart... ....................................................................... 10 Specified Condition Quickstart ... ........................................................................... 11 KN Values Quickstart ... ......................................................................................... 12 Limiting KG Quickstart ... ...................................................................................... 13 Floodable Length Quickstart... ............................................................................... 14 Longitudinal Strength Quickstart... ........................................................................ 15 Tank Calibrations Quickstart ... .............................................................................. 16

Chapter 3 Using Hydromax... ............................................................................................... 17 Getting Started ... .................................................................................................... 18 Installing Hydromax ... ................................................................................. 18 Starting Hydromax... .................................................................................... 18

Hydromax Model ... ................................................................................................ 19 Preparing a Design in Maxsurf ... ................................................................. 19 Opening a New Design ... ............................................................................. 22 Opening an Existing Hydromax Design File ... ............................................ 23 Updating the Hydromax Model ... ................................................................ 25 Hydromax Sections Forming... .................................................................... 25 Checking the Hydromax model ... ................................................................ 29 Setting Initial Conditions ... .......................................................................... 31 Working with Loadcases... ........................................................................... 33 Modelling Compartments ... ......................................................................... 40 Forming Compartments ... ............................................................................ 52 Compartment Types... .................................................................................. 55 Sounding Pipes ... ......................................................................................... 57 Damage Case Definition... ........................................................................... 58 Key Points (e.g. Down Flooding Points) ... .................................................. 60 Margin Line Points ... ................................................................................... 62 Modulus Points and Allowable Shears and Moments ... .............................. 63 Floodable Length Bulkheads ... .................................................................... 63 Stability Criteria... ........................................................................................ 63

Analysis Types ... .................................................................................................... 64 Upright Hydrostatics... ................................................................................. 65 Large Angle Stability... ................................................................................ 67 Equilibrium Analysis ... ................................................................................ 70 Specified Conditions... ................................................................................. 73 KN Values Analysis... .................................................................................. 75 Limiting KG... .............................................................................................. 78 Floodable Length ... ...................................................................................... 81 Longitudinal Strength ... ............................................................................... 84 Tank Calibrations... ...................................................................................... 87 Starting and Stopping Analyses... ................................................................ 90 Batch Analysis ... .......................................................................................... 91

Analysis Settings... ................................................................................................. 94

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Heel... ........................................................................................................... 94 Trim ... .......................................................................................................... 95 Draft... .......................................................................................................... 96 Displacement ... ............................................................................................ 96 Specified Conditions... ................................................................................. 97 Permeability... .............................................................................................. 97 Tolerances... ................................................................................................. 98

Analysis Environment Options .... ........................................................................ 100 Fluids Analysis Methods .... ....................................................................... 100 Density of Fluids.... .................................................................................... 101 Waveform .... .............................................................................................. 103 Grounding.... .............................................................................................. 104 Hog and Sag.... ........................................................................................... 105 Stability Criteria.... ..................................................................................... 106 Damage.... .................................................................................................. 106

Analysis Output.... ................................................................................................ 107 Reporting .... ............................................................................................... 108

Copying & Printing.... ................................................................................ 109 Select View from Analysis Data.... ............................................................ 110 Saving the Hydromax Design .... ................................................................ 111 Exporting .... ............................................................................................... 112

Chapter 4 Stability Criteria.... ............................................................................................... 113 Criteria Concepts.... .............................................................................................. 114 Criteria Procedures.... ........................................................................................... 118

Starting the Criteria dialog.... ..................................................................... 118 Resizing the Criteria dialog .... ................................................................... 119 Working with Criteria.... ............................................................................ 119 Editing Criteria .... ...................................................................................... 122 Working with Criteria Libraries.... ............................................................. 123

Criteria Results.... ................................................................................................. 126 Nomenclature .... ................................................................................................... 128

Definitions of GZ curve features .... ........................................................... 128 Glossary .... ................................................................................................. 131

Chapter 5 Hydromax Reference.... ....................................................................................... 133 Windows .... .......................................................................................................... 134

View Window .... ........................................................................................ 134 Loadcase Window.... .................................................................................. 135 Damage Window .... ................................................................................... 136 Input Window .... ........................................................................................ 136 Results Window.... ..................................................................................... 138 Graph Window.... ....................................................................................... 140 Report Window.... ...................................................................................... 143

Toolbars .... ........................................................................................................... 147 Menus.... ............................................................................................................... 149

File Menu.... ............................................................................................... 149 Edit Menu .... .............................................................................................. 150 View Menu .... ............................................................................................ 152 Analysis Menu .... ....................................................................................... 153 Case Menu .... ............................................................................................. 156 Display Menu.... ......................................................................................... 157 Window Menu .... ....................................................................................... 159 Help Menu .... ............................................................................................. 159

Appendix A Calculation of Form Parameters .... ................................................................. 161

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Definition and calculation of form parameters .... ...................................... 161 Potential for errors in hydrostatic calculations .... ...................................... 168 Reference Designs .... ................................................................................. 169 Reference Calculations .... .......................................................................... 170

Appendix B Criteria file format .... ...................................................................................... 172 Appendix C Criteria Help.... ................................................................................................ 176

Parent Heeling Arms.... ........................................................................................ 177 Heeling Arm Definition .... ......................................................................... 177

Parent Heeling Moments.... .................................................................................. 184 Parent Stability Criteria.... .................................................................................... 186

Criteria at Equilibrium.... ........................................................................... 186 GZ Curve Criteria (non-heeling arm) .... .................................................... 187 Heeling arm criteria (xRef).... .................................................................... 203 Heeling arm criteria .... ............................................................................... 203 Multiple heeling arm criteria .... ................................................................. 220 Heeling arm, combined criteria.... .............................................................. 226 Other combined criteria .... ......................................................................... 230

Appendix D Specific Criteria .... ........................................................................................... 233 Heeling arms for specific criteria - Note on unit conversion.... ................. 233 ISO 12217: Small craft – stability and buoyancy assessment andcategorisation..... ........................................................................................ 239

Appendix E Reference Tables .... ......................................................................................... 242 File Extension Reference Table.... ............................................................. 242 Analysis settings reference table.... ............................................................ 243

Index.... ................................................................................................................................. 244

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About this Manual

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About this ManualThis manual describes how to use Hydromax to perform hydrostatic and stabilityanalyses on you Maxsurf design.

Chapter 1 Introduction Contains a description of Hydromax functionality and its interface to Maxsurf

Chapter 2 Quickstart Gives a quick walk through the analysis tools available in Hydromax.

Chapter 3 Using Hydromax Explains how to use Hydromax' powerful floatation and hydrostatic analysis routines to

best advantage.

Chapter 4 Stability Criteria

Gives details of the stability criteria that may be evaluated with Hydromax.

Chapter 5 Hydromax Reference Gives details of Hydromax' windows and each of Hydromax' menu commands.

If you are unfamiliar with Microsoft Windows ® interface, please read the owner'smanual supplied with your computer. This will introduce you to commonly used termsand the basic techniques for using any computer program.

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Chapter 1 Introduction

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Chapter 1 IntroductionHydromax is a hydrostatics, stability and longitudinal strength program specificallydesigned to work with Maxsurf. Hydromax adds extra information to the Maxsurf

surface model. This includes: compartments and key points such as downflooding pointsand margin line.

Hydromax’ analysis tools enable a wide range of hydrostatic and stability characteristicsto be determined for your Maxsurf design. A number of environmental setting optionsand modifiers add further analysis capabilities to Hydromax.

Hydromax is designed in a logical manner, which makes it easy to use. The followingsteps are followed when performing an analysis:

• Input model

• Analysis type selection

• Analysis sett ings• Environment options

• Criteria specification and selection

• Run analysis

• Output

Hydromax operates in the same graphical environment as Maxsurf; the model can bedisplayed using hull contour lines, rendering or transparent rendering. This allows visualchecking of compartments and shows the orientation of the vessel during analysis.

Input Model

Maxsurf design files may be opened directly into Hydromax, eliminating the need fortime-consuming digitising of drawings or hand typing of offsets. This direct transfer

preserves the three-dimensional accuracy of the Maxsurf model.

Tanks can be defined and calibrated for capacity, centre of gravity and free surfacemoment. Tanks and compartments can be flooded for the purpose of calculating theeffects of damage.

A number of loadcases can be created. The loadcase allows static weights and tank-fillings to be specified and calculates the corresponding weights and centres of gravity aswell as the total weight and centre of gravity of the vessel under the specified loadingcondition.

Other input consists of: tank sounding pipes; key points, such as downflooding points,immersion and embarkation points; margin lines and section modulus.

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Analysis Types

Hydromax contains the following analysis tools:• Upright hydrostatics

• Large angle stability

• Equilibrium analysis

• Specified Conditi on analysis

• KN values and cross curves of stability

• Limiting KG analysis

• Floodable Length analysis

• Longitudi nal Strength analysis

• Tank Calibrations

Although common analysis settings are used where possible, different analyses mayrequire different settings. For example: the upright hydrostatics analysis simply requiresa range of drafts; whereas the longitudinal strength analysis requires a detailed loaddistribution. The analysis settings for each analysis type are explained in detail in theanalysis synopsis below.

Analysis Settings

The analysis settings describe the condition of the vessel to be tested. For example, arange of drafts in the case of upright hydrostatics, or a range of heel angles for a largeangle stability analysis.

The following analysis settings are available:• Heel

• Trim

• Draft

• Displacement

• Permeability

• Specified conditio ns

The analysis settings are specified prior to running the analysis. Settings that are notrelevant to the selected analysis type are greyed out in the Analysis menu.

Environment Options

Environmental options are modifiers that may be applied to the model or its environment

that will affect the results of the hydrostatic analysis.

Depending on the analysis being performed, different environmental options may beapplied to the Hydromax:

• Type of Fluid Simulation

• Density (of fluids)

• Wave forms

• Grounding

• Hogging and sagging

• Intact and Damage condition

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Stability Criteria

Hydromax has the capability to calculate compliance with a wide range of stabilitycriteria. These criteria are either derived from the properties of the stability curvecalculated from a Large Angle Stability analysis or from the vessel’s orientation andstability properties calculated from an Equilibrium analysis. Limiting KG and Floodable

length analyses also use stability criteria.

Hydromax has an extensive range of stability criteria to determine compliance with awide range of international stability regulations. In addition, Hydromax has a generic setof parent criteria from which virtually any stability criterion can be customized.

Output

Views of the hull are shown for each stage of the analysis, complete with immersedsectional areas and actual waterlines. The centres of flotation, gravity and buoyancy arealso displayed. Heeled and trimmed hullforms and water plane shapes may be printed.

Results are stored and may be reviewed at any time, either in tabular form, or as graphsof the various parameters across the full range of calculation. All results are accumulatedin the Report window (which can be saved, copied and printed), or output directly to aWord document.

The criteria checks are summarised in tables listing the status (pass/fail) of eachcriterion. The criterion settings and intermediate calculation data may also be displayedif required.

For a brief overview of the different analysis that Hydromax has available, continuereading Chapter 2 Quickstart .

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Chapter 2 Quickstart

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Chapter 2 QuickstartThis chapter will briefly describe each analysis type and its output. For each analysistype, a list of the required settings as well as the available environment options is given.

Hydromax contains the following analysis types• Upright Hydrostatics

• Large Angle Stability

• Equilibrium Condition

• Specified Conditio n

• KN Values

• Limiting KG Quickstart

• Floodable Length

• Longitudinal Strength


Each analysis has different settings that may be applied

Heel

Trim

Draft

Displacement

Specified conditions

• Permeability

• Loadcase

• Tank and compartment definitio n

Hydromax offers different environment options that may be applied to the analyses• Fluid Densities

• Treatment of fluids i n tanks: flu id simul ation or co rrected VCG

• Wave form

• Grounding

• Hog and sag

• Damage

Hydromax offers an extensive range of stability criteria that are applicable toequilibrium, large angle stability, limiting KG and Floodable length analysis.

Chapter 3 Using Hydromax will describe each of the analysis types, settings andenvironment options in more detail.

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Upright Hydrostatics QuickstartFor Upright Hydrostatics, heel is fixed at zero heel, trim is fixed at a user defined valueand draft is varied in fixed steps. Displacement and centre of buoyancy and otherhydrostatic data are calculated during the analysis.

Upright hydrostatics requirements• Range of drafts to be analysed

• VCG (for calculation of some stability characteristics such as GMt and GMl only)

• Trim

Upright hydrostatic options• Fluid Densities

• Wave form

• Hog and sag

• Damage

• Compartment definition (in case of damage)

The results are tabulated and graphs of the hydrostatic data, curves of form and sectionalarea at each draft are available.

For more detailed information please see: Upright Hydrostatics on page 65.

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Large Angle Stability QuickstartFor the analysis of Large Angle Stability, displacement and centre of gravity arespecified in the loadcase. A range of heel angles are specified and Hydromax calculatesthe righting lever and other hydrostatic data at each of these heel angles by balancing theloadcase displacement against the hull buoyancy and, if the model is free-to-trim, thecentre of gravity against the centre of buoyancy such that the trimming moment is zero.

Large angle stability requirements• Range of heel angles to b e analysed

• Trim (fixed or free)

• Loadcase

• Tank definitio n in the case of tank loads being inclu ded in the Lo adcase (and/or forthe definition of d amage)

Large angle stability options• Fluid Densities


• Wave form

• Hog and sag

• Damage


• Key points

• Margin line and deck edge

• Analysis of stab il it y cr iteri a

The key output value is GZ (or righting lever), the horizontal distance between thecentres of gravity and buoyancy. A graph of these values at the various heel angles formsa GZ curve. Various other information is often overlaid on the GZ curve, includingupright GM, curves for wind heeling and passenger crowding levers and the angle of thefirst downflooding point. These additional data depend on which (if any) stability criteriahave been selected.

The sectional area curve at each of the heel angles tested may also be displayed.

If large angle stability criteria have been selected for analysis, these results will also bereported in the criteria results table and they may lead to additional curves beingdisplayed on the GZ curve.

Downflooding angles for any key points, margin line and deck edge will also becomputed and tabulated.

For more detailed information please see: Large Angle Stability on page 67.

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Equilibrium Condition QuickstartEquilibrium Analysis uses the Loadcase, to calculate the displacement and the locationof the centre of gravity. Hydromax iterates to find the draft, heel and trim that satisfyequilibrium and reports the equilibrium hydrostatics and a cross sectional areas curve.

Equilibrium analysis requirements• Loadcase


• Compartment definit ion and d amage case (in case of damage)

Equilibrium analysis options• Fluid Densities


• Wave form• Hog and sag

• Grounding

• Damage


• Key points

• Margin line and deck edge

• Analysis of equi libr ium cri ter ia

Equilibrium analysis result table lists the hydrostatic properties of the model. If a waveform has been specified there will be a number of columns; each column contains theresults for a different position of the vessel in the wave as given by the wave phasevalue. The sectional area curve is also calculated, as is the freeboard to any defined key

points, margin line and deck edge. Any equilibrium criteria will also be evaluated andtheir results reported.

For more detailed information please see: Equilibrium Analysis on page 70.

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Specified Condition QuickstartIn the specified condition each of the three degrees of freedom, for which the hydrostatic

properties of the model are to be calculated, can be set.

Specified Condition Requirements• Specified Conditio ns Input Dialog

If fixed trim is specified, you may enter the trim or specify the forward and aft drafts(these are at the perpendiculars as specified in the Frame of Reference dialog).

Specified Conditions Options• Fluid Densities

• Wave form

• Hog and sag

• Grounding• Damage

• Tank and Compartment definition (in case of damage)

The output for the specified condition consists of a curve of cross sectional areas andhydrostatics of the vessel in the specified condition.

For more detailed information please see Specified Conditions on page 73.

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KN Values QuickstartKN values or Cross Curves of Stability are useful for assessing the stability of a vessel ifits VCG is unknown. They may be calculated for a number of displacements before theheight of the centre of gravity is known. The KN data may then be used to obtain the GZcurve for any centre of gravity height (KG) using the following formula:

GZ = KN - KG * sin(Heel)where GZ is the righting lever measured transversely between the Centre of Buoyancyand the Centre of Gravity, and KG is the distance from the baseline to the vessel'seffective Vertical Centre of Gravity.

KN Values Analysis Requirements• Range of displacements to be analysed

• Range of heel angles to b e analysed


• Estimate of VCG (provides more accurate result if free-to-trim)

KN Values Analysis Options• Fluid Densities

• Wave form

• Hog and sag

• Damage


Output is in the form of a table of KN values and a graph of Cross Curves of Stability.

If the analysis is performed free-to-trim and an estimate of the VCG is known, this may be specified. The computed KN results will then give a more accurate estimate of GZ forKG close to the estimated VCG since the effects of VCG on trim have been moreaccurately accounted for.

For more detailed information please see KN Values Analysis on page 75.

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Limiting KG QuickstartThe Limiting KG analysis may be used to obtain the highest vertical position of thecentre of gravity (maximum KG) for which the selected stability criteria are just passed.This may be done for a range of vessel displacements. At each of the specifieddisplacements, Hydromax runs several Large Angle Stability analyses at different KGs.The selected stability criteria are evaluated; the centre of gravity is increased until one ofthe criteria fails.

Limiting KG Analysis Requirements• Range of displacements to be analysed

• Range of heel angles to b e analysed


• Stability criteria for which limiting KG is to be found

Limiting KG Analysis Options• Fluid Densities

• Wave form

• Hog and sag

• Damage


• Key points (if required fo r criteria)

• Margin line and deck edge (if required for criteria)

A graph of maximum permissible GZ plotted against vessel displacement is produced as

well as tabulated results indicating which stability criteria limited the VCG. If limitingcurves are required for each of the stability criteria individually, this may be done in theBatch Analysis mode.

A check will be made to ensure that any selected equilibrium criteria are passed,however at least one large angle stability criterion is required. Only relevant criteria will

be used, i.e. if a damage case is chosen, only damage criteria will be evaluated; if theintact condition is used, only intact criteria will be evaluated. Some criteria, such asangle of maximum GZ, are very insensitive to VCG and may prevent the analysisconverging. If the analysis is unable to converge for a certain displacement this will benoted and the next displacement tried.

For more detailed information see Limiting KG on page 78.

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Floodable Length QuickstartThis analysis mode is used to compute the maximum compartment lengths based onuser-specified equilibrium criteria. Floodable Lengths may be computed for a range ofdisplacements; the LCG may be specified directly or calculated from a specified initialtrim. In addition a range of permeabilities may be specified. The VCG is also required toensure accurate balance of the CG against the CB at high angles of trim. As well as thestandard deck edge and margin line immersion criteria (one of which must be specified)the user can also add criteria for maximum trim angle and minimum required values oflongitudinal and transverse metacentric height.

Floodable Length Analysis Requirements• Range of displacements to be analysed

• VCG

• Range of permeabilities to be analysed

• Trim (free- to- trim to either ini tial trim or specified LCG)

• Floodable length criteria to be tested

• Margin line and deck edge (required for criteria)

Floodable Length Analysis Options• Fluid Densities

• Wave form

• Hog and sag

The output is in the form of tabulated Floodable Lengths for each displacement and permeability. The data is tabulated for each of the stations as defined in Maxsurf. Thedata is also presented graphically.

For more detailed information please see Floodable Length on page 81.

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Longitudinal Strength QuickstartHydromax calculates the net load from the buoyancy and weight distribution of themodel. That data is then used to calculate the bending moment and shear force on thevessel.

Longitudinal Strength Analysis Requirements• Loadcase (including distribut ed loads if required)


• Compartment definit ion and d amage case (in case of damage)

Longitudinal Strength Analysis Options• Fluid Densities

• Treatment of flu ids in tanks: fluid si mulation is always used for Long itudinal

Strength analysis• Wave form

• Hog and sag

• Grounding

• Damage


• Al lowab le shear and bending moment

The longitudinal strength graph and tables contain all information on weight and buoyancy distribution, the shear force and bending moment on the vessel. If defined,graphs of allowable shear and bending moment are superimposed on the graph.

For more detailed information please see Longitudinal Strength on page 84.

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Tank Calibrations QuickstartTanks can be defined and calibrated for capacity, centre of gravity and free surfacemoment (FSM). Fluid densities and tank permeabilities can be varied arbitrarily. Tankcalibrations are for the upright (zero heel) vessel, but the vessel's trim may be specified.Hydromax uses its fluid simulation mode to calculate the actual position of the fluids inthe tanks, taking into account the vessel trim. Tank ullages are measured from the top ofthe sounding pipe to the free surface of the liquid within the tank along the sounding

pipe and in a similar manner, soundings are measured from the bottom of the sounding pipe to the free surface.Tank calibration analysis requirements

• Tank definitio ns

• Sounding pipe definitio n (if required)

• Sounding int ervals for calibration levels

• Trim

Tank calibration analysis options• Fluid Densities

• Treatment of fluids i n tanks: flu id simul ation always selected

• Hog and Sag

• Damage: Intact c ase always selected

For each tank, a table of capacities, volumes etc. is calculated. These results are presented in both tabular and graphical forms.

For more detailed information please see Tank Calibrations on page 87.

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Chapter 3 Using Hydromax

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Chapter 3 Using HydromaxThis chapter describes

• Getting Started , installation and starting the program

• Hydromax Model , opening and validating the Maxsurf model

• Analysis Typ es

• Analysis Sett ings

• Analysis Environment Options

• Anal ysi s Output , reporting

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Getting StartedThis section contains everything you need to do to start using Hydromax

• Installing Hydromax

• Starting Hydromax

Installing HydromaxInstall Hydromax by inserting the CD and running the Setup program, then follow theinstructions on screen.

Note:Before installing any program from the Maxsurf suite for the first time,

please read the purchase letter (also referred to as installation manual).

Starting HydromaxAfter installation, Hydromax should be accessible through the Start Menu. Simply selectHydromax from the Maxsurf menu item under Programs in the Start menu.

Windows Registry

Certain preferences used by Hydromax are stored in the Windows registry. It is possiblefor this data to become corrupted, or you may simply want to revert back to the defaultconfiguration. To clear the Hydromax preferences, start the program with the Shift keydepressed. You will be asked if you wish to clear the preferences, click OK, doing thiswill reset all the preferences.

The following preferences are stored in the registry:• Colour settings of contours and background

• Fonts

• Window size and location

• Size of resizing di alogs (alternatively, these may be reset by ho lding down t he shiftkey when activating them)

• Density of fl uids

• Permeabilities for floodable length analysis

• Location of files

• Units for data input and results output

• Convergence tol erance (Error values)

• Maximum number of loadcases

Note:The default density for the fluid labelled "Sea Water" is stored in thewindows registry. All hydrostatic calculations use this. Check the density ofseawater after resetting your preferences.

It is recommended to save your customized densities with your projectusing the File | Save Densities As command.

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Hydromax ModelThis section describes how to open a Maxsurf model in Hydromax and provides someimportant information to ensure that your model is correctly interpreted by Hydromax.

• Preparing a Design in Maxsurf

• Opening a New Design

• Opening an Existing Hydromax Design File

• Updating the Hydromax Model

• Hydromax Sections Forming

• Checking the Hydromax model

After checking the Hydromax model, the next step is to check the Hydromax settingsand initial analysis conditions.

• Setting Initial Conditio ns

Depending on the analysis performed, you may need to set up the following additionalmodel data:

• Working with Loadcases

• Modelling Compartments

• Forming Compartments

• Compartment Types

• Damage Case Definiti on

• Sounding Pipes

• Key Points (e.g. Down Floodin g Points)

• Margin Line Points

• Modulus Points and Allowable Shears and Moments

• Stability Criteria

Preparing a Design in MaxsurfThere are several important checks that must be carried out in Maxsurf before opening adesign in Hydromax:

• Setting the Zero Point

• Setting t he Frame of Reference

• Surface Use • Skin Thickness

• Outside Arrows

• Trimming

• Coherence of the Maxsurf surf ace model

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Setting the Zero Point

Ensure that the zero point is correctly setup in Maxsurf. A consistent zero point andframe of reference should be used for the model throughout the Maxsurf suite. InHydromax you have the option of displaying longitudinal measurements such as LCB orLCF from the model zero point or amidships.

Setting the Frame of Reference

It is vital that the Frame of Reference is correctly setup in Maxsurf before attempting toanalyse the model in Hydromax. The Frame of reference should not be changed inHydromax. The frame of reference defines the fore and aft perpendiculars, the baselineand the datum waterline; midships is automatically defined midway between the

perpendiculars. By convention, in the profile and plan views, the vessel’s bow is on theright.

The perpendiculars define the longitudinal positions of the vessel’s draft marks andcannot be coincident. The base line is the datum from which the drafts and KG aremeasured.

Surface Use

In Maxsurf you can choose between two types of surface use

HullHull surfaces are used to define the watertight envelope of the hull.

Internal structureInternal structure surfaces are used for all other surfaces (any surfaces which donot make up the watertight envelope) and also surfaces which are to be used inHydromax to define the boundaries of tanks and compartments that have complexshapes.

The following table describes the difference between each surface use in Hydromax:

Included: Hull Shell InternalStructure

Hydrostatic sections

Selection of tank/compartment boundariesSkin thickness applied to the surface

Verify that all surfaces that are to be used as tank/compartment boundaries are defined asInternal Structure. If a surface is defined as internal structure, it is not included as part ofthe hull shell by Hydromax, i.e. internal surfaces will be ignored in the forming ofhydrostatic sections.

Skin Thickness

If skin thickness is to be used in hydrostatic calculations, ensure that the thickness and projection direction have been specified for the hull shell surfaces. Thickness can bespecified differently for each hull surface, resulting in more accurate hydrostatics. Toactivate skin thickness in Hydromax ensure that the “Include Skin Thickness” option isselected when reading the file or calculating the hull sections.

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NoteTank boundaries made from internal structures surfaces do not have skinthickness. To include skin thickness, the internal structure surface should be

placed to model the inside of the tank if the tank wall has significantthickness.

Skin thickness for hull surfaces will be treated so that the hull sections go tothe outside of the plate whilst any tanks are trimmed to the inside of the

plate.

Outside Arrows

The surfaces’ outside arrows define the orientation of the surfaces. Ensure that you haveused the Outside Arrows command from the Display menu to tell Maxsurf whichdirection points outwards (towards the seawater) for each surface. The surface directionmay then be flipped by clicking on the end of the arrow.

Trimming

Ensure that all surfaces are trimmed correctly. You should have completely closedtransverse sections or sections with at most one opening.

Correct Section with no opening.

Correct section with one opening: this section will be closed across the top.

Also see:Hydromax Sections Forming on page 25 Checking the Hydromax model on page 29

Coherence of the Maxsurf surface model

Hydromax will generally have no problem correctly interpreting your design as long asthe following requirements for the Maxsurf model are observed:

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• Make sure that each surf ace touches its adj acent surfaces at its edge, preferably bybonding the edges together

• Where surfaces intersect, trim away the excess regions of the surface; e.g. the partof the keel that is inside the hull and the part of t he hull that is in side the keel

• Do not have surfaces that cannot be closed in an unambiguous f ashion, i.e. a

maximum of one gap in a transverse section through the hull.• Remember that the inner porti ons of each intersecting contour w ill be trimmed off

• Check surface use; internal structure surfaces are ignored when forming the hullsections in Hydromax

Note:For internal structure surfaces that will be used to define tank (orcompartment boundaries) the same requirements apply.

Also see:Checking the Hydromax model on page 29.

Opening a New DesignFile opening in Hydromax is window specific, i.e. Hydromax will automatically look forcompartment definition files when you are in a Compartment Definition window and aloadcase in a Loadcase window.

To open a design for analysis, ensure that the design view window is active, then selectOpen Design from the File menu. Choose a Maxsurf design file (.msd).

The following dialog will appear:

Calculate new Sections

Choosing Calculate Sections will calculate the specified number of sections through thehull. These will then be used for the Hydrostatics calculations.

The meaning of (ignore existing data, if any) is explained in Opening an ExistingHydromax Design File .

Include Plating Thickness

At this stage, any surface thickness specified in the Maxsurf Surface Properties dialogmay be included.

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Use Trimmed Surfaces

If the Maxsurf model has trimmed surfaces, the Use Trimmed Surfaces item should beticked.

Stations

When calculating stations, you may select how many stations should be used. Reducingthe number of stations will speed up the analysis time but reduce the accuracy,conversely increasing the number of stations will increase the analysis time but lead tohigher accuracy results.

The first option allows you to use the station grid created in Maxsurf. This is extremelyuseful for hulls that have features such as keels or bow thrusters that need to beaccurately modelled and may need a locally denser station spacing to do so. It alsoallows designs with significant longitudinal discontinuities in their sectional areas tohave stations specified either side of the discontinuity, avoiding any errors inherent inthe integration of evenly spaced stations. For example, if it was known that a design hada significant discontinuity in its sectional area curve at amidships, by specifying onestation 1mm aft of amidships and one station 1mm forward of amidships thisdiscontinuity can be modelled very accurately.

The upper limit for the number of stations is 200.

Surface Precision

The Surface Precision options has two functions:• Setting f or calculating the hydrostatic sections

• Setting u sed to form new compartments or tanks.

The precision at which the design was saved in Maxsurf is included in the Maxsurfdesign file (.msd). Hydromax recognises this precision setting and will and set theSurface Precision button accordingly.

Note:Maxsurf surface trimming information may vary for different precisions.Therefore it is recommended not to change the precision setting whenopening the Maxsurf design file in Hydromax.

Opening an Existing Hydromax Design FileAfter saving the Maxsurf design file for the first time in Hydromax, a “Hydromax

Design file” (.hmd) is created. The Hydromax design file will consist of the hydrostaticsections and all input data such as compartment definitions, key points, sounding pipesetc. Hydromax also allows saving of all input and output files into individual files.

To open an existing design, there are two options:

Double click on the .hmd file from any Windows explorer window

Use the Hydromax Open command form the file menu and select the .msdfile

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An existing Hydromax design consists of a number of files with different file extensions.

When Hydromax opens a .msd file, it will look for a .hmd file with the same name as the.msd file. For example: when opening OSV.msd, the OSV.hmd file is found. TheCalculate Sections dialog now has the option to read the sections from the file.

Ensure “Read existing data and sections” is selected and click OK.

Hydromax will now open the .hmd file. This contains hydrostatic sections informationand all input information from last time the .hmd file was saved, i.e. compartmentdefinitions, loadcases, damage cases, key points etc.

Notes:1) When selecting “Read existing data and sections (do not update geometry)” theMaxsurf surface information is not recalculated. This means that changes to thehull shape in the Maxsurf Design file, are not automatically incorporated. You willload your existing sections, loadcases and compartment definitions etcetera. See:Updating the Hydromax Model on page 25 for more information.

2) Calculate new sections (ignore existing data, if any) means that Hydromax willrecalculate the hull sections and ignore any data stored in the .hmd file. You willhave to reload your individual loadcases and compartment definition files etceteraafter you have selected this option and pressed OK. For more information on file

properties and extensions in Hydromax, please see: File Extension Reference

Table on page 242.

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Updating the Hydromax ModelTo update the hydrostatic sections to the latest Maxsurf Design File, select “RecalculateHull sections” in the analysis menu after reloading the Maxsurf Design File.This function can also be used to include/exclude surface thickness or change the

number of sections and to change use/not use trimmed surfaces without reloading theMaxsurf Design File.

The “Recalculate Hull Sections” command recalculates Hull surfaces as well as TankBoundary surfaces (Internal Structure surfaces in Maxsurf). Any tanks and loadcaseswill also be updated with this command.

Note:Changes to the Maxsurf design are only recalculated after the new Maxsurfdesign has been re-loaded into Hydromax. This means that if the model issimultaneously being edited in Maxsurf and Hydromax, it is necessary to:1) save and close the model in Hydromax2) save in Maxsurf3) open in Hydromax, using “Read existing data and sections” to make surethe loadcase, compartment definition etc remain part of the Hydromaxdesign file.4) use the “Recalculate Hull Sections” from the analysis menu.

Hydromax Sections FormingHydromax works by applying trapezoidal integration to data calculated from a series ofcross sections taken through the Maxsurf model surfaces. Hydromax will automaticallyform these sections, called “Hydromax sections”, “hydrostatic sections” or just

“sections”. Hydromax deals only with sections that are completely closed, or can beunambiguously closed. This section outlines the section forming process in Hydromaxand may be helpful whilst preparing a Maxsurf design for Hydromax. Whilst it is always

preferable to give Hydromax a completely closed model with no ambiguities, Hydromaxwill try to resolve any problems with the model definition in the manner outlined in thefollowing sections.

The following cases can occur:• Single surface

• Multiple surface, closed section lines; e.g. via bonded edges, compacted contr olpoints, trimming etc

• Multiple surface, small gaps w ithin tolerance• Multiple surface, one opening per surface

• Multiple surface, multiple openings per su rface

Single Surface

Where a hull consists of an open shell (e.g. a hull surface with no deck), Hydromax willautomatically close the section with a straight line connecting the opening ends.

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If, however, the section is made up of two line segments, (e.g. having both a gap at thecentreline as well as an open deck), an ambiguity exists as to how the two line segmentswill be connected. This is not an acceptable shape.

In the example above, if either the top or bottom gap had been closed in Maxsurf thedesign would cease to be ambiguous.

Multiple Surfaces, One Closed Section

Multiple surfaces that are trimmed correctly, bonded together or use compacted control points will not cause any problems when opened in Hydromax. Hydromax will form aclosed section through multiple surfaces by linking the curve segments together.

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Note: Over compacted control pointsA common problem with compacted control points occurs when the numberof compacted control points is equal to or exceeds ( ≥ ) the surface order(read: stiffness).

The maximum number of compacted control points is the surface order –1.

Multiple Surfaces, Small Gaps Within Tolerance

Hydromax will link curve segments together if they are only separated by a smallamount. The user cannot change these tolerances, because there are too manydependencies in the program.

Multiple Surfaces, One Opening Per Surface

Each surface will be closed by a straight line linking the ends of the opening.

Where surfaces intersect, each surface will be closed before being intersected withanother. The excess portions of the curve will be trimmed off to form a single continuouscontour.

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Multiple Surfaces, Multiple Openings Per Surface

Same as for a single surface, Hydromax deals only with sections that are completelyclosed, or can be unambiguously closed.

Ambiguous Sections (e.g. decks, bulwarks)

A common example of ambiguous sections is a model with multiple decks. Hydromaxwill have difficulties distinguishing the intended main deck.

The example above has bulwarks; generally these will be treated correctly by Hydromaxand trimmed off, depending on the height of the bulwark relative to the rest of thesection. To prevent ambiguities it is recommended to trim the bulwark in Maxsurf. If the

bulwark’s volume is expected to influence the hydrostatic calculations, the bulwark’svolume has to be properly modelled in Maxsurf.

Hydromax first closes the individualsurfaces

Hydromax closes the outside contour andtrims remnants

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Checking the Hydromax modelBefore starting any analysis you should check whether Hydromax has been able tocorrectly interpret your design. The following tools are available to validate theHydromax model.

• Show Single Hull Section • Checking the Sectional Area Curve

• Using Rendering t o Check the Model

Note:Sections that are not formed correctly cause the majority of problems withHydromax models. Therefore, checking your sections after opening thedesign in Hydromax is strongly recommended. Incorrect sections in themodel will give incorrect results.

These sections should be continuous with no gaps and no unexpected lines.In particular, look closely at intersections between surfaces to make surethat Hydromax has interpreted the shape correctly.

Show Single Hull Section

In the body plan view, you can step through the sections one-by-one to verify that theyhave been correctly calculated. This is done by selecting Show Single Hull Section inBody Plan view from the Display menu. You can then click in the inset box to view thesections, the left and right arrow cursor keys will enable you to step through the sectionsone-by-one. This works the same as the Maxsurf body plan window and is an extremely

powerful tool to validate your Hydromax model. For more information see the Maxsurf

manual.

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Checking the Sectional Area Curve

Another way of checking the Hydromax model is to perform a specified conditionanalysis at quite deep draught and look carefully at the sectional area curve in the graphwindow. If this displays any unexpected spikes or hollows Hydromax may not havecorrectly interpreted the hull shape. This is not a foolproof method since it does not

necessarily highlight problems in the non-immersed part of the hull.

This Cross Sectional Area curve indicates there may be a problem with section forming from 12 m to 16 m.

Using Rendering to Check the Model

The model may also be rendered, which makes it easier to see if there are any areas ofthe model which have not been properly defined. Select Render from the Display menuwhilst in the perspective view and turn on the sections:

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Note:In rare instances incorrect rendering may occur. This does not necessarilymean that the model is incorrect. As long as the sections are formedcorrectly, the model is correct.

Setting Initial ConditionsAll Hydromax calculations are performed in the frame of reference of the model.Hydromax uses the APP and FPP together with the baseline and the zero point for allcalculations and gives the results in the units specified in the display menu.

Note:Before you run any analysis using Hydromax, it is important that you set upthe required initial conditions for the design.

Coordinate System

Hydromax uses the Maxsurf coordinate system:

+ve forward -ve aft+ve starboard -ve port+ve up -ve down

View window View directionBody plan From the stern, looking fwdPlan From above, Port side above the centrelineProfile From Starboard, bow to the right.

Frame of Reference and Zero Point

It is essential that a frame of reference be specified. This should be done in Maxsurf and

not in Hydromax. Draft and trim are measured on the forward and aft perpendiculars. Ifthese are not in the correct positions, some analysis results will be meaningless.

See: Setting the Zero Point and Setting the Frame of Reference on page 20.

Note:Changing the zero point in Maxsurf will not update the compartmentdefinition, loadcase and other input values. Changing the zero point afteryou have started analysing the model in Hydromax is not recommended.

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Customising Coefficients

In Hydromax you may choose between the length between perpendiculars and thewaterline length for the calculation of Block, Prismatic and Waterplane AreaCoefficients.

The LCB and LCF can be displayed in the Results windows relative to the specified ZeroPoint, Amidships location, Aft Perpendicular, Fwd Perpendicular or from the Aft,Middle or fwd end of the actual waterline. You can also specify whether you want theforward (towards the bow) or the aft (towards the stern) to have a positive sign. Finallyyou can chose whether you want the LCB and LCF to be displayed as a length or as a

percentage of the waterline or LPP length as specified in the Length for Coefficients.

Setting Units

The units used may be specified using the Units command. In addition to the length andweight (mass) units, units for force and speed (used in wind heeling and heeling due to

high-speed turn etc. criteria) and the angular units to be used for areas under GZ curves,may also be set. The angular units for measuring heel and trim angles are alwaysdegrees. Units may be changed at any time.

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Other Initial Conditions

See:Fluids Analysis Methods on page 100 Density on page 101

Working with LoadcasesLoadcases define the loading condition of the vessel. Static weights that make up thevessel lightship are specified here as well as tank filling levels, expressed as either a

percentage of the full tank capacity or as a weight.

Creating a new Loadcase File

To create a load case, switch to the loadcase view by selecting Loadcase from theLoadcase sub-menu in the Window menu. Then select “New Load Case” from the Filemenu or press Ctrl+N. A new load spreadsheet will be displayed in the Loadcasewindow. The default loadcase will contain a lightship entry and an entry for each tank(with a default filling of 50%).

The tabs in the bottom of the window can be used to skip through the different loadcasesin the design.

Create New Loadcases based on TemplateTo avoid rework, an existing loadcase may be used as a template when creating a newloadcase. To do this,

In the loadcase window, select the Loadcase you wish to use as a template

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Loading a Saved Loadcase

You can load a saved loadcase into your loadcase window by:

Select an empty tab in the loadcase window that you wish to load theloadcase into

Empty tab.

If there are no empty tabs, you should either increase the maximum number of loadcases(see below), or close an existing loadcase.

Select File | Open Load Case

Select the .hml file you wish to open.

Setting the Maximum Number of Loadcases

The maximum number of loadcases (up to twenty-five) that can be loaded in Hydromaxat any one time is set by selecting “Max. Number of Loadcases” from the Case menu.You may then enter the maximum number of load cases you require.

You must restart Hydromax for this change to take effect. In most cases, you will onlyneed to set this once to the maximum number of loadcases you are ever likely to use. Forconvenience of use, a sensible number is recommended.Each loadcase can be selected and used for analysis. Each may be saved and loadedindependently, effectively allowing you as many loadcases as you require.

Note:When loading a design that has more loadcases than the maximum you havecurrently set in Hydromax, you will receive a warning and the file will not

be loaded. You must increase the maximum number of allowable loadcasesand restart Hydromax before you can load the design.

Closing a Loadcase

Select the tab of the loadcase you wish to close in the Loadcase window

Select File | Close Load Case

Adding and Deleting Loads

To add an extra load to the loadcase,

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Select Add Load from the Edit menu or press Ctrl+A.

A new load will be inserted into the table above the currently selected row. You canrepeat this process for as many loads as you wish.

If you want to remove a load from the table, simply click anywhere in the row you want

to remove, and choose Delete Load from the Edit menu (or highlight the complete row by clicking the grey cell to the left of the row and press the Delete key). If you wish todelete several loads simultaneously, click and drag so that all of the loading rows thatyou wish to delete are selected, then select Delete Load.

Editing Loads

Click on the cell containing the load name and type in a name for this load, for example"Lightship", and press the Tab key to go to the next column in the table (or simply clickdirectly in the cell you wish to edit).

For each item in the list you can specify a quantity. This is used to calculate the totalweight of that item. For example: if the item was “crew” with a weight per unit, youcould specify the quantity and unit weight, and the total weight of crew would beautomatically calculated. The weight of each item should be entered in the next column.

The weight must always be positive. If for some reason you wish to have an upward(negative) load, you can do so by entering a negative quantity – this can be useful if youwant to apply a pure moment to the model by applying equal magnitude, but oppositesign loads to the vessel in the loadcase.

Tab to the next column and enter the horizontal lever for the item. After you type in thisnumber, press enter and the total LCG will be automatically re-calculated and displayedin the bottom row of the table. The CG position will also be shown and updated in the

View windows if Large Angle Stability, Longitudinal Strength or Equilibrium analysisare selected.

Note:Levers, as with all other measurements in Hydromax, are measured fromthe Zero Point.

Loadcase Sorting

A number of tools are available for controlling the order in which items and tanks occurin the loadcase. You may move selected items and tanks up and down in the loadcase;you may also sort selected items by name, fluid type (for tanks) etc.

Insert row | Delete row | Sort rows | Move row(s) up | Move row(s) down

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Sort selected columns

After moving loads, subtotals and subsubtotals, you may have to use Analysis | UpdateLoadcase ( button) to update the subtotals and subsubtotals. To ensure dataconsistency, Hydromax does this automatically prior to running an analysis.

Loadcase FormattingHydromax allows you to improve the presentation of the Load Case window by adding

blank, heading or sub-total lines in the table.

Adding Component or Heading LinesComponents or headings can be included in a load case by preceding the text witha period (.) character.

Adding Blank LinesA blank line can be added into the load case by placing a dollar ($), apostrophe (‘)or full-stop(.) character in the Item Name field.

Adding Totals or Subtotals

A subtotal can be displayed for several loads within a load case. To do this theitem name field must commence with the word ‘ total ’ or ‘ subtotal ’.

Sub-subtotalsSub-sub-totals may also be inserted. Sub-subtotals must start with the text“subsubtotal ”.

Grouping Similar TanksTanks are listed in the loadcase in the order they are defined in the CompartmentDefinition table. If you wish to change the order in which tanks appear in theloadcase, it is necessary to reorder them in the Compartment Definition table. See:Compartment and Tank Ordering on page 50.

Loadcase Colour Formatting

Different colours can be defined for fixed mass items and tanks; alternatively, tanks may be displayed in the same colour as the fluid they contain (As defined in Analysis | Fluidsdialog).

View | Colour menu when Loadcase window is frontmost

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Longitudinally Distributed Loads

Distributed loads can be entered in the Loadcase window in the aft limit and forwardlimit cells. The aft limit and forward limit columns only appear when LongitudinalStrength analysis is selected and the distributed loads will only have an effect on theresults in this analysis mode. The “Long. Arm” column defines the longitudinal positionof the centre of the load; the fore and aft limits define the longitudinal extents of theload.

If the longitudinal arm is changed in the Loadcase window, the forward and aft limitswill be moved by the same amount.

For an evenly distributed load, the centre of gravity should be midway between theforward and aft limits.

Evenly distributed loads. Red = green and divided in the centre.

For trapezium shaped distributed loads the centre of gravity is not midway between the boundaries, but within the middle third 1/3 of the centre.

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Also see:Update Loadcase on page 155

Free surface correction

If the corrected VCG fluid option has been chosen, the Loadcase will sum the freesurface moments, divide by the total displacement to obtain the VCG correction andadjust the VCG accordingly to obtain the corrected fluid VCG.

Fluid simulationIf the Fluid simulation option is selected in the analysis menu, no correctionis made to the upright VCG. Instead, at every step of the analysis,Hydromax calculates the actual position of the fluid in the tanks taking intoaccount heel and trim, making the tanks’ free-surface parallel to the seasurface, thus the actual vessel CG is recalculated accounting exactly for thestatic shift of the fluids in slack tanks.

When the corrected VCG method is selected in the analysis menu, it is possible tochoose the type of free surface moment to be applied for each tank in a HydromaxLoadcase. The options available are

MaximumHydromax will use the maximum free surface moment of the tank in uprightcondition for all fluid levels.

ActualHydromax uses the free surface moment for the current fluid level of the tank inupright condition.

IMO

Hydromax uses IMO MSC75.(69) Ch 3.3 for the calculation of the free surfacemoment. This method approximates the movement of fluid due to heeling and is

based on the fluid shift in a 50% full rectangular, box-shaped-tank. For othershapes and fillings of tanks it will not correctly approximate the free surfacemoment.

User specifiedA user specified value is used for all levels and heel angles.

Note:All VCG correction methods, except the user specified method, set the freesurface moment to zero for fillings < 0.1% and ≥ 98%. This is allowed byclassification societies and is an approximation of reality since the tank isalmost empty or full and the shift in fluid mass is negligible.

Modelling CompartmentsThis section will describe in detail how to model different types of tanks andcompartments.

Besides a general explanation on how to model tanks using the compartment definitiontable, this section contains a number of important sections that the user should be awareoff when modelling tanks:

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• Number of Sections in Tanks on p age 54

• Tank and Compartment Permeability on page 49

Creating a Compartment definition file (.htk)

Select the Compartment Definition table by clicking on the CompartmentDefinition tab at the bottom of the Input window.

Select New Compartment Definition from the File menu

, this will give you a new set of compartment definitions with one default tank.

Adding and Deleting Compartments

Before you can start adding compartments, make sure you have created a Compartmentdefinition file, see above.

Compartments may be added or deleted by

Select Add or Delete Compartment from the Edit menu.

Add will add a tank after the currently selected compartment and Delete will delete thecurrently selected compartment(s). The accelerator keys Ctrl+A and the Delete key mayalso be used to add and delete entries respectively.

Modelling Box Shape Tanks

Simple tanks and compartments are created by specifying six values that define a box-shaped boundary for the tank. This box will be called the Boundary Box . The boundary

box is made up of the fore and aft extremities of the tank, the top and bottom, and the port and starboard limits of the tank. Each value defines one of the six planes of the tank.

The column headings in the Compartment Definition table include terms such as 'F

Bottom, 'A Top', 'F Port' and 'A Starboard'. The 'F' and 'A' abbreviations stand forForward and Aft, in other words the two ends of the compartment. You will notice thataft columns contain the word "ditto". This means that the value is identical at the aft endof the tank to the forward end, resulting in a parallel tank.

When the “Update Loadcase” command from the Analysis menu is used, or an analysisstarted, Hydromax will form the sections that define the tanks and compartments. This isdone by finding the intersection of the tank bounding box and the hull. Thus it is notnecessary to make the tanks fit the hull manually – this is done automatically byHydromax.

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Box shaped compartments can be formed from the numerical values in the compartment definition table.

See Longitudinal Extents of Boundary Box on page 54 for some recommendationsregarding setting the boundary box.

Modelling Tapered Tanks

The default is for compartments to have parallel sides. If you wish to define taperedcompartments, it is possible to enter different transverse and vertical values for the

points defining the compartment ends.

If a different value is entered in one of the “ditto” columns, a tapered tank will result.Tanks can be tapered or sloped in Plan or Profile views. Hydromax does not have amechanism for creating a sloped tank boundary in the Body Plan view.

By changing the “ditto”-input fields, tapered tanks can be formed

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Note:Tapering can be done in Plan and in Profile view. Tapered tanks in BodyPlan view have to be created using a boundary surface. See ModellingTanks Using Boundary Surfaces on page 43.

Linked TanksTanks, compartments and non-buoyant volumes may be linked. This means that althoughthey are defined as separate tanks, they act as a single tank with a common free surface.To link tanks, compartments or non-buoyant volumes, first make them the same type asthe parent and give them the same name. The easiest way to do this is to copy and pastethe name from the Name column of the parent row into the Name column of the linkedtank row. They may then be linked to the parent by typing l or linked in the Typecolumn. Linked tanks and compartments do not have to be physically linked in space.However, the fluid in a linked tank or damaged compartment is always assumed to beable to flow freely between the linked volumes.

Modelling Tanks Using Boundary Surfaces

Tanks, compartments and non-buoyant volumes may have their boundaries defined bysurfaces as well as being constrained to particular dimensions. This allows for themodelling of arbitrarily shaped tanks.

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Forming tanks using boundary surfaces

The surfaces to be used to define the tank boundaries are selected by clicking in theBoundary Surfaces column in the middle of the Compartments Definition table. A dialogwill appear that allows you to select which surfaces form the boundary of the tank. If atank uses boundary surfaces, the cell in the Boundary Surfaces column is coloured blue.

If you wish to use a Maxsurf surface to define a tank or compartment, tick next to thesurface name in the Boundary Surface list. Note that symmetrical surfaces appear twiceas there will be a starboard and a port side copy of the surface. The Starboard surface isfirst in the list and the Port surface second. The port surface is also identified with thesuffix (P) after the name.

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Note:Only internal structure surfaces appear in the boundary surfaces list.

Symmetrical surfaces are duplicated, with the port-side surface having “(P)”appended to the surface name.

After selecting the internal surfaces, it is necessary to type in the extents ofthe boundary box. Hydromax will automatically set the “Fore” and “Aft”limits of the boundary box to just within the longitudinal limits of theBoundary Surface. This ensures that at least 12 sections are inserted in thetank.

Also see:Forming Compartments on page 52

Number of Sections in Tanks on page 54 Longitudinal Extents of Boundary Box on page 54

Modelling External Tanks

External tanks may not be modelled in Hydromax. However, it is normally possible toadd "Hull" surfaces in the Maxsurf model, which will enclose the external tanks. Thetanks can then be modelled in Hydromax.

Additional box-shaped hull surfaces used to define deck tanks

Modelling Non-Buoyant Volumes

Non-buoyant volumes are effectively permanently flooded compartments. They cannormally be modelled using trimmed hull surfaces. However, there are occasions whereit is more convenient to use non-buoyant volumes. In some cases, where the volume to

be flooded forms sections within the hydrostatic section, this is the only option, e.g.

waterjet ducts. The choice whether to use trimmed surfaces or non-buoyant volumes is primarily determined by the length of the non-buoyant volume relative to the length ofthe vessel.

Using trimmed hull surfacesWhen the length of the non-buoyant volume, relative to the length of the model, islarge enough; the non-buoyant volume can be calculated accurately from the hullsections. If possible, trimmed surfaces should be used. The picture below is a goodexample of when to use trimmed surfaces.

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Propeller tunnels modelled with trimming surfaces

Using tank type: Non-buoyant volumeIn some cases using trimmed surfaces is just not possible. For example, when thesections of the non-buoyant volume are entirely enclosed within the hull sections(as is the case for a water jet duct) the use of a non-buoyant volume is the onlyway in which these features can be modelled.

Water-jet ducts modelled as non-buoyant volumes

Another occasion when non-buoyant volumes should be used, is when the lengthof the compartment relative to the length of the hull is too small to calculate itsvolume from the hull sections. A good example of this is a bow thruster on a longship. If the vessel is very long, and the thruster duct is of small diameter, theremay not be sufficient sections to model it accurately (even if you use themaximum of 200 sections for the Hydromax model). In this case you are better offmodelling the thruster duct as internal structure and using these surfaces to definea non-buoyant volume. For example: in the image below the bow thruster volumeis only calculated with one section.

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For more information, see Number of Sections in Tanks on page 54.

Tip: Besides increasing the number of sections through the bow thruster from 1 to 12,modelling the thruster duct as a non-buoyant volume has the additional advantage of being able to specify a Tank and Compartment Permeability , and hence also account forthe thruster.

Bow thruster tube modelled as two non-buoyant volumes

Tanks within Compartments

When a tank is defined within a compartment, Hydromax will automatically deduct thevolume of the tank from the compartment volume using a “linked neg. (negative)compartment”. This is necessary for damage cases where the compartment is floodedand the volume of the tank should be treated completely separately from thecompartment.

Linked negative compartments are deleted and recreated whenever a tank or

compartment is added, deleted or modified. Negatively linked compartments aredisplayed on the bottom of the Compartment Definition table solely for reference purposes and are not under direct user control. This means that linked negativecompartments cannot be added, deleted or modified.

Linked negative compartments are named based on both the parent compartment as wellas the tank from which the linked negative compartment was derived. For example alinked negative compartment might be named “Compartment3 (Stbd Hydr Oil)” toreflect that it is derived from the intersection of Compartment3 with the Stbd Hydr Oiltank.

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Tanks Overlapping

As mentioned earlier in this manual, only compartments and non buoyant volumes ortanks can overlap with each other. Tanks or compartments of the same type (eg twotanks) can not overlap. A tank and a non-buoyant volume are also not allowed tooverlap.

Hydromax will first try to form tank sections and then check whether these sectionsoverlap tank sections of adjacent tanks. When two conflicting or overlapping tanks orcompartments are detected during the forming process, you will receive an errormessage:

Notice that the compartment definition row number of the tank is given in brackets

i.e. tank #8 intersects tank #3.

Troubleshooting Overlapping TanksSometimes the reason for the conflict can be quite simple: eg an overlapping boundary

box. However, when you are modelling tanks using boundary surfaces, the surface boundaries act as a boundary between two adjacent tanks and the bounding box extentsare allowed to overlap. In these cases, it can be quite difficult to see why the tanksoverlap, especially if you have a large number of tanks already defined.

By temporarily deleting all tanks except for the one that does not form, it often becomesclear why the tank overlaps. In the case of the image above, the tank’s fwd most sectiongoes all the way to the CL (probably because the fwd boundary box extent is just fwd ofthe boundary surfaces or exactly on the edge of a boundary surface). This causes this

particular tank to “overlap” with surrounding tanks.

Procedure to Fix Overlapping Tanks:

Save Model

Go into Comp def window

Save comp def

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Delete all tanks except for one you wish to investigate

form tanks, inspect tank sections

Try to fix tank definition, eg by selecting additional boundary surfaces

Now that you know how to fix it..

Close comp def file. Do NOT save!!

Open saved Comp def file

Fix compartment.

Save & move on to next compartment.

Tank and Compartment Permeability

Tanks may have two permeabilities; one, which is used when the tank is intact, and theother when it is damaged. Compartments and non-buoyant volumes have only one

permeability, thought it is listed in both columns. The compartment permeability isapplied when the compartment is flooded in a damage condition and the non-buoyantvolume permeability is applied at all times since it is always flooded.

In the case of damaged tanks and compartments, the permeability fraction is also appliedto the free-surface-moment contribution of that tank or compartment.

Permeability of CompartmentsAs opposed to tanks, compartments typically have structure (other than platestiffeners) and equipment inside. In case of large variations in permeability withina compartment it is recommended to model separate linked compartments withseparate permeability to increase accuracy.For example an engine room with engines and auxiliaries at the tanktop could bedivided up in a lower- and an upper engine room compartment. The lower

compartment will have a permeability of, for example, 60% and the uppercompartment a permeability of 95%. Depending on the level of accuracy required,the engines and equipment could also be modelled individually as empty tanks.

Relative Density of Tank Fluids

Relative Density (Specific Gravity) values can be typed directly into the RelativeDensity column of the Compartment Definition table.

Alternatively the fluid type can be entered into the Fluid Type column, either as thename or as one of the single letter codes (when entering the name, auto complete is used,so it is normally only necessary to type the first few letter of the name). If a fluid type isentered, the relative density value is obtained from the value specified in the Densitydialog. Whenever values are changed in the Density dialog (see Density of Fluids on

page 101), all entries for that fluid in the compartment definition are automaticallyupdated.

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Tanks and Surface Thickness

If you have specified that Hydromax should include the surface thickness, the tanks,compartments and non-buoyant volumes will correctly account for the surface thicknessand its projection direction: the tanks will go to the inside of the hull shell.

Note:Thickness of boundary surfaces are not taken into account, hence youshould design these surfaces to the inside of the tank.

Compartment and Tank Ordering

Tanks defined in the Compartment Definition table appear in the loadcase in the sameorder as they are defined in the Compartment Definition table. To reorder the tanks:

Copy the tank definition data to Excel

Sort the rows in to the desired order

Paste the data from Excel back into the Compartment Definition table.

Take care if you have linked tanks – unlink them first.

Compartment and Tank Visibility

When creating complicated tank plans, it is often useful to check individual tanks.Selected tanks may be displayed in the following manner:

Define a damage case

Select only damaged tanks and compartments for display, turn off thedisplay of intact tanks and compartments.

Select whether you want to see the tank outline or the tank sections (tankssections are preferable when checking that tanks have been formedcorrectly since it is these sections which are used to determine the tankvolume and other properties).

Choose the damage case from the Analysis toolbar

Set any of the tanks and compartments you wish to be visible to damagedin the damage case window.

You can make the damage case window quite small and tile it next to the perspectiveview. Use this to quickly turn tanks on and off by changing their damage status.

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Using a damage case to quickly change the tank and compartment visibility

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Step 1: Close Internal Structure Surface

Hydromax will close the Internal Structure Surface contour by drawing a straight line between the ends of theopening.

Hydromax uses the same method for forming the tank section from the boundarysurfaces as for forming the hydrostatic sections through the hull. As with the hull

sections, the surfaces selected to form the tank boundary must form closed sectioncontours at all longitudinal positions through the tank. The area inside the selectedsurfaces will define the tank contour.

Make sure that the boundary surfaces:• Form a closed section cont our, or

• There is no more than one opening – the opening wil l be closed with a straight li ne

Note:Hydromax will close the section contour of the selected boundary surfacesonly. Often a tank is not formed as expected because only one side of theinternal structure surface was selected for example the portside (p).

Another common cause of unexpected results is trimming. If you selected“use trimmed surfaces” while opening the Maxsurf model, Hydromax willuse the trimmed internal structure surface. Usually the internal structuresurfaces are best to be left untrimmed .

Step 2: Clip to Boundary SurfaceUsing the closed surface section contour Hydromax can now form a closed compartmentsection. The tank or compartment looks like this at this stage:

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Step 3: Clip to HullHydromax will clip the compartment section to the hull.

Step 4: Clip to Boundary Box

Finally the compartment section is clipped to the boundary box. The boundary box isformed from the numerical input in the Compartment definition table.

Number of Sections in Tanks

The volume of a tank or compartments is calculated by integrating section propertiesalong the length of the tank. Thus it is important to have a sufficiently large number ofsections to accurately model the tank. Hydromax will normally place twelve sections

between the forward and aft limits defining the tank. If this results in a section spacinggreater than the spacing for the hull spacing, additional sections will be inserted into thetank so that the tank section spacing match the hull section spacing.

Also seeLongitudinal Extents of Boundary Box on page 54

Longitudinal Extents of Boundary Box

For tanks near the ship’s extremities it is good practise to set the “Fore” and “Aft” limitsin the compartment table to just inside the hull surface (say 1mm). The followingexample illustrates why:

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• If the boundary box is set like this:

The number of hull sections is dependent on the section spacing in the model.

• But if the boundary box is set just in side the forward limit of the bulbous bow:

To recap – Near the ship’s extremities, the longitudinal extents should not be set toextreme values, they should be set to just inside the extents of the hull surfaces to ensurethat at least 12 sections are used to calculate the tank volumes.

For internal structure surfaces that are used as boundary surface, Hydromax willautomatically set the “Fore” and “Aft” limits of the boundary box to just within thelongitudinal limits of the boundary surface. This ensures that at least 12 sections areinserted in the tank.

Note that transversely and vertically there are no such restrictions.

Also see Number of Sections in Tanks on page 54 Forming Compartments on page 52

Compartment TypesFive compartment types can be created using the Compartment Definition table - tanks,linked tanks, compartments, linked compartments and non-buoyant volumes.

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TanksWill be included in the tank calibration output and are automatically added to theloadcase.

Linked TanksWill have their volume added to the parent tank with the same tank name. They donot have a separate entry in the loadcase. In addition, if a tank is damaged, anytank that it is linked to will also be regarded as damaged. Tanks need not beadjoining to be linked, they can be remote from one another. In this case the tanklinking simulates tanks with cross connections.

CompartmentsAre only used to specify compartmentation for damage. They are not included inthe tank calibration output and will not be added to the loadcase.

Linked CompartmentsWork in the same way as linked tanks. This allows you to damage a complexcompartment configuration by linking compartments together and damaging the

parent compartment.

Non-Buoyant VolumesAre only used to specify compartments of the vessel which are permanentlyflooded up to the static waterline. They are ideal for defining water-jet ducts,moon pools, etc. and essentially behave as damaged compartments. They are notincluded in the tank calibration output and will not be added to the loadcase.

To change the type of a tank, type the first character of the tank type ( t , c or n ) in theType column of the Compartment Definition table and then press Enter. This willautomatically set the tank/compartment to the correct type.

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Sounding PipesHydromax allows sounding pipes to be defined for each tank. One sounding pipe pertank is permitted and up to nine vertices per sounding pipe, allowing inclined, bent orcurved sounding pipes to be modelled.

Hydromax creates a default sounding pipe when the tank is formed (either by running ananalysis, or using one of the following commands: Analysis | Recalculate Tanks andCompartments; or Analysis | Update Loadcase. The default sounding pipe is placed atthe longitudinal and transverse position of the lowest point of the tank. If the lowest

point of the tank is shared between several locations (e.g. the bottom of the tank is flateither longitudinally or transversely) the default sounding pipe location is placed at theaft-most low point and as close to the centreline as possible. The top of the sounding

pipe is taken to be level with the highest point of the tank and the default sounding pipeis assumed to be straight and vertical. Automatically created sounding pipes will berecalculated if the tank geometry changes. However, once the sounding pipe has beenedited manually, any changes to the sounding pipe due to tank geometry changes willalso have to be made manually.

Edit Sounding Pipes

To customise a sounding pipe, you need to use the Sounding Pipes table in the Inputwindow, shown below.

You can activate this window by selecting from the Windows | Input | Sounding Pipesmenu, by clicking on the tabs at the bottom of the Input window, or by clicking on the

icon in the window toolbar.

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To add vertices to create a bent sounding pipe, make the sounding pipe type UserDefined, then click on the first row of a particular sounding pipe and choose Edit | Addor use the Ctrl+A key combination. A new row will be added to the sounding pipe andthe longitudinal position, offset and height of the vertex can be edited. Unwantedvertices can be deleted by clicking on the relevant row in the table and selecting Edit |Delete or by hitting the Delete key. Note that each successive vertex in a sounding pipemust be no higher than the previous vertex i.e. it is not acceptable to have S-bends in thesounding pipes.

Calibration Increment

Hydromax allows user definable increments (or: intervals) for tank soundings. This isdone by specifying a numerical value for the increment for each tank in the CalibrationSpacing column of the Sounding Pipes Input window.

Type the value of the desired calibration increment in the CalibrationSpacing cell for the tank calibration you wish to modify.

If no increment is entered, Hydromax uses its default value based on a reasonabledivision of the depth of the tank. In this case the Sounding Pipes table will display“Auto” in the Calibration Increment column for the tank.

NoteIncrements are measured along the sounding pipe, not along the verticalaxis of the tank. If the sounding pipe is inclined or if it has multiple angles,soundings will step evenly along the inclined length of the sounding pipe.

Damage Case Defin itionIn all but the floodable length and tank calibration analysis modes, Hydromax is capableof including the effects of user-defined damage. Hydromax allows the user to set up anumber of damage cases. Volumes that are permanently flooded should be defined asnon-buoyant volumes.

Adding a Damage Case

To add a damage case, make the Damage window active and select Add Damage Casefrom the Case menu. You may specify a name for the Damage Case in the dialog. Eachnew damage case will have a column in the Damage Window and a tick may be placedto indicate which tanks and compartments are damaged for that particular Damage Case.The new damage case is added after the currently selected damage case column, to inserta damage case immediately after the intact case, select the intact case column. Severaldamage cases may be added in one go by selecting a number of columns.

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Deleting a Damage Case

To delete damage cases, simply select the columns to be deleted in the Damage Windowand select Delete Damage Case from the Case menu. Note that it is not possible to deletethe intact case.

Renaming a Damage Case

The name of the current damage case may be changed by selecting Edit Damage Casewhen the damage case window is active, the current damage case is selected from theAnalysis toolbar – see below.

Selecting a Damage Case

The current damage case is selected from the Analysis toolbar.

The Loadcase and View windows will reflect the damage defined in the current damagecase. To perform analyses for the intact vessel, select Intact as the current damage case.

Any subsequent analyses will take into account the damaged compartments. Note thatcarrying out a Tank Calibration analysis will force the intact case to be selected. This isalso the case for the Floodable Length analysis which effectively sets up its ownlongitudinal extent of damage.

When tanks have been damaged, their weights and levers are no longer displayed in theLoadcase window and the word ‘Damage’ is displayed in the quantity column. This is

because Hydromax uses the “Lost buoyancy” method rather than “Added mass”.

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Links to Tanks or Compartments

Downflooding points may be linked to tanks or compartments. Select the tank orcompartment from the combo-box in the Linked to column of the Down Flooding Pointstable in the Input window:

Downflooding points that are linked to tanks or compartments, which are damaged in thecurrently selected damage case, will be ignored when computing the downfloodingangle. These downflooding points will appear italicised and an asterisk (*) is postfixed tothe downflooding point’s name in the DF Angles table of the Results window:

The downflooding angles for each of the points are displayed in the results window. Thedownflooding angles are computed during a large angle stability analysis; the freeboardsafter an Equilibrium or Specified Condition analysis. Immersed points are highlighted inred in the Freeboard column. In addition to the Key Points results, immersion angles orfreeboards (depending on the analysis) are also given for the margin line and deck edge.In the Name column the longitudinal position where immersion first takes place (or thelowest freeboard) is given.

Note:Linking a downflooding point to a tank does not mean that Hydromax willconsider a tank damaged when the downflooding point is submerged. This

form of automatic flooding is not supported in Hydromax yet.

Margin Line PointsThe margin line is used in a number of the criteria. Hydromax automatically calculatesthe position of the margin line 76mm below the deck edge when the hull is first read in.If necessary, the points on the margin line may be edited manually in the Margin LinePoints window (the deck edge is automatically updated so that it is kept 76mm above themargin line).

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It is only necessary to modify the height value of the margin line points. Once this has been done for all the points that need to be changed, selecting Snap Margin Line to Hullin the Analysis menu will project all of the points horizontally onto the hull surface,ensuring that the margin line follows the hull shape precisely. Asymmetric margin linesand deck edges are not supported.

Points may be added or deleted as required using the procedure described in Adding KeyPoints and Deleting Key Points on page 61.

Modulus Points and Allowable Shears andMomentsThe Modulus window can be used to enter maximum allowable shear forces and bendingmoments for each section. One or more points can be entered in this window. Allowableshear force and/or bending moment can be specified at each point. The modulus value isnot currently used as deflections are not calculated.

To start a table of allowable shear forces and bending moments, bring the Modulus tableto the front and choose New Modulus Points from the File menu with the Moduluswindow frontmost. The allowable values can be saved and recalled as text files by usingOpen and Save from the File menu. New allowable values can be inserted by selectingAdd from the Edit menu and entering a longitudinal position as well as an allowableshear and/or moment.

Points may be added or deleted as required using the procedure described for the key points.

These allowable values are displayed as lines on the longitudinal strength graph.

Floodable Length BulkheadsBulkheads entered in the Input window are used for Floodable Length analysis in orderto optionally plot the compartment lengths in the floodable length graph for easyverification that the critical compartment lengths are not exceeded.

The Bulkheads are automatically sorted by longitudinal position. For more informationsee Floodable Length on page 81.

Stabil ity CriteriaStability criteria may be evaluated after a Large Angle Stability analysis and after anEquilibrium analysis. Stability criteria are required to perform a limiting KG andFloodable Length analysis. Please refer to Chapter 4 Stability Criteria starting at page113 for information on defining and selecting criteria.

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Analysis TypesAfter specifying the input values and checking the Hydromax model, the analysis can be

performed. In this section the different analysis types available in Hydromax will bedescribed.

The following analysis types are available in Hydromax:• Upright Hydrostatics

• Large Angle Stability

• Equilibrium Analysis

• Specified Condition s

• KN Values Analysis

• Limiting KG


• Longitudi nal Strength


Also, some general information is given on:• Starting and Stopping Analyses

• Batch Analysis

The required analysis settings and environment options will be discussed separately andin more detail in the next two sections of this chapter.

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Upright HydrostaticsUpright hydrostatics lets you determine the hydrostatic parameters of the hull at a rangeof drafts, at zero or other fixed trim.

Choosing Upright HydrostaticsSelect Upright Hydrostatics from the Analysis Type option in the Analysis menu ortoolbar.

Upright Hydrostatic Analysis Settings

The following analysis settings apply for Upright Hydrostatic Analysis:• Draft from the Analysis menu, specify range of drafts for analysis

• Trim from the Analysis menu, you may specify a fixed trim for all drafts

A range of drafts for upright hydrostatic calculations can be specified using the Draftscommand from the Analysis menu.

Initial and final drafts can be entered, together with the number of drafts to be used. TheVertical Centre of Gravity is also required for the calculation of GM etc. This isspecified as KG, i.e. from the baseline, which is not necessarily the vertical zero datum.

When a design is first opened, the initial draft defaults to the draft at the DWL inMaxsurf. Similarly the VCG defaults to the height of the DWL.

Upright Hydrostatics Environment Options

The following environments can be applied to the upright hydrostatics analysis:• Density fro m the Analysis menu

• Wave Form (if any)

• Hog and Sag

• Damage (or Intact) from the Analysis toolbar

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Large Angle StabilityLarge angle stability lets you determine the hydrostatic parameters of the hull at a rangeof heel angles either with or without trim or free-to-trim.

Choosing Large Angle StabilitySelect Large Angle Stability from the Analysis menu or toolbar.

Large Angle Stability Settings

The following analysis settings apply for Large Angle Stability Analysis:• Displacement and Centre of Gravity usi ng t he Loadcase window

• Heel from the Analysis menu, select range for analysis

• Trim (fixed or free) from the Analysis menu

If criteria are being evaluated, the heel range and heel angle steps should be chosen

accordingly, to ensure accurate evaluation of the criteria.

NoteYou can select positive heel direction (port or starboard). However, you canenter negative values and test full 360 degrees of stability if you wish. Somecriteria require calculations of GZ at negative heel. The criteria are onlyevaluated on the side of the graph that corresponds to positive heel angles.

For example: when using a -180 to 180 heel range, the results may be twoangles of vanishing stability, the one that would be reported in the criteriawould be the one with a positive heel angle (even if the one at negative heeloccurred at an angle closer to zero).

Also see: Heel on page 94 in the Analysis Settings section.

Large Angle Stability Environment Options

The following environments can be applied to the large angle stability analysis:• Fluid simulation of tank fluid s centre of gravity

• Density


• Hog and sag (if any)



Large Angle Stability Results

Large Angle Stability Analysis results are:• Hydrostatic data table for each angle of heel

• GZ curve

• Stability Criteria evaluation

• Downflooding angles to key points, deck edge and margin line

• Curve of areas at each heel angl e

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Downflooding AngleAfter a Large Angle Stability analysis, the Key Points Data table lists thedownflooding angles of the margin line, deck edge and defined Key Points. Inaddition, the first downflooding point is marked on the large angle stability graph.Only the positive downflooding angles are displayed, hence if there is any

asymmetry, the large angle stability analysis should be carried out heeling both tostarboard and to port. For the margin line and deck edge the longitudinal positionat which immersion first occurred is provided.

Downflooding points that are linked to tanks or compartments that are damaged inthe currently selected damage case, will be ignored when computing thedownflooding angle. These downflooding points will appear italicised, and anasterisk (*) is postfixed to the downflooding point’s name in the Key Point Datatable of the Results window.

A downflooding angle of zero degrees indicates that the key point is immersed atzero degrees of heel.

Also see:Select View from Analysis Data on page 110 .

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Equilibr ium AnalysisEquilibrium analysis lets you determine the draft, heel and trim of the hull as a result ofthe loads applied in the table in the Loadcase window. The analysis can be carried out inflat water or in a waveform.

Choosing Equilibrium Analysis

Select Equilibrium from the Analysis Type option in the Analysis menu.

Equilibrium Analysis Settings

• Displacement and Centre of Gravity usi ng t he Loadcase window

Also see:Setting the Frame of Reference on page 20

Equilibrium Analysis Environment Options

The following environments can be applied to the Equilibrium analysis:• Fluid simulation of tank fluid centre of gravity

• Density


• Hog and Sag (if any)


• Grounding (if any)

• Criteria

Equilibrium ResultsEquilibrium Results are:

• Hydrostatic data

• Freeboard of key points, deck edge and margin line

• Criteria evaluation

• Time stepping animation

• Curve of areas

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Hydrostatic data

Height/freeboard above free surfaceThe freeboard of each Key Point is also calculated. The freeboard is for the vesselcondition currently displayed in the Design view and is recalculated after eachEquilibrium and Specified Conditions analysis. The freeboard calculated is thevertical distance of the Key Point above the local free surface; hence the local freesurface height if a waveform is selected will be taken into account.

Freeboard of key points.

Negative freeboards, i.e. where the Key Points are immersed are displayed in red.The longitudinal positions at which the minimum freeboard for the margin lineand deck edge occurred are also specified.

Stability Criteria EvaluationThe criteria results are displayed in the Criteria tab in the results window.

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Equilibrium Animation in WavesIf performed in conjunction with analysis in waves, the Equilibrium analysis willautomatically phase-step the waveform through a complete wavelength. This givesten columns of results, one for each position of the wave crest. If necessary theresults of this phase stepping can be animated giving a simple, quasi-static

simulation of the hull motion in waves (Display | Animate).

Note:This simulation only includes static behaviour at each wave phase, and doesnot cover dynamic or inertial forces. This can be done using Seakeeper.

Equilibrium Concept

The definition of equilibrium is “Position or state where object will remain ifundisturbed”. You can distinguish equilibrium into two types:

• Stable, when disturbed the object will return to i ts equilibrium posi tion

• Unstable, when disturbed the object will not return to its equilibri um position

With ships, an unstable equilibrium can exist when the KG > KM, i.e. the centre ofgravity is above the metacentre (negative GMt). In real world a ship in unstableequilibrium will roll from the upright unstable equilibrium position to a position of stable

equilibrium and assume an “angle of loll”. Since Hydromax starts the equilibriumanalysis in upright position, it has no way of determining whether the equilibrium isstable or unstable. This means that unstable equilibrium may be found instead of thestable equilibrium. Therefore it is recommend to check the value of GMt yourself afterdoing an equilibrium analysis or perform a Large Angle Stability analysis and look at theslope of the GZ curve through the equilibrium heel angle.

Stable equilibrium Unstable equilibrium

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Unstable equilibrium

Stable equilibrium”Angle of loll”

The graph above shows the results of a Large Angle Stability analysis for a vessel withnegative initial GMt. In practice this vessel would have a loll angle of approximately 25degrees. If an equilibrium analysis is performed for this vessel with the transverse armset to zero, Hydromax will find the unstable equilibrium position with zero degrees ofheel.

In practice, it is desirable to find the stable equilibrium position. To do this, first ensurethat the tolerances (Edit | Preferences ) are set as sensitive as possible. This will ensurethat the smallest possible heeling moment is required to find stable equilibrium position.Then create a very small heeling moment by offsetting one of the weight items in theloadcase window TCG by just a fraction. The equilibrium analysis will now find thestable equilibrium position.

Note:It is good practice to always perform a Large Angle Stability analysis aswell as the equilibrium analysis to check if the vessel is in stable or unstableequilibrium. This is most likely to occur if the VCG is too high and thevessel has negative GM when upright. The problem can be overcome byoffsetting the weight of the vessel transversely by a small amount.

Specified ConditionsSpecified Condition analysis lets you determine the hydrostatic parameters of the vessel

by specifying the heel, trim and immersion. Heel can be specified by either the angle ofheel or the TCG and VCG. Trim can be specified by the actual trim measurement, or theLCG and VCG. Immersion can be specified by either the displacement or the draft.

Choosing Specified Conditions

Select Specified Conditions from the Analysis Type option in the Analysis menu ortoolbar.

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KN Values AnalysisKN Values Analysis allows you to determine the hydrostatic properties of the hull at arange of heel angles and displacements to produce the cross curves of stability diagram.

Choosing KN Values AnalysisSelect KN Values from the Analysis Type option in the Analysis menu or toolbar.

KN Values Analysis Settings

The analysis settings required for KN Values analysis are:• Heel from the Analysis menu, select range for analysis


• Displacement from the Analysis menu, select range for analysis and specifyestimate of VCG if known

The heel angles used may differ from those used in the Large Angle Stability andLimiting KG analyses. To set the range of angles, select Heel from the Analysis menu.

A range of displacements for KN calculations can be specified using the Displacementcommand from the Analysis menu. Initial and final displacements can be entered,together with the number of displacements required.

The VCG can also be entered (specified from the vertical zero datum). Traditionally, KNcalculations are calculated assuming the VCG at the baseline (K). However if theanalysis is being calculated free-to-trim and an estimate of the VCG is known, theaccuracy of the KN calculations (for VCGs in the vicinity of the estimated VCG) may beimproved by calculating the GZ curve using the estimated VCG position – this willreduce the error in the trim balance due to the vertical separation of CG and CB becausethis vertical separation is specified more accurately than simply assuming the VCG at the

baseline.If a VCG estimate is specified, the KN values are still presented in the normal mannerwith the KN values calculated as follows:

KN(φ) = GZ( φ) + KG_estimated sin( φ)

For information on Trim settings for KN Analysis, see: Trim for KN, Limiting KG andFloodable Length analyses on page 96.

Also seeKN Value Concepts on page 76

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KN Values Analysis Environment Options

• Density




KN Values Analysis Results

KN Value Concepts

The righting lever, GZ, may be calculated from the KN cross curves of stability (at thedesired displacement) for any specified KG using the following equation: .

GZ = KN - KG sin( φ)

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Limiting KGLimiting KG analysis allows you to analyse the hull at a range of displacements todetermine the highest value of KG that satisfies the selected stability criteria. GZ curvesare calculated for various KG values. After each cycle, the selected criteria are evaluatedto determine whether the CG may be raised or must be lowered.

When comparing the results of a limiting KG analysis to that of a Large Angle Stabilityanalysis, it is essential that the same heel angle intervals are used and that the free-to-trim options and CG are the same. Some criteria, notably angle of maximum GZ, areextremely sensitive to the heel angle intervals that have been chosen.

Choosing Limiting KG

Select Limiting KG from the Analysis Type option in the Analysis menu or toolbar.

Limiting KG Settings

The initial conditions required for Limiting KG analysis are:• Displacement from the Analysis menu, select range for analysis

• Heel from the Analysis menu, select range for calculation of GZ curves


The range of displacements to be used is set in the same way as they are set in the KNanalysis.

The heel angles used may differ from those used in the Large Angle Stability and KNanalyses. To set the range of angles, select Heel from the Analysis menu. See LargeAngle Stability on page 67 for further details.

For information on Trim settings for Limiting KG Analysis, see: Trim for KN, LimitingKG and Floodable Length analyses on page 96.

Note:Since Limiting KG can be quite a time consuming analysis, you may wishto use a smaller number of heel angles than for the Large Angle Stabilitycalculations. (However this will cause some loss of accuracy.)

Limiting KG calculations will be significantly faster if the trim is fixed.

Limiting KG Environment Options• Fluid simulation of tank fluid centre of gravity

• Density




• Criteria

Limiting KG Results

Limiting KG analysis results are

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• Limiting KG values, for each displacement and the li miting criterion.

• Limiting KG vs displacement graph

The Limiting KG value is measured from the baseline, which is not necessarily the sameas the zero point.

The Limiting KG analysis also checks that any selected equilibrium based criteria are passed at each VCG that it tries. However, you must still have at least one Large AngleStability criterion selected.

Criteria are only evaluated on the positive side of the GZ curve, so if there is any form ofasymmetry, it may be necessary to run the analysis heeling the vessel to both starboardand port (this can be done automatically in the Batch Analysis).

After a Limiting KG analysis has completed, the results in the Criteria results tabledisplay “Not Analysed”, this is because they do not necessarily refer to the final KG andwould be misleading. If you require the limiting KG for each criterion individually orwish to perform a Large Angle Stability and Equilibrium analysis at each of thedisplacements and the corresponding limiting KG, this can be done in the BatchAnalysis.

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Some criteria may depend on the vessel displacement and or vessel’s VCG. Where thesevalues are explicit in the criterion’s definition in Hydromax, the correct values ofdisplacement and VCG will be used in the evaluation of these criteria. However,

problems can arise if the criterion is only available in its generic form – most commonlyheeling arm criteria where the heeling arm is specified simply as a lever and not as amoment. In this case, since the heeling arm is not related to the vessel displacement in itsdefinition within Hydromax, the heeling arm will remain constant for all displacements(where it is perhaps desired that the heeling arm should vary with displacement. Forexample in the case where the heeling moment, rather than the heeling arm is constant).

Important:For important information on varying displacement while evaluating criteriasee Important note: heeling arm criteria dependent on displacement on page183.

Also see:Convergence Error on page 98 in the Analysis Settings section.

Limiting KG Concepts

Hydromax will iterate to a KG value that just passes all criteria you have specified in thecriteria dialog. Hydromax will start with a set start KG value (e.g. 1 meter), run a largeangle stability analysis and check the selected criteria. If any of the criteria fail,Hydromax will lower the KG and try again. If the criteria pass, Hydromax will raise theKG value and try to make the criteria fail. Hydromax will continue doing this until thelimiting KG value has been iterated to within 0.1mm. If this tolerance is not achieved ina certain number of iterations, Hydromax will move on to the next displacement.

When performing a Limiting KG analysis, Hydromax will evaluate any equilibrium-

based criteria that are selected for testing and act accordingly. However, at least one GZ- based criterion must also be selected. This is because to perform a sensible search,Hydromax must have at least one criterion that will improve by reducing the VCG;Hydromax assumes that raising the VCG will make criteria more likely to fail and thatreducing the VCG will make the criteria more likely to pass. This is not necessarily thecase for equilibrium-based criteria such as freeboard requirements or for GZ-basedcriteria such as Angle of maximum GZ; if only these types of criteria are selected,Hydromax may have difficulty in finding a true limiting KG and specify convergenceerrors.

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Floodable LengthThe Floodable Length analysis allows you to calculate the longitudinal distribution ofmaximum length of compartments that can be flooded with the vessel still passingspecified equilibrium criteria. The results are presented as the maximum length ofcompartment plotted (or tabulated) against the longitudinal position of thecompartment’s centre. Traditionally the criterion of margin line immersion is used tocompute the Floodable Length curve. The Floodable Length may be computed for arange of displacements and compartment permeabilities.

Choosing Floodable Length

Select Floodable Length from the Analysis Type option in the Analysismenu or toolbar.

Floodable Length Analysis Settings

The initial conditions required for Floodable Length analysis are:• Trim (free-to-trim, either initial trim or specified LCG)

• Displacement, select range and sp ecify VCG

• Permeability, select range

• Bulkhead location (if applicable)

The analysis is always carried out free-to-trim, but the centre of gravity can either bespecified directly in the Trim dialog or it is computed from the specified initial trim. Forinformation on Trim settings for Floodable Length Analysis, see: Trim for KN, LimitingKG and Floodable Length analyses on page 96.

The range of displacements to be used is set in the same way as they are set in the KNand Limiting KG analyses. The VCG must also be specified since the Floodable lengthanalysis is very sensitive to accurate trim calculations. This means that the verticalseparation of CG and CB is accounted for in the trim balance.

The permeability dialog is used to specify the permeabilities to be used for the FloodableLength analysis; the permeability is applied over the entire length of the vessel and isalso applied to the free-surface when calculating the reduction of waterplane area andinertia.

This permeability is unrelated to the permeability when defining compartments and isonly used for floodable length calculations.

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Floodable Length Environment Options

• Density



• Damage: no damage case may be selected as this i s automati cally defin ed by theanalysis. The Intact conditio n i s automatically selected and the Damage toolbar isdisabled

• Criteria from the Analysis menu, select which criteria should be evaluated

Criteria must be specified from the analysis menu. These are used to compute theFloodable Lengths.

Note that internally, Hydromax will treat the vessel sinking or the trim exceeding +/-89ºas a criterion failure.

Floodable Length results

The results of the analysis are given in tabulated format at the stations defined in theMaxsurf grid spacing as well as graphical format. The tabulated data is linearlyinterpolated from the graphical data. (The raw graph data can be accessed by doubleclicking the graph.)

There are several graph plot options available in the Data | Data format dialog (when thefloodable length graph is topmost). The vessel profile (centreline buttock) may also bedisplayed. All compartment standards up to the maximum specified will be plotted.

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Floodable lengths graph options:• Fix the y-axis so t hat it i s the same scale as the x-axis.

• Plot the diff erent comp artment standards u p to a specified maximum value.

• Vessel profile (shown in light g rey)

• Floodable Length Bul kheads locations are specified in a table in the Input window .The graph upd ates in real time as you adjust the bulkhead locations so once youhave calculated the floodable lengths, you can quickl y adjust the bul kheadlocations so that the vessel meets the r equired compartment standard.

If the analysis is unable to find a condition where the vessel passes the selected criteria,the following dialog will be displayed. The vessel sinking or the criteria failing in theintact condition could cause this.

Floodable Length Concepts

The analysis is performed by defining a flooded compartment, with the centre of thecompartment at a section under investigation. The length of this flooded compartment is

increased section-by-section until one of the criteria is failed. The compartment is thenmoved progressively forward along the vessel. This process may be visualised by turningon the display of the Hydromax sections.

Note: Speed versus Ac curacyThe analysis will be both considerably more accurate and slower with alarger number of sections in the Hydromax model; it is recommended that aminimum of 100 sections be used for most situations.

The speed of the analysis can be increased quite considerably by increasingthe allowable tolerances in the Edit | Preferences dialog.

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Longitudinal StrengthLongitudinal Strength lets you determine the bending moments and shear forces createdin the hull due to the loads applied in the Loadcase window. The analysis can be carriedout in flat water or in a specified waveform.

Choosing Longitudinal Strength

Select Longitudinal Strength from the Analysis Type option in the Analysis menu ortoolbar.

Longitudinal Strength Settings

The initial conditions required for Longitudinal Strength analysis are:• Displacement and Centre of Gravity usi ng t he Loadcase window

• Distributed loads using the Loadcase window

When the Longitudinal Strength analysis mode is selected, two extra columns appear in

the Loadcase window. These are used to specify the longitudinal extents of the load. Atrapezium shaped distributed load is derived from the centre and fore and aft extents ofthe load. See the Loadcase Longitudinally Distributed Loads section on page 38 for moredetails.

Longitudinal Strength Environment Options

• Density


• Hog and Sag


• Grounding (if any)

• Criteria, allowable shears and moments from Input window

Note that Hydromax will always use the fluid simulation method when performing alongitudinal strength analysis. For more information on how Hydromax can take fluidsin tanks into account see Fluids Analysis Methods on page 100.

Longitudinal Strength Results

The output from the longitudinal strength calculations is a graph of weight, buoyancy,net load, shear force and bending moment along the length of the hull. If defined,allowable shear forces and bending moments are overlayed on the graph.

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Name of Curve DescriptionWeight Vessel mass / unit lengthBuoyancy Buoyancy distribution / unit length = immersed cross sectional

area * density. Damaged tanks and compartments reduce the buoyancy.

Net Load Weight – BuoyancyShear

Shear Force = ∫ x

AftSt dx x NetLoad )(

MomentBending Moment = ∫−

x

AftSt

dx xShearForce )(

Allowable shearand moment

Allowable shear and bending moments as specified in the inputModulus table.

This data is also displayed in the “Long. Strength” tab in the Results window. You candisplay this table by choosing Longitudinal Strength from the Results sub-menu underthe Window menu.

NoteMake sure you have defined sections in your model in Maxsurf. Withoutthis, the longitudinal strength table will be empty.

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Tank CalibrationsTank Calibration allows you to determine the properties of the tanks you have defined inthe Compartment window, at a range of capacities.

Choosing Tank Calibrations

Select Tank Calibrations from the Analysis Type option in the Analysis menu or toolbar.

Tank Calibration Input

• Tank definitio ns and boundaries

• Permeability

• Fluid type

All required Tank Calibration Analysis input can be specified in the CompartmentDefinition table.

Note: Note that permeability and relative density values can be changed after thetanks have been calibrated, the capacities and free surface moments will beupdated automatically.

Also see:Relative Density of Tank Fluids on page 49

Tank Calibration Settings

• Trim, fixed trim

Tank Calibration Environment Options


• Density

Tank Calibration Results

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In the Window | Graphs menu each tank can be selected for display in the Graphwindow. For more information see Chapter 5 Hydromax Reference .

Sounding pipes and tank calibration results

If the vessel is trimmed, there are ranges of tank volumes that will show the samesounding/ullage. (The same effect can occur if the sounding pipe does not reach thelowest or highest point in the tank – remember that this can change as the vessel trims,which is effectively what is happening in the figures below). These points occur whenthe tank is near empty or near full, see below (increasing the trim, will exacerbate this

phenomenon):

Figure a Zero trim

Figure b

Trim by bow, near-emptytank

Figure c Trim by bow, near-full tank

Figure a shows a sounding pipe that extends the whole height of the tank, with thevessel at zero trim. Here all tank filling levels will have a valid sounding.

Figure b shows the vessel with (bow down) trim and a small amount of fluid in the tank.Here there will be a range of tank filling levels which all show zero sounding.

Figure c shows the vessel with the same trim, but with the tank nearly full. Here therewill be a range of tank filling levels that all show maximum sounding.

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Starting and Stopping AnalysesTo start the analysis, choose Start Analysis from the Analysis menu or toolbar.Hydromax will step through the parameter ranges specified, floating the hull toequilibrium conditions where required. Hydromax will redraw the contents of thewindows to display the current hull position for each iteration.

Calculations may be interrupted at any time by selecting Stop Analysis from theAnalysis menu or toolbar.

If you have stopped the analysis, you can resume calculation by selecting ResumeAnalysis from the Analysis Menu or toolbar.

There may be a slight time delay on all of these operations while the current cycle isfinished.

You can also switch application by clicking in the window of any background program.Hydromax will continue to calculate in the background although its speed will bereduced. The drawing of the vessel at each step of the analysis can be quite timeconsuming. If you are not interested in seeing the progress of the analysis, switch to atable window and maximise it to speed up the analysis. Should the analysis take longerthan about 45 seconds, Hydromax will flash and beep to indicate that the analysis has

been completed.

The start, pause and resume functions are also available in the Analysis toolbar:

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Batch Analysis

Batch Analysis Concepts

Hydromax has basic batch processing capability. With a single command, Hydromaxwill run Large Angle Stability and Equilibrium analyses for all combinations of load anddamage cases. Further, Limiting KG and KN calculations can be made for each damagecondition. There are other options which allow the analysis to be performed heeling to

both port and starboard. For the Limiting KG analysis you may also check the LimitingKG for each criterion individually. You may also choose to perform a Large AngleStability and Equilibrium analysis at the final VCG.

The aim of the batch processing function is to:• Provide the user with a simple and consistent w ay of carrying out Large Angle

Stability and Equilibrium analyses on a large number of load and damage cases.

• Facilitate time consumin g Limit ing KG analyses, especially where results for allindividual criteria are required.

• Enable Limiting KG and KN analyses to be performed automatically for all damagecases.

• Facilitate testing with heel to port and starboard for vessels wit h asymmetricloading and/or damage conditions (or hull s).

• Facilitate export of t he data from Hydromax and import into MS Excel for postprocessing and r eport generation.

• Provide all relevant results and the data required to be able to reproduce the ru ns,i.e.: analysis parameters, fil e name etc.

Before you can perform a Batch Analysis it is recommended that you run a number ofAnalyses manually to check whether the Model has been defined correctly and allAnalysis Settings and Environment conditions have been set correctly.

Batch Analysis – Procedures

Once the loadcases, damage cases, key points, criteria and analysis parameters for therequired analyses have been set up, the Batch Analysis is started

• Analysis | Start Batch Analysis

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Batch analysis runs all combination of loadcases and damage cases.

Tip: Under most operating systems, minimising Hydromax can reduce the time requiredto perform the calculations. This is because time consuming redrawing of the designwindows, graphs and tables is avoided.

Batch Analysis Settings

Analysis parameters such as trim, heel angles etc. are set in the normal way for eachanalysis type included in the Batch analysis. For example, if you want the Large AngleStability to use a fixed trim of 0.5 m:

• first select th e Large Angle Stability analysis type from the analysis menu

• set the trim to Fixed trim and 0.5 m

• then select Analysis | Batch Analysis

Batch Analysis Environment Options (Criteria)

Any Analysis Environment Options specified prior to a Batch Analysis will be usedduring the Batch Analysis. Any criteria that have been set are evaluated at the end ofeach analysis and the results of these are also output to the text file.

Important:For important information on varying displacement while evaluating

criteria, see Important note: heeling arm criteria dependent on displacement on page 183.

Batch Analysis Results

Before analysis starts, you will be prompted to enter the name and location of the filewhere Hydromax will write the results of the batch analysis. Once the analysis iscomplete, this tab delimited text file may be imported directly into MS Excel for further

processing.

Because the analyses are simply carried out one after the other, it is not possible to go back to the results for a specific analysis from within Hydromax; only the results of thefinal analysis will be stored in Hydromax.

At the bottom of the dialog is a check box which allows users to select whether theresults of a batch analysis should go to the Report window in Hydromax as well as the

batch analysis text file. When the option for Sending the results to Word is selected inthe Edit | Preferences dialog, the batch analysis will automatically create a Worddocument.

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Warning:Sending the results to the Report can slow down analysis considerably andalso consume considerable system resources. For large batch analysis, it isadvisable not to include the results in the report. The report is stored inmemory and if you have insufficient memory, it is possible that your

computer will become very slow to respond and under some circumstanceswith certain operating systems even cause Hydromax to crash.

Also see: Reporting on page 108.

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Analysis SettingsIn the previous sections opening and preparing a model in Hydromax was discussedtogether with descriptions of the different Analysis types. This section will describe thefollowing analysis settings:

• Heel

• Trim

• Draft

• Displacement

• Specified Condition s

• Permeability

Hydromax will allow specification of only those analysis settings that apply to thecurrently selected analysis type.

In hydrostatic analysis, there are three degrees of freedom: Trim, Heel and Draft.Hydromax matches the trim, heel and draft with the vessel’s mass and centre of gravityor visa versa. This way the volume of the displaced hull matches the required mass andthe centres of gravity and buoyancy lie one above the other in a vertical line. Forexample: it can match a specified heel, trim and draft by varying the displacement andcentre of gravity; or it can match a specified displacement and centre of gravity byvarying the heel, trim and draft. Combinations of both are also possible. The followingtable is a very simplified representation of the degrees of freedom and their weightcounterpart:

Degree of Freedom Weight1 Draft Displacement2 Trim Longitudinal Centre of Gravity (LCG)3 Heel Transverse Centre of Gravity (TCG)

In fact it is a rather more complicated situation than that suggested by the table above, because vertical centre of gravity is also important and also because most of thevariables are coupled.

The various analysis types and settings can be thought of as setting one variable in each pair to a fixed value and deriving the others from the analysis.

For example: the Upright Hydrostatics analysis consists of fixing heel and trim and

stepping through a series of fixed drafts. In this case the LCB and TCB (and thereforethe required LCG and TCG) are calculated from the underwater hullshape at each draft.For an equilibrium analysis all degrees of freedom are derived from the centre of gravityand Displacement. In the Specified Condition Analysis any combination of the variable

pairs may be specified.

HeelThe Heel dialog from the analysis menu is used to specify the range of heel angles to beused for Large Angle Stability, KN and Limiting KG analyses. Heel angles between -180° and +180 ° may be specified. The heel steps must be positive. If only one set ofsteps is required, simply put 0 in the other steps.

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If there is any asymmetry in the vessel due to either: hull shape, key points, loading,damage, etc., and there is any doubt as to which will be the worst heel direction, then theanalysis should be carried out for both heel to starboard and heel to port to find the most

pessimistic condition.

If all the heel angle intervals are 10 deg or less, Hydromax will fit a cubic spline to theGZ curve and use this to interpolate for values between the tested heel angles. If any stepis greater than 10 deg, Hydromax will not do any curve fitting and linear interpolationwill be used.

Note:For the angle of equilibrium to be found (when analysing criteria), it isessential that the GZ curve crosses the GZ=0 axis with positive slope. It is

possible that the GZ at zero heel may be very slightly positive (due toasymmetry or rounding error) for this reason, it is advisable to test at leastone negative heel angle, at say -5 degrees, to ensure that the equilibriumangle is identified.

It is good practise to start the heel range at an angle of approximately -30°.This is to allow roll back angle criteria to be evaluated correctly.

Note:The heel angles to be used are specified independently for each analysismode. This can be a source of apparent differences in the results from thedifferent analyses.

TrimFor most analyses you may specify whether the vessel is free-to-trim or has fixed trim.Select Trim in the Analysis menu to bring up the Trim dialog.

Specification of different trim options is dependent on the type of analysis currently selected.

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Trim may be specified for Upright Hydrostatics, Large Angle Stability, KN AnalysisLimiting KG, Floodable Length and Tank Calibrations. (For the Specified Conditionanalysis, the trim may be specified in the Specified Conditions dialog.) Equilibrium andLongitudinal Strength analyses always use a free trimming (and free heeling) analysis sothat there is no trimming (or heeling) moment applied to the vessel at the finalequilibrium.

Trim for KN, Limiting KG and Floodable Length analyses

Fixed trim(KN and Limiting KG analyses only).The analysis is carried out with the specified fixed trim; the vessel is not free-to-trim as it heels. Although considerably faster, this analysis will tend to over-estimate ship stability properties such as GZ.

Free-to-trim using a specified initial trim valueUsing this method, for each displacement, the LCB of the intact vessel at thespecified trim and zero heel is computed. The LCG is calculated using this value

and the VCG. Calculations at each heel angle of the large angle stability analysisare then done free-to-trim using the derived LCG and VCG. Thus, for eachdisplacement, the upright, intact vessel trim will be the same, but the LCG will bedifferent.

Free-to-trim to a specified LCG valueWith this method, a specified constant LCG is maintained for each displacement.This LCG is then used to compute the free-to-trim vessel orientation at each heelangle as the large angle stability analysis is performed. Thus, for eachdisplacement, the LCG will be the same, but the upright vessel trim will bedifferent.

DraftThe draft dialog is used to specify the range of drafts to be used for the Uprighthydrostatics analysis.

The VCG specified in the draft dialog is used for the calculation of upright stabilitycharacteristics such as GMt only, and is specified in terms of KG – i.e. from the

baseline, which is not necessarily the vertical zero datum.

DisplacementThe displacement dialog is used to specify the range of displacements to be used for theKN, Limiting KG and Floodable Length calculations.

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The VCG may also be specified, in this case it is measured from the vertical zero datum.

For KN analysis, the VCG will only have an effect if the analysis is free-to-trim. It will be used to determine the LCG if an initial trim value is specified. It will also be used toimprove the accuracy of the KN results.

For Floodable Length calculations, which are always calculated free-to-trim, the VCGwill be used to calculate the LCG if an initial trim value is specified. Also, because theanalysis is very sensitive to trim, the VCG is needed to provide an accurate balance ofthe trimming moment. (As the trim angle increases the longitudinal movement of thecentre of gravity due to its vertical position becomes more important.)

In the case of the Limiting KG analysis, the actual VCG is used and the VCG input fieldwill state “not applicable”.

Specified Conditions

The specified conditions analysis setting is only available for the specified conditionanalysis.

See Specified Conditions on page 73.

PermeabilityThe Permeabilities are set in a table in the Permeability dialog. Use the Add and Delete

buttons to add or delete rows from the table. The permeabilities may be sorted by doubleclicking on the permeability column heading. The last set of permeabilities used will berecalled from the registry when Hydromax is started.

The Permeability dialog is used to specify the permeabilities to be used for the Floodable

Length analysis; the permeability is applied over the entire length of the vessel.

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This permeability is unrelated to compartment, tank or non-buoyant volume permeabilityand is only used for floodable length calculations.

Individual Permeability of Tanks and Compartments

The individual permeability of each compartment (or tank) is specified in theCompartment definition table. The compartment, tank and non-buoyant volume permeabilities are used when calculating the effects of damage, and/or calculating theweights of fluids in tanks in the loadcase.

Also see:Modelling Compartments on page 40

TolerancesIn the Edit | Preferences dialog of Hydromax, calculation tolerances can be set. Thisdefines the tolerances that Hydromax uses to determine when to finish iteration during

• Large Angle Stability• Equilibrium analysis

• Specified conditio ns

• KN calculations


• Longitudinal Strength

Ideal tolerances can range between 0.00001% and 0.1% (1 gram in 10 tonnes ofdisplacement). Acceptable tolerances can range from 0.001% to 1.0%. Acceptabletolerances should always be greater than Ideal tolerances.

Convergence Error

Hydromax will attempt to solve most analysis to within the ideal tolerance. If this is notachieved within a certain number of iterations, but the acceptable error has beenachieved, Hydromax will continue. If convergence to within the acceptable error has not

been achieved, Hydromax will display a warning.

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One of the most common causes of non-convergence is if the specified displacementexceeds the volume of the completely submerged vessel and it sinks. Also convergencemay be poor if the trim angle approaches ±90°. If Hydromax thinks that it is likely thatthe model has sunk (waterplane area is zero at the current condition) the following dialogwill be displayed. The specified displacement and the actual displacement at the currentiteration are provided for information.

NoteThis warning is not displayed during batch analysis, instead the warning iswritten in the batch file.

If there is a convergence problem, which appears not to be due to sinking, then thefollowing dialog will be displayed.

This problem can sometimes occur if the specified displacement is extremely small andthe vessel has a large flat bottom, producing a highly non-linear waterplane area vs. draft

plot. Other causes of non-convergence can be non-linear moment to trim vs. trim anglecurve or moment to heel vs. heel angle curve.

Note:There are occasions when convergence will not necessarily occur within themaximum allowable number of iterations. If Hydromax fails to converge itwill give you a warning, but will allow you the option of continuing thesearch. If you choose to continue, Hydromax will search for the equilibrium

position indefinitely . If the search is unsuccessful after a reasonable periodof time, you can interrupt Hydromax by pausing the analysis.

The analysis will also fail to converge if the trim becomes excessive. All analyses otherthan Floodable Length will fail if the trim exceeds +/-45º; in the case of the FloodableLength analysis, this limit is increased to +/-89º.

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Analysis Environment OptionsThe analysis can be performed in different environments; this section describes theanalysis environment options available in Hydromax in more detail:

• Fluids Analysis Methods

• Density

• Waveform

• Grounding

• Hog and Sag


• Damage

Fluids Analysis Methods

Hydromax allows you to specify two different ways of simulating any fluids contained intanks or compartments. Selecting Fluids in the Analysis menu opens the Fluids Analysisdialog.

NoteMost documented stability criteria assume that the corrected VCG methodhas been used. Although the computational potential is available, authoritieshave not adopted this more accurate calculation of the shift in centre ofgravity due to fluid movement.

Fluid analysis method: Use corrected VCG

Tank capacities and free surface moments are calculated for the upright hull (zero trimand zero heel). The effective rise in VCG due to the tanks' free surface is calculated bysumming the free surface moment of all the tanks filled to less than 98% capacity anddividing by the total vessel displacement (the free surface moment to be applied isspecified in the loadcase).

This method should be used when compiling a stability booklet for a design, as itcorresponds with the traditional approach used by naval architects and classificationsocieties worldwide. It is reasonably accurate at low angles of heel and trim.

In this case, the loading window will include a column for free surface moment and cellsfor corrected fluid VCG. These values are automatically calculated from the maximumfree surface moments of the tanks, calculated in the upright condition. There are severalFSM types available. For more information, see Working with Loadcases on page 33.

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Fluid analysis method: Simulate fluid movement

This method is a faithful simulation of the static movement of the centre of gravity of thefluid in each tank. Every tank is rotated to the heel and trim angle being analysed.Hydromax iterates to find the fluid level for the rotated tank at the specified capacity.The new centre of gravity is calculated for each tank and used in the analysis. The newLCG, VCG and TCG are calculated for the whole design and used in the calculation ofGZ, KG, and GM.

This approach is used when the stability of a vessel is being investigated and the closest possible simulation of the hull's behaviour is required. It is particularly useful at high

angles of heel or trim, or with tanks whose heeled water plane area may be significantlydifferent from the upright case (i.e. tall narrow tanks, or wide shallow tanks). The

penalty of using this approach is that the calculation time is longer, however the resultsare significantly more accurate.

When fluid simulation method is selected, free surface moments and corrected fluid VCG are not applicableand are not displayed in the loadcase.

When selected, fluid simulation is used for analyses that use a loadcase, i.e. Large AngleStability, Equilibrium Condition and Longitudinal Strength (the Longitudinal Strengthanalysis always uses fluid simulation). When fluid simulation is used in one of theseanalyses, the actual fluid level in the tank, filled to the volume specified in the loadcase,will be displayed in the View window. Otherwise the complete tank will be shown.

Density of Fluids

Where necessary, the density of sea water (the fluid in which the vessel is floating) andfluids commonly carried on board can be adjusted using the Density dialog.

Density using the current units, or non-dimensional relative density (specific gravity),may be specified. Alternatively, density may be specified using Barrels as the unit ofvolume. Conversions are performed automatically. Relative density is calculated relativeto a fluid having a density of 1000.0 kg/m 3.

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By assigning a code to the fluid you can easily apply the fluid type in the CompartmentDefinitions table. Tanks that have been specified as containing one of these fluids will beupdated automatically when the density of the fluid is changed in the Density dialog.Tank calibrations results and loading conditions will also be updated.

NoteThe vessel's hydrostatics are always calculated assuming the vessel isfloating in the fluid labelled "Sea Water". This is the first fluid in the list

printed in bold font. If the vessel is to float in a different fluid, it isnecessary to change the density of this fluid. Note that only the customfluids may have their names changed. Thus, if you wanted to carry out ananalysis for a vessel in fresh water, you would change the density of "SeaWater" to 1000.0 kg/m 3.

Saving and Loading Densities

Densities listed in the Density table can be saved and loaded using the File menu.

The densities file may be edited manually if desired. There is one row for each of the 18fluid types. The four columns, each separated by a tab character. These are fluid name ,

fluid code , relative density , colour respectively (the colour is in hexadecimal for the red,green, blue components and are probably much more easily edited in the Density dialog.The name and code for the first entry, Sea Water, cannot be changed (any changes madewill be ignored). All other entries may be edited (the same restrictions area applied as

when editing through the Density dialog).Sea Water S 1.0250 6D00FF00FF00Water Ballast B 1.0250 6D006D00FF00Fresh Water W 1.0000 FF005F005F00Diesel D 0.8400 FF005B00FF00Fuel Oil F 0.9443 6D00FF006D00Lube Oil L 0.9200 7F007F007F00

ANS Crude C 0.8883 3F003F003F00Gasoline leaded G 0.7499 FF0000007F00Unlead. Gas. U 0.7499 FF007F007F00JFA J 0.8203 7F007F00FF00MTBE M 0.7471 F600FA00C900Gasoil GO 0.8524 FF00FF007F00Slops SL 0.9130 FF006F00FF00Custom 1 C1 1.0000 D6000300D600Custom 2 C2 1.0000 D600D6000300

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Custom 3 C3 1.0000 0300D600D600Custom 4 C4 1.0000 D60003000300Custom 5 C5 1.0000 DF00DF00DF00

If you make an error, you can always reset the densities to their default values in theDensities dialog.

Also see:Windows Registry on page 18

WaveformHydromax is capable of analysing hydrostatics and stability in arbitrary waveforms aswell as for a level water plane. To specify a waveform, select the Waveform commandfrom the Analysis menu:

The water plane can be specified as flat, or as a sinusoidal or trochoidal waveform. If awaveform is specified, the wavelength, wave height and phase offset can be specified.The wavelength defaults to the waterline length of the hull at the DWL. If thewavelength is modified the wave height defaults to a standard metric wave, equivalentto:

Once a wavelength has been set, the wave height can be modified to give a non-standardheight.

The phase offset governs the position of the wave crest aft of the forward end of theDWL, as a proportion of the wavelength. The phase offset varies between 0 and 1, bothof which correspond to a wave crest at the forward end of the DWL.

For example, a phase offset of 0.5, with a wavelength equal to the waterline length, willgive a single wave crest at amidships.

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GroundingGrounding is an additional analysis environment option for the Equilibrium orLongitudinal Strength analysis. It is possible to specify grounding on one or two pointsof variable length. The Equilibrium analysis will determine whether the hull is grounded

or free floating and will trim the hull accordingly. Damage can be specified concurrentlywith grounding.

If the vessel touches one or both grounding points, this will be reflected in the results:

The displacement column will show the total grounding reaction force in brackets;the sum of the buoyancy and the grounding reactions equals the loadcasedisplacement.

The effective centre of gravity will be modified by the grounding reactions – amass is effectively being removed from the vessel; this will bring the effectivecentres of gravity and the centre of buoyancy in line vertically. The value of KG,GMt and GMl are all calculated to the effective centre of gravity. Remember thatKG is measured in the upright vessel reference frame (normal to the baseline);whilst GMt and GMl are the actual vertical separation of the metacentres abovethe centre of gravity in the trimmed reference frame normal to the sea surface.

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Note:Grounding points are considered to span the transverse extents of the hulland therefore constrain the heel to zero. The length of the grounding pointsis only used when considering the load distribution for LongitudinalStrength analysis and not to determine the pivot point. The vessel is

considered to pivot at the centre of the grounding point.

When two grounding points are entered, the first point (edit boxes on theleft) must refer to the forward grounding point; the second grounding pointis the aft grounding point.

Note: Fixed zero heel during grounding analysisThe equilibrium analysis will only consider the longitudinal balance ofmoments, i.e. the vessel will not be balanced in heel and the vessel willremain upright (zero heel) even if the transverse metacentric height is lessthan zero.

Hog and SagHydromax has the option to apply hog or sag during the calculations.

Hog or sag is distributed in a parabolic curve centred at either the amidships location, ora specified longitudinal position relative to the zero point. This is called the “centre ofdeflection”.

When hog is specified the centre of deflection and frame of reference at that locationremain stationary and the ends of the hull are deflected downward.

When sag is specified the centre of deflection and frame of reference at that locationremain stationary and the ends of the hull are deflected upwards.

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Note:Hog and sag apply to all analysis modes including tank calibrations, whichwill vary slightly with changes in hog and sag.

Stabil ity CriteriaStability criteria may be seen as the “environment of authorities” that the ship will bedeployed in.

For more information see Chapter 4 Stability Criteria starting at page 113 .

DamageYou can specify whether the model is to be analysed in intact or damaged conditionusing the Analysis Toolbar .

Also see:Damage Case Definition on page 58

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Analysis OutputHydromax will produce the following output data:

• Hydromax model visualisation

• Result data tables per analysis• Graphs per analysis

• Report

o Report wind ow

o Streamed directly to a Word document

In this section:• Reporting

• Copying

• Select View from An alysis Data

• Saving the Hydromax Design • Exporting

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ReportingHydromax has several options to do your reporting:

• Batch Analysis text file and/or streaming to Report window

• Automaticall y generate a report in the Report Window for each analysis run• Automaticall y Streaming results t o Word

• Manually copy and paste tables and graphs from the Results Window and GraphWindow

The most efficient method depends on the number of loadcases and damage cases youhave to analyse and the output you require.

Form small number of loadcases and damage cases you can do a manual copy and pasteof the results into a report. This then allows you to validate the results at the same time.

For large numbers of cases, it is recommended to use batch analysis. Batch Analysisresults saved as text files do not include graphs. Select the option to send the results tothe report window if you require Graphs. Additionally, if the option to Stream the reportto Word has been selected in the Edit | Preferences dialog a word document isautomatically generated after a Batch Analysis.

Streaming results to Word

It is possible to stream the Analysis results directly to Word. To do this:• Edit | Preferences

• Select the option to Send the Report t o Word

This will send the Report document to Word instead of to the Report window. After youhave run an analysis a Word document is created and opened automatically. This alsoapplies to Batch Analysis.

Tips:

See:Copying Tables on page 109 for tips on how to include the table header in a copy

paste to for example ExcelGraph Formatting on page 142 for tips on how to format your graph prior tocopying to another application.

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Data Format on page 157 for tips on how to specify what should be displayed andcustomise how to display tables (vertical or horizontal).

Copying & PrintingA range of options for transferring data from Hydromax to other programs such asspreadsheets and word processors is provided through copy and paste functions. Thisdata transfer works both ways: e.g. copying and pasting data to and from Excelspreadsheets allows you to use the full spreadsheet capabilities of Excel on yourHydromax model.

Copying Hull Views

Pictures of the hull in the View windows may be copied to the Clipboard using the Copycommand from the Edit menu. A dialog appears after selecting the Copy command thatwill allow you to set the scale of the copied picture.

These pictures can then be pasted into other applications or the Hydromax Reportwindow.

To copy a simple bitmap image of the view at the current resolution, use Ctrl+I;additionally, a bitmap of the current image may be saved by pressing Ctrl+Shift+I

Copying Tables

Tables may be copied to the clipboard. Simply select a cell, row, column, range of cellsor the whole table and then choose the Copy command or Ctrl+C.

The data copied from the table will be placed on the clipboard and can then be pastedinto a spreadsheet or word processor for further work.

Note:Copying data from the table with the Shift key depressed, will also copy thecolumn headings.

Printing

Each of the windows in Hydromax may be printed. Simply bring the window you wishto print to the front and choose Print from the File menu. Views of the hull in the Viewwindow may be printed to scale as in Maxsurf.

Prior to printing you may wish to set up the paper size and orientation by using the Page

Setup command from the File menu.

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Print Preview

The page to be printed is initially displayed in print preview mode. To print the pageclick the Print button, otherwise click the Cancel button.

The printing may be forced to be black and white. Choose the Colours button and select

the options required. Note that the print preview is not refreshed after these changes, butthe selection will be reflected in the printout.

The titles may be edited by clicking the Titles button.

Graph Printing to Scale

When printing the graph, it is possible to ensure that the graph is plotted to a sensiblescale so that measurements can be made directly from the graph. To do this, hold theshift key down when selecting the print command for the graph. You will be asked if youwant to print the graph to scale or to fill the page:

The scale used will depend on the length units that are currently selected. If these aremetric, then the graph will be plotted so that the grid lines are at one of the followingintervals (If the current length units are imperial then similar intervals will be used, butthey will be inches instead of cm.): 1.0cm, 2.0cm, 2.5cm, 5.0cm.

Exporting a Bitmap Image

You may also export a bitmap of the rendered perspective view with the File | Export |

Bitmap Image command.

Select View from Analysis DataFor most analyses, each step from the analysis can be visualised when the analysis hascompleted. For example: the angle of downflooding can be visualised by returning to theStability table in the results window, selecting the column at the required heel angle andselect “Select View From Data” in the Display menu.

In the View window the hull will be displayed in the selected position. This can also bedone for Upright Hydrostatics and the different wave phase calculations for anEquilibrium analysis in a waveform.

The Select View from Data can also be used to display the Curve of Areas graph foreach intermediate analysis stage, see Graph type on page 141 .

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Saving the Hydromax DesignHydromax design data may be saved

• Saving in a Hydromax Design File

• Saving Input Files separately

Saving in a Hydromax Design File

To save the design in one file, ensure that the View window is topmost and select Savefrom the File menu. The Hydromax data is saved in a .hmd file with the same name asthe design.

Saving Input Files separately

In addition to saving all the data together, the data in the individual tables such asloadcases, damage cases, compartment definition, key points etc., may also be savedseparately.

For more information on file properties and extensions in Hydromax, please see:File Extension Reference Table on page 242.

NoteAlthough all Hydromax model data is saved in the .hmd file automaticallyevery time you press Save from any of the design windows, it isrecommended to also save the Hydromax input files separately. This givesthe option of loading common data into different design files. E.g. forcomparing the characteristics of vessels which have only minor differencesin hull shape and identical tank layouts and loadcases.

Saving Loadcases to a FileOnce you have set up a loading spreadsheet, you can save it in a file on disk. Thisallows the same loading spreadsheet to be recalled at any time for use with thesame design or with any other hull.

To save the loadcase table, ensure the Loadcase window is topmost on the screenand choose Save Load Case from the File Menu. Selecting this option saves all theloads displayed in the current tab in the Loadcase window.

Saving Damage Cases to a FileBring the Damage window to the front and select Save Damage Cases or SaveDamage Cases As from the file menu.

Saving Compartment Definitions to a FileTo save a compartment definition to a file, bring the Input window to the front andchoose the compartment definition table; select Save Compartment Definitionfrom the File menu. You will be asked to name the file and select where it is to besaved.

Saving Input Window TablesTo save a input window table to a file, bring the Input window to the front andchoose the required input table; select Save from the File menu. You will be askedto name the file and select where it is to be saved.

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Saving Results to a File

Once you have performed an analysis, the data generated may be saved as a text file.This allows for further calculations to be done in a spreadsheet or for formatting to bedone in Word, Excel or other programs.

To save the data, ensure the Results window is topmost on the screen and choose thetable containing the data you wish to save. Select Save or Save As from the File Menu.

Selecting this option saves all the data currently displayed in the Results window. TheResults files are saved as tab delimited text, meaning that they can be read directly intospreadsheets such as Excel with values being placed in individual spreadsheet cells.

ExportingThe data export function in Hydromax is similar to Maxsurf. Some Hydromax-specificexport features are described below.

Data export dialog in Hydromax.

DXF exportContains all lines displayed in the active design window as closed poly-lines. Inaddition, each tank, compartment and non-buoyant volume is exported on aseparate layer. This export function is particularly useful to export tankarrangement drawings.

Note:

The layer name is the same as the compartment name, so it is important tohave unique compartment names.

For more information on data export of DXF and IGES, please see the “ Output of Data ”section in the Maxsurf manual.

Exporting the Model to Hydromax Version 8.0

After Hydromax version 8, a major change to the Hydromax file structure was made.Hydromax models created in versions greater than version 8.0 can be exported using theFile | Export menu so that it is compatible with Hydromax version 8.0. All key pointswill become downflooding points in the version 8 file and any tank sounding pipeinformation will be lost.

http://www.fdsfiles.com/webmanuals/maxsurf/msmanual.htm#output_of_data

http://www.fdsfiles.com/webmanuals/maxsurf/msmanual.htm#output_of_data

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Criteria ConceptsHydromax includes a wide range of template criteria (or: parent criteria) as well as pre-defined custom criteria such as IMO, HSC, DNV, ISO and more. Hydromax uses asingle dialog to control all the stability criteria. This makes it quick and easy to set whichcriteria should be included for analysis and to change criteria parameters. It is also

possible for users to create their own custom sets of criteria. Users may save, import andedit their criteria sets. These custom criteria files may be easily transferred via email.

Criteria may be identified as intact or damage criteria (or both). This ensures that thecorrect criteria are evaluated and displayed during normal and batch analysis. Althoughall criteria are displayed in the criteria table, only criteria that are applicable are added tothe report; i.e.: if the intact case is being computed, only the criteria that are selected forevaluation during an intact analysis will be evaluated and added to the report, similarlyfor the damage cases.

Criteria results are added to the Report after a Large Angle Stability or Equilibriumanalysis. However, only the applicable criteria are added to the report (although all aredisplayed in the Results table); i.e. after an Equilibrium analysis only those criteria thatare evaluated from Equilibrium data are added, and after a Large Angle Stability analysisonly GZ based criteria are added to the report.

Help information relating to the use and parameters of each criterion is displayed in thelower right hand corner of the dialog.

Criteria List Overview

Hydromax includes a wide range of criteria. These criteria are listed using in a treecontrol on the left-hand side of the criteria dialog. This section describes how this list of

criteria can be divided up in to Parent heeling arms, Parent criteria, predefined customcriteria and user created custom criteria. This section also explains how all criteria can bedivided up into two different criteria types: equilibrium and GZ curve based.

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The criteria tree list

Parent Heeling ArmsIn most cases a ship is subject to specific heeling moments. Those heeling momentare then used in a number of different criteria. The Hydromax criteria list containsParent Heeling Arms that can be copied into a custom criteria folder and thencross-referenced into the stability criteria.

The advantage of using cross-referenced Heeling Arms is that a heeling arm isnow defined (and edited) in only one place. This ensures that all criteria which usea specific heeling arm use exactly the same heeling arm. Another benefit is that,since the heeling arm is defined in one place, it is only displayed once in the GZgraph and not duplicated for each criterion that uses it.

Parent CriteriaThe Parent Criteria group contains all the parent criteria types that are available inHydromax. Each parent criterion allows you to perform a specific calculation;these are the fundamental criteria from which criteria for specific codes arederived.

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Parent criteria are special in that you cannot rename, delete or add criteria to theParent Criteria group. Also the parent criteria settings cannot be saved, they willalways revert to their default values when Hydromax is restarted. This is becausethe parent criteria are intended for use as templates from which you can deriveyour own custom criteria. This is done by dragging the required parent criteria into the “My custom criteria” group or any other group you create.

To distinguish the Parent criteria from your derived criteria, they are displayed inbold text in the Criteria list.

Predefined Custom CriteriaA number of criteria files containing criteria for specific codes are supplied withHydromax. These may be found in the “HMSpecificCriteria” folder. This foldercan be found in the Maxsurf root directory: c:\program files\Maxsurf.

Most specific criteria are locked; those that are not locked require your ship designdata to be input.

Also seeWorking with Criteria Libraries on page 123 Appendix D Specific Criteria on page 233.

Custom CriteriaYou can create your own set of criteria in the tree as well. This is explained in thesection on Working with Criteria on page 119 .

Types of criteria

There are two fundamental types of criteria:

Equilibrium criteriaEquilibrium criteria are evaluated after an Equilibrium analysis and refer only tothe condition of the vessel in its equilibrium state For example: margin lineimmersion tests, freeboard measurements, trim angle, metacentric height, etc. Thistype of criterion is also used by the Floodable Length analysis. Equilibrium

criteria can be recognised by the icon.

Criteria derived from measurements of the GZ curve.These are calculated after a Large Angle Stability analysis and during a LimitingKG analysis. For example, area under GZ curve between specified limits, angle ofmaximum GZ, etc. These criteria are often referred to as Large Angle Stability(LAS) or GZ criteria.

Note that there is some cross-over between the criteria types, notably angle ofequilibrium heel. This can be measured from the GZ curve by looking for an up-crossingof the GZ=0 axis. The equilibrium heel angle is also a fundamental output of theEquilibrium analysis. The same also applies for GMt. For this reason, in some criteriasets some criteria are included twice, once in the form of an Equilibrium criterion andagain as a Large Angle Stability criterion.

For a criterion to be used in the search for maximum VCG in the Limiting KG analysis,it must be a LAS criterion. This is because it is only this type of criteria that is morelikely to pass as VCG is reduced. A check is also made to ensure that any selectedEquilibrium criteria are passed, but they cannot be included directly in the search

algorithm.

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You will notice that different icons are used to differentiate between different types ofcriteria. These icons are derived from the parent criterion type. The different types ofcriteria and their icons are described below:

Folder icon, create separate folders to store related criteria. All folders musthave unique names (even if the parent folders have different names).Equilibrium criterion. These criteria are evaluated only after an equilibriumanalysis has been performed.GZ criterion. These criteria make measurements from the GZ curved obtainedfrom a Large Angle Stability analysis.GZ area criterion

GZ criterion with heeling arm

GZ area criterion with heeling arm

GZ criterion with several heeling arms and their combinations

GZ area criterion with several heeling arms and their combinationsCombined GZ criterion. These criteria perform several individual tests on theGZ curve. e.g. STIX.Combined GZ heeling arm criterion. These criteria perform several individualtests on the GZ curve including a heeling arm. e.g. Weather criterion.

See next: Criteria Procedures

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Criteria ProceduresThis section describes how to work with the stability criteria dialog.

• Starting the Criteria dialog

• Resizing the Criteria dialog • Working with Criteria

• Editing Criteria

• Working with Criteria Libraries

Starting the Criteria dialogThe criteria dialog allows you to select which criteria are selected for inclusion in theanalysis and change their parameters. To bring up the Criteria dialog, select Criteria fromthe Analysis menu:

or use the Criteria button, , in the analysis toolbar:

The criteria dialog is shown below:

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Note:The Floodable Length analysis uses its own set of criteria. The criteriacommand will bring up the Floodable Length Criteria dialog when theFloodable Length analysis is selected.

Resizing the Criteria dialogThe dialog may be resized and a vertical and horizontal slider can be used to resize thewidth of the Criteria List and the height of the Criterion Details areas.

Note that if, in the unlikely event that the dialog items vanish due to resizing the dialog,the dialog size can be reset by holding down the “Shift” key when you open the dialog.

Working with CriteriaIn the Concepts section it was explained how the criteria are listed in a tree list. Thissection explains how to create and customise your own criteria from the Parent HeelingArms and Criteria provided with Hydromax.

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View a video that shows how to for example create a custom heeling arm criterion.

Using the Criteria Tree List

The tree works in much the same way as the file folders in Windows Explorer:

Click on the “+” sign to expand the folder (or double click on it).

Click on the “-” sign to collapse the group (or double click on it).

Click on an item’s name or icon to select it

Once selected, click again on the on the item’s name to edit its name

Some short-cut keys for the tree list:Tree control smart keys FunctionAlt+Keypad * Recursively expands the current group

completelyRight Arrow or Alt+Keypad + Expands the current group

Left Arrow or Alt+ Keypad - Collapses the current groupUp Arrow Move one item up treeDown Arrow Move one item down treeSpace Include criterion for analysis

Criteria Tree Right-click Context Menu

Several options are available by right-clicking on a criterion or criterion group:

Criterion right-click menu

Include for Analysis:Toggle whether the criterion (or all criteria within the group) should be evaluated.

Intact:Toggle whether the criterion (or all criteria within the group) should be evaluatedfor intact conditions.

Damage:Toggle whether the criterion (or all criteria within the group) should be evaluatedfor damaged conditions.

Lock:Toggle whether the criterion (or all criteria within the group) are locked. If acriterion is locked, this prevents inadvertent editing of its parameters. Locking isused for criteria belonging to specific codes where the required values are fixed.

https://www.formsys.com/maxsurf/videos/new-in-version-12/new-analysis-features/xref-heeling-arms-in-hydromax-criteria#Q_sCzHHHkUUuLPACDqxc0A


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In other cases, where the items are mutually exclusive, the check boxes act as radio buttons and only one may be selected. This occurs, for example, with the “Value of GMtat” criterion:

Finally a check box can be used to select whether a specific effect should be included,for example, GZ curve reduction in the wind heeling criteria:

Criterion Pass/Fail Test

There are some subtle differences between the wordings for different criteria. Forexample one criterion may state “Shall be greater than…”, whereas another may state“Shall not be less than…”. Hydromax allows you to make this distinction by selectingthe required comparison from a combo-box in the criterion row of the details table:

Description Symbol Logical testShall be greater than > Greater thanShall not be less than ≥ Greater than or equal toShall be less than < Less thanShall not be greater than ≤ Less than or equal to

Damage and Intact

Criteria may be defined as intact or damage stability criteria (or both). Intact criteria areonly evaluated for the intact case and damage criteria are evaluated when a damage casehas been selected (irrespective of whether there are actually any damaged compartmentsor tanks in the damage case). Criteria that are defined for both are always evaluated.

These options may either be set using the right-click menu or by ticking the appropriate boxes in the bottom of the dialog:

Intact and Damage tick-boxes.

Working with Criteria LibrariesIt is possible to load and save the criteria. The parent criteria, built into Hydromax arenot saved, only the criteria that you create or import will be saved.

Default Criteria Library File

When starting, Hydromax will try to open the default criteria library file called:“Hydromax Criteria Library.hcr” from the directory in which the Hydromax programresides. By default this is c:\program files\Maxsurf\ Hydromax Criteria Library.hcr. Ifthis file cannot be found, you will be prompted to locate a criteria file:

You may select an alternative file or click the Cancel button to proceed and be given thedefault criteria, which consists of the Parent criteria and a “My Custom Criteria” group.

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The default criteria library will be automatically updated every time the criteria dialog isclosed. Even if you loaded an alternative file, updates will be saved in the default criterialibrary, either overwriting the existing one or creating a new one.

Note

It is good practise to save the criteria file with the project in the projectfolder. That way, when at a later stage you need to re-analyse the project, allcriteria are still available. See Saving Criteria below.

Saving Criteria

It is also possible to save the criteria into a new file. This can be useful when you aredefining new custom sets of criteria that you wish to keep separate or when definingcriteria sets for different vessels. Choose Save Criteria As from the File menu. This willsimply export all the custom criteria (parent criteria are not saved) to the specified file.Further updates will, however, continue to be saved to the default criteria library file thatwas opened when Hydromax was first started, so if you want to save any further changesyou will have to resave as described above.

Importing Criteria and Specific Criteria Files

New criteria may be added to your criteria list by importing them – choose ImportCriteria from the File menu. You will then be asked if you wish to keep the existingcriteria:

If you choose “Yes” your existing criteria will be kept, if you choose “No”, all existingcriteria except the parent criteria will be removed and replaced by those in the file youare opening. The default criteria library will be over-written with the new criteria so ifyou wish to keep any custom criteria that you may have added to your default criterialibrary, you must save them in a new file first.

Note that when keeping your existing criteria, it is important to ensure that the groupnames in the file you are importing are not the same as those that already exist. If thisdoes occur, the imported criteria will be found in the original groups, not in the newgroups.

A number of criteria containing criteria for specific codes are supplied with Hydromax.These may be found in the “HMSpecificCriteria” folder.

You can import several criteria files in one go using Shift, or Ctrl select to selectmultiple files in the Open Hydromax Criteria dialog.

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Criteria File Format

The criteria are saved in a Hydromax criteria file with the extension .hcr. The file is anormal PC text file, which may be edited manually so as to generate custom criteria. Thetypical format of the file is given in the following file: c:\ProgramFiles\Maxsurf\\HMCriteriaHelp\CriteriaHelp.html. Editing this file will also allow youto add your own help text or associate rich text format help files (rtf) files with yourcriteria.

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Criteria Resul tsAfter a Large Angle Stability or Equilibrium analysis, criteria are evaluated and theresults displayed in the Stability Criteria table in the Results window. Criteria can also bere-evaluated without having to redo the analysis when “Close and Recalculate” isselected in the criteria dialog. This allows you to edit criteria parameters or selectedcriteria and re-evaluate using the existing analysis results. After calculation the relevantcriteria are also added to the Report.

Criteria Results Table

The tested criteria are listed one above the other. Intermediate values are displayed.Values that could not be calculated, e.g.: angle of vanishing stability, angle ofequilibrium, etc., have n/a in the Actual and/or Value column. This is normally due to aninsufficient range of heel angle having been used.

Results may be displayed in “Verbose” or “Compact” format (see above). The format for

the results table and the report are specified separately. Chose the Display | Data Formatcommand when the Stability Criteria results are displayed:

Stability criteria results window: compact format

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Stability criteria results window: verbose format

Report and Batch Processing

As noted earlier, only the relevant criteria results are added to the Report and/or Batchfile. Criteria that are not relevant, i.e. any criteria that have a “not analysed” result, arenot added to the Report (although they are displayed in the Criteria Results table). Forexample damage criteria during intact analysis or Equilibrium criteria during a LargeAngle Stability analysis are not added to the report.

Also seeReporting on page 108 Batch Analysis on page 91

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Typical GZ curve

Unusual GZ curve with double peak

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GZ curve with heeling arm superimposed

GZ Definitions

The table below defines how Hydromax calculates the various features of the GZ curve:

Angle of vanishingstability

The angle of vanishing stability is the smallest positiveangle where the GZ curve crosses the GZ=0 axis withnegative slope.

Angle of vanishingstability withheeling arm curve

The angle of vanishing stability with a given heeling armis the smallest positive angle where the GZ curve crossesthe heel arm curve and where the GZ-Heel Arm curvehas negative slope.

Downfloodingangle

The downflooding angle is the smallest positive angle atwhich a downflooding point becomes immersed.

Equilibrium angle The equilibrium angle is the angle closest to zero wherethe GZ curve crosses the GZ=0 axis with positive slope.

Equilibrium anglewith heeling armcurve

The equilibrium angle with a given heeling arm is theangle closest to zero where the GZ curve crosses the heelarm curve where the GZ-Heel Arm curve has positiveslope.

First peak in GZcurve

In some cases, the GZ curve may have multiple peaks;this often occurs if the vessel has a large watertightcabin. The angle of the first peak is the lowest positiveangle at which a local maximum in the GZ curve occurs.

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GM L or GM T Vertical separation of the longitudinal or transversemetacentre and centre of gravity. The location of themetacentre is computed from the water-plane inertia, notthe slope of the GZ curve. Note that the centre of gravityused is the upright centre of gravity corrected by the free

surface moments of partially filled tanks in their uprightcondition, rotated to the specified heel (and trim) angle.GZ Curve The curve of vessel righting arm (GZ) plotted against

vessel heel angleHeeling arm curve A curve of heeling lever, which is superimposed on the

GZ curve. This is typically used to assess the effects ofexternal heeling moments, which are applied to thevessel. These include the effects of wind, passengercrowding, centripetal effects of tuning, etc. Dependingon the moment that they represent, the heeling armcurves will have different shapes.

The heeling arms are never allowed to be negative; if thecos function goes negative, the heeling arm is made zero.If the heeling arm has a power of cos greater than zero,the heeling arm is forced to be zero at heel angles greaterthan 90° and less than -90°.

Maximum GZ Positive angle at which the value of GZ is a maximumMaximum GZabove heeling armcurve

Positive angle at which the value of (GZ - heel arm) is amaximum

GlossaryThe table below describes some commonly used terms:

φ Angle of heel measured from upright.Deck Slope /maximum slope

The maximum slope of an initially horizontal, flat deck atthe resultant vessel heel and trim. i.e. combined effect ofheel and trim.

Gust Ratio Used for some wind heeling criteria, the Gust Ratio is theratio of the magnitude of the gust wind heeling arm to thesteady wind heeling arm.

g = 9.80665ms-2

1998 CODATA recommended value for standardacceleration of gravityRoll back angle A negative heel angle change. Often a roll back angle is

measured from some equilibrium position; the resultingheel angle after the roll back has been applied is morenegative than the original. Commonly used in wind andweather criteria to account for the action of waves rollingthe vessel into the wind. If a criterion uses a roll backangle, it is often necessary to calculate the GZ curve fornegative angles of heel.

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Chapter 5 Hydromax Reference

Page 133

Chapter 5 Hydromax ReferenceThis chapter contains brief descriptions of the tools available in Hydromax:

• Windows

• Toolbars

• Menus

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WindowsHydromax uses a range of graphical, tabular, graph and report windows.

• View Window

• Loadcase Window • Damage Window

• Input Window

• Results Window

• Graph Window

• Report Window

View WindowThe View window displays the hull, frame of reference, immersed sections of the hulland any compartments, and the centroids of gravity, buoyancy, and flotation. These

positions are represented by:

c b centre of buoyancyc g centre of gravityc f centre of flotationK location of keel (K) for KN

during KN analysis

You can choose which type of view is displayed by selecting from the Window menu orthe View toolbar.

The Zoom, Shrink, Pan and Home View commands from the View menu may be usedand work in exactly the same way as in Maxsurf. If a Perspective view is shown, youmay also use the Pitch, Roll and Yaw indicators to change the angle of view. Please referto the Maxsurf manual if you are unfamiliar with these functions.

You may set the visibility of the various display elements by using the Visibilitycommand from the Display menu. Two sets of visibility flags are maintained, one is usedfor all analyses other than tank calibration and the other is used for when the tankcalibration analysis is selected.

If a view window is visible when an analysis is being carried out, it will display the hull

shape using the correct heel trim and immersion for the current step of the analysis.After an analysis, the Select View from Data command in the Display menu may be usedto move the hull to a selected position from the Results window.

The view of the tanks, compartments and non-buoyant volumes can be toggled betweenan outline view and a view of the sections.

Perspective view

In the perspective view, the model may be rendered.

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The rendered view also enables tanks and compartments to be more easily visualised,especially when the hull shell is made transparent.

The rendering options are to be found in the Display menu, with further lighting optionsin the Render toolbar.

Please refer to the Maxsurf manual for more information on the different renderingoptions available in perspective view.

Note:

Fastest performance will be achieved by reducing the amount of redrawingthat is required from Hydromax. For this reason, it is best to turn offsections, and especially waterlines, when performing an analysis. You maythen turn them on again after the analysis has completed. For fastest

performance, e.g. when running in Batch mode, minimise the Hydromaxwindow so that no redrawing occurs.

Loadcase WindowIn the Loadcase window a spreadsheet table of all loads and tanks is displayed.

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• Compartment Definitio n

• Sounding Pipes

• Key Points

• Margin Line Points

• Modulus Points

The input window contains tabs on the bottom that allow you to quickly browse throughthe different input tables.

Compartment Definition

This table can be used to define the tanks and compartments in the Hydromax models.For more information see Modelling Compartments on page 40 in the Analysis Inputsection.

Sounding Pipes

This table is used to define the tank sounding pipes and calibration intervals. Defaultvalues are provided but these may be edited if necessary.

Key Points

There are several types of Key Points:• Down Flooding points

• Potential Down floodin g points

• Embarkation poin ts

• Immersion Points

Only downflooding points are used in determining the downflooding angle, which isused in criteria evaluation.

Margin Line Points

The margin line is used in a number of the criteria. Hydromax automatically calculates

the position of the margin line 76mm below the deck edge when the hull is first read in.If necessary, the points on the margin line may be edited manually in the Margin LinePoints window (the deck edge is automatically updated so that it is kept 76mm above themargin line).

Modulus Points

This table is used to define the allowable limits for shear force and bending momentduring the longitudinal strength calculations.

Bulkheads

See Floodable Length Bulkheads on page 63 .

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Results WindowThe Results window contains ten tables, one for each of the different analysis types pluscriteria results and key points results tables. When switching mode, the currentlyselected results table will change to reflect the current analysis mode. Note that results

are never invalidated if analysis options are modified – it is up to the user to ensure thatthe results are recalculated as necessary.

Setting the Data Format

It is possible to configure Hydromax so that only the results that you wish to see aredisplayed. To do this, choose Data Format from the Display menu.

A dialog similar to the one above will appear. Items that are selected with a tick will bedisplayed in the Results window and on any printed output. Items that are not selectedare still calculated during the analysis cycle, but are not displayed. You may change thedisplay format at any time after the analysis without having to redo the calculations.

Data Layout

Most analysis data can be formatted vertically or horizontally to fit better on the screenor the printed page. For example, with Upright Hydrostatics, the data can be formatted sothat each draft has a column of results, or so that each draft is on a separate row.

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To change the format, select Data Format from the Display menu, and select either thehorizontal or vertical layout button.

Key Points Data Result Window

Key points data is calculated for Large Angle Stability, Equilibrium and Specifiedcondition Analysis. The DF angle column is only visible when the analysis mode is setto Large Angle Stability and the Freeboard column is only displayed when the analysismode is set to Equilibrium or Specified condition.

Stability Criteria Result Window

If stability criteria are turned on in the analysis menu, they will be evaluated duringLarge Angle Stability, Limiting KG and Equilibrium analyses. The results of the criteriaevaluation are presented in this table after Large Angle Stability and Equilibriumanalyses. Criteria results are not displayed in this table after a Limiting KG analysis. Theresults may be displayed in compact format:

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Alternatively, the results can be displayed in verbose format, where all the intermediatecalculations are shown, by selecting the desired format in the Display | Data formatdialog.

Graph WindowThe Graph window displays graphs, which show the results of the current analysis.Hydromax will automatically display the graph that displays the result of the current

analysis when you select Graph from the Windows menu or press the toolbar button.Alternatively you can select a specific graph using the Windows | Graphs menu item.Only the graphs that are applicable to the current analysis can be displayed.

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Graphs can be copied using the Edit | Copy command.

Graph type

Hydromax can graph many types of data depending on the type of analysis being performed. These graphs include Upright Hydrostatics, Curves of Form, Curve of Areas,

Righting Lever (GZ curve), Longitudinal Strength, Floodable Length and TankCapacities. These can all be displayed via the Graphs item in the Windows menu.

Tip: You can use the Select View from Analysis Data option (page 110 ) to see the Curveof Areas for each heel angle and/or intermediate stage during the analysis.

Interpolating Graph Data

To display an interpolated value from one of the curves, use the mouse to click anywhereon the curve. The data in the lower left corner of the window will change to display thecurve name and co-ordinates of the mouse on the curve. Click anywhere on the dashedline and drag it with the mouse; as you move the cursor the interpolated values will bedisplayed.

Note:In case multiple curves are plotted in the same graph you can switch between the curves by clicking on them. Hydromax will ignore the exact position you click on the curve to allow reading all related interpolatedvalues along the black dashed line.

GZ Graph

The GZ value, Area and corresponding heel angle can be measured by using the slider;the slider data is displayed at the bottom of the Graph window. The area is integratedfrom zero heel angle to the location of the graph slider.

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Note:Because the horizontal axis scale is always in degrees, the area is alwaysgiven in units of length.degrees and cannot be displayed in units oflength.radians.

NoteThe lower integration limit is always zero (irrespective of the equilibrium

angle). Thus if you require the area between two limits, you must subtractthe area at the lower limit from the area at the higher limit.

Curve fitting for GZ graph

A curve fit will be performed if all the heel angle intervals are less than or equal to 10 ˚ .If this is the case, a parametric cubic spline is used to fit a smooth curve through thecalculated GZ data at the specified heel angles. This ensures that the fitted line goesexactly through the calculated GZ points. If you wish to prevent this curve fitting, add aheel angle interval of greater than 10 ˚ as the final step. This can sometimes be useful ifyou expect a discontinuity in the GZ curve.

Graph data

The graphed data can be obtained by double clicking on the graph. Since the graph datacontains more data points than most tables in the results window, this double click can

be extremely helpful to export the analysis data to for example Excel fro further processing. Especially in the case of the sectional area curve, where there is no tabulardata available.

Also see: Copying Tables on page 109.

Graph Formatting

When you are in the Graph window you can use the View | Colour dialog to change thecolours of the curves in the graph as well as the background. The View | Font command

allows you to change the text size and font size.

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Copying Graphs

You can copy the contents of the Graph window using the Copy command or Ctrl+C. Note that the picture is placed in the clipboard as a meta-file which can be resized inWord or Excel.

NoteWhen the graph is pasted in Microsoft Word ®, the graph can be edited byright clicking on the graph and selecting “edit picture”.

Report WindowHydromax contains a Report window. This window is used to create a progressivesummary of the analyses that have been carried out. This report can be edited via Cut,Copy and Paste; printed, saved to and recalled from a disk file.

Report Window Page Setup

When you are in the Report window, the File | Page setup command allows you tocustomise the page orientation and size you wish to use for reporting. This is important because, inserted tables will be automatically formatted to fit the current page set up.However, once the tables have been placed into the report, their formatting will not bechanged by changes to the print set up. Hence it is often most convenient to select thedesired report page set up before any analyses have been made. You can for examplechoose the landscape Page Setup prior to running an analysis to make the tables fit

better.

Hydromax will split most results tables so they fit the specified page set up. However, both Loadcase and Criteria results tables will not be split.

Editing a ReportThe Report window has it's own toolbar permanently attached to the view, as well as aruler showing you tab stops, indentation and margin widths. Underneath all of this youhave your actual editing area.

As the built-in report window only has basic editing and formatting functionality, it isrecommended that the report window be used only to accumulate the results. Once allthe results have been gathered in the report window, these should be saved and opened ina word processor such as Microsoft Word or Open Office for formatting:

• set the results tables up as you w ant them to appear in the report (the report usesthe same column widths, fonts etc.); do the same for the graph w idow;

• choose an appropriate paper size for the report (the tables will b e split to fit thi spaper size, so cho osing a wi de paper size will prevent all but the widest tablesfrom being split);

• copy and paste the Hydromax report in to Microsoft word. Use the Format | Auto format function i n Word (wi th the defaul t sett ings) to set the correct styles forthe different levels of heading in the document, this will facilitate generating a tableof contents and also allows you t o re-format the various styles (or import a customset of styles using the style organiser in Word).

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The Ruler allows you to set left, right, centre, and decimal tab stops. The tab stops arevery useful for creating columns and tables. A paragraph can have as many as 20 tab

positions.

The 'left' tab stop indicates where the text following the tab character will start. To createa left tab stop, click the left mouse button at the specified location on the ruler. The lefttab stop is indicated on the ruler by an arrow with a tail toward the right.

The 'right' tab stop aligns the text at the current tab stop such that the text ends at the tabmarker. To create a right tab stop, click the right mouse button at the specified locationon the ruler. The right tab stop is indicated on the ruler by an arrow with a tail toward theleft.

The 'centre' tab stop centres the text at the current tab position. To create a centre tabstop, hold the shift key and click the left mouse button at the specified location on theruler. The centre tab stop is indicated on the ruler by a straight arrow.

The 'decimal' tab stop aligns the text at the decimal point. To create a decimal tab stop,hold the shift key and click the right mouse button at the specified location on the ruler.The decimal tab stop is indicated on the ruler by a dot under a straight arrow.

To move a tab position using the mouse, simply click the left mouse button on the tabsymbol on the ruler. While the mouse button is depressed, drag the tab to the desiredlocation and release the mouse button.

To clear a tab position, simply click on the desired tab marker and drag it off the ruler.

Normally, a tab command is applicable to every line of the current paragraph. However,if you highlight a block of text before initiating a tab command, the tab command is then

applicable to all the lines in the highlighted block of text.

Keyboard Support for Reports

In addition to menu support, there are also several useful keystrokes that are availablewhile editing the report. These are listed below for convenience:

Ctrl+B Toggle Bold on/offCtrl+U Toggle Underline on/off

Ctrl+PageUp Position at the top of the reportCtrl+PageDown Position at the bottom of the report

Ctrl+Enter Insert a page break

Opening and Saving the Report

The report can be saved to a file or read in from a file using the Save and Open Menucommands with the report window highlighted. This is useful if you wish to append ananalysis to a report that had been calculated at some time in the past. (Load in the oldreport, perform the analyses; the new results will be appended to the end of the reportwhich may then be resaved).

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Pasting images into the report

Sometimes, it is desirable to insert schematic images of the vessel into the report. This isvery easily done, by copying an image from one of the design views and then pasting itinto the report at the desired location. Ensure that the colors selected will be easilyvisible in the white background of the report view.

Depending on which Microsoft operating system you are using (notably Win98), theimage may not maintain its aspect ratio and may be pasted into the report as a square. Toovercome this problem, paste the image into Microsoft Word first, then copy it fromWord back into the Hydromax report window.

Changing the scale will affect the size of the image, and hence the thickness of the lines.For example, copying the image at 1:100 instead of 1:50 will effectively double thethickness of the lines if you make the images the same size in the report. Remember thatyou can change the font size in the design window.

MS AP FP

BaselinecgTank 1

cgTank 2

cgTank 3

cgTank 4

hatch 1 hatch 2 hatch 3cf

cb

cg

zero pt.

Image copied at 1:500 (Word image displayed at 200%)

MS APFP

BaselinecgTank 1

cgTank 2

cgTank 3

cgTank 4

hatch 1 hatch 2hatch 3

cf

cb

cg

zero pt.

Image copied at 1:250 (Word image displayed at 100%)

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ToolbarsHydromax has a number of icons arranged in toolbars to speed up access to somecommonly used functions. You can hold your mouse over an icon to reveal a pop-up tipof what the icon does.

File Toolbar

The File toolbar contains icons that execute the following commands: New - Open - Save - Cut - Copy - Paste - Print

Edit Toolbar

The Edit toolbar contains icons that execute the following commands:Add Row - Delete Row | Sort Loadcase Rows – Move Loadcase Row up – MoveLoadcase Row Down

View Toolbar

The View toolbar contains icons that execute the following commands:Zoom – Shrink – Pan – Home View – Rotate – Assembly window.

The Rotate command is only available in the Perspective window. The Assemblywindow is not available in Hydromax.

Analysis Toolbar

The Analysis toolbar contains icons for selecting the current analysis, loadcase anddamage case:Analysis Type - Current Loadcase - Current Damage Case

The Analysis toolbar also contains icons that execute the following commands:Criteria (dialog) | Start Analysis - Pause Analysis - Resume Analysis | Update TankValues in Loadcase

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MenusThe following section describes all of the menu commands available in the Hydromax

program.• File Menu

• Edit Menu

• View Menu

• Anal ysi s Menu

• Case Menu

• Display Menu

• Window Menu

• Help Menu

File MenuThe File menu contains commands for opening and saving files and printing.

New

Creates a new table for whichever input table is frontmost, e.g: when the LoadcaseCondition is the frontmost window, the New command will create a new loadingcondition. When the Compartment Definition table is frontmost, New creates a newcompartment definition.

Open

When no design is open, selecting the Open command will show a dialog box with a list

of available Maxsurf designs. Select the design you wish to open, click the Open button.The requested design will be read in and its hull shape calculated for use in Hydromax.

If a design is already open, the Open command will open whichever file corresponds tothe frontmost input window.

Close

The Close command will delete the data in the frontmost window. Hydromax will askwhether you wish to save any changes.

Selecting Close when one of the design view windows is frontmost will close the currentMaxsurf design.

Save

Selecting Save will save the contents of the frontmost window to a file on the disk.

Save As

Selecting Save As performs the same function as save but allows you to specify a newfilename preventing the original file from being overwritten.

Export

Selecting Export enables you to export a Hydromax file as a variety of different fileformats such as:

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DXF or IGES.DXF exports sections as closed poly-lines. In addition, each tank, compartmentand non-buoyant volume is exported on a separate layer (the layer name being thesame as the compartment name, so it is important to have unique compartmentnames).

IGES exports the NURB surface data. See the Maxsurf manual for moreinformation.

Hydromax v8.0 fileAlso allows users to export Hydromax files that are compatible with earlierversions of Hydromax.

Export BitmapAllows you to export the rendered image as a bitmap file at the specifiedresolution. This command is only available when the Perspective window isfrontmost with rendering turned on.

Import Criteria

Imports criteria from the selected criteria files. Current criteria may be kept or discarded.

Save Criteria As

Exports the current criteria set to the specified file. It is good practice to save the criterialibrary with each project in a project folder.

Load Density Table

Loads a density table saved in Hydromax, see below.

Save Densities As

Saves the Fluid densities table, see Density of Fluids on page 101.

Page Setup

The Page Setup dialog allows you to change page size and orientation for printing.

Print

The Print command allows you to print the contents of the frontmost window on thescreen.

Exit

Exit will close Hydromax and all the data windows. If you have any data or results,which have not been saved to disk, Hydromax will ask you if you wish to save them

before quitting.Edit MenuThe Edit menu contains commands for working with tables.

Undo

Undo may be used with desk accessories, but cannot be used on Hydromax drawingwindows or data windows.

Cut

Cut may be used in the Report window but cannot be used on Hydromax drawing or data

windows.

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Copy

The Copy command allows you to copy data from any of the windows, including thedesign view, input tables, results tables and graph window.

Paste

Choose the Paste command to Paste data into the Loadcase window or other input tables,or the Report window. Paste cannot be used in the View, Graph or Results windows.

Select All

Selects the entire Report.

Fill Down

Copies text in a table down a column like a spreadsheet.

Table

Performs operations on Hydromax's Report window.

Insert New TableCreate a new table in the Report.

Insert RowInsert a new row into the current table in the Report.

Split CellSplit the currently selected cell into two separate cells in a table in the Report.

Merge CellsMerge the selected cells in a table into a single cell in the Report.

Delete CellsDelete current cell, column or row or a range of cells, columns or rows in theReport.

Row PositioningSet Justification for the current table row or an entire table in the Report.

Cell BorderSet Cell Border Width for a single cell or range of cells in the Report.

Cell ShadingSet Cell Shading Percentage for a single cell or a range of cells in the Report.

Show GridToggle table grid lines in the Report.

Add

The Add command is used to add an entry to the input tables.

Delete

The Delete command will delete rows from the input tables. If no rows are selected, thelast row in the window will be deleted, otherwise all selected rows will be deleted.

Add Surface Areas

This command automatically adds the surface areas and centres of gravity of all hullsurfaces into the current loading condition. This is useful for estimating the initial weightof hull plating.

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Preferences

The Hydromax preferences dialog allows you to set your analysis tolerances (or: errorvalues) and select the option to stream the report to a Microsoft Word document.

Also see:

Tolerances on page 98 Streaming results to Word on page 108.

View MenuThe View menu contains commands for controlling the views in the graphics windows.

Zoom

The Zoom function allows you to examine the contents of the design view windows indetail by enlarging the selected area to fill the screen.

Shrink

Choosing Shrink will reduce the size of the displayed image in the design view windows by a factor of two.

Pan

Choosing Pan allows you to move the image around within the View window.

Home View

Choosing Home View will set the image back to its Home View size.

Set Home View

Choosing Set Home View allows you to set the Home View in the View window. To set

the Home View, use Zoom, Shrink, and Pan to arrange the view, then select Set HomeView from the View menu.

Rotate

Activates the Rotate command, which is a virtual trackball which lets you freely rotate adesign in the Perspective view window.

Colour

The Colour function allows you to set the colour of lines, labels, and graphs.

Remember to always be careful when using colour. It is very easy to get carried awaywith bright colours and end up with a garish display that is uncomfortable to work with.In general it is best to use a neutral background such as mid grey or dull blue and uselighter or darker shades of a colour rather than fully saturated hues.

From the scrollable list, select the item whose colour you wish to change. The item’scurrent colour will be displayed on the left of the dialog. To change the colour click inthe box and select a new colour from the palette.

When Loadcase window is frontmost, Colours for the loadcase items can be set. SeeLoadcase Colour Formatting on page 37.

Font

Font command allows you to set the size and style of text.

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The text style chosen will affect the display and printing of all text in the Report,

Loadcase, Graph, Curve of Areas, and Results windows.Toolbar

Allows you to turn the Toolbars on and off.

Status Bar

Allows you to turn the Status Bar on and off at the bottom of the screen.

Full Screen

Maximises screen layout.

Analysis MenuThe Analysis menu can be used to change the current analysis mode. It also containscommands to set the input data and analysis settings and environment options requiredfor the current analysis.

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Fluids

Allows you to specify whether to use Corrected VCG method or Simulate FluidMovement method when treating the fluid contained in slack tanks.

Also see:

Free surface correction on page 40.Density

This command allows you to set the density of fluids used in the analysis. See Density on page 101.

Waveform

The Waveform command allows you to perform analysis for a flat waterplane orsinusoidal or trochoidal waveforms.

Hog and Sag

Allows you to define the amount of hog or sag to be applied to the hull when calculatingthe vessel’s hydrostatics.

Criteria

The criteria menu item will bring up the criteria dialog. This allows you to specify whichcriteria will be checked during the analysis.See Criteria on page 114 .

When the floodable length analysis is selected, the criteria command will bring up aFloodable Length Criteria dialog with criteria that only apply to floodable lengthanalysis.

GroundingSpecifies grounding on one or two points of variable length for use with the Equilibriumand Longitudinal Strength analyses.

Update Loadcase

Checks for changed tanks and makes sure that any tanks and compartments that have not been formed are correctly calculated. It then updates the loadcase with the correctcapacities and free surface moments for the tanks. Also recalculates totals and sub-subtotals after a row sorting or moving command.

Also see:Tank Loads on page 39

Recalculate Tanks and Compartments

Forces all tanks and compartments to be re-formed from their initial definition. Thiscommand also updates the loadcase.

If any of the tank boundaries are made up from boundary surfaces, it is better to use“Recalculate Hull Sections ” after re-opening the Maxsurf model to make sure the latestinternal structure surfaces are being used as well.

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Delete Damage Case

Deletes the current damage case(s) in the Damage Case window.

Edit Damage Case

Allows the name of the selected damage case, other than the intact case, to be edited.

Max. Number of Loadcases

Allows the user to set the number of loadcases that can be defined. A maximum of 25loadcases may be specified.

Display MenuThe Display menu contains commands for controlling the data, which are displayed inthe graphics and other windows.

Data Format

Data Format allows you to choose which stability data are tabulated. A dialog box allowsyou to choose from a range of stability variables. See Setting the Data Format on page138.

Coefficients

Allows you to customise how you wish to calculate the coefficients as well as the displayformat for the LCB and LCF.

See Customising Coefficients on page 32 for more information.

Units

The units used may be specified using the Units command. In addition to the length and

mass units classes, units for speed (used in wind heeling and heeling due to high-speedturn etc. criteria) and the angular units to be used for areas under GZ curves, may also beset. The angular units for measuring heel and trim angles are always degrees. SeeSetting Units on page 32 for more information.

Select View from Data

This function may be used to synchronise the display in the Design View window withone of the sets of data in Results window. The view may be set from any of the resultsfrom Upright Hydrostatics, Large Angle Stability or Equilibrium analyses. Simplyhighlight the column or row that corresponds to the condition you wish to view andselect “Select View From Data”; the Design View will change to match the condition inthe selected row or column in the Results window.

Visibility

The visibility of tanks, compartments, labels, hull contours, and other items in the designview may be set by using this dialog.

Grid

The grid submenu allows you to hide the grid or show the grid with or without stationgrid labels. The grid can only be displayed when the vessel is in upright position on itsdesign waterline. The option to display the grid will be greyed out when the ship iscurrently displayed in, for example, a trimmed state at the end of an equilibrium analysis.Switching analysis type puts the boat back into upright position on its design waterline.

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Zero Point

Access to the Zero Point is intended for information only. You are not expected tochange the Zero Point in Hydromax.

This function sets the longitudinal and vertical reference point for all measurements,

including the centre of gravity. It is highly recommended that the correct zero point beset in Maxsurf prior to loading the design into Hydromax. This will ensure that aconsistent zero point is used in all the programs.

Window MenuFor the items in this menu, each represents a Hydromax window. Selecting the item

brings the appropriate window to the front.

Cascade

Displays all the Windows behind the active Windows.

Tile HorizontalLayout all visible windows across the screen.

Tile Vertical

Layout all visible windows down the screen.

Arrange Icons

Rearranges the icons of any iconised window so that they are collected together at the bottom of the Maxsurf program window.

View Direction

Select the desired view direction from the sub-menu. The selected design window willthen be brought to the front.

Loadcase

Brings the Loadcase window to the front. The Loadcase window allows you to enter aseries of component weights, together with their longitudinal and vertical distances fromthe zero point. These inputs are used to calculate the total Displacement and Centre ofGravity for Stability, KN and Equilibrium analysis.

Input

Choose from the Input item to bring the desired Input window to the front and displaythe Compartment Definition, Key Points, Margin Line Points or Modulus table.

Results

Choose from the Results item to bring the desired Results window to the front anddisplay the desired table.

Graph

Brings the selected Graph window to the front. The Graph window displays a number ofdifferent graphs, depending on which analysis mode is currently active.

Help Menu

Provides access to Hydromax Help.

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Hydromax Help

Invokes Hydromax Help.

Hydromax Automation Reference

Invokes the Automation Reference help system.

Online Support

Provides access to a wide range of support resources available on the internet.

Check for Updates

Provides access to our website with the most recent version listed.

About Hydromax

Displays information about the current version of Hydromax you are using.

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Appendix ACalculation of Form ParametersThis Appendix explains how the calculation of form parameters (C B, CP, AM, etc.) is achieved in

Hydromax, and investigates why differences with other hydrostatics packages may occur.Definition and calculation of form parametersBelow is a summary of the definitions of basic vessel particulars and form parameters used inHydromax.

Measurement Reference Frames

Results in Hydromax are given from the vessel’s zero point. However, because Hydromax treatstrim exactly (the hull is rotated not sheared when trim occurs), there are two frames ofreference:

Ship or upright frame of referenceThe “ship” or “upright” reference frame is that of the upright vessel with zero-trim. Herethe baseline is horizontal and the perpendiculars are vertical. “Longitudinal”measurements are made parallel to the baseline and “vertical” measurements are

perpendicular to the baseline.

World or trimmed frame of referenceThe “world” or “trimmed” reference frame is that of the trimmed vessel. Here the

baseline is no longer horizontal and neither are the perpendiculars vertical.“Longitudinal” measurements are made parallel to the horizontal, static waterline and“vertical” measurements are perpendicular to the waterline

Rotated reference frame (red) and measurements in the two reference frames:

Measurements in the upright vessel reference frame (green) and trimmed reference frame (blue)

The majority of measurements are given in the “ship” frame of reference. These includelongitudinal centres of gravity, floatation and buoyancy (LCG, LCF, LCB); and measurementsfrom the keel such as KB and KG. Measurements such as GM are measured in the “world”frame of reference, i.e. GM is the true vertical separation of the metacentre and the centre ofgravity with the vessel inclined. It is for this reason the LCG and LCB values in the “ship”frame of reference are not the same if there is any vertical separation between the CG and CBeven though the vessel is in equilibrium; it is the LCG and LCB in the “world” reference framethat are the same.

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Appendix A

Page 163

Some of the more common lengths that may be used to characterise a vessel.

In Hydromax you may choose between the length between perpendiculars and the waterlinelength for the calculation of Block, Prismatic and Waterplane Area Coefficients. SelectCoefficients from the Display menu:

Beam

It is normal to use the maximum waterline beam for calculation of coefficients, and this may beof the DWL or the waterline under consideration. However, there may be times when it isappropriate to use the maximum immersed beam (e.g. submarine, vessel with tumble-home or

blisters). For the calculation of section area coefficients it is normal practice to use the beam anddraft of the section in question.

Vessel with tumble-home

Catamarans and other multihull vessels pose another difficulty. In some cases the overall beamis of importance, in others, the beam of the individual hulls may be required.

Hydromax uses the total waterline beam of immersed portions of the section forcalculation of block coefficient and other form parameters. For the case of a monohull thiswill be the normal waterline beam. For catamarans this will be twice the demihull beam(remember that the total displaced volume is used and hence the block coefficient is thesame as that of a single demihull). For the section shown below, the beam used would bethe sum of B1, B2 and B3.

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Multihull beams

Draft

The draft is normally specified from a nominal datum. Normally this datum is the lowest part ofthe upright hull. However, for vessels with raked keel lines or yachts, the datum may beelsewhere. In Hydromax drafts are defined from the datum line. However, there are also

occasions when the immersed depth of the section is a more relevant measure of draft, this isoften the case when form parameters are calculated.

Hydromax uses the depths that stations extend below the waterline for calculation of formcoefficients. For calculations of block coefficient, the greatest immersed section depth isused; for calculations of section area coefficients, the immersed depth of the section inquestion is used. Both depths are measured in upright position.

Draft measurements

Draft measurement at heel angleWhen the vessel is heeled, the draft is measured through the intersection of the uprightwaterline and the centreline, perpendicular to the heeled waterline (see figure below).Essentially the draft is measured along the heeled and trimmed perpendiculars on thecentreline. It is for this reason that as the heel approaches 90degrees, the draft becomesvery large.

Draft measured along the inclined perpendicular lines

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Appendix A

Page 165

Midship Section

It is current usual practice to define the midship section as midway between the perpendiculars,however for some vessels it is defined as the midpoint of the DWL. For vessels with no parallelmid-body, the section with greatest cross-sectional area may also be of particular interest.

When comparing form coefficients such as C P and C M , remember that Hydromax uses thestation with the maximum immersed cross-sectional area at the waterline underconsideration.

Block Coefficient

Principles of Naval Architecture defines the block coefficient as:

"the ratio of the volume of displacement of the moulded form up to any waterline to the volumeof a rectangular prism with length, breadth and depth equal to the length, breadth and mean draftof the ship at that waterline."

However, the actual definitions of the length, beam and draft used vary between authorities.Length may be LBP, LWL or some effective length. The beam may be at amidships or the

maximum moulded beam of the waterline; or may be defined according to another standard –this may be important for hulls with significant tumble-home or blisters below the waterline.

Hydromax uses the length of the waterline under consideration, L, the maximumwaterline beam of that waterline, B. The draft is the depth below the waterline of thedeepest section, T. Note that B and T need not occur at the same longitudinal station.

T B LC B

⋅⋅

∇=

Midship Section Coefficient

Principles of Naval Architecture defines the midship coefficient as:

"The ratio of the immersed area of the midship station to that of a rectangle of breadth equal tomoulded breadth and depth equal to moulded draft at amidships."

It should be noted that, for sections that have significant tumble-home or blisters below thewaterline, the midship section coefficient can be greater than unity.

The midship section coefficient used by Hydromax, is calculated at the station withmaximum cross-sectional area. The beam used is the waterline beam at this station, b, andthe draft is the immersed depth of the station, t.

t b

AC M

⋅=max

Prismatic Coefficient

Principles of Naval Architecture defines the prismatic coefficient as:

"The ratio between the volume of displacement and a prism whose length equals the length ofthe ship and whose cross-section equals the midship section area."

Again the definition of midship section and vessel length depend on the standard being used.

Hydromax uses the length of the waterline under investigation, L, and the maximum

immersed cross-section area Amax.

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Appendix A

Page 167

⎟⎟

⎠

⎞⎜⎜

⎝

⎛ −= −

pp

f a

L

T T 1tanθ

where: θ is the trim angle; T a , T f are the aft and forward drafts at the corresponding perpendiculars and LPP is the length between perpendiculars.

Maximum deck inclinationThe inclination angle is a combination of heel and trim angle. Hydromax calculates the steepestslope of the deck when the ship is trimmed and/or heeled. Deck camber and initial deck slopeare not taken into account.

For example:

The Max deck inclination is themaximum slope of the deck whencombining the trim and heel angleof the vessel, assuming the deckinclination is zero when the vessel isin upright position.

Immersion

The weight required to sink the model one unit-length below its current waterline. The unit-length can be either in cm or inch depending on your unit settings.

MTc or MTi

The required moment to make the vessel trim one unit-length. That can be either cm or inchdepending on your unit settings.

RM at 1 deg

The righting Moment at 1 degree heel angle, calculated by

)1sin(** GMt Displ RM =

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Appendix A

Page 168

Potential for errors in hydrostatic calculationsThere are a number of potential sources of error when calculating the hydrostatic properties ofimmersed shapes. These mainly occur from the integration method used, and occur in both handcalculations, and most automatic calculations carried out by computers. Both methods usenumerical integration techniques, which are normally either based on Simpson's rule or theTrapezium rule. As with all numerical integration schemes, the accuracy increases as the stepsize is reduced, hence computer calculations offer an enormous advantage compared with handcalculations, due to the increased speed and accuracy with which these calculations may becarried out. With hand calculations, it is normal to use perhaps 21 sections and perhaps 3-5significant figures; with computer calculations, it is quite feasible to use 200 sections or morewith 10s of significant figures. These effects are noted from comparing the results of differenthydrostatics packages on the same hullform. In general, differences for basic parameters such asdisplacement etc. are under 0.5% (note that, in general, agreement of hand calculations to within2% is considered good). Differences in derived form parameters may show considerablevariation. However, this is primarily due to differences in the definitions used – see discussionabove.

The 0.5% error discrepancy noted above, may be attributed to a number of causes:• Convergence limits wh en balancing a hull to a specified displacement or centre of gravity.

• Different n umber of integration stations used, and t heir distrib ution. Where there are largechanges in shape, such as near the bow and stern, the stations should be more closelyspaced. This can be of particular importance if the waterline intersects the stem profilebetween two sections.

• Differences in the hull d efinition, and number of interpolation p oints used to define eachsection. If the surface is exported as DXF poly-lines then the precision used and thenumber of str aight-line sections used to make up the pol y-line are important.

• The integration method used: t rapezium, Simpson, or higher order methods.

Integration of wetted surface area

At first glance, it may seem that wetted surface area may be calculated by simply integrating thestation girth along the length of the hull, in a similar way that one might integrate the stationcross-sectional area along the length of the hull to obtain the volume. However, this is not thecase, and the wetted surface area can only be accurately found by summing elemental areas overthe complete surface. Further, the error due to integrating girths along the vessel length cannot

be removed simply by increasing the number of integration stations. The only accuratenumerical method is to sum the areas of individual triangles interpolated on the parametricsurface.

The differences are easily shown by considering the surface area of half a sphere. This is givenanalytically by: 22 R A π = , where R is the radius of the circle.It may be shown that the area obtained by integrating the girth of the sphere along its length isgiven by:

2

22' R

A π = , note that this is with an infinite number of integration steps, and hence the

integration of section girths underestimates by error factor of 27.1/45.02

22

2

== π π π

R R

, or

approximately 27%.However, for normal ship hulls the differences will be much less, due to the greatly reducedlongitudinal curvature. Surface areas calculated by the 'Calculate Areas' dialog in Maxsurf are

the most accurate, since they are derived from the actual parametric definition of the surface.Those calculated by Hydromax and most other hydrodynamics packages, which use a number ofvertical stations to define the hull, will be subject to the error described above.

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Appendix A

Page 169

Reference DesignsA folder of reference hull shapes is included with Maxsurf and Hydromax. These designs are ofsimple geometric shapes and can be used to validate calculations performed by Hydromax.Below is a table of results derived analytically from these shapes compared with resultsobtained from Maxsurf and Hydromax at different precisions.

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A p p

e n

d i x A

P a g

e

1 7 0

R e

f e r e n c e

C a l c u

l a t i o n s

H y d r o s t a t i c s c a l c u l a t i o n s

f o r v a r i o u s r e f e r e n c e

d e s i g n s , c o m p a r i s o n o f M a x s u r f a n d

H y d r o m a x w i t h a n a l y t i c a l v a l u e s

s p h e r e 1 0 m d i a m a t 5 m

d r a f t

V o l u m e

m ^ 3

W P A r e a

m ^ 2

V C B

m

L C B

m

T r a n s .

I m ^ 4 L o n g .

I m ^ 4 V o l u m e

W P A r e a

T r a n s .

I

L o n g .

I

A n a l y t i c a l l y

d e r i v e d

2 6 1 . 7 9 9 3 9

7 8 . 5 3 9 8 2

- 1 . 8 7 5 0

4 9 0 . 8 7 3 8 5 2

4 9 0 . 8 7 3 8 5

% e r r o r

% e r r o r

% e r r o r

% e r r o r

H y d r o m a x

H i g h P r e c i s i o n

2 6 0 . 4 9 9 8

7 8 . 3 8 1

- 1 . 8 7 4 0

4 8 8 . 6 8 0 7 2 6 9 4 8 9 . 1 4 2 4 7

- 0 . 5 0 %

- 0 . 2 0 %

- 0 . 4 5 %

- 0 . 3 5 %

H y d r o m a x

L o w

P r e c i s i o n

2 6 0 . 3 4 2 7 9

7 8 . 3 5 7

- 1 . 8 7 4 0

4 8 8 . 5 6 4 7 4 1

4 8 8 . 9 3 8 7 3

- 0 . 5 6 %

- 0 . 2 3 %

- 0 . 4 7 %

- 0 . 3 9 %

M a x s u r f H

i P r e c i s i o n

2 6 1 . 5 3 2

7 8 . 3 4 1

- 1 . 8 7 5 0

4 9 0 . 5 7

4 8 5 . 7 6 1

- 0 . 1 0 %

- 0 . 2 5 %

- 0 . 0 6 %

- 1 . 0 4 %

M a x s u r f L o w

P r e c i s i o n

2 5 7 . 1 0 5

7 7 . 8 4 9

- 1 . 8 7 1 0

4 8 3 . 1 9 1

4 8 0 . 8 9

- 1 . 7 9 %

- 0 . 8 8 %

- 1 . 5 7 %

- 2 . 0 3 %

1 0 m C y l i n d e r

1 0 m d i a m

. a t 5 m

d r a f t

V o l u m e

m ^ 3

W P A r e a

m ^ 2

V C B

m

L C B

m

T r a n s .

I m ^ 4 L o n g .

I m ^ 4 V o l u m e

W P A r e a

T r a n s .

I

L o n g .

I


d e r i v e d

3 9 2 . 6 9 9

1 0 0

- 2 . 1 2 2 0

8 3 3 . 3 3 3 3 3 3

8 3 3 . 3 3 3 3 3

% e r r o r

% e r r o r

% e r r o r

% e r r o r

H y d r o m a x


3 9 1 . 9 9 1

1 0 0

- 2 . 1 2 1 0

8 3 3 . 3 3 3 3 3 3

8 3 3 . 3 3 3 3 3

- 0 . 1 8 %

0 . 0 0 %

0 . 0 0 %

0 . 0 0 %

H y d r o m a x

L o w

P r e c i s i o n

3 9 1 . 9 9 1

1 0 0

- 2 . 1 2 1 0

8 3 3 . 3 3 3 3 3 3

8 3 3 . 3 3 3 3 3

- 0 . 1 8 %

0 . 0 0 %

0 . 0 0 %

0 . 0 0 %

M a x s u r f H

i P r e c i s i o n

3 9 2 . 5 2 2

1 0 0

- 2 . 1 2 2 0

8 3 3 . 3 3 3

8 3 3 . 3 3 3

- 0 . 0 5 %

0 . 0 0 %

0 . 0 0 %

0 . 0 0 %

M a x s u r f L o w

P r e c i s i o n

3 8 9 . 8 7 4

1 0 0

- 2 . 1 1 8 0

8 3 3 . 3 3 3

8 3 3 . 3 3 3

- 0 . 7 2 %

0 . 0 0 %

0 . 0 0 %

0 . 0 0 %

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A p p e n

d i x A

P a g e

1 7 1

B o x

2 0 m l o n g 1 0 m b e a m a t 5 m

d r a f t

V o l u m e

m ^ 3

W P A r e a

m ^ 2

V C B

m

L C B

m

T r a n s .

I m ^ 4 L o n g .

I m ^ 4 V o l u m e

W P A r e a

T r a n s .

I

L o n g .

I


d e r i v e d

1 0 0 0

2 0 0

- 2 . 5

0

1 6 6 6 . 6 6 6 6 6 6 6 6 6 6 . 6 6 6 7

% e r r o r

% e r r o r

% e r r o r

% e r r o r

H y d r o m a x


1 0 0 0

2 0 0

- 2 . 5

0

1 6 6 6 . 6 6 6 6 6 6 6 6 6 6 . 6 6 6 7

0 . 0 0 %

0 . 0 0 %

0 . 0 0 %

0 . 0 0 %

H y d r o m a x

L o w

P r e c i s i o n

1 0 0 0

2 0 0

- 2 . 5

0

1 6 6 6 . 6 6 6 6 6 6 6 6 6 6 . 6 6 6 7

0 . 0 0 %

0 . 0 0 %

0 . 0 0 %

0 . 0 0 %

M a x s u r f H

i P r e c i s i o n

1 0 0 0

2 0 0

- 2 . 5

0

1 6 6 6 . 6 6 7

6 6 6 6 . 6 6 7

0 . 0 0 %

0 . 0 0 %

0 . 0 0 %

0 . 0 0 %

M a x s u r f L o w

P r e c i s i o n

1 0 0 0

2 0 0

- 2 . 5

0

1 6 6 6 . 6 6 7

6 6 6 6 . 6 6 7

0 . 0 0 %

0 . 0 0 %

0 . 0 0 %

0 . 0 0 %

P a r a b o l i c W i g l e y t y p e H u l l , L

W L = 1 5 m , B

= 1 . 5 m

, D = 0 .

9 3 7 5

V o l u m e

m ^ 3

W P A r e a

m ^ 2

V C B

m

L C B

m

T r a n s .

I m ^ 4 L o n g .

I m ^ 4 V o l u m e

W P A r e a

T r a n s .

I

L o n g .

I


d e r i v e d

9 . 3 7 5

1 5

- 0 . 3 5 2 0

1 . 9 2 8 7 5

1 6 8 . 7 5

% e r r o r

% e r r o r

% e r r o r

% e r r o r

H y d r o m a x


9 . 3 6 4

1 4 . 9 8 5

- 0 . 3 5 2 0

1 . 9 2 5 2 7

1 6 8 . 4 6 8 5

- 0 . 1 2 %

- 0 . 1 0 %

- 0 . 1 8 %

- 0 . 1 7 %

H y d r o m a x

L o w

P r e c i s i o n

9 . 3 5 1

1 4 . 9 8

- 0 . 3 5 2 0

1 . 9 2 4 1 8

1 6 8 . 3 7 7 3

- 0 . 2 6 %

- 0 . 1 3 %

- 0 . 2 4 %

- 0 . 2 2 %

M a x s u r f H

i P r e c i s i o n

9 . 3 7 2

1 4 . 9 9 9

- 0 . 3 5 1 0

1 . 9 2 7

1 6 8 . 6 3

- 0 . 0 3 %

- 0 . 0 1 %

- 0 . 0 9 %

- 0 . 0 7 %

M a x s u r f L o w

P r e c i s i o n

9 . 3 0 2

1 4 . 9 4 2

- 0 . 3 5 1 0

1 . 9 1

1 6 7 . 6 2 1

- 0 . 7 8 %

- 0 . 3 9 %

- 0 . 9 7 %

- 0 . 6 7 %

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Appendix B

Page 172

Appendix BCriteria file formatThe criteria are saved in a Hydromax criteria file with the extension .hcr. The file is a normal

PC text file, which may be edited manually so as to generate custom criteria. The typical formatof the file is given below:

Please refer to the file C:\Program Files\Maxsurf\HMCriteriaHelp\CriteriaHelp.html for a fulllist of all the parameters for all the different criteria types.

Hydr omax Cr i t er i a Fi l e[ uni t s ]Lengt hUni t s = mMassUni t s = t onneSpeedUni t s = kt sAngl eUni t s = deg

GZAr eaGMAngl eUni t s = deg[ end]

[ cr i t er i onGr oup]Gr oupName = Speci f i c Cr i t er i aPar ent Gr oupName = r oot[ end]

[ cr i t er i onGr oup]Gr oupName = My Cust om Cr i t er i aPar ent Gr oupName = r oot[ end]

[ cr i t er i onGr oup]Gr oupName = STI X i nput dat aPar ent Gr oupName = Speci f i c Cr i t er i a[ end]

[ c r i t er i on] Type = CTSt dAr eaUnder GZBet weenLi mi t sRul eName = STI X i nput dat aCr i t Name = GZ ar ea t o t he l esser of downf l oodi ng or …Cr i t I nf o = Ar ea under GZ cur ve bet ween speci f i ed heel …Cr i t I nf oFi l e = HMCr i t er i aHel p\ St i xHel p. r t f

Locked = t r ueGr oupName = STI X i nput dat a Test I nt act = t r ue Test Damage = f al se Test = f al seCompar e = Gr eat er ThanUseLoHeel = f al seUseEqui l i br i um = t r ueUseHi Heel = f al seUseFi r st Peak = f al seUseMaxGZ = f al seUseFi r st DF = t r ue

UseVani shi ngSt ab = t r ueLoHeel = 0. 0Hi Heel = 30. 0

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Appendix B

Page 173

Requi r edVal ue = 0. 000[ end]

[ c r i t er i on] Type = CTSt dAngl eOf Vani shi ngSt abRul eName = STI X i nput dat aCr i t Name = Angl e of vani shi ng st abi l i t yCr i t I nf o = Cal cul at es t he angl e of vani shi ng s t abi l i t y…Cr i t I nf oFi l e = HMCr i t er i aHel p\ St i xHel p. r t fLocked = t r ueGr oupName = STI X i nput dat a

Test I nt act = t r ue Test Damage = f al se Test = f al seCompar e = Gr eat er ThanRequi r edVal ue = 0. 0[ end]

The file must have “ Hydr omax Cr i t er i a Fi l e ” in the first row. The first section of thefile is the units section and this specifies the units that are to be used in the file. There are twoangular units:Angl eUni t s Specifies the units for angular measurements,

e.g. range of stabilityGZAr eaGMAngl eUni t s Specifies the angle units used for area under

GZ graph and for GM.

The criteria then appear after the units section and as many criteria as required may be included.The common parameters for all criteria are as follows:

Type Describes the type of criterionRul eName Text which specifies the rule to which the

criterion belongsCr i t Name Text which specifies the criterion’s nameCr i t I nf o Verbose description of the criterionLocked Whether the criterion may be edited in

Hydromax or not. If Locked is set to true, it isnot possible to edit the criterion’s parametersin Hydromax

The other parameters that may be set depend on the criterion type. The available criterion typesare as follows:Criteria at equilibriumCTSt dEqui Angl e Angle of equilibriumCTSt dEqui Fr eeboar d Freeboard at equilibriumCTSt dEqui GM GM at equilibriumGZ curve criteriaCTSt dVal ueOf GMAt Value of GM at specified

heel angleCTSt dVal ueOf GZAt Value of GZ at specified

heel angle.CTSt dVal ueOf MaxGZ Maximum value of GZ in

specified rangeCTSt dRat i oOf GZVal ues Ratio of two GZ values at

specified heel angles.

CTSt dAngl eOf MaxGZ Angle at which maximumGZ occurs.CTSt dAngl eOf Equi l i br i um Angle of equilibrium.

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Appendix B

Page 174

CTSt dAngl eOf Downf l oodi ng Angle at which first downflooding point isimmersed.

CTSt dAngl eOf Vani shi ngSt ab Angle of vanishingstability.

CTSt dRangeOf St abi l i t y Range of positivestability.

CTSt dAr eaUnder GZBet weenLi mi t s Area under GZ curveCTSt dHSCMonoAr eaUnder GZBet weenLi mi t s Area under GZ curve –

required area depends onupper limit, linear

CTSt dHSCMul t i Ar eaUnder GZBet weenLi mi t s Area under GZ curve –required area depends onupper limit, exponential

Heeling arm criteriaCTSt dHeel Val ueOf GMAt Equi l i br i um Value of GM at angle of

equilibrium with specifiedheel arm.

CTSt dHeel Val ueOf GZAt Equi l i br i um Value of GZ at angle ofequilibrium with specifiedheel arm.

CTSt dHeel Val ueOf MaxGZAboveHACTSt dHeel Rat i oOf GZVal uesCTSt dHeel Angl eOf MaxGZAboveHACTSt dHeel Angl eOf Equi l i br i um Angle of equilibrium with

specified heel arm.Generic heeling arm

CTSt dPassenger Cr owdi ngAngl eOf Equi l i br i um Angle of equilibrium withspecified heel arm.Passenger crowdingheeling arm

CTSt dHi ghSpeedTur nAngl eOf Equi l i br i um Angle of equilibrium withspecified heel arm.Turning heeling arm

CTSt dDer i vedHeel Ar mAngl eOf Equi l i br i um Derived wind heelingCTSt dHeel Angl eOf Vani shi ngSt ab Angle of vanishing

stability with specifiedheel arm.

CTSt dHeel RangeOf St abi l i t y Range of stability withgeneric wind heeling arm

CTSt dHeel Ar eaBet weenGZAndHABet weenLi mi t s Area between GZ curve

and heeling armCTSt dHeel Rat i oOf Ar eas1Tur ni ng Area ratio, method 1using generic heeling arm

CTSt dHeel Rat i oOf Ar eas1Li f t i ng Area ratio, method 1using sin+cos heeling arm

CTSt dHeel Rat i oOf Ar eas2 Ratio of areas based onUS Navy wind heelingcriterion.

Multiple heeling arm criteriaCTSt dMul t i Heel Rat i oOf GZVal ues GZ ratio for combined

heeling armsCTSt dMul t i Heel Angl eOf Equi l i br i um Angle of equilibrium for

combined heeling armsCTSt dMul t i Heel Ar eaBet weenGZAndHABet weenLi mi t s Area between GZ curve

and heeling arm, for

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Appendix B

Page 175

combined heeling armsCTSt dMul t i Heel Rat i oOf Ar eas1Tur ni ng Ratio of areas method 1

for combined heelingarms

Heeling arm, combined criteriaCTSt dHeel Gener i cTur ni ng Combined criteria for

turningCTSt dHeel Gener i cLi f t i ng Combined criteria for

lifting of heavy weightsCTSt dHeel Gener i cWi ndHeel i ng Combined angle of

equilibrium, ratio of GZvalues and ratio of areascriteria for specifiedheeling arm; based on US

Navy wind heelingcriterion. Uses genericheeling arm

CTSt dHeel Wi ndHeel i ng Combined angle of

equilibrium, ratio of GZvalues and ratio of areascriteria for specifiedheeling arm; based on US

Navy wind heelingcriterion. Uses windheeling arm

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Appendix C

Page 176

Appendix CCriteria HelpIn this Appendix all individual Parent Criteria are explained in detail. This information can also

be found in the lower right of the Criteria Dialog in the Criteria Help section.In this section:

• Parent Heeling Arms

• Parent Heeling Moments

• Parent Stability Criteria

For all general help on criteria or working with the criteria dialog, see Chapter 4 StabilityCriteria on page 113 .

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Appendix C

Page 178

Also see the next section: Heeling arms for specific criteria - Note on unit conversion section on page 233.

Note:When you are working with the parent heeling arms, make sure you copy them intoa custom heeling arms folder before editing them. Same as for the Parent criteria,

the Parent heeling arms will be reset to their default values each time you start upHydromax.

General heeling arm

The general form of the heeling arm is given below:

)(cos)( φ φ n A H = where:φ is the heel angle, A is the magnitude of the heeling arm,

ncos describes the shape of the curve.

Typically n=1 is used for passenger crowding and vessel turning since the horizontal lever forthe passenger transverse location reduces with the cosine of the heel angle. For wind n=2 isoften used for heeling because both the projected area as well as the lever decrease with thecosine of the heel angle. However, some criteria, such as IMO Severe wind and rolling (weathercriterion) have a heeling arm of constant magnitude, in this case n=0 should be used.

Make sure you read Important note: heeling arm criteria dependent on displacement on page183.

General heeling arm with gust

Some criteria require a Gust Ratio, this is the ratio of the magnitude of the wind heeling armduring a gust to the magnitude of the wind heeling arm under steady wind.

steady

gust

H

H GustRatio =

Both the steady and the gust heel arm have the same shape.

)(cos)( φ φ nsteady A H =

)(cos)( φ φ ngust GustRatio A H ××=

where:

φ is the heel angle, A is the magnitude of the heeling arm,


It should be noted, that in this case, the definition of gust ratio is the ratio of the heeling arms.Some criteria specify the ratio of the wind speeds; if it is assumed that the wind pressure is

proportional to the square of the wind seed, the ratio of the heel arms will be the square of theratio of the wind speeds.

General cos+sin heeling arm

Some criteria, notably lifting of weights, require a heeling arm with both a sine and cosine

component:)(sin)(cos)( φ φ φ mn B Ak H +=

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Appendix C

Page 179

It should be noted that provided the indices are both unity, the same heeling arm form may beused for computing towing heeling arms of the form:

( ))sin()cos()( δ φ δ φ φ +++= B Ak H in this case a constant angle (in the case of towing, the angle of the tow above the horizontal) isincluded.

It may be shown that this is equivalent to:( ))sin()cos()( φ φ φ DC k H += where:

)(tan1 2

2

δ α −+= R

C , )tan( δ α −= C D , 222 B A R += and A

B=α tan

Make sure you read Important note: heeling arm criteria dependent on displacement on page183.

User Defined Heeling Arm

A user-defined heeling arm may be used in the criteria. With the heeling arm, the user canspecify the number of points and the shape of the heeling arm curve.

This heeling arm can then be cross-referenced into any of the heeling arm criteria. First, thenumber of points is specified and then for each point the angle and magnitude of the curve can

be specified. These should be comma delimited for example <45 , 1.2> for a heeling armmagnitude of 1.2 meters at 45 degrees angle of heel. (To aid input of the data, if only one valueis supplied it is taken as the heel angle – and the magnitude is left unchanged, and if a value

preceded by a comma is given, this is taken as the magnitude – and the heel angle is leftunchanged.) A single coefficient may be adjusted and this is used as a multiplication factor(whist the shape of the curve remains unchanged).

Passenger crowding heeling arm

The magnitude of the heel arm is given by:

)(cos)( φ φ n pas pc

MDn H Δ

=

where:

pasn is the number of passengers M is the average mass of a single passenger

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Appendix C

Page 180

D is the average distance of passengers from the vessel centrelineΔ is the vessel mass (same units as M )

The heeling arm parameters are specified as follows:

Option Description Units

number of passengers:nPass

Number of passengers none

passenger mass: M Average mass of one passenger massdistance fromcentreline: D

Average distance of the passengers fromthe centreline

length

cosine power: n Cosine power for curve - defines shape none

Wind heeling arm

In the case of the wind pressure based formulation, the wind heeling arm is given by:( ) )(cos)( φ φ n

w g H hPA

a H Δ−=

where:a is a constant, theoretically unity A is the windage area at height h Δ is the vessel massP is the wind pressure

H is the vertical centre of hydrodynamic resistance to the wind force

In the case of the wind velocity based formulation, the wind heeling arm is given by:

( ) )(cos)(2

φ φ nw g

H h Ava H Δ

−=

where:a is now effectively an average drag coefficient for the windage area multiplied by the airdensity and has units of densityv is the wind speed.And the other parameters are described as above.

Option Description Unitsconstant: a Constant which may be used to modify

the magnitude of the heel arm, normallyunity for pressure based formulation or0.5 ρair CD for the velocity formulation;where ρair is the density of air and C D isan average drag coefficient for thewindage area

none for

pressure basedformulation;mass/length3 forvelocity

basedformulation

wind model Pressure or Velocity (type “P” or “V”)

wind pressure orvelocity

Actual velocity of pressure - depends onwind model

mass/(time 2 length) orlength/time

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area centroid height: h Height of user defined total or additionalwindage area

length

total area: A User may specify either a total windagearea

length 2

additional area: A Or, an area to be added to the windagearea computed by Hydromax based on

the hull sections

length 2

height of lateralresistance: H

There are four options for specifying H(all options are calculated with the vesselupright at the loadcase displacement andLCG):User specified

length

H = mean draft / 2 H is taken as half the mean draft. lengthH = vert. centre of

projected lat. u'waterarea

H is taken as the vertical centre ofunderwater lateral projected area.

length

H = waterline H is taken as the waterline length


Turning heeling arm

The magnitude of the heel arm is derived from the moment created by the centripetal forceacting on the vessel during a high-speed turn and the vertical separation of the centres of gravityand hydrodynamic lateral resistance to the turn. The heeling arm is obtained by dividing theheeling moment by the vessel weight. The heeling arm is thus given by:

)(cos)(2

φ φ nt h

Rgv

a H =

where (in consistent units):a is a constant, theoretically unityv is the vessel velocity R is the radius of the turnh is the vertical separation of the centres of gravity and lateral resistance


Option Description Unitsconstant: a Constant which may be used to modify the

magnitude of the heel arm, normally unitynone

vessel speed: v Vessel speed in turn length/timeturn radius: R Turn radius may be specified directly lengthturn radius, R, as

percentage of L WL Or, as some criteria require, as percentageof L WL

%

Vertical lever: h There are four options for specifying h (alloptions are calculated with the vesselupright at the loadcase displacement andLCG):User specified

length

h = KG h is taken as KG - position of G above baseline in upright condition

length

h = KG - mean draft / 2 h is taken as KG less half the mean draft. lengthh = KG - vert. centre of

projected lat. u'waterh is taken as the vertical separation of thecentres of gravity and underwater lateral

length

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area projected area.cosine power: n Cosine power for curve - defines shape none

Lifting heeling arm

This is used to simulate the effect of lifting a weight from its stowage position. The magnitude

of the heel arm is given by:[ ])sin()cos()( φ φ φ vh

M H lw +

Δ=

where: M is the mass of the weight being liftedh is horizontal separation of the centre of gravity of the weight in its stowage position and thesuspension positionv is vertical separation of the centre of gravity of the weight in its stowage position and thesuspension positionΔ is the vessel mass (same units as M )


Option Description UnitsMass being lifted: M Mass of weight being lifted massvertical separation ofsuspension fromstowage position: v

Vertical separation of suspension pointfrom weight’s original stowage position onthe vessel. This value is positive if thesuspension position is above the originalstowage position.

length

horizontal separation ofsuspension from

stowage position: h

Horizontal separation of suspension pointfrom weight’s original stowage position on

the vessel This value is positive if thehorizontal shift of the weight should

produce a positive heeling moment.

length

Towing heeling arm

The magnitude of the heel arm is given by:

[ ])sin()(cos)( τ φ τ φ φ +++Δ

= hvgT

H ntow

where:T is the tension in the towline or vessel thrust, expressed as a force.h is horizontal offset of the tow attachment position from the vessel centrelinev is vertical separation tow attachment position from the vessel’s vertical centre of thrustΔ is the vessel massn is the power index for the cosine term which may be used to change the shape of the heelingarm curveτ is the (constant) angle of the towline above the horizontal. It is assumed that the towline issufficiently long that this angle remains constant and does not vary as the vessel is heeled.



tension or thrust: T Tension in towline or vessel thrust forcevertical separation of

propeller centre and towVertical separation tow attachment

position from the vessel’s vertical centrelength

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attachment: v of thrust. This value is positive if thetowline is above the thrust centre.

horizontal offset of towattachment: h

Horizontal offset of the tow attachment position from the vessel centreline. Thisvalue is positive if the offset is in thedirection of the tow.

length

angle of tow abovehorizontal: tau Angle of tow above the horizontal angle


Areas and levers

Some criteria require the evaluation of above and below water lateral projected areas and theirvertical centroids. The user may also specify additional areas and vertical centroids or the totalareas and vertical centroids. In all cases the vertical centroids are given in theMaxsurf/Hydromax co-ordinate system; i.e.: from the model’s vertical datum, positive upwards.

Centroids of area are calculated for the upright vessel (zero trim and heel) at the mean draft. Theareas are calculated from the hydrostatic sections used by Hydromax; thus, increasing thenumber of sections will increase the accuracy of the area calculation; further, only “Hull”surfaces are included in the calculation - “Structure” surfaces are ignored.

The vertical position of the keel, K, is assumed to be at the baseline (as set up in the Frame ofReference dialog), even if the baseline does not correspond to the physical bottom of the vessel.

Important note: heeling arm criteria dependent on displacement

Some heeling arm criteria are dependent on the displacement of the vessel for the calculation ofthe Heeling Arm. For example, the value “ A” in:

)(cos)( φ φ n A H =

,is manually calculated from:

Δ= M

A , where

M = heeling momentΔ = displacement.

This means that the heeling arm will vary with the displacement. Hydromax will not take thechange in displacement into account.

When evaluating these criteria that are dependent on displacement, care has to be taken to make

sure any change in displacement is taken into account. For large angle stability this means thatevery loadcase will have its own set of criteria. For Limiting KG and Batch analysis, there aretwo options:

1. Calculate the worst-case lever based on the displacement and VCG that result in the worstlever and see if the criterion is actually a limiting one for KG.2. Calculate limiting KG at single displacements and change the heeling arm for eachdisplacement.

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Parent Heeling MomentsHeeling moments work the same way as Parent Heeling Arms in that they can be crossreferenced into criteria. The advantage of using heeling moments is that they provide a constantheeling moment (varying heeling arm) as the vessel displacement changes (due to differentloadcases or during a limiting KG analysis).

These are in addition to the existing specific heeling arm curves for passenger crowding, windheeling etc., which take account of the vessel displacement as required.


The following heeling moments are available in the Hydromax criteria dialog:• General heeling mo ment

• General cos+sin heeling moment

• General heeling mo ment with gust

• User Defined Heeling Moment

General heeling moment

The general form of the heeling moment is given below. It allows you to specify a constantheeling moment as opposed to a constant heeling arm :

)(cos)( φ φ n A H Δ

=

where:φ is the heel angle, A is the magnitude of the heeling moment (mass.length) and Δ the vessel displacement

(mass); thus Δ A

is the magnitude of the heeling arm (length).ncos describes the shape of the curve.

Typically n=1 is used for passenger crowding and vessel turning since the horizontal lever forthe passenger transverse location reduces with the cosine of the heel angle. For wind n=2 isoften used for heeling because both the projected area as well as the lever decrease with thecosine of the heel angle. However, some criteria, such as IMO Severe wind and rolling (weathercriterion) have a heeling arm of constant magnitude, in this case n=0 should be used.

General cos+sin heeling moment

Some criteria, notably lifting of weights, require a heeling moment with both a sine and cosinecomponent:

( ))(sin)(cos)( φ φ φ mn B Ak

H +Δ

=

where:φ is the heel angle, A and B the magnitudes of the cosine and sine components of the heeling moment

(mass.length) and Δ the vessel displacement (mass); thusΔ A and

Δ B are the magnitude of the

heeling arm (length).

It should be noted that provided the n and m indices are both unity, the same heeling momentform may be used for computing towing heeling moments of the form:



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( ))sin()cos()( δ φ δ φ φ +++Δ

= B Ak

H

in this case a constant angle (in the case of towing, the angle of the tow above the horizontal) isincluded.

It may be shown that this is equivalent to:

( ))sin()cos()( φ φ φ DC k H +Δ

=

where:

)(tan1 2

2

δ α −+= R

C , )tan( δ α −= C D , 222 B A R += and A

B=α tan

General heeling moment with gust

Some criteria require a Gust Ratio, this is the ratio of the magnitude of the wind heeling armduring a gust to the magnitude of the wind heeling arm under steady wind.

steady

gust

H H =GustRatio

The general form of the heeling moment is given below. It allows you to specify a constantheeling moment as opposed to a constant heeling arm . Both the steady and the gust heel momenthave the same shape.

)(cos)( φ φ nsteady

A H Δ

=

)(cosGustRatio)( φ φ ngust

A H ××

Δ=

where:φ is the heel angle, A is the magnitude of the heeling moment (mass.length) and Δ the vessel displacement

(mass); thusΔ A is the magnitude of the heeling arm (length).


It should be noted, that in this case, the definition of gust ratio is the ratio of the heeling arms.

Some criteria specify the ratio of the wind speeds; if it is assumed that the wind pressure is proportional to the square of the wind seed, the ratio of the heel arms will be the square of theratio of the wind speeds.

User Defined Heeling Moment

With the User Defined Heeling Moment, the user can specify the number of points and theshape of the heeling moment curve. Defining User Defined Heeling Moments works in muchthe same as for User Defined Heeling Arm . This heeling moment can then be linked into aHeeling arm criteria (xRef) for evaluation.

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Parent Stability CriteriaThe parent criteria are divided up into different categories:

• Criteria at Equilibri um

• GZ Curve Criteria (non -heeling arm)

• Heeling arm crit eria (xRef) • Heeling arm criteria

• Multiple heeling arm criteria

• Heeling arm, combined criteria

• Other combi ned criteria

Criteria at EquilibriumThese criteria are calculated after an equilibrium analysis and relate to the equilibrium positionof the vessel after the analysis. The equilibrium criteria are only displayed in the report if you

run an equilibrium analysis.

Maximum value of Heel, Trim or Slope at Equilibrium

This criterion may be used to check the value of maximum Heel, Pitch or Maximum Slope(compared with an originally horizontal and flat deck).

Option Description UnitsThe angle of Choose from the following (case

insensitive auto-completion is used):HeelPitch

MaxSlope

deg

Shall be less than /Shall not be greater than

Permissible value deg

Minimum Freeboard at Equilibrium

Checks whether the minimum freeboard is greater than a minimum required value. This could be used to check margin line or downflooding point immersion.

Option Description UnitsThe value of Choose from the following (case

insensitive auto-completion is used):

MarginlineDeckEdgeDownfloodingPointsPotentialDfloodingPointsEmbarkationPointsImmersionPoints

length

Shall be greater than /Shall not be less than

Permissible value length

Maximum Freeboard at Equilibrium

Check that the maximum freeboard is less than a maximum required value. This could be usedto check that an embarkation point is sufficiently close to the waterline.


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The value of Choose from the following (caseinsensitive auto-completion is used):MarginlineDeckEdgeDownfloodingPointsPotentialDfloodingPoints

EmbarkationPointsImmersionPoints

length



To check that the freeboard lies within a specified range, use a combination of both forms of theminimum/maximum freeboard criteria.

Value of GM T or GM L at Equilibrium

This criterion is used to check that the GM (transverse or longitudinal) exceeds a specifiedminimum value.

Option Description UnitsThe value of Choose from the following (case

insensitive auto-completion is used):GMtransverseGMlongitudinal)

length



GZ Curve Criteria (non-heeling arm)

These criteria, calculated from the GZ curve, are calculated from the Large Angle Stabilityanalysis in Hydromax.

Value of GMt at

Finds the value of GMt at either a specified heel angle or the equilibrium angle. The criterion is passed if the value of GMt is greater then the required value. GMt is computed from waterplane inertia and immersed volume.

Option Description UnitsValue of GMt at either

specified heel angle User specified heel angle deg

angle of equilibrium See Nomenclature degShall be greater than /Shall not be less than


Value of GZ at

Finds the value of GZ at either a specified heel angle, first peak in GZ curve, angle of maximumGZ or the downflooding angle. The criterion is passed if the value of GZ is greater then therequired value.

Option Description UnitsValue of GZ at either

specified heel angle User specified heel angle degangle of first GZ peak See Nomenclature degangle of maximum GZ See Nomenclature deg

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first downfloodingangle

See Nomenclature deg



Value of Maximum GZ

Finds the maximum value of GZ within a specified heel angle range. The criterion is passed ifthe value of GZ is greater than the required value. If you want to check the value of GZ at acertain angle you can set both specified angles as the required angle. If any of the calculatedangles for the upper limit are less than the lower limit, they will be ignored when selecting thelowest. If all the upper limit values are less than the lower limit, then the criterion will fail. Thisfunctionality is to allow criteria such as “The maximum GZ at 30deg or greater”.

Note: Upper limit and analysis heel angle rangeIt is required that the range of heel angles specified for the Large Angle Stabilityanalysis is equal, or exceeds, the upper range heel angle specified in the criterion.

Option Description UnitsValue of maximum GZ

in the range from thegreater of

Lower limit for heel angle range, thegreater of the following:

specified heel angle User specified heel angle degangle of equilibrium See Nomenclatureto the lesser of Upper limit for heel angle range, the lesser

of the following:specified heel angle User specified heel angle; this should

normally be specified and be less than orequal to the upper limit of the range ofheel angles used for the Large AngleStability analysis.

deg

angle of first GZ peak See Nomenclature degangle of maximum GZ See Nomenclature degfirst downfloodingangle




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Value of Maximum GZ

Value of GZ at Specified Angle or Maximum GZ below Specified Angle

If the angle at which maximum GZ occurs is greater than a specified value, the value of GZ atthe specified angle is calculated. Otherwise the value of maximum GZ is calculated. Therequired GZ value depends on the angle at which the maximum occurs, see graph below.

Option Description Unitsheel angle at whichrequired GZ is constant

If the angle of maximum GZ is greaterthan or equal to this value, the requiredvalue of GZ is constant and is taken at thisspecified angle. Otherwise the requiredvalue of maximum GZ varies as ahyperbolic function with the angle ofmaximum GZ. This is

0φ .

deg

required value of GZ atthis angle is

Required value of GZ at the heel anglespecified above. This is ( )0φ GZ .

length

limited by first GZ peakangle

Angle at which GZ is measured may belimited to the location of the first peak inthe GZ curve.

deg

limited by firstdownflooding angle

Angle at which GZ is measured may belimited to first downflooding angle.

deg


Permissible value. length

If 0maxφ φ ≥

GZ then ( )0φ GZ must be greater than the specified, constant value.

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If0max

φ φ <GZ

thenmaxGZ must be greater than ( )0

0

max

φ φ

φ GZ

GZ

where:

0φ is the specified angle at which the required GZ value becomes a constant

maxGZ φ is the heel angle at which the maximum GZ of value occurs

( )0φ GZ is the GZ value at 0φ and maxGZ is the maximum value of GZ.

Variation of required GZ with angle of maximum GZ

The angle at which the GZ was measured is listed in the results.

Value of RM at Specified Angle or Maximum RM Below Specified Angle

As above (Value of GZ at specified angle or maximum GZ below specified angle) except therighting moment rather than the righting lever is specified, measured and compared.

The righting moment RM is given by:gGZ RM ρ ∇=

where:∇ is the vessel volume of displacement ρ is the density of the liquid the vessel is floating in

g is acceleration due to gravity = 9.80665m/s 2

GZ is the righting lever.

Ratio of GZ Values at Phi1 and Phi2

Calculates the ratio of the GZ values at two specified heel angles. The criterion is passed if theratio is less then the required value.

( )( )2

1Ratioφ φ

GZ GZ =

Option Description UnitsRatio of GZ values at phi1 and phi2

Phi1, first heel angle,

the lesser of

First heel angle, the lesser of the

following:specified heel angle User specified heel angle degangle of first GZ peak See Nomenclature deg

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Option Description Unitsangle of maximum GZ See Nomenclature degfirst downfloodingangle


Phi2, second heel angle,the lesser of

Second heel angle, the lesser of thefollowing:

specified heel angle User specified heel angle degangle of first GZ peak See Nomenclature degangle of maximum GZ See Nomenclature degfirst downfloodingangle



Permissible value %

Ratio of GZ values at phi1 and phi2

Angle of Maximum GZ

Finds the angle at which the value of GZ is a maximum positive value, heel angle can be limited by first peak in GZ curve and/or first downflooding angle. The criterion is passed if the angle isgreater then the required value.

Option Description UnitsAngle of maximum GZ

limited by first GZ peak angle

The angle of maximum GZ shall not begreater than the angle at which the first GZ

peak occurs

deg

limited by firstdownflooding angle

The angle of maximum GZ shall not begreater than the angle at which the firstdownflooding occurs

deg



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Angle of Equilibrium

Finds the angle of equilibrium from the intersection of the GZ curve with the GZ=0 axis. Thecriterion is passed if the equilibrium angle is less then the required value.

Option Description UnitsAngle of equilibrium



Ratio of equilibrium heel angle to the lesser of

The equilibrium angle and the lesser of the selected angles are compared. If the ratio is less thanthe required value, then the criterion is passed. Using a ratio gives more flexibility, e.g.: it is

possible to check that the equilibrium angle does not exceed half (or any other fraction) thedownflooding angle.

The user may choose the type of Key point to define the downflooding angle (downflooding point, potential downflooding point, embarkation point, immersion point).

If the equilibrium angle is negative, the user is advised that the vessel should be heeled in theopposite direction and the criterion is failed.

Option Description UnitsRatio of equilibrium angle to the lesser of:

spec. heel angle Specified heel angle degangle of margin lineimmersion

Angle of first immersion of the margin line deg

angle of deck edgeimmersion

Angle of first immersion of the deck edge deg

first flooding angle ofthe

Smallest immersion angle of the specifiedtype of Key Point

deg

angle of first GZ peak Angle of first local peak in GZ curve degangle of max. GZ Angle at which maximum GZ occurs degangle of vanishingstability

Angle of vanishing stability deg


Permissible value %

Equilibrium heel angle satisfies either

This criterion is nothing more than two “Ratio of equilibrium heel angle to the lesser of”criteria. The actual criterion is passed if either of the individual criteria is passed. This type ofcriterion is used to formulate criteria such as:

The maximum allowable angle of equilibrium is 15 degrees in the damagecondition, but this can be allowed to increase to 17 degrees if the deck edge is notimmersed.

Angle of Downflooding

Finds the angle of first downflooding. The criterion is passed if the downflooding angle isgreater then the required value.


Angle of downfloodingShall be greater than /Shall not be less than


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Angle of Margin Line Immersion

Finds the first/minimum angle at which the margin line immerses. The criterion is passed if thesmallest angle at which the margin line immerses is greater then the required value.

Option Description UnitsAngle of margin line immersionShall be greater than /Shall not be less than


Angle of Deck Edge Immersion

Finds the first/minimum angle at which the deck edge immerses. The criterion is passed if thesmallest angle at which the deck edge immerses is greater then the required value.


Angle of deck edge immersionShall be greater than /Shall not be less than


Angle of Vanishing Stability

Finds the angle of vanishing stability from the intersection of the GZ curve with the GZ=0 axis.The criterion is passed if the angle of vanishing stability is greater then the required value.

Option Description UnitsAngle of vanishing stability



Range of Positive Stability

The angular range for which the GZ curve is positive is computed. The criterion is passed if thecomputed range is greater then the required value.

Option Description UnitsRange of positive stability

from the greater of Lower limitspecified heel angle User specified heel angle degangle of equilibrium See Nomenclature degto the lesser of Upper limit of the rangefirst downfloodingangle


angle of vanishingstability




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GZ Area between Limits type 1 - standard

The area below the GZ curve and above the GZ=0 axis is integrated between the selected limitsand compared with a minimum required value. The criterion is passed if the area under thegraph is greater than the required value.


GZ area between limits type 1 - standardfrom the greater of Lower limit for integration, from greatest

angle ofspecified heel angle User specified heel angle degangle of equilibrium See Nomenclature degto the lesser of Upper limit of integration, from lesser

angle ofspecified heel angle User specified heel angle degspec. angle aboveequilibrium

User specified heel angle above theequilibrium heel angle

deg






Permissible value length.angle

GZ area between limits type 1 - standard

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Option Description Unitsto the lesser of Upper limit of integration, from smallest

angle ofspecified heel angle User specified heel angle degspec. angle aboveequilibrium

User specified heel angle above theequilibrium heel angle

deg





lower heel angle Minimum angle that requires a GZ areagreater than... Until this angle the requiredGZ area is constant

deg

required GZ area atlower heel angle

Value of GZ area that is required until thelower heel angle

length.angle

higher heel angle Angle from which the required GZ arearemains constant onwards

deg

required GZ area athigher heel angle

Value of GZ area that is required from thehigher heel angle onwards

length.angle



GZ area between limits type 2 - HSC monohull type

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Option Description Unitshigher heel angle Heel angle at which required GZ area is

specifieddeg

required GZ area athigher heel angle

Value of GZ area that is required until thehigher heel angle

length.angle

Shall be greater than /

Shall not be less than


GZ area between limits type 3 - HSC multihull type

Ratio of GZ area between limits

This criterion calculates the ratio of the two areas between the GZ curve and the GZ=0 axis.

Ratio =( )2Areaabs

1Area =

( )

( ) ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∫

∫

φ φ

φ φ

φ

φ

φ

φ

d GZ

d GZ

4

3

2

1

abs

, where “abs” means the absolute value of.

Option Description UnitsRatio of GZ area between limits

Area 1 from the greater of Area 1 lower integration limit, 1φ

specified heel angle User specified heel angle degangle of equilibrium See Nomenclature degArea 1 to the lesser of Area 1 upper integration limit, 2φ deg

specified heel angle User specified heel angle degangle of first GZ peak See Nomenclature degangle of maximum GZ See Nomenclature degfirst downflooding angle See Nomenclature deg

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Option Description Unitsangle of vanishing stability See Nomenclature degArea 2 from the lesser of Area 2 lower integration limit, 3φ

specified heel angle User specified heel angle degangle of first GZ peak See Nomenclature deg

angle of maximum GZ See Nomenclature degfirst downflooding angle See Nomenclature degangle of vanishing stability See Nomenclature degArea 2 to Area 1 upper integration limit, 4φ

specified heel angle User specified heel angle degShall be greater than /Shall not be less than

Permissible value %

This criterion is designed to be calculated on the positive side of the GZ curve only; GZ areas below the GZ=0 axis on the negative heel angle side of the GZ curve are not considered

positive. Typically, Area 1 would be from equilibrium to vanishing stability and Area 2 would be from vanishing stability to 180 deg, see graph below.

In the example below, the lower and upper integration limits for Area 1 are equilibrium andvanishing stability, respectively and the limits for Area 2 are vanishing stability and 180 deg.

Ratio of GZ area between limits – Example 1

In the following example the upper limit for Area 1 has been set to the downflooding angle. Thelimits for Area 2 remain unchanged.

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In the final example, the lower integration range for Area 2 has been reduced to thedownflooding angle. Note that Area 2 is now A1 – A2.


Ratio of positive to negative GZ area between limits

This criterion calculates the ratio of GZ area above the GZ=0 axis to that below the axis in thegiven heel angle range.


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Option Description UnitsRatio of positive to negative GZ area

between limitsin the heel angle range from User specified lower limit heel angle degto User specified upper limit heel angle degShall be greater than /Shall not be less than

Permissible value %

Ratio =( )2Areaabs

1Area ,

where “abs” means the absolute value of. And the areas are defined as follows:

If both heel angle limits are ≥ zero: Area 1 is the total area between the GZ curve and GZ=0axis, where the value of GZ > 0; Area 2 is the total area between the GZ curve and GZ=0 axis,where the value of GZ < 0. Area 1 is positive, Area 2 is negative.

Ratio of positive to negative GZ area between limits.

Positive heel: lower limit = 0deg, upper limit = 180deg.

If both heel angle limits are < zero: Area 1 is the total area between the GZ curve and GZ=0axis, where the value of GZ < 0; Area 2 is the total area between the GZ curve and GZ=0 axis,where the value of GZ > 0. Area 1 is positive, Area 2 is negative.

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Ratio of positive to negative GZ area between limits.Negative heel: lower limit = -180deg, upper limit = 0deg.

If the lower heel angle limit < zero, and the upper heel angle limit > zero (the upper limit isassumed to be greater than the lower limit): Area 1 is the total area between the GZ curve andGZ=0 axis, where the value of GZ > 0 for heel angles ≥ 0 plus the area between the GZ curveand GZ=0 axis, where the value of GZ < 0 for heel angles < 0; Area 2 is the total area betweenthe GZ curve and GZ=0 axis, where the value of GZ < 0 for heel angles ≥ 0 plus the area

between the GZ curve and GZ=0 axis, where the value of GZ > 0 for heel angles < 0. Area 1 is positive, Area 2 is negative.

Ratio of positive to negative GZ area between limits.Positive and negative heel: lower limit = -180deg, upper limit = 180deg.

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Heeling arm cr iteria (xRef)The cross-reference heeling arm criteria are set up to allow you to define heeling arms orheeling moments in a central location and then cross-reference or link them into the criteria. Thecriteria themselves work much the same as the Heeling arm criteria (page 203), except for thefact that you don’t have to specify the heeling arm for each criterion separately, but can simplyselect which heeling arm you wish to apply.


After you have defined your heeling arms, these can be cross-referenced into new heeling armcriteria:

The heeling arms are cross-referenced simply by selecting the desired heeling arm from the pull-down list:

For information on defining heeling arms or moments, see Parent Heeling Arms on page 177 .

Heeling arm cri teriaThese criteria are derived from the GZ curve which is calculated from the Large Angle Stabilityanalysis in Hydromax. If the user has specified any heeling arm, these are also drawn in the GZcurve. Most criteria are made up of a generic form of the criterion including a general heelingarm, and in some cases, the same criteria are given with a specific heeling arm (e.g. due to wind

pressure, passenger crowding or vessel turning).



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NoteThe heeling arm is specified for each criterion individually. If you would like to beable to define general heeling arms or moments and apply those to several criteria,

please see:- Parent Heeling Arms on page 177,- Heeling arm criteria (xRef) on page 203.

The heeling arm criteria available in the Hydromax Criteria dialog are listed below. Alsoavailable are:

• Multiple heeling arm criteria

• Heeling arm, combined criteria

Value of GM T at equilibrium - general heeling arm

Calculates the transverse metacentric height (GM T) at the intersection of the GZ and heel armcurves. The criterion is passed if the GM T value is greater then the required value. GM T iscomputed from the waterplane inertia and the displaced volume at the equilibrium heel angle.

Uses the general heel arm as described in § General heeling arm .

Ratio of GM T and heeling arm

Calculates the following ratio and the criterion is passed if the ratio exceeds the specified value.)()sin( φ φ HAGM >

Where the heel angle, φ , is the lesser of: a user-specified heel angle; angle of margin lineimmersion; angle of deck edge immersion; or first flooding angle of the specified key pointtype. In addition, this angle may also be multiplied by a user-specified factor. The specifiedcross-referenced heel arm is then evaluated at this heel angle to give: )(φ HA . Finally, Thetransverse GM is taken at a user-specified heel angle or angle of equilibrium (without heel arm).

Ratio of GMt and heel arm criterion

Uses the general heel arm as described in § General heeling arm .

Value of GZ at equilibrium - general heeling arm

Calculates the value of the GZ curve at the equilibrium intersection of the GZ and heel armcurves. The criterion is passed if the GZ value is greater then the required value.

Uses the general heel arm as described in § General heeling arm

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Page 205

Value of GZ at equilibrium - general heeling arm

Value of maximum GZ above heeling arm - general heeling arm

Finds the maximum value of (GZ - heel arm) at or above a specified heel angle. The firstdownflooding angle may be selected as an upper limit. The criterion is passed if the value of(GZ - heel arm) is greater then the required value.

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Page 206

Value of maximum GZ above heeling arm - general heeling arm

The upper limit may be specified as a certain percentage of the selected limits. This is applied toall selected upper angle limits, including “specified heel angle”. However this option wouldnormally be used to specify an upper limiting angle of “half the angle of margin lineimmersion”.

Maximum ratio of GZ to heeling arm - general heeling arm

This criterion calculates the maximum ratio of GZ : Heeling arm (for the same heel angle)within the range of heel angles specified. The value of GZ at this heel angle must be greaterthan zero. If the heeling arm is zero or negative in the range, then the point with maximum

positive GZ (where the heeling arm ≤ 0.0) will be selected.


Examples:

Upper limit is 50% of angle of margin line immersion (43 ° / 2 = 21.5 °). In the range 0 ° to 21.5 °, the maximum ratio ofGZ:heel arm occurs at 21.5 °. At this heel angle the value of GZ is 0.553m and the heel arm 0.930m giving a ratio of

59%.

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Appendix C

Page 207

In this case a constant heeling arm is used, thus the maximum ratio occurs at the angle of maximum GZ (62.4 °). At thisheel angle the value of GZ is 1.122m and the heel arm 0.5m giving a ratio of 224%.

Finally, the downflooding angle is 94.3 °, at this heel angle the heel arm is zero (thus the ratio infinite). Hence thecriterion is passed. The angle and value of GZ is given for the location where it is a maximum (in the region where theheel arm is zero; the exact value will depend slightly on the heel angles tested in the Large Angle Stability analysis.)

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Appendix C

Page 208

The same is true if an unusual user-defined heeling arm is used. In this case the heeling arm is zero between 50 ° and70 °. Hence the maximum ratio reported is infinity and occurs at the angle where GZ is maximum in this heel angle

range.

Ratio of GZ values at phi1 and phi2 - general heeling arm

Used to check the ratio of GZ values at two points on the GZ curve. The heel arm is used todefine the equilibrium angle and the heel angle where (GZ - heel arm) is maximum. Thecriterion is passed if the ratio is less than the required value.

Ratio =

( )( )2

1

φ φ

GZ GZ

Angle of maximum GZ above heeling arm - general heeling arm

Calculates the heel angle at which the difference between the GZ curve and the heeling arm isgreatest (GZ - Heel Arm is maximum, positive). The criterion is passed if the angle is greaterthen the required value.

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Appendix C

Page 209

Angle of maximum GZ above heeling arm - general heeling arm

Angle of equilibrium - general heeling arm

Calculates the angle of equilibrium with a General heeling arm applied. The equilibrium angleis the smallest positive angle where the GZ and heeling arm curves intersect and the GZ curvehas positive slope. The criterion is passed if the equilibrium angle is less then the required value.

Angle of equilibrium - general heeling arm

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Appendix C

Page 210

Angle of equilibrium ratio - general heeling arm

Calculates the ratio of the angle of equilibrium (with a General heeling arm applied) to another,selectable angle. The angle of equilibrium is computed as described in § Angle of equilibrium -general heeling arm .

Ratio =specified

mequilibriu

φ

φ

The other angle used to compute the ratio may be one of the following:Required angle for ratio calculation Auto complete textMarginline immersion angle MarginlineImmersionAngleDeck edge immersion angle DeckEdgeImmersionAngleAngle of first GZ peak DownfloodingAngleAngle of maximum GZ MaximumGZAngleFirst downflooding angle FirstGZPeakAngleAngle of vanishing stability with heel arm VanishingStabilityWithHeelArmAngle

Angle of equilibrium - passenger crowding heeling arm

Calculates the angle of equilibrium with the heeling arm due to passenger crowding applied.The heeling arm is calculated from the number, weight and location of the passengers, see§Passenger crowding .

Angle of equilibrium - high-speed turn heeling arm

Calculates the angle of equilibrium with the heeling arm due to high speed turning applied. Theheeling arm is calculated from the turn radius, vessel speed and height of the vessel’s centre ofgravity, see § Turning .

Angle of vanishing stability - general heeling arm

Calculates the location of the first intersection of the GZ curve and heel arm curve where theslope of the GZ curve is negative. The criterion is passed if the angle is greater then the requiredvalue. This criterion should not be confused with the range of positive stability.

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Appendix C

Page 211

Angle of vanishing stability - general heeling arm

Range of positive stability - general heeling arm

Computes the range of positive stability with the heeling arm.[Range of stability] = [Angle of vanishing stability] – [Angle of equilibrium]The criterion is passed if the value of range of stability is greater then the required value.

Range of positive stability - general heeling arm

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Appendix C

Page 212

GZ derived heeling arm - general heeling arm

This criterion is used to calculate the amplitude of a heeling arm derived from the value of GZat a certain heel angle. The GZ value used to define the heeling arm is the GZ at one of thefollowing heel angles:

• specified angle of heel

• angle of first peak in GZ curve

• angle at which maximum GZ occurs

• angle of first downflooding

• immersion angle of margin li ne or deck edgeThe heeling arm is then calculated as described by the equation below, and is then comparedwith a minimum required value.

φ α φ

n

GZ A

cos=

where: A Amplitude of heeling arm

n Shape of heeling arm ( n = 0 for constant heeling arm)φ Specified heel angle

φ GZ Value of GZ at specified heel angle

α Required ratio = φ φ HAGZ /

GZ area derived heeling arm - general heeling arm

This criterion is used to calculate the amplitude of a heeling arm derived from the area under theGZ curve between specified limits. The area under both the GZ and heeling arm curves isintegrated between the same specified limits, see below.

Lower integration limit, 1φ :• specified angle of heel

• angle of equilibri um

Upper integration limit, 2φ :

• spec. heel angle

• spec. angle above equilibri um

• angle of fi rst GZ peak

• angle of max. GZ

• first downflooding angle

• angle of vanishing stabili ty

It is also possible to specify a minimum heel angle for the upper integration limit. Any negativeareas (due to negative GZ) up to this minimum upper integration heel angle will be deductedfrom the total area under the GZ curve.

The amplitude of the heeling, which satisfies the equation below arm is then found andcompared with a minimum required value.

α

φ φ φ

φ

φ φ

φ

∫∫ =

2

12

1

dd cos

GZ A n

A Amplitude of heeling armn Shape of heeling arm ( n = 0 for constant heeling arm)φ heel angleGZ GZ curve

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α Required ratio

GZ area derived heeling arm (type 2) - general heeling arm

This criterion is used to simulate the effects of wind heeling whilst the vessel is rolling inwaves. Because of the many different ways in which this criterion is used it has several optionsfor defining the way in which the areas are calculated. With the wind pressure acting on it, thevessel is assumed to roll to windward under the action of waves and then roll to leeward. Therollback angle is taken from the equilibrium angle with the wind heeling arm.

A heeling arm of prescribed shape is found such that the specified area ratio is met. Theamplitude of the heeling arm is then compared with a required minimum value.

The roll back may be specified as either:• a fixed angular roll back from the angle of equilibrium with the wind heel arm;

• roll b ack to the vessel equilibrium angle ignori ng the wind heeling arms (i.e.: where the GZcurve crosses the GZ=0 axis with positive slope); or

• roll back to a specified heel angle.

NoteThe Large Angle Stability analysis heel angle range should include a sufficientnegative range to allow for the rollback angle. For more information see: § Heel .

Area 1 = ( )∫ −2

1

)(armheel)(φ

φ φ φ φ d GZ

Area 2 = ( )∫ −2

1

)()(armheelφ

φ φ φ φ d GZ

Ratio = 2Area1Area

GZ area derived heeling arm (type 2) - general heeling arm

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Appendix C

Page 214

Angle of equilibrium - derived wind heeling arm

The derived wind heeling criterion is used to check that the steady heel angle due to wind pressure exceeds a certain value. The steady heel arm is derived from a gust of specified ratio.The wind gust will cause the vessel to heel over to the lesser of a specified heel angle, angle ofthe first GZ peak, angle of maximum GZ or the first downflooding angle.The vessel is assumed to be safe from gusts up to the specified ratio, if the angle of steady heelis greater than the angle. This means that the lesser of: a specified heel angle, first peak in GZcurve, angle of maximum GZ or the first downflooding angle, should be large enough towithstand a gust from a steady wind heeling angle larger than ….

Angle of equilibrium - derived wind heeling arm

Ratio of equilibrium angles - derived heeling arm

This criterion is used to compare the equilibrium angles with two different heeling arms. Thefirst equilibrium angle, φ1, is the angle of equilibrium with a derived heeling arm. The secondequilibrium angle, φ2, is the angle of equilibrium with a specified heeling arm.The derived heeling arm is chosen such that the areas, A 1 and A 2, are in the specified ratio.There are several options which can be used to define the upper and lower ranges for the areaintegrations. The specified heeling arm is specified by an amplitude and cosine power; the samecosine power is used for both the specified and the derived heeling arms.

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Appendix C

Page 215

Ratio of equilibrium angles - derived heeling arm

Area 1 = ( )∫ −2

1

)(armheel)(φ

φ φ φ φ d GZ

Area 2 = ( )∫ −2

1

)()(armheelφ

φ φ φ φ d GZ

Ratio of areas = 2Area1Area

φ1 = Angle of equilibrium with heeling arm derived from required area ratio (purple heelingarm)

φ2 = Angle of equilibrium with specified heeling arm (orange heeling arm)

The criterion is passed if the ratio φ2 : φ1 is less than the required value. Thus if it is requiredthat φ2 be less than φ1, then the ratio φ2 : φ1 must be less than unity.

Option Description UnitsA Magnitude of specified heeling arm lengthn Cosine power to describe shape of both

specified and derived heelning armsrequired area ratioArea1 / Area2

The required area ratio used to find thederived heeling arm magnitude

options Specify lower integration limit for Area1 deg

options Specify upper integration limit for Area1 degoptions Specify lower integration limit for Area2; the

upper integration limit is always the angle ofdeg

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Appendix C

Page 216

equilibrium with derived heel armrequired value Specifies the maximum allowable ratio of

equilibrium heel angle with the specified heelarm to the equilibrium heel angle with thederived heel arm (phi2 / phi1). This value isnormally less than or equal to 100%,indicating that the equilibrium heel angle withthe specified heel arm must be less than theequilibrium heel angle with the derived heelarm


GZ area between limits - general heeling arm

Computes the area below the GZ curve and above the heel arm curve between the specified heelangles. The criterion is passed if the area is greater than the required value.

Area =( )∫ −2

1

)(armheel)(φ

φ φ φ φ d GZ

GZ area between limits - general heeling arm

Ratio of areas type 1 - general heeling arm

The ratio of the area between the GZ curve and heel arm and the area under the GZ curve iscomputed. This criterion is based on the area ratio required by various Navies’ turning and

passenger crowding criteria. Type 1 stands for which areas are being integrated to calculate theratio (see graph). The criterion is passed if the ratio is greater than the required value.

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Appendix C

Page 217

Area 1 =( )∫ −2

1

)(armheel)(φ

φ φ φ φ d GZ

;

Area 2 =∫ 4

3

)(φ

φ φ φ d GZ

;

Ratio = 2Area1Area


Ratio of areas type 1 - general cos+sin heeling arm

This is a very similar criterion to § Ratio of areas type 1 - general heeling arm; the onlydifference being the shape of the heel arm. In this criterion the heel arm has both a sine and acosine component. This is used to simulate the effects of lifting weights and is used by several

Navies.The modified form of the heeling arm is given below, for further information also see § Generalcos+sin heeling arm

)(sin)(cos)( φ φ φ mn B Ak H +=

Area 1 =( )∫ −2

1

)(armheel)(φ

φ φ φ φ d GZ

;

Area 2 = ∫4

3)(

φ

φ φ φ d GZ ;

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Appendix C

Page 219

Ratio of areas type 2 - general wind heeling arm


The ratio of the area under the GZ curve to the area under the heel arm curve is computed. Thiscriterion is based on the area ratio required by BS6349-6:1989. The criterion is passed if theratio is greater than the required value. Areas under the GZ=0 axis are counted as negative.

Area GZ = ∫ 2

1

)(φ

φ φ φ d GZ ;

Area HA = ∫ 2

1

)(armheelφ

φ φ φ d ;

Ratio =HAAreaGZArea

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Appendix C

Page 220


Multiple heeling arm criteriaThese criteria are used to check the effects of combinations of three heeling arms:

• Passenger crowd ing

• Turning

• Wind

The combined heeling arms are computed by adding the values of the individual heeling arms ateach heel angle.

Ratio of GZ values at phi1 and phi2 - multiple heeling arms

Checks the ratio of GZ values as per § Maximum ratio of GZ to heeling arm - general heelingarmThis criterion calculates the maximum ratio of GZ : Heeling arm (for the same heel angle)within the range of heel angles specified. The value of GZ at this heel angle must be greaterthan zero. If the heeling arm is zero or negative in the range, then the point with maximum

positive GZ (where the heeling arm ≤ 0.0) will be selected.


Examples:

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Appendix C

Page 221

Upper limit is 50% of angle of margin line immersion (43 ° / 2 = 21.5 °). In the range 0 ° to 21.5 °, the maximum ratio ofGZ:heel arm occurs at 21.5 °. At this heel angle the value of GZ is 0.553m and the heel arm 0.930m giving a ratio of

59%.

In this case a constant heeling arm is used, thus the maximum ratio occurs at the angle of maximum GZ (62.4 °). At thisheel angle the value of GZ is 1.122m and the heel arm 0.5m giving a ratio of 224%.

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Appendix C

Page 222

Finally, the downflooding angle is 94.3 °, at this heel angle the heel arm is zero (thus the ratio infinite). Hence thecriterion is passed. The angle and value of GZ is given for the location where it is a maximum (in the region where theheel arm is zero; the exact value will depend slightly on the heel angles tested in the Large Angle Stability analysis.)

The same is true if an unusual user-defined heeling arm is used. In this case the heeling arm is zero between 50 ° and70 °. Hence the maximum ratio reported is infinity and occurs at the angle where GZ is maximum in this heel angle

range.

Ratio of GZ values at phi1 and phi2 - general heeling arm and uses the following s pecificheeling arms:

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Appendix C

Page 223


• Turning

• Wind

Ratio of GZ values at phi1 and phi2 - multiple heeling arms

Angle of equilibrium - multiple heeling armsChecks the equilibrium heel angle as per § Angle of equilibrium - general heeling arm and usesthe following specific heeling arms:


• Turning

• Wind

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Appendix C

Page 224

Angle of equilibrium - multiple heeling arms

GZ area between limits - multiple heeling arms

Checks the area under the heel angle as per § GZ area between limits - general heeling arm anduses the following specific heeling arms:


• Turning • Wind

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Appendix C

Page 225

GZ area between limits - multiple heeling arms

Ratio of areas type 1 - multiple heeling arms

Checks the area under the heel angle as per § Ratio of areas type 1 - general heeling arm anduses the following specific heeling arms:


• Turning • Wind

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Appendix C

Page 226

Ratio of areas type 1 - multiple heeling arms

Heeling arm, combined criteriaSeveral criteria require the evaluation of several individual criteria components. Although it is

possible to evaluate these criteria by evaluation of their individual components, for simplicitythe common combinations have been combined into single criteria.

Note:At least one of the individual criteria has to be selected.

Combined criteria (ratio of areas type 1) - general heeling arm

This is a combined criterion where three individual criteria must be met. These are:1. Angle of steady heel must be less than a specified value. The Angle of steady heel isobtained as per § Angle of equilibrium - general heeling arm .2. The area ratio must be greater than a specified value. The area ratio is evaluated as per §Ratio of areas type 1 - general heeling arm 3. The ratio of the value of GZ at equilibrium to the value of maximum GZ must be less than aspecified value.

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Appendix C

Page 227

Combined criteria (ratio of areas type 1) - general heeling arm

Combined criteria (ratio of areas type 1) - passenger crowding

This criterion is essentially the same as its generic form: Combined criteria (ratio of areas type1) - general heeling arm , however the heel arm is the specific passenger crowding form.

Combined criteria (ratio of areas type 1) - high-speed turn

This criterion is essentially the same as its generic form: Combined criteria (ratio of areas type1) - general heeling arm , however the heel arm is the specific high-speed turning form.

Combined criteria (ratio of areas type 1) - general cos+sin heeling armThe lifting criterion is the same as the Combined criteria (ratio of areas type 1) - general heelingarm except that the heel arm has both a cos and sin component.

Combined criteria (ratio of areas type 1) – cos+sin heeling arm

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Appendix C

Page 228

Combined criteria (ratio of areas type 1) - lifting weight

This criterion is essentially the same as its generic form: Combined criteria (ratio of areas type1) - general cos+sin heeling arm , however the heel arm is the specific lifting of a heavy weightform.

Combined criteria (ratio of areas type 1) - towing

This criterion is essentially the same as its generic form: Combined criteria (ratio of areas type1) - general cos+sin heeling arm , however the heel arm is the specific towing form.

Combined criteria (ratio of areas type 2) - general wind heeling arm

This is a widely applicable wind heeling criterion in its most generic format. The heeling arm isspecified simply by a magnitude and cosine power. Optionally, a gust wind can be applied.1. Angle of steady heel must be less than a specified value. The angle of steady heel is obtainedas per Angle of equilibrium - general heeling arm .2. The area ratio must be greater than a specified value. The area ratio is evaluated as per Ratioof areas type 2 - general wind heeling arm .3. The ratio of the value of GZ at equilibrium to the value of maximum GZ must be less than aspecified value.


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Appendix C

Page 229

Area definition

If required, a reduction of the GZ curve may be applied. If this is done, all calculations are doneusing a reduced GZ’ curve which is computed at each heel angle as follows:

)(cos)()(' φ φ φ m BGZ GZ −=

This criterion may be used to evaluate the following specific criteria (as well as many others ofsimilar format):

• US Navy DDS079-1: §079-1-c(9) 1, §079-1-c(9) 4,

• Royal Navy NES 109: §1.2.2, §1.3.5, §1.4.2 Initial impu lse and Wind heeling crit eria

• RAN A015866: §4.4.4.2, §4.8, §4.9.5

• IMO A.749(18) Code on i ntact stabil ity: §3.2

• IMO MSC.36(63) High-speed craft code §2.3.3.1

• ISO/FDIS 12217-1:2002(E) Small Non-Sailin g Boats §6.3.2

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Appendix C

Page 230

Combined criteria (ratio of areas type 2) - wind heeling arm

This criterion is exactly the same as § Combined criteria (ratio of areas type 2) - general windheeling arm except that the magnitude of the heeling arm is automatically calculated from thewind pressure (or velocity), projected area and area lever information.

Area definition


Other combined criteriaOther criteria, which do not easily fall into the categories above, are found here.

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Appendix C

Page 231

Other criteria - STIX

The stability index criterion or STIX criterion as described in ISO/FDIS 12217-2:2002(E) isused to assess the stability of sailing craft. The required input parameters are described below.Please refer to ISO/FDIS 12217-2:2002(E) for exact definitions of parameters and how theyshould be calculated.

Option Description Unitsdelta Adjustment to STIX rating, either 0 or 5.5=δ if the vessel, when fully flooded

with water, has reserve buoyancy and positive righting lever at a heel angle of 90º. 0=δ in all other cases.

AS, sail area ISO 8666 Sail area as defined in ISO 8666. Note thatno additional windage areas are calculated

by Hydromax for this criterion.

length 2

height of centroid ofAS

Height of sail area centre of effort frommodel’s vertical datum (not necessarily the

waterline, this is not the same as the STIXvariable CEh which is measured from thewaterline, positive up).

length

LH, length Hull length as defined by ISO 8666. Thismay be either specified or calculated byHydromax. Hydromax calculates this

parameter as the overall length of thevessel (all hull surfaces) in the upright,zero trim condition.

length

BH, beam of hull Hull beam as defined by ISO 8666. Thismay be either specified or calculated by

Hydromax. Hydromax calculates this parameter as the overall beam of the vessel(all hull surfaces) in the upright, zero trimcondition.

length

LWL, length waterline Hull waterline length in the current loadcondition as defined by ISO 8666. Thismay be either specified or calculated byHydromax. Hydromax calculates this

parameter as the waterline length of thevessel (all hull surfaces) at zero heel and atthe loadcase displacement and centre ofgravity; if the analysis is carried out free-to-trim, the waterline of the trimmed vesselis used.

length

BWL, beam waterline Hull waterline beam in the current loadcondition as defined by ISO 8666. Thismay be either specified or calculated byHydromax. Hydromax calculates this

parameter as the waterline beam of thevessel (all hull surfaces) at zero heel and atthe loadcase displacement and centre ofgravity; if the analysis is carried out free-to-trim, the waterline of the trimmed vessel

is used.

length

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Option Description Unitsheight of immersed

profile area centroidHeight of centre of the lateral projectedimmersed area of the hull from model’svertical datum (not necessarily thewaterline, this is not the same as the STIXvariable LPh ); may be specified or

calculated by Hydromax. Hydromaxcalculates this parameter at zero heel and atthe loadcase displacement and centre ofgravity; if the analysis is carried out free-to-trim, the waterline of the trimmed vesselis used.

length


Hydromax uses the numerical STIX ratingvalue rather than the STIX design category.

Hydromax calculates the various factors and STIX rating according to ISO/FDIS 12217-2:2002(E). Note that a downflooding angle is required to calculate the STIX index. Hence, if no

downflooding points are defined, or defined downflooding points do not immerse within theselected heel angle range, the angle of downflooding is taken to be the largest heel angle tested.This affects the calculation of the Wind Moment and Downflooding factors.

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Appendix D Specific CriteriaIn this appendix:

• Heeling arms for specific criteria - Note on unit con version

• ISO 12217: Small cr aft – stabilit y and buoyancy assessment and categori sation .

Heeling arms for specific cri teria - Note on unitconversionThere are quite a few different ways in which different authorities define their heeling arms. Theapproach that has been taken in Hydromax is to reflect the physics of what is generating theheeling moment.

Be careful as some criteria specify heeling arms and some specify heeling moments or“moments” in mass.length. All Hydromax criteria use a heeling arm since this is what isultimately plotted on the GZ curve. To obtain the heeling arm from the heeling moment, it is

necessary to divide by vessel weight ( Δg ); and in the case of “moments” in mass.length, it isnecessary to divide by vessel mass.

Hydromax uses an internal conversion of knots to m/s based on the International Nautical milewhich is defined as exactly 1852m (International Hydrographic Conference, Monaco, 1929).Thus 1 knot = 1852/3600 = 0.5144444... m/s.(Note that the UK nautical mile is 6080ft = 1853.184m; giving a conversion multiplier for knotsto m/s of 0.51477333...)

In the following section, the conversions for some common criteria have been explained.

IMO Code on Intact Stability A.749(18) amended to MSC.75(69)

3.1.2.6 - Heeling due to turningHeeling moment defined by:

⎟ ⎠ ⎞

⎜⎝ ⎛ −Δ=

2196.0

20 d

KG LV

M tonne R [kNm]

Where:

R M = heeling moment in tonne.m

0V = service speed in m/s

L = length of ship at waterline in m

tonneΔ = displacement in tonned = mean draft mKG = height of centre of gravity above keel in m

Hence the heeling arm, g M H R R Δ= /1000 [m], is given by:

⎟ ⎠ ⎞

⎜⎝ ⎛ −=

Δ⎟ ⎠ ⎞

⎜⎝ ⎛ −Δ=

2196.0

100021000

196.02

02

0 d KG

LgV

gd

KG LV

H R [m]

Where:g = standard acceleration due to gravity = 9.80665 m/s 2

Δ = displacement in kg

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Page 234

The heeling arm in Hydromax is defined as:

h Rg

V a H R

2

= [m],

Where:

V = vessel speed in m/s R = radius of turn in mh = height of centre of gravity above centre of lateral resistance in ma = non-dimensional constant (theoretically unity)

Thus equating the required IMO heeling arm to the Hydromax heeling arm, we obtain:

⎟ ⎠ ⎞

⎜⎝ ⎛ −=

2196.0

20

2d

KG LgV

h Rg

V a

Equating similar terms:

⎟ ⎠ ⎞⎜

⎝ ⎛ −=

2d KGh

0V V = and assuming that the ratio of the turn radius to the vessel length is 5.1:1, we obtain:

%510= L R

and

9996.0%510196.0 =×=a

Note that it suffices that 196.0= R L

a and any ratio of turn radius to vessel length and constanta that satisfies this relationship may be chosen, the choice of a ratio of 5.1:1 merely gives aconstant approaching the theoretically correct value of unity.

3.2 - Severe wind and rolling criterion (weather criterion)Heeling arm defined by:

tonnew g

PAZ l Δ

=81.9

1 1000 [m]

Where:

1wl = heeling arm in mP = wind pressure in Pa A = projected lateral windage in m 2

Z = vertical separation of centroids of A and underwater lateral area in m

tonneΔ = displacement in tonne

81.9g = IMO assumed value of gravitational acceleration - 9.81m/s 2


Δ−

= g H hPAa H w )( [m]

Where:

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Appendix C

Page 235

g = standard acceleration due to gravity = 9.80665 m/s 2

Δ = displacement in kgh = height of centroid of A in m

H = height of centroid of underwater lateral area in m

a = non-dimensional constant (theoretically unity)


tonnegPAZ

g H hPA

a Δ=

Δ−

81.91000)(

Equating similar terms:

Z H h =− and

99966.081.9

80665.9

81.9

===g

ga

IMO HSC Code MSC.36(63)

Annex 6 1.1.4 - Heeling moment due to wind pressureHeeling moment defined by:

PAZ M v 001.0= [kNm]Where:

v M = heeling moment in kNmP = wind pressure in Pa

A = projected lateral windage in m2

Z = vertical separation of centroids of A and underwater lateral area in m

Hence the heeling arm, g M H vv Δ= /1000 [m], is given by:

gPAZ

gPAZ H R Δ

=Δ

= 1000001.0

[m]Where:


Δ = displacement in kg


Δ−=

g H hPA

a H w)(

[m]Where:






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Appendix C

Page 236

Δ=

Δ−

gPAZ

g H hPA

a)(

Equating similar terms: Z H h =−

and0.1=a

Annex 7 1.3 - Heeling due to windHeeling arm defined by:

tonne

PAZ HL Δ

=98001

[m]

Where:

1 HL = heeling arm in m

P = wind pressure in Pa A = projected lateral windage in m 2

Z = vertical separation of centroid of A and half the lightest service draft inm

tonneΔ = displacement in tonne


Δ−=

g H hPA

a H w)(

[m]



H = height of half the lightest service draft in m



Equating similar terms: Z H h =−

and

00068.18.9

80665.99800

=Δ

Δ=ΔΔ=

tonne

ga

Where the effect of wind plus gust is required, the factor a should be multiplied by the gustfactor – typically 1.5. Hence, in the case of wind plus gust, a becomes 1.50102

USL code (Australia)

USL C.1.1.3 - Wind heeling momentUSL wind heeling “moment” is specified as:

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)(000102.0 H hPA M −= [tonne.m]

Where:h = height of centroid of A in m


P = wind pressure in Pa

A = projected lateral windage in m 2

Thus the heeling arm is given by:

Δ−= 1000

)(000102.0 H hPA H [m]


Δ−=

g H hPA

a H )(

[m]


Δ = displacement in kga = non-dimensional constant (theoretically unity)

Thus equating:

Δ−=

Δ−= 1000

)(000102.0)(

H hPAg

H hPAa H

simplifying and rearranging:

0002783.180665.9102.00.1000000102.0 =×=××= ga

USL C.1.1.4 - Heeling moment due to turningUSL wind heeling “moment” is specified as:

Lhv

M tonnesktsΔ=

2

0053.0 [tonne.m]

Where:

ktsv = vessel speed in knots

tonneΔ = displacement in tonneh = height of centre of gravity above centre of lateral resistance in m L = waterline length of vessel in m

Thus the heeling arm is given by:

0.10001

0053.02

×Δ

Δ= L

hv H tonneskts

[m]

Where:Δ = displacement in kg


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h Rg

V a H

2

= [m],

Where:V = vessel speed in m/s R = radius of turn in mh = height of centre of gravity above centre of lateral resistance in ma = non-dimensional constant (theoretically unity)

Thus equating the required USL heeling arm to the Hydromax heeling arm, we obtain:

0.10001

0053.022

×Δ

Δ= L

hvh

Rg

V a tonneskts

simplifying and rearranging:

0.10001

5144.013.53.5 22

2

L Rg

V v

L Rga tonneskts =ΔΔ=

finally, with g = 9.80665 [ms -2]:

L R

a 196424.0=

Assuming that the ratio of the turn radius to the vessel length,%509=

L R

gives a value for a :

999798.0%509196424.0 =×=a

Note that it suffices that 196424.0=

L

R

a , and any ratio of turn radius to vessel length andconstant a that satisfies this relationship may be chosen, the choice of a ratio of 509% merelygives a constant approaching the theoretically correct value of unity.

ISO 12217-1:2002(E)

This section explains how the ISO 12217-1 code calculates the heeling arm and how you canreplicate this calculation with a Hydromax criterion.

“6.3.2 Rolling in beam waves and windThe curve of righting moments of the boat shall be established up to the downflooding angle orthe angle of vanishing stability or 50°, whichever is the least, using annex D. The heeling

moment due to wind, MW, expressed in newton metres, is assumed to be constant at all anglesof heel and shall be calculated as follows:

M W = 0.3 A LV * (A LV / LWL + T M )* v W 2

Where LWL is the waterline length;T M is the draught at the mid-point of the waterline length, expressed in metres;vW = 28 m/s for design category A, and 21 m/s for design category B;

A LV is the windage area as defined in 3.3.7, but shall not be taken as less than 0.55*L H * B H .”

Basically they are using moment = force * lever, wherethe force is calculated as 0.3 * A LV * vW

2, andthe lever is ( A LV / LWL + T M )

This lever is a bit confusing so let’s concentrate on that.

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Hydromax’ wind heeling arm calculation uses H for the vertical height of the hydrodynamiccentre (underwater area) and h as the vertical height of the aerodynamic centre (windage area) –all measured consistently from the zero point, positive up.

Thus the lever is (h-H) in Hydromax should be the same as the ( A LV / LWL + T M ) lever from ISO.You can calculate ( A LV / LWL + T M ) manually and then make sure the (h-H) value in Hydromax isthe same by specifying:

Velocity based heeling arm;H = 0.0;h = ( A LV / LWL + T M );a = 0.3 kg/m 3

Note: the centre of the windage area -h- applies to the additional windage area or the totalwindage area depending on which option you have selected. Make sure you check your totalwindage lever in the intermediate results in the criteria results tab of the Results window.

For example, supposing we have a vessel with the following characteristics: Displacement 105.7 tonne = 1037 kN L

H 24 m

B H 5 m LWL 21.1 mT M 1.9 mvW 28 m/s for design category A

A LV 72 m 2 ( this is greater than 0.55 L H B H = 66 m 2)Thus according to the ISO 12217 formula, the heeling moment is given as:

M W = 0.3 * 72 * (72 / 21.1 + 1.9) * 28 2 = 89961 NmThus the heeling arm = M W / Displacement = 89961 / 1037000 = 0.0868 m

The input for Hydromax requires:Total area A = 72 m 2;

area centroid height: h = A LV / LWL + T M = 72 / 21.1 + 1.9 = 5.312 m;a = 0.3 kg/m 3 giving the expected result for heeling arm amplitude:

Intermediate results for the wind heeling arm.

ISO 12217: Small craft – stabi li ty and buoyancyassessment and categor isation.This section gives some details on implementing the ISO 12217 stability criteria in Hydromax.

See also the note on converting units for the definition of the heeling arms in ISO 12217-1:2002(E) .

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Part 1: Non-sailing boats of hull length greater than or equal to 6m

In many cases the user must determine the required pass value for the criteria, which depends onthe category and length of vessel being tested. In most cases the default required value wouldexceed the worst case.

6.1.2: Downflooding heightMinimum freeboard to downflooding points must be determined from Figures 2 and 3 (Section6.1.2) and entered into the required value field; the default value is set at 1.42m which is slightlygreater than the height required for a category A vessel of 24m in length.

6.1.3: Downflooding angleMust be greater than a certain value as determined according to the design category; see Tables3 and 4 (Sections 6.1.3, 6.2). The default value is set to 49.7

6.2: Offset-load testThere are several ways of evaluating this criterion:

1. Define a heeling arm and calculate the intersection of the heeling arm with the GZcurve to determine the angle of equilibrium.

2. Specify a loadcase with the offset load specified and carry out an equilibrium analysis.Verify that the angle of equilibrium does not exceed the maximum permissible value.An additional requirement in this section is that a specified freeboard must be exceeded.

6.3: Resistance to wind and wavesDetermine the windage area and lever and enter them in the appropriate fields in the criterion.Also determine the required wind speed and roll-back angle (depending on the design category)and enter these values.

In Hydromax, there is no option for placing the height, H, of the centre of lateral resistance atthe bottom of the vessel, so this must be specified manually (it is measured from the model zero

point, positive upwards).

6.3.3: Resistance to wavesThis criterion comprises two parts, one to check that the righting moment is sufficient and asecond to determine whether the righting lever is sufficient.

6.4: Heel due to wind actionDetermine the parameters required for calculation of the wind heeling moment as per 6.3, butnote the different wind speeds to be used. Determine the limiting heel angle from Table 4(Sections 6.2)

Part 2: Sailing boats of hull length greater than or equal to 6m

6.2.2: Downflooding heightMinimum freeboard to downflooding points must be determined from Figure 2 (Section 6.2.2)and entered into the required value field, the default value is set at 1.42m which is slightlygreater than the height required for a category A vessel of 24m in length.

6.2.3: Downflooding angleMust be greater than a certain value as determined according to the design category, see Tables3 (Sections 6.2.3). The default value is set to 40

6.3: Angle of vanishing stabilityDetermine the required angle of vanishing stability which depends on design category andvessel displacement. The default value is 130.

6.4: Stability index (STIX)

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Determine the required STIX value depending on the design category, see Table 5 (Section6.4.9). Also specify the sail area and vertical position of the sail area centroid and enter thesevalues in the appropriate fields in the criterion. If desired you can specify the other values or letHydromax calculate them for you.

6.5: Knockdown-recovery testThe test can be approximated by examining the angle of vanishing stability in the floodedcondition. If the flooded vessel has positive GZ at the knockdown angle, it should self right.

6.6.6: Wind stiffness testDetermine the wind heeling moment as defined in 6.6.6 for the wind speed of interest (Table 6,Section 6.6.7). Convert this to a heeling lever. Calculate the GZ curve with the crew seated towindward, this criterion will then look at the angle of equilibrium of the vessel under theapplied wind heeling arm.

Part 3: Boats of hull length less than 6m

These criteria are evaluated after an equilibrium analysis under the specified loading condition.

Non-Sailing Boats:6.2.2: Downflooding-height testsDetermine the required downflooding height and specify the appropriate loading condition. Thecriterion is evaluated after an equilibrium analysis.

6.3: Offset-load testThis criterion is most effectively evaluated by performing an equilibrium analysis with therequired offset loading condition

Sailing Boats:7.2: Downflooding heightMinimum freeboard to downflooding points must be determined from Figure 2 (Section 6.2.2)

and entered into the required value field, the default value is set at 1.42m which is slightlygreater than the height required for a category A vessel of 24m in length.

7.5: Knockdown-recovery testThe test can be approximated by examining the angle of vanishing stability in the floodedcondition. If the flooded vessel has positive GZ at the knockdown angle, it should self right.

7.6.6: Wind stiffness testDetermine the wind heeling moment as defined in 6.6.6 for the wind speed of interest (Table 6,Section 6.6.7). Convert this to a heeling lever. Calculate the GZ curve with the crew seated towindward, this criterion will then look at the angle of equilibrium of the vessel under theapplied wind heeling arm.

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Appendix EReference TablesThis appendix contains the following reference tables:

• File Extension Reference Table • Anal ysi s sett ings reference table

File Extension Reference TableThe following table lists files that are used in Hydromax. The .hmd file contains all theadditional information that defines the Hydromax model and you need only save this file whenworking in Hydromax. However, if you wish to transfer loadcases or compartment definitionsfrom one model to another, this can be done by going to the appropriate window and saving it toa separate file.

File Extension Description

Maxsurf Design .msd Contains control point and surface information. E.g. precision, flexibility, thickness, outside arrows,trimming, colour

When opening a .msd file Hydromax looks for a .hmdfile with the same name.

Hydromax Design .hmd Contains hydrostatic sections information and all Inputinformation that may also be stored separately in thefiles below

The .hmd file does not contain:- Maxsurf surface information- Links to or information on the Stability Criteria

Library- Links to or information on the Results tables- Links to or information on the Report

Separate Input files Extension DescriptionLoadcase .hml Each loadcase can be saved separatelyCompartments .htk The compartment definition can be saved separatelyDamage cases .dcs The damage case definition can be saved separatelyAll Input window tables .txt All tables in the input window can be saved as text

files. Downflooding/embarkation points, margin lines,sounding pipes and modulus

Output files Extension DescriptionAll Result Window tables .txt Result tables can be saved separately

Results tables can not be opened in HydromaxReport .rtf The report can be saved separatelyLibrary Extension DescriptionHydromax Criteria Library .hcr The library is not related to the Hydromax Design File,

i.e. is not model related. The library is loaded when the program starts, not when the model is opened. Formore information see the section on criteria.

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Linking to tanks or compartments ........... 62Draft ........................................65, 96, 154, 164DWL ............................................................ 65DXF export ................................................ 112

E

Edit Loadcase............................................. 156Edit Menu .................................................. 150Edit Toolbar ............................................... 147Edit,

Add......................................................... 151Delete ..................................................... 151

Equilibrium ............................................ 10, 70Equilibrium Condition ................................. 10Export......................................................... 149Export Bitmap............................................ 150Exporting ................................................... 112

External Tanks ............................................. 45 F

File Extension Table .................................. 242File Menu................................................... 149File Toolbar................................................ 147File,

Close ...................................................... 149Exit......................................................... 150Hydromax Version 8.0........................... 112

New ........................................................ 149Open................................................. 22, 149

Save........................................................ 149Save As .................................................. 149Fill Down ................................................... 151Floodable Length ......................................... 14Floodable Length Criteria dialog............... 155Flooding ....................................................... 60Fluid analysis method ................................ 100Fluid VCG............................................ 40, 101Fluids ......................................................... 155Font ............................................................ 152Form parameters ........................................ 161Frame of Reference........................ 20, 31, 158Free Surface Moment........................... 40, 100Free Surface Moment, options ..................... 40Freeboard ..................................................... 71Full Screen ................................................. 153

G

Graph ......................................................... 159Curve of Areas ....................................... 141Curves of Form ...................................... 141Data interpolation................................... 141double click............................................ 142get data ................................................... 142Righting Lever (GZ) .............................. 141

Type ....................................................... 141Graph colours............................................. 142Graph Formatting....................................... 142Graph Printing to Scale.............................. 110Graph Window........................................... 140Graphs........................................................ 141Grid ............................................................ 157Grounding .......................................... 104, 155GZ .................................................................. 9

H

Heel ...................................................... 94, 154Heeling Moments....................................... 184Help Menu ................................................. 159Hog and Sag....................................... 105, 155Home View ........................................ 134, 152Horizontal lever ........................................... 36

Hull SectionsRecalculate ............................................. 156Hydromax v8.0 file .................................... 150

I

Immersion .................................................. 167Immersion Angles........................................ 69Initial Conditions ......................................... 31Input ........................................................... 159Input Tables, saving ................................... 111Input Window ............................................ 136Insert New Table........................................ 151

Insert Row.................................................. 151Installing Hydromax .................................... 18ISO 12217-1............................................... 238

K

Key points ............................................ 60, 137adding....................................................... 61Data .......................................................... 69deleting..................................................... 61editing ...................................................... 61Results.................................................... 139

KN Values.............................................. 12, 75

L

Large Angle Stability ............................... 9, 67lateral projected area .................................. 183LCB, LCG.................................................. 166Length ........................................................ 162Libraries ..................................................... 123Limiting KG................................................. 78Linked negative compartments .................... 47Loadcase .............................................. 33, 159

Adding and Deleting loads....................... 35Distributed loads ...................................... 38Editing loads ............................................ 36

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Free surface correction............................. 40maximum number............................ 35, 157Renaming ................................................. 34saving ..................................................... 111Tank loads................................................ 39Update ...................................................... 39

Loadcase Colour Formatting........................ 37Loadcase Formatting.................................... 37

Blank lines ............................................... 37Grouping tanks......................................... 37Headings lines .......................................... 37Totals ....................................................... 37

Loadcase Sorting.......................................... 36Loadcase Template ...................................... 33Loadcase Window...................................... 135Loading a Saved Loadcase........................... 35Longitudinal Strength ............................ 15, 84

M

Margin Line points............................... 62, 137Margin Line, Snap to hull .......................... 156Maximum deck inclination ........................ 167Maximum shears and moments ................... 63Measurement reference frames .................. 161Menus......................................................... 149Merge Cells................................................ 151Midship Section......................................... 165Midship Section Coefficient ...................... 165Modulus points........................................... 137

Modulus Window......................................... 63Moment to trim .......................................... 167

N

Non-Buoyant Volume Definition................. 40

O

Online Support ........................................... 160Outside arrows ............................................. 21overlap ......................................................... 48

P

Page Setup.................................................. 150Pan ..................................................... 134, 152Paste ........................................................... 151Permeability ..............................14, 47, 97, 154Perspective view ........................................ 134Precision, surface ......................................... 23Preferences........................................... 18, 152Print............................................................ 150Print Preview.............................................. 110Printing....................................................... 109Printing to scale.......................................... 110Prismatic Coefficient ................................. 165

R

Ratio of equilibrium angles - derived heelingarm ......................................................... 214

Reference Calculations .............................. 170Reference Designs ..................................... 169

Relative Density................................... 49, 101Render........................................................ 158Render Transparent.................................... 158Report Window.......................................... 143

Keystrokes ............................................. 145Reporting ................................................... 108Results........................................................ 159Results Window......................................... 138Results, saving ........................................... 112Resume Analysis.................................. 90, 156Righting Moment ....................................... 167Rotate ......................................................... 152Row Positioning......................................... 151

S

Save............................................................ 112Saving Densities ........................................ 102Section, show single................................... 158Sectional Area Curve ................................... 30Sections, Forming ........................................ 25Select All.................................................... 151Select View from Data....................... 110, 157Set Analysis Type ...................................... 156Set Home View .......................................... 152Shift Key ...................................................... 18Show Grid .................................................. 151Show single hull section .............................. 29Shrink................................................. 134, 152Simulate fluid movement........................... 101Skin Thickness ............................................. 20Sounding Pipes .................................... 57, 137

Calibration Increment .............................. 58Edit........................................................... 57

Specific Gravity ................................... 49, 101Specified Condition ........................11, 73, 154

Specified Conditions, dialog........................ 97Split Cell .................................................... 151Stability booklet ......................................... 100Stability criteria............................................ 63Stability Criteria Results ............................ 139Stability criteria, Angle of deck edge

immersion .............................................. 193Stability criteria, Angle of downflooding .. 192Stability criteria, Angle of equilibrium...... 192Stability criteria, Angle of equilibrium -

derived wind heeling arm....................... 214Stability criteria, Angle of equilibrium -

general heeling arm........................ 209, 210

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Stability criteria, Angle of equilibrium - high-speed turn heeling arm........................... 210

Stability criteria, Angle of equilibrium -multiple heeling arms............................. 223

Stability criteria, Angle of equilibrium - passenger crowding heeling arm............ 210

Stability criteria, Angle of margin lineimmersion .............................................. 193

Stability criteria, Angle of maximum GZ .. 191Stability criteria, Angle of maximum GZ

above heeling arm - general heeling arm208Stability criteria, Angle of vanishing stability

............................................................... 193Stability criteria, Angle of vanishing stability -

general heeling arm................................ 210Stability criteria, Areas and levers ............. 183Stability criteria, check boxes.................... 122

Stability criteria, Combined criteria (ratio ofareas type 1) - general cos+sin heeling arm............................................................... 227

Stability criteria, Combined criteria (ratio ofareas type 1) - general heeling arm ........ 226

Stability criteria, Combined criteria (ratio ofareas type 1) - high-speed turn............... 227

Stability criteria, Combined criteria (ratio ofareas type 1) - lifting weight .................. 228

Stability criteria, Combined criteria (ratio ofareas type 1) - passenger crowding........ 227

Stability criteria, Combined criteria (ratio of

areas type 1) - towing............................. 228Stability criteria, Combined criteria (ratio of

areas type 2) - general wind heeling arm228Stability criteria, Combined criteria (ratio of

areas type 2) - wind heeling arm............ 230Stability criteria, copying criteria............... 121Stability criteria, criteria library file .......... 123Stability criteria, damage and intact settings

............................................................... 123Stability criteria, defining custom criteria.. 121Stability criteria, equilibrium..................... 186Stability criteria, General cos+sin heeling arm

............................................................... 178Stability criteria, General heeling arm ....... 178Stability criteria, glossary .......................... 131Stability criteria, Gust ratio........................ 178Stability criteria, GZ area between limits -

general heeling arm................................ 216Stability criteria, GZ area between limits -

multiple heeling arms............................. 224Stability criteria, GZ area between limits type

1 - standard............................................. 194Stability criteria, GZ area between limits type

2- HSC monohull type ........................... 195

Stability criteria, GZ area between limits type3 - HSC multihull type........................... 197

Stability criteria, GZ area derived heeling arm- general heeling arm ............................. 212

Stability criteria, GZ area derived heeling arm(type 2) - general heeling arm................ 213

Stability criteria, GZ curve features........... 128Stability criteria, GZ definitions ................ 130Stability criteria, GZ derived heeling arm -

general heeling arm................................ 212Stability criteria, GZ, non-healing arm ...... 187Stability criteria, heeling arm definition .... 177Stability criteria, heeling arm dependency on

displacement .......................................... 183Stability criteria, heeling arm units............ 233Stability criteria, Heeling due to bollard-pull

............................................................... 182

Stability criteria, Heeling due to lifting ofweights ................................................... 182Stability criteria, Heeling due to passenger

crowding ................................................ 179Stability criteria, Heeling due to towing .... 182Stability criteria, Heeling due to turning.... 181Stability criteria, Heeling due to wind ....... 180Stability criteria, IMO Code on Intact Stability

A.749(18)............................................... 233Stability criteria, IMO HSC Code MSC.36(63

............................................................... 235Stability criteria, importing................ 123, 124

Stability criteria, ISO 12217 ...................... 239Stability criteria, list................................... 114Stability criteria, Maximum Freeboard at

equilibrium............................................. 186Stability criteria, Maximum ratio of GZ to

heeling arm - general heeling arm.. 206, 220Stability criteria, Maximum value of heel,

pitch or slope at equilibrium .................. 186Stability criteria, Minimum Freeboard at

equilibrium............................................. 186Stability criteria, moving criteria ............... 121Stability criteria, Other criteria - STIX ...... 231Stability criteria, parent criteria ......... 115, 186Stability criteria, pass/fail test .................... 123Stability criteria, Range of positive stability

............................................................... 193Stability criteria, Range of positive stability -

general heeling arm................................ 211Stability criteria, Ratio of areas type 1 -

general cos+sin heeling arm................... 217Stability criteria, Ratio of areas type 1 -

general heeling arm................................ 216Stability criteria, Ratio of areas type 1 -

multiple heeling arms............................. 225

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Stability criteria, Ratio of areas type 2 -general wind heeling arm....................... 218

Stability criteria, Ratio of areas type 3 -general heeling arm................................ 219

Stability criteria, Ratio of GM T and heelingarm ......................................................... 204

Stability criteria, Ratio of GZ area betweenlimits ...................................................... 198

Stability criteria, Ratio of GZ values at phi1and phi2.................................................. 190

Stability criteria, Ratio of GZ values at phi1and phi2 - general heeling arm............... 208

Stability criteria, Ratio of GZ values at phi1and phi2 - multiple heeling arms............ 220

Stability criteria, Ratio of positive to negativeGZ area between limits .......................... 200

Stability criteria, report and batch processing

............................................................... 127Stability criteria, results ............................. 126Stability criteria, saving ............................. 124Stability criteria, selecting for analysis...... 121Stability criteria, tree list ............................ 120Stability criteria, User Defined Heeling Arm

............................................................... 179Stability criteria, USL code........................ 236Stability criteria, Value of GMt at ............. 187Stability criteria, Value of GMt at equilibrium

- general heeling arm ............................. 204Stability criteria, Value of GMt or GMl at

equilibrium............................................. 187Stability criteria, Value of GZ at................ 187Stability criteria, Value of GZ at equilibrium -

general heeling arm................................ 204Stability criteria, Value of GZ at specified

angle or maximum GZ below specifiedangle....................................................... 189

Stability criteria, Value of maximum GZ .. 188Stability criteria, Value of maximum GZ

above heeling arm - general heeling arm205Stability criteria, Value of RM at specified

angle or maximum RM below specifiedangle....................................................... 190

Start Analysis ....................................... 90, 156Start Batch Analysis................................... 156Starting Hydromax....................................... 18Status Bar ................................................... 153Stop Analysis ....................................... 90, 156Streaming results to Word ......................... 108Surface Use .................................................. 20

T

Table .......................................................... 151Tank

adding, deleting........................................ 41

Fluids ....................................................... 49Ordering ................................................... 50Permeability....................................... 47, 49Saving .................................................... 111Surface Thickness .................................... 50Visibility .................................................. 50

Tank Calibrations................................... 16, 87Tank Type

external..................................................... 45linked ....................................................... 43simple....................................................... 41tapered...................................................... 42

tanksoverlap ..................................................... 48

TanksRecalculate ............................................. 155

Tanks within Compartments ........................ 47

Tanks, boundary surfaces .................................... 43complex.................................................... 43

Non-Buoyant Areas ................................. 45Recalculate ............................................. 147

Tile Horizontal ........................................... 159Tile Vertical ............................................... 159Tolerances .................................................... 98Toolbars ............................................. 147, 153Trapezoidal integration ................................ 25Trim ..................................................... 95, 154

Fixed ........................................................ 96

Free-to-trim to a specified LCG value..... 96Free-to-trim using a specified initial trim

value..................................................... 96Trim angle.................................................. 166Trimmed surfaces, checking ........................ 21

U

Undo........................................................... 150Units..................................................... 32, 157Update Loadcase........................................ 155Upright Hydrostatics................................ 8, 65

V Validate Hydromax model........................... 29View Direction........................................... 159View Menu ................................................ 152View Toolbar ............................................. 147View Window ............................................ 134Visibility .................................................... 157Visibility Toolbar....................................... 148

W

Waterplane Area Coefficient ..................... 166Wave definition.......................................... 103Wave height ............................................... 103

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Waveform .................................................. 155sinusoidal ............................................... 103trochoidal ............................................... 103

Wavelength ................................................ 103Wetted surface area, integration of ............ 168Window Menu ........................................... 159Window Toolbar ........................................ 148Windows Registry........................................ 18

Hydro Max

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