Chuong 1 _ Trai Dat Va Cach Bieu Thi

TRC A

(GEODESY)

GV: o Hu S

Khoa Xy dng

[email protected]

GV: o Hu S

Khoa Xy dng

Chng 1:

TRI T V CCH BIU TH

MT T

NI DUNG CHNG 1

Hnh dng - kch thc tri t v cch biu th

mt t

Cc h ta - cao

Khi nim v bn

Phn mnh v nh s hiu bn

1.1 HNH DNG V KCH THC

TRI T 1.1.1 Hnh dng

B mt tri t c din tch S 510,2 triu km2. Trong

: i dng chim 71%

Lc a chim 29%

L mt g gh, li lm; ch cao nht +8882m (nh

Hymalaya), ch thp nht -11032m (h Marian Thi

Bnh Dng, gn Philippines)

u th k 20 (Listinger c), a ra khi nim

mt Geoid v dng mt ny biu th b mt tri t

Mt Geoid : l mt nc bin trung bnh yn tnh, ko

di xuyn sut qua cc lc a hi o to thnh mt mt

cong khp kn (Mt Geoid cn c gi l mt thy

chun lc a, hay mt nc gc tri t)

Hnh nh tri t chp t v tinh

Mt Geoid c dng lm mt quy chiu ca h thng

cao

Mt Geoid c c tnh:

+ Mt Geoid khng phi l mt ton hc

+ Ti mi im trn mt Geoid u vung gc vi

phng ca ng dy di ti im .

1.1.2 Kch thc.

Do mt Geoid khng phi l mt ton hc, nn khi

tnh ton - biu din kch thc Tri t chng ta phi

dng b mt khc gn trng vi Geoid v phi l mt

ton hc, l mt Ellipsoid tri t (Gi tt l

Ellipsoid), cn tho mn:

- Tm Ellipsoid trng vi tm Geoid

- Mt phng xch o Ellipsoid trng vi mt phng

xch o Geoid

- Th tch Ellipsoid tri t = th tch Geoid

- Tng bnh phng chnh cao t mt Ellipsoid ti

mt Geoid l nh nht ([h2] =min)

c im ca Ellipsoid:

- Ellipsoid l mt mt biu din c bng phng

trnh ton hc v hu ht mi tnh ton Trc a thc

hin trn mt ny (gi l Mt quy chiu)

- Ti mi im, b mt Ellipsoid lun vung gc vi

phng php tuyn.

c trng cho Ellipsoid

+ Bn trc ln (bn knh ln): a

+ Bn trc nh (bn knh nh): b

+ dt a

ba

2 2 2

2 2 2

Ph.trnh:

1.X Y Z

a a b

Geoid

Ellipsoid

O

b a

Tc gi

(Ellipsoid)

Quc

gia

Nm Bn trc ln a (m)

Bn trc nh b (m)

dt

Delambre Php 1800 6.375.653 6.356.564 1:334,0

Everest Anh 1830 6.377.276 6.356.075 1:300,8

Bessel c 1841 6.377.397 6.356.079 1:299,2

Clark Anh 1980 6.378.249 6.356.515 1:293,5

Krasovski Nga 1940 6.378.388 6.356.863 1:298,3

WGS84 M 1984 6.378.137 6.356.752,3 1:298,257

Mt s Ellipsoid tri t

1.2.1 Khi nim

Trong trc a,

tin cho vic thit k

k thut, ngi ta

tm cch biu din b

mt tri t ln mt

phng. Phng php

ny cho php chng

ta thu nh b mt tri

t vi chnh xc

cn thit.

1.2 CCH BIU TH MT T

V b mt tri t l b mt t nhin v cng phc

tp, v vy biu din ln mt phng ta phi chiu b

mt tri t ln mt Ellipsoid hoc mt cu ri thu nh

mt cu tri t theo t l mong mun. Bng php chiu

xuyn tm ngi ta tip tc chiu hnh cu tri t ln

mt tr, mt nn, theo cc phng php khc nhau.

Sau ct mt tr, mt nn, theo mt ng sinh c

chn trc v tri ra mt phng.

Phng php chiu ny lm cho b mt qu t b

bin dng. S bin dng ph thuc vo im chiu v cc

im trn mt t cng nh phng php chiu.

1.2.2 nh v cc im trn mt t

V tr khng gian cc im trn mt t c xc nh

bng 2 yu t:

1. To a l (, ) hoc to vung gc phng (x, y) trn mt quy chiu Ellipsoid

2. cao ca im so vi mt Geoid

xc nh v tr cc im A,B,C trong khng gian ta

chiu chng xung mt Geoid theo phng dy di ta

c cc im a, b, c.

Trong trng hp biu din b mt tri t trong mt

phm vi khng ln, vi yu cu chnh xc khng cao

chng ta coi b mt tri t c chiu trc tip ln mt

phng

B

A

C

c

b

a

P

1.3 H TO A L Trong ton hc cng nh trong trc a, xc nh to

ca mt im, chng ta cn xc nh quan h gia im

vi mt h trc c chn lm gc.

P

P1

O M

M

Q Q1

xc nh to a l ca mt im trn b mt

tri t, Gi s phng php tuyn trng vi phng dy

di v mt Geoid trng vi mt Ellipsoid trn xoay ca

tri t.

Cc yu t c chn lm gc trong h to a l

nh sau:

- Tm O ca tri t c chn lm gc to

- Hai mt phng gc l mt phng kinh tuyn gc v mt

phng xch o

T hnh v:

- P, P1: l cc Bc v cc Nam ca tri t

- PP1: trc xoay ca tri t

- Q, Q1: l cc Ty v cc ng ca tri t

- G (Greenwich): V tr i thin vn Greenwich ngoi

Lun n

hiu r h to a l, chng ta c mt s khi

nim sau:

- Mt phng kinh tuyn l mt phng i qua trc xoay PP1

ca tri t

- Mt phng v tuyn l mt phng vung gc vi trc xoay

PP1

- ng kinh tuyn l giao tuyn ca mt phng kinh tuyn

vi mt cu tri t

- ng v tuyn l giao tuyn ca mt phng v tuyn vi

mt cu tri t

- Mt phng kinh tuyn gc l mt phng kinh tuyn i qua

G (Mt phng kinh tuyn gc chia tri t ra lm hai na

ng bn cu v Nam bn cu)

- Mt phng xch o l mt phng v tuyn i qua tm O

ca tri t

To a l ca im M(M ,M)

M (v ): l gc hp bi mt phng xch o v ng

dy di qua M

M (kinh ): l gc hp bi mt phng kinh tuyn gc v

mt phng kinh tuyn i qua im M

Trn xch o =0, trn kinh tuyn gc =0

Thng quy c:

M t xch o ln gi l v Bc (00 900)

M t xch o xung gi l gi l v Nam (00 900)

M t kinh tuyn gc G sang ng gi l kinh ng (00

1800)

M t kinh tuyn gc G sang Ty gi l kinh Ty (00

1800)

1.4 H TO VUNG GC KHNG GIAN

OXYZ (H T. A TM)

H ta vung gc khng gian: l h thng gm

im gc to v 3 trc to X, Y, Z xc nh

trong khng gian Euclide 3 chiu: h quy chiu ny

c s dng trong o c v tinh v nhng bi ton

trc a ton cu.

1.5 H TO VUNG GC PHNG Trong trc a h to vung gc phng ngc vi h

to vung gc cc; trc X theo phng ng, trc

Y theo phng ngang

Qua nhiu thi k khc nhau th c nhng h to cng

khc nhau (ngay c Vit nam cng nh th gii)

y

x

O

th hin mt khu vc trn b mt tri t ln mt

phng ngi ta phi s dng cc php bn . Thng qua

cc php chiu bn nh ngha cc h ta vung gc trc a

Cc li chiu bn thng dng:

- Hnh tr ngang,

- Hnh tr ng,

- Hnh nn,

- Phng v,

1.5.1 Php chiu Gauss, H to vung gc phng

Gauss Kruger

Php chiu ny s dng Ellipsoid Krasovski vi cc

thng s

a= 6.378.245 m , b= 6.356.863 m, = 1/298,3

Php chiu Gauss l php chiu hnh tr ngang ng gc.

Trong php chiu ny tri t c chia thnh 60 mi

chiu 60 v c nh s tng ng t 1 60 bt u t

kinh tuyn gc Greenwich (00) sang ng vng qua Ty

ri tr v knh tuyn gc.

Mi mi chiu c gii hn bi kinh tuyn ty - bn

tri v kinh tuyn ng - bn phi (2 kinh tuyn bin). V

kinh tuyn gia ca mi chiu c gi l kinh tuyn

trc, i xng vi 2 kinh tuyn bin.

T=60(n-1), G=6

0.n-30, P=60 .n

Vi n l s th t ca mi chiu

GP'

O

P

Sau khi chia ra tng mi chiu v xc nh kinh tuyn

trc ca mi mi chng ta cho qu cu tri t tip xc

vi mt trong ca mt hnh tr ngang theo ng kinh

tuyn trc.

Ly tm chiu O l tm tri t ln lt chiu cc mi ln

mt tr tng mi mt, sau va xoay va tnh tin hnh

cu n mi s 2 tng ng vi on chn cung trn xch

o

v tip tc cho n ht

Sau ct mt tr theo hai ng sinh KK ri tri ra mt

phng ta c nh hnh sau

kmR

L 84,666180

6..0

0

x

y

K

K'

c im ca mi mi chiu:

- Bo ton v gc

- Xch o c chiu thnh ng thng v lm trc Y

- Kinh tuyn trc (gia) c chiu thnh on thng v

chn lm trc X; X Y

- Kinh tuyn trc khng b bin dng sau khi chiu

- Cc kinh tuyn v v tuyn khc b thay i sau khi chiu

- Cng xa kinh tuyn trc bin dng cng ln

to Y lun dng ngi ta di kinh tuyn trc v

pha Ty 500km, X dng di X v Nam 10000km

Vit Nam h to Gauss c thnh lp nm 1972

gi l h to HN72, chn Ellipsoid quy chiu Kraxosky

gc t ti i thin vn Punkv (Lin X c) truyn to

ti Vit Nam thng qua h to quc gia Trung Quc.

1.5.2 Php chiu v h to vung gc phng UTM

(Universal Transverse Mercator)

500 km

x

xch ao

cat tuyen

kinh tuyen truc

y

Php chiu UTM s dng Ellipsoid WGS 84

Thng s Ellipsoid WGS 84

Bn trc ln a = 6.378.137 m

Bn trc nh b = 6.356.752,3 m

dt cc = 1 / 298,257

Php chiu UTM cng l php chiu hnh tr ngang

ng gc nhng mt tr khng tip xc vi mt Ellipsoid

ti kinh tuyn trc m ct mt Ellipsoid ti 2 ct tuyn

cch kinh tuyn trc 180km

c im ca mi mi chiu.

- Bo ton v gc (ng dng)

- Xch o thnh ng thng ngang kinh tuyn trc

- Hai ct tuyn h s bin dng m = 1 (khng bin dng)

- Kinh tuyn trc m = 0,9996

Vng trong ct tuyn m < 1 (bin dng m)

Vng ngoi ct tuyn m > 1 (bin dng dng)

K t ngy 12/08/2000 Vit Nam s dng thng nht

trn phm vi ton quc h to vung gc UTM gi l

VN2000, chn Ellipsoid quy chiu WGS 84, im gc to

l im gc ca li GPS cp 0 ti H Ni.

1.5.3 H ta c lp (t do)

Y

X

O

1.6 H CAO Mt Geoid c chn lm mt quy chiu cho cao.

cao ca mt im l khong cch tnh theo phng

dy di t im ti mt Geoid

A

B

H

H

g g

A

B

Mat thuy chuan gia nh

Geoid (mat thuy chuan goc)

Ellipsoid trai at

- Nu mt chun gc (l mt Geoid), ta c cao tuyt i

- Nu mt thy chun l mt gi nh ta c cao gi nh

- Khong cch t mt im ti mt Ellipsoid theo phng php

tuyn gi l cao trc a

- Hiu s cao gia 2 im (chnh cao) l khong cch theo

phng dy di gia 2 mt thy chun i qua 2 im .

Trong trc a khng o c cao trc tip m ch o

c chnh cao gia cc im.

Trc 1975, Bc Vit Nam mt thy chun gc c chn i

qua trm Nghim triu Hn du Sn Hi Phng.

Nam Vit Nam chn mt thy chun gc Mi Nai H Tin

Sau 1975, Vit Nam mt thy chun gc c chn i qua

trm Nghim triu Hn du Sn Hi Phng

HH.Dau = HM.Nai + 0,167 m

T 2001, thng nht trn lnh th VN ch s dng cao HD

CC H TA C TI VIT NAM

Thi Php thuc: Ellipsoid Clark (Anh), im gc ti H

ni, php chiu Bonne v h thng im to ph trm

ng dng; lm c s cho lp bn 1/100.000 v

1/200.000 khu vc ng Dng.

Min Nam VN t 1954-1975: h Indian 54 vi Ellipsoid

Everest (Anh), im gc ti n , php chiu UTM v

h thng im to ph trm Nam Vit Nam, h cao

Mi Nai, H Tin;

Min Bc t 1959 bt u xy dng h thng li Trc a

v h quy chiu v kt thc nm 1972 => h HN-72 vi

Ellipsoid Krasovski , im gc ti Punkovo chuyn v VN

ti i thin vn Lng HN (thng qua im Ng Lnh

Trung Quc), php chiu Gauss- Kruger, h cao Hn

du, Hi phng

Quan h gia cao Hn du v cao Mi nai

HH = HM + 0,167 m

T 1992-1994: nh v li Ellipsoid Krasovski ph hp

Vit Nam.

T 1996-2000: Xy dng h VN-2000 vI Ellipsoid

WGS-84 c nh v ph hp vi lnh th Vit nam,

im gc to N00 t ti Vin nghin cu a

chnh, ng Hong Quc Vit, H ni; php chiu

UTM, h cao Hn du - Hi phng.

H Quy chiu WGS 84

1.7 KHI NIM BN .

1.7.1 nh ngha bn Bn l hnh v thu nh trn giy cc hnh chiu bng

ca nhng phn b mt tri t, c k n s bin dng

do nh hng ca cong tri t, theo mt quy lut ton

hc no .

Bn l biu hin thu nh ca b mt tri t ln mt phng theo mt quy lut ton hc xc nh, th hin bng

cc k hiu quy c c bit; trn trng thi, s phn

b v mi quan h gia cc hin tng t nhin, kinh t,

vn ha, x hi c chn lc v khi qut ha ph hp

vi mc ch s dng c th ca bn

1.7.2 Phn loi bn :

a. Phn loi theo mc ch: Ph thng, chuyn ngnh

b. Phn loi theo ni dung

* Bn a l chung: Bn a hnh, Bn a hnh

khi qut, Bn Khi qut.

* Bn a l chuyn (gi tt l bn chuyn ):

Cng nghip, Nng nghip, Du lch, a cht, Thy vn,

Kh hu, Th nhng, Thc vt, ng vt

c. Phn loi theo t l

Bn t l ln, trung bnh, nh

d. Phn loi theo phm vi din tch

Ton cu, i dng, lc a, chu lc, quc gia, tnh,

huyn, x

1.7.3 T l bn a) nh ngha:

T l bn l t s gia chiu di ca mt on thng

trn bn vi chiu di nm ngang tng ng ca n

ngoi thc a (thc t).

T l bn k hiu 1:M hoc

T l bn l mt phn s c t s l n v, cn mu

s thng l nhng s trn trm, trn nghn,..

b) Phn loi bn a hnh theo t l

- T l ln:

- T l trung bnh:

- T l nh:

;5000

1;

2000

1;

1000

1;

500

1

;000.50

1;

000.25

1;

000.10

1

1.000.000

1;

500.000

1;

250.000

1;

100.000

1

tt

bd

SM

1 S

c. chnh xc (sai s) ca t l bn

t = 0,1xM (mm)

M: Mu s t l bn

t: sai s c bn quy ra thc t

1.7.4 Thc t l c gi tr chiu di on thng ngoi thc a tng

ng biu din trn bn mt t l no c nhanh

chng v d dng, ngi ta dng thc t l:

C hai loi thc t l:

+ Thc t l thng

+ Thc t l xin (cho chnh xc cao hn)

1.7.5 Biu din a vt trn bn . - K hiu theo t l

- K hiu phi t l

- K hiu na t l

- K hiu ch gii

1.7.6 Biu din a hnh trn bn . - Phi cnh, t bng (t s dng)

- Ghi cao v ng bnh (phng php ph bin)

1.7.7 Bn s. D liu c lu tr di dng file v hin th trn cc

thit b in t.

u im:

chnh xc, lu tr, cp nht x l thng tin, tt hn

hn so vi bn giy

1.8 CHIA MNH V NH S HIU BN .

Bn a hnh ni ring cng nh cc loi bn khc

c biu din nhiu loi t l khc nhau.

Mc ch ca chia mnh v nh s hiu tin cho qun

l v s dng bn .

S hiu bn cn gi l danh php bn (hay

phin hiu bn ).

Trn th gii v Vit nam tng tn ti nhiu kiu t

danh php bn khc nhau.

Lu : mi loi bn c cc quy nh v t l v cch

chia mnh nh s hiu khc nhau

Di y trnh by cch chia mnh v phin hiu

(danh php) bn a hnh theo kiu hin nay ang

c s dng Vit Nam

T bn a hnh c bn c t l 1:1.000.000, trn

c s t bn ny tin hnh chia mnh v nh s hiu

cho cc t bn t l ln hn (theo s chia mnh

trang tip sau)

T bn t l 1:1.000.000 c hnh thnh theo

php chiu hnh nn, c dng hnh thang (l giao ca

hng v ct) nh sau:

- Theo v tuyn t xch o v hai cc Bc, Nam ta

chia ra cc di 40 v t tn bng cc ch ci Latin:

A,B,C, . . . (b ch ci I v O)

- Theo kinh tuyn chia tri t ra cc mi 60 (nh

vy c 60 mi) v nh s t 1 60.

nh s th t t Ty sang ng (bt u t kinh tuyn

1800)

Mi s 1 nm gia kinh tuyn 1800 v 1740T

Mi s 2 nm gia kinh tuyn 1740T v 1680T

Nu kinh tuyn nh s lin tc t 0 3600, th mi 1? mi 2?

Ch : Mi bn khc mi chiu. S th t mi chiu

c nh s bt u t kinh tuyn gc Greenwich (00)

v ng sang Ty. Cn mi bn c nh s t

kinh tuyn 1800 v Ty sang ng. Nh vy s hiu

mi chiu v s th t ct ca t bn 1:1.000.000 lch

nhau 30 n v.

V d: = 1050 ng, tc mi chiu th 18 ct ca t bn 1:1.000.000 l 18 + 30 = 48.

1.8.1. Phin hiu bn a hnh t l 1:1.000.000

giao nhau gia hng v ct ni trn s c biu din

thnh 1 t bn t l 1:1.000.000

Tn ca t bn ny ghp t k hiu Hng s hiu

Ct

S chia mnh sau th hin cch chia mnh v nh s

hiu cc t bn t l khc nhau.

3 x 3 = 9

c, d

1, 2

3, 4

a, b

A, B

C, D

3, 4

1, 2

C, D

A, B

25.000

10.000

1

III, IV

I, II

2 x 2 = 4

2 x 2 = 4

1

1.000

5.000

2.000

1

1

2 x 2 = 4

2 x 2 = 4

50.000

250.000

500.000

1.000.000

1

1

1

2 x 2 = 4

1

2 x 2 = 4

1

8 x 12 = 96

100.000

1

241, 242,. . .256

1, 2 , . . . 16

13, 14, 15, 16

1, 2 , 3, 4

.

.

.

4 x 4 = 16

500

1

g, h, k

.

.

.

a, b, c

.

.

.

85, 86, . . . 96

1, 2 , . . . 12

.

.

.

16 x 16 = 256

1.8.2 Phin hiu bn a hnh t l 1:500.000

T mnh bn 1:1.000.000 c chia ra thnh 2x2 = 4

mnh bn t l 1:500.000, v ghi k hiu A, B, C, D

theo nguyn tc t tri qua phi t trn xung di.

Tn: ghp t tn t c s chia ra n k hiu

BA

C D

F-48

(1:1.000.000)

F-48-D

(1:500.000)

1.8.3 Phin hiu bn a hnh t l 1:250.000

T mnh bn 1:500.000 chia ra thnh 2x2 = 4 mnh

bn t l 1:250.000 v nh s 1, 2, 3, 4 theo nguyn

tc t tri qua phi t trn xung di.

F-48-D

(1:500.000)

3

1

F-48-D-4

(1:250.000)

4

2

1.8.4 Phin hiu mnh bn t l 1:100.000

T mnh bn t l 1:1.000.000 chia ra thnh 8x12 =

96 mnh bn t l 1:100.000, v nh s t 1, 2, ,

95, 96 theo nguyn tc t tri qua phi t trn xung di

F-48-96

(1:100.000)

F-48

(1:1.000.000)

1 2 3 4 5 6 7 8 9 10 11 12

13 24

969785


T mnh bn 1:100.000 chia ra thnh 2x2 = 4 mnh

bn t l 1:50.000 v nh s 1, 2, 3, 4

F-48-96-D

(1:50.000)D

B

F-48-96

(1:100.000)

C

A


T mnh bn t l 1:50.000 chia ra thnh 2x2 = 4

mnh bn t l 1:25.000 v nh k hiu a, b, c, d

F-48-96-D

(1:50.000)

c

a

d

b

F-48-96-D-d

(1:25.000)


T mnh bn 1:25.000 c chia ra thnh 2x2 = 4

mnh bn t l 1:10.000 v nh s 1, 2, 3, 4

F-48-96-D-d-4 (1:10.000)

F-48-96-D-d (1:25.000)

3

1

4

2


T mnh bn t l 1:100.000 c chia ra thnh

16x16 = 256 mnh bn t l 1:5.000 v nh s t 1,

2, , 255, 256

32

122

17

1 43

F-48-96

(1:100.000)

65 87 109 11

F-48-96(256)

(1:5.000)

13 14 15 16

256255241

240


T mnh bn t l 1:5.000 c chia ra thnh 3x3 = 9

mnh bn t l 1:2.000 v nh k hiu a, b, c, d, e, f,

g, h, k

F-48-96(256-k)

(1:2.000)

F-48-96(256)

(1:5.000)

g

a

d

h

e

b

k

c

f


T mnh bn t l 1:2.000 c chia ra thnh 2x2 = 4

mnh bn t l 1:1.000 v nh s I, II, III, IV

F-48-96(256-k-IV)

(1:1.000)

F-48-96(256-k)

(1:2.000)

III

I

IV

II

1.8.11 Phin hiu mnh bn a hnh t l 1:500

T mnh bn t l 1:2.000 c chia ra thnh 4x4 =

16 mnh bn t l 1:500 v nh s 1, 2, , 15, 16

F-48-96(256-k)

(1:2.000)

9

1

12

4

F-48-96(256-k-16)

(1:500)

2 3

8765

10 11

13 14 15 16

Cch chia mnh v nh s hiu theo quc t

(SV tm c trong cc ti liu)

Chuong 1 _ Trai Dat Va Cach Bieu Thi

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