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S KHC BIT GIA TA VUNG GC PHNG UTM VI H TA VUNG GC PHNG A DIN CHN TRI

NCS. L VN HNG Vin KHCN Xy dng

Tm tt: Trong thc t vic bnh sai tnh ton mng li trc a c thc hin hon ton trn b mt Elipsoid sau c th s dng trong trc a cng trnh, chng c tnh chuyn v ta a din chn tri hoc v ta vung gc UTM. Vic kho st s khc bit gia h ta a din chn tri v h ta vung gc phng UTM trong trc a cng trnh l mt vn cn lu .

1. t vn

Ngy nay vic ng dng cng ngh nh v ton cu (GPS) trong cng tc lp li trc a c s dng kh ph bin. Kt qu o GPS s xc nh c ta khng gian Xi, Yi, Zi hoc ta trc a Bi, Li, Hi ca cc im trong h to WGS-84 hoc trong h quy chiu quc gia VN2000.

s dng chng trong trc a cng trnh cn phi tnh chuyn ta trc a B, L v h ta vung gc phng x,y theo php chiu hnh tr ngang gi gc (UTM). Nu nh cao ca khu o khng qu ln v vic chn kinh tuyn trc ca php chiu UTM hp l th bin dng chiu di kh nh, nhng i vi trng hp chn kinh tuyn trc khng ph hp v cao khu vc xt kh ln th bin dng chiu di l ng k.

Trong thc t, ngoi h ta vung gc phng UTM ngi ta c th s dng h ta vung gc khng gian a din chn tri cho cc cng trnh tp trung trn mt din tch khng ln [1,2]. thit lp h ta ny, cn chn 1 im quy chiu, ti thit lp ma trn xoay R v im cng chnh l im gc ca h ta a din.

C th tnh ton kho st bin dng chiu di trong cc trng hp cao (H) ca khu o khc nhau v s khc bit gia hai h ta a din chn tri v h ta vung gc phng UTM. Trn c s c th a ra kt lun v kh nng ng dng ca tng h ta trong trc a cng trnh.

2. C s l thuyt

2.1 Ta vung gc phng theo php chiu hnh tr ngang gi gc UTM

Theo php chiu UTM, v tr ca mt im trn mt Ellipsoid c xc nh qua ta phng x, y theo cng thc sau [1, 2]:

)]tt543t31111385(Bcos40320

lBsinN}t)t.2(

)t321()t61(28)t2411(8{Bcos.720lBsinN

)t4(Bcos24l.BsinNBcos

2lBsinNX[mx

64278

42

22232456

22342

00

(1)

trong , Xo l chiu di cung kinh tuyn t xch o n v B.

)]tt179t47961(Bcos5040

lN

}tt.2)t81(

)t61(4{Bcos120lN)t(Bcos

6lNBcosl.N[my

64277

4222

2355

233

0

(2)

trong , hiu kinh oLL , vi oL l kinh ca kinh tuyn trung ng:

tgBt (3)

2

22

e1Bsine1

MN

;

322

2

)Bsine1()e1(aM

(4)

Trong cc cng thc tnh i ta (1), (2), gi tr m0 l t l bin dng chiu di trn kinh tuyn trung ng

ca mi chiu. Nu l php chiu Gauss-Kriuger th m0 = 1, nu l php chiu UTM theo mi O6 th m0 = 0,9996, v nu l php chiu UTM theo mi O3 th m0=0.9999 [4].

Z

Y

X

y

z

Lo

Bo

O

x

H

o

G

a) H ta a din chn tri

X (N)

Y (E)O

500 km

Ct

tuy

n

Ct

tuy

n

kinh

tuy

n

b) H ta vung gc UTM

Hin nay theo quy nh ca nh nc cc bn t l nh v ln u s dng h ta VN2000, php chiu UTM mi 6o hoc mi 3o.

2.2 H ta vung gc khng gian a din chn tri

H ta a din chn tri c s dng trong trc a v tinh, trc a thin vn, ch yu l lin quan n im quan st v tinh, thin vn. H ta ny c thit lp da vo mt im quy chiu B0, L0, H0 hoc x, y, z trn mt t (mang tnh a phng). Quan h gia to vung gc khng gian a tm v h ta khng gian a din chn tri c biu din thng qua cc cng thc di y[2]:

zyx

=

00000

00

00000

sinBsinLcosBcosLcosB0cosLsinL

cosBsinLsinBcosLsinB.

002

0

0000

0000

sin].)1([

sincos)(coscos)(

BHeNZ

LBHNYLBHNX

(5)

trong :

X, Y, Z - to vung gc khng gian a tm; B0, L0, H0 - to trc a ca im trng tm li ( hay gc to ca h to a din); N0 - bn knh cong vng thng ng th nht i qua h to a tm.

0N =2

2 2 2 2cos sina

a Bo b Bo (6)

a, b - bn trc ln v bn trc nh ca Ellipsoid WGS 84; e - tm sai th nht ca Ellipsoid.

e = 2 2a ba

(7)

Hnh 1. H ta a din chn tri v h ta vung gc UTM

3. Tnh ton kho st sai khc gia hai h ta Sau khi bnh sai GPS s xc nh c ta khng gian Xi, Yi, Zi hoc ta trc a Bi, Li, Hi ca cc

im trong h to WGS-84 v s dng chng trong trc a cng trnh cn phi tnh chuyn v h ta a din chn tri hoc v h ta vung gc UTM. Mun chuyn ta ca mt im bt k t mt cong (mt Ellipsoid WGS 84) v mt phng (a din hoc UTM) u gy ra bin dng v chiu di v din tch. Chng ta tin hnh kho st xc nh c gi tr bin dng ny.

Chn li kho st gm 20 x 20 , mi c kch thc B, L = 10". Mi mt li c ta Bi, Li, Hi (c 441 mt li) ti cc vng c cao khc nhau. C th:

- Ti vng ng bng chn cao ca cc im trong mt li u bng 6m v ta trc a B, L, H ca im bn tri pha di tng ng l 2100'0", 105045'0", 6m;

- Ti vng trung du chn cao ca cc im trong mt li u bng 100m v ta trc a B, L, H ca im bn tri pha di tng ng l 2100'0", 105045'0", 100m;

- Ti vng ni chn cao ca cc im trong mt li u bng 700m v ta trc a B, L, H ca im bn tri pha di tng ng l 2100'0", 105045'0", 700m. 3.1 Xc nh khong cch (1)i gd gia cc im trong h ta khng gian Xi, Yi, Zi ca mt li vi im

quy chiu T ta ca cc im kho st Bi, Li, Hi tnh chuyn v Xi, Yi, Zi theo [2,3], sau ta tnh c khong

cch theo cng thc (8) (1) 2 2 2i g i g i g i gd X Y Z (8)

Chiu di (1)i gd l khong cch khng gian gia cc im c cng cao trc a, coi l khong cch thc.

3.2 Xc nh khong cch (2)i gd gia cc im trong h ta a din xi, yi, ca mt li vi im quy chiu T ta ca cc im kho st Bi, Li tnh chuyn v xi, yi, theo [2,3], sau ta tnh c khong cch

theo cng thc (9) (2) 2 2

i g i gi gd x y

(9)

Chiu di (2)i gd l chiu di trn mt phng nm ngang (mt phng chn tri) i qua im quy chiu.

3.3. Xc nh khong cch (3)i gd gia cc im trong h ta vung gc phng UTM xi, yi ca mt li vi im quy chiu T ta ca cc im kho st Bi, Li tnh chuyn v xi, yi theo [2,3] s dng kinh tuyn trung ng 105o,

mi chiu 3o (mo=0,9999), sau ta tnh c khong cch theo cng thc (10)

gigigid 22)3( yx (10)

Trong : i - im xt th i; g - im quy chiu (im gc hoc im trng tm); X, Y, Z ; x, y; x, y - gia s ta gia im xt v im quy chiu.

3.4 Kho st bin dng chiu di gia h ta a din chn tri v h ta vung gc phng UTM Gi tr bin dng chiu di gia ta vung gc khng gian v ta a din.

(1) (2) (1) (2)i g i g i gd d

(11)

Gi tr bin dng chiu di gia ta vung gc khng gian v ta vung gc UTM (1) (3) (1) (3)i g i g i gd d

(12)

3.5 Kt qu tnh ton T nhng cng thc trn v s liu kho st tin hnh tnh ton cho c kt qu di y:

a. Kt qu kho st vng ng bng (h=6m)

Ta trc a Ta khng gian Tn im B( 0 ' ") L( 0 ' ") H(m) X(m) Y(m) Z(m) 22 21 00 10.00 105 45 0.00 6 -1616960.0552 5733307.8876 2271684.287 36 21 00 10.00 105 47 20.00 6 -1620851.1030 5732209.0730 2271684.287 98 21 00 40.00 105 47 10.00 6 -1620483.2161 5731969.3716 2272545.6091 176 21 01 20.00 105 46 10.00 6 -1618695.8828 5732015.9181 2273693.9646 219 21 01 40.00 105 46 20.00 6 -1618913.7926 5731725.0619 2274268.1109 220 21 01 40.00 105 46 30.00 6 -1619191.6725 5731646.5680 2274268.1109 221 21 01 40.00 105 46 40.00 6 -1619469.5487 5731568.0606 2274268.1109

Ta a din Ta UTM Tn im x(m) y(m) z(m) x(m) y(m) 22 -2768.1841 -2887.5346 1.2573 2323334.9885 577970.2265 36 -2767.9733 1155.0139 0.7084 2323354.4501 582013.3135 98 -1845.3123 866.2604 0.3272 2324275.6427 581719.9826 176 -615.1196 -866.2604 0.0886 2325497.3605 579981.3995 219 -0.0100 -577.5069 0.0261 2326113.8308 580267.1797 220 -0.0025 -288.7535 0.0065 2326115.2298 580555.9237 221 0.0000 0.0000 0.0000 2326116.6338 580844.6679

b. Kt qu kho st vng trung du (h=100m)


Ta a din Ta UTM Tn

im x(m) y(m) z(m) x(m) y(m) 22 -2768.2251 -2887.5772 1.2573 2323334.9885 577970.2265 36 -2768.0143 1155.0309 0.7084 2323354.4501 582013.3135 98 -1845.3397 866.2732 0.3272 2324275.6427 581719.9826 176 -615.1287 -866.2732 0.0886 2325497.3605 579981.3995 219 -0.0100 -577.5155 0.0261 2326113.8308 580267.1797 220 -0.0025 -288.7577 0.0065 2326115.2298 580555.9237 221 0.0000 0.0000 0.0000 2326116.6338 580844.6679

c. Kt qu kho st vng ni (h=700m)


Ta a din Ta UTM Tn

im x(m) y(m) z(m) x(m) y(m) 22 -2768.4869 -2887.8487 1.2575 2323334.9885 577970.2265 36 -2768.2761 1155.1395 0.7085 2323354.4501 582013.3135 98 -1845.5142 866.3546 0.3272 2324275.6427 581719.9826 176 -615.1869 -866.3546 0.0886 2325497.3605 579981.3995 219 -0.0100 -577.5698 0.0261 2326113.8308 580267.1797 220 -0.0025 -288.7849 0.0065 2326115.2298 580555.9237 221 0.0000 0.0000 0.0000 2326116.6338 580844.6679

d. Bng kt qu kho st bin dng chiu di: Tn im Khong cch kho st (m) Chnh lch khong cch (m) STT

u - Cui Khng gian (KG) a din

(DD) UTM KG - DD KG - UTM

Vng kho st

1 221 - 22 4000.0876 4000.0874 3999.9955 0.0002 0.0921

2 221 - 36 2999.2889 2999.2888 2999.2319 0.0001 0.0570 3 221 - 98 2038.5251 2038.5251 2038.4858 0.0000 0.0394 4 221 - 176 1062.4402 1062.4402 1062.4178 0.0000 0.0224 5 221 - 219 577.5069 577.5069 577.4950 0.0000 0.0120 6 221 - 220 288.7535 288.7535 288.7476 0.0000 0.0059 7 221 - 221 0.0000 0.0000 0.0000 0.0000 0.0000

Vng ng bng

(h=6m)

1 221 - 22 4000.1467 4000.1465 3999.9955 0.0002 0.1512 2 221 - 36 2999.3333 2999.3332 2999.2319 0.0001 0.1015 3 221 - 98 2038.5553 2038.5553 2038.4858 0.0000 0.0696 4 221 - 176 1062.4559 1062.4559 1062.4178 0.0000 0.0381 5 221 - 219 577.5155 577.5155 577.4950 0.0000 0.0205 6 221 - 220 288.7577 288.7577 288.7476 0.0000 0.0102 7 221 - 221 0.0000 0.0000 0.0000 0.0000 0.0000

Vng trung du

(h=100m)

1 221 - 22 4000.5239 4000.5237 3999.9955 0.0002 0.5284 2 221 - 36 2999.6167 2999.2319 2998.9862 0.0001 0.3849 3 221 - 98 2038.7479 2038.7479 2038.4858 0.0000 0.2622 4 221 - 176 1062.5560 1062.5560 1062.4178 0.0000 0.1382 5 221 - 219 577.5698 577.5698 577.4950 0.0000 0.0748 6 221 - 220 288.7849 288.7849 288.7476 0.0000 0.0373 7 221 - 221 0.0000 0.0000 0.0000 0.0000 0.0000

Vng ni (h=700m)

4. Kt lun

Qua cc kt qu tnh ton trn c th thy rng:

- Trong h ta vung gc khng gian a din chn tri, mt phng x,y ca h ta i qua im quy chiu c cao xp x cao trung bnh ca khu vc kho st, do cao khu o khng nh hng n bin dng chiu di cnh khi chiu ln mt phng nh trong php chiu UTM;

- Ti cc vng c cao khc nhau, khong cch ca cc im sau khi chuyn v h ta vung gc khng gian a din chn tri gn nh trng vi khong cch thc, xt cho bn knh ti trn 4km;

- Khong cch ca cc im sau khi chuyn v h ta vung gc UTM i vi vng ng bng, trung du v vng ni c s khc bit r rt. i vi vng trung du v vng ni, nh hng ca cao n bin dng chiu di l kh ln;

- H ta vung gc khng gian a din chn tri c th s dng cho cc cng trnh c hnh th khng ko di m nm gn trong mt din tch gn vung hoc gn trn vi bn knh khng qu 5km.

TI LIU THAM KHO

1. NG NAM CHINH, NGC NG, Gio trnh nh v v tinh (A), Trng i hc M a cht, H Ni, 2012.

2. NG NAM CHINH, H quy chiu trc a, Bi ging cao hc, Trng i hc M a cht, H Ni, 2009.

3. GS.TSKH HONG NGC H, Bnh sai tnh ton li trc a v GPS, Nh xut bn Khoa hc v k thut, 2006.

4. TCXDVN 309:2004, Cng tc trc a trong xy dng - Yu cu chung.

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