Proiect Geodezie FINALL

U.S.A.V.C. CLUJ-NAPOCA FACULTATEA DE HORTICULTURA SECTIA M.T.C

PROIECT GEODEZIE

HERLEA DAN RADU AN IV, GRUPA 2 MTC

1

STABILIREA REELEI DE RIDICARE LANT DE TRIUNGHIURIPunctele de sprijin vor fi determinate planimetric n sistemul de coordonate Stereografic 1970 i altimetric n sistem de cote Marea Neagr 1975. Pentru asigurea unei precizii planimetrice de 5 cm i altimetrice de 1cm, punctele reelei de triangulaie au fost verificate, dup care s-a trecut la ndesirea acestora .:A B C D x 584712.515 586780.315 584702.733 587235.887 y 393564.1296 394477.271 404064.118 405042.402

3

5

6

7

1

1

1

1

2 1

3

7 1 6 2 4

1

8 2 3 1 9 1 2 2 0 2

2

4

1

2

4

9

8

1

1

0

5

1

Reeaua de triangulatie Verificarea reelei se face cu scopul de a localiza i apoi de a elimina acele puncte care , datorit unor cauze , au fost deplasate de la poziiile iniiale.Verificarea reelei se va realiza din punct de vedere planimetric i altimetric.

2

Rezolvarea retelei din punct de vedere planimetric

Den.unghi 1 2 3 [] 4 5 6 [] 7 8 9 [] 10 11 12 [] 13 14 15 [] 16 17 18 [] 19 20 21 [] 22 23 24 []

Val.unghi 73.7355 69.0669 57.1982 200.0006 58.5179 79.4529 62.0298 200.0006 60.3452 67.4485 72.2069 200.0006 70.2261 67.4485 62.326 200.0006 70.2156 67.4391 62.3459 200.0006 64.3212 69.4373 66.2421 200.0006 68.2605 63.4712 68.2689 200.0006 59.9432 63.8177 76.2397 200.0006

sin 0.916096657 0.884256872 0.782373201 0.795114904 0.948365791 0.827343593

w

6

6 0.812192286 0.872100447 0.906206045 6 0.892613281 0.872100447 0.829948032 6 0.892538913 0.872028186 0.830122366 6 0.847020627 0.886959008 0.862671631 6 0.878270638 0.839848073 0.878333722 6 0.808492243 0.842790093 0.931155954 6

d 0.437680343 0.52812803 0.796052192 w1 0.762731031 0.334447637 0.678915225 w2 0.718290285 0.561090065 0.466600706 w3 0.505059896 0.561090065 0.672139332 w4 0.505266919 0.561284221 0.67168562 w5 0.627564437 0.520709695 0.586276876 w6 0.544437955 0.646333007 0.54426691 w7 0.727906592 0.638643459 0.391579044 w8

Compensarea Unghiurilor Stabilirea numrului ecuaiilor de condiier = -2p+4=24-(2*10)+4=8 unde : r - numarul total de ecuatii de conditii p - numarul total de puncte din retea - numarul total de unghiuri masurate in reteaua geodezica w1 = l1-p1+1=17-10+1=8 unde : w1 - numarul conditiilor geometrice de figura l1 - numarul laturilor cu viza dubla 3

p1 - numarul punctelor stationabile w2 = 0 ecuatii de punct central S = l-2p+3=17-(2*24)+3=0 unde: s - numarul conditiilor de laturi l - numarul total de laturi din retea p - numarul total de puncte din retea

Conditia de baza:r = w1+w2+S 8=8+0+0 nb = Nb-1 nb = 2-1=1 unde: nb - numarul conditiilor de baze Nb - numarul bazelor masurate sau cele calculate din coordinate n = N-1 n = 2-1=1 unde: n - numarul conditiilor de orientari N - numarul orientarilor

Stabilirea conditiilor geometrice:

(1^) - valoarea cea mai probabila a unghiului 1^ - valoarea unghiului masurat

(1^)+(2^)+(3^)=200g (4^)+(5^)+(6^)=200 (7^)+(8^)+(9^)=200g g

(1^)=1^+v1 (2^)=2^+v2 (3^)=3^+v3 (4^)=4^+v4 (5^)=5^+v5 (6^)=6^+v6 (7^)=7^+v7 (8^)=8^+v8g g g

(9^)=9^+v9 (10^)=10^+v10 (11^)=11^+v11 (12^)=12^+v12 (13^)=13^+v13 (14^)=14^+v14 (15^)=15^+v15 (16^)=16^+v16

(10^)+(11^)+(12^)=200g (13^)+(14^)+(15^)=200 (16^)+(17^)+(18^)=200 (19^)+(20^)+(21^)=200

(22^)+(23^)+(24^)=200g

4

Sistemul ecuatiilor de erori:v1+v2+v3+1^+2^+3^-200g=0 v4+v5+v6+4^+5^+6^-200g=0 v7+v8+v9+7^+8^+9^-200g=0 v10+v11+v12+10^+11^+12^-200g=0 v13+v14+v15+13^+14^+15^-200g=0 v16+v17+v18+16^+17^+18^-200g=0 v19+v20+v21+19^+20^+21^-200g=0 v22+v23+v24+22^+23^+24^-200g=0

v1+v2+v3+w1=0 v4+v5+v6+w2=0 v7+v8+v9+w3=0 v10+v11+v12+w4=0 v13+v14+v15+w5=0 v16+v17+v18+w6=0 v19+v20+v21+w7=0 v22+v23+v24+w8=0 d1*v1-d3*v3+dv*v5-d6*v6+d9*v9-d8*v8+d11*v11-d12*v12+d15*v15-d17*v17-d18*v18+d21*v21-d20*v20+d23*v23d24*v24+w9=0 unde: w1=1+2+3 - 200 w2=4+5+6 - 200 w3=7+8+9 - 200 w4=10+11+12 - 200 w5=13+14+15 - 200 w6=16+17+18 - 200 w7=19+20+21 - 200 w8=22+23+24 - 200w9 = cc (1 P2 ) P1

unde: P1=DA-B *sin (1^)*sin (5^)*sin (9^)*sin (11^)*sin (15^)*sin (17^)*sin (21^)*sin (23^) P2=DC-D *sin (2^)*sin (6^)*sin (8^)*sin (12^)*sin (14^)*sin (18^)*sin (20^)*sin (24^) cc=636620 d1=ctg 1 d2=ctg 2 d3=ctg 3 5

d4=ctg 4 .. d23=ctg 23 d24=ctg 24 Pentru rezolvarea sistemului de 10 ecuaii cu 24 de necunoscute se pune condiia; ca [vv] sa fie egal cu minim i astfel se ajunge la sistemul normal de ecuaii de forma: [aa]k1+[ab]k2+[ac]k3+[ad]k4+[ae]k5+[af]k6+[ag]k7+[ah]k8+[ai]k9+w1 = 0 [bb]k2+[bc]k3+[bd]k4+[be]k5+[bf]k6+[bg]k7+[bh]k8+[bi]k9+w2 = 0 [cc]k3+[cd]k4+[ce]k5+[cf]k6+[cg]k7+[ch]k8+[ci]k9+w3 = 0 [dd]k4+[de]k5+[df]k6+[dg]k7+[dh]k8+[dh]k9+w4 = 0 [ee]k5+[ef]k6+[eg]k7+[eh]k8+[ei]k9+w5 = 0 [ff]k6+[fg]k7+[fh]k8+[fi]k9+w6 = 0 [gg]k7+[gh]k8+[gi]k9+w7 = 0 [hh]k8+[hi]k9+w8= 0 [ii]k9+w9= 0

6

Tabelul coeficientilor ecuatiilor normale:a 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 e 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 f 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 g 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 h 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 i 0.437680343 -0.52812803 s 1.4376803 0.471872 1 1 1.3344476 0.3210848 1 0.4389099 1.4666007 1 1.5610901 0.3278607 1 0.4387158 1.6716856 1 1.5207097 0.4137231 1 0.353667 1.5442669 1 1.6386435 0.608421

0.334447637 -0.678915225 -0.561090065 0.466600706 0.561090065 -0.672139332 -0.561284221 0.67168562 0.520709695 -0.586276876 -0.646333007 0.54426691 0.638643459 -0.391579044

7

aa 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3

ab 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

ac 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

ad 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

ae 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

af 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

ag 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

ah 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

ai 0.43768 0.52813 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.09045

as 1.43768 0.471872 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.909552

bb 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3

bc 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

bd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

be 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

bf 0

bg 0

bh 0

bi 0

bs 0

cc 0

cd 0

ce 0

cf 0

cg 0

ch 0

ci 0

cs 0

dd 0

de 0

8

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0.334448 -0.67892 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.34447

0 0 1 1.334448 0.321085 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.655532

0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 -0.56109 0.466601 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.09449

0 0 0 0 0 1 0.43891 1.466601 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.905511

0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 3

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

df 0 0

dg 0 0

dh 0 0

di 0 0

ds 0 0

ee 0 0

ef 0 0

eg 0 0

eh 0 0

ei 0 0

es 0 0

ff 0 0

fg 0 0

fh 0 0

9

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0.56109 -0.67214 0 0 0 0 0 0 0 0 0 0 0 0 -0.11105

0 0 0 0 0 0 0 1 1.56109 0.327861 0 0 0 0 0 0 0 0 0 0 0 0 2.888951

0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 3

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 -0.56128 0.671686 0 0 0 0 0 0 0 0 0 0.110401

0 0 0 0 0 0 0 0 0 0 1 0.438716 1.671686 0 0 0 0 0 0 0 0 0 3.110401

0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 3

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

fi 0 0 0

fs 0 0 0

gg 0 0 0

gh 0 0 0

gi 0 0 0

gs 0 0 0

hh 0 0 0

hi 0 0 0

hs 0 0 0

ii 0.191564 0.278919 0

is 0.629244 -0.24921 0

ss 2.066925 0.222663 1

10

0 0 0 0 0 0 0 0 0 0 0 0 0 0.52071 0.58628 0 0 0 0 0 0 0.06557

0 0 0 0 0 0 0 0 0 0 0 0 1 1.52071 0.413723 0 0 0 0 0 0 2.934433

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 3

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.64633 0.544267 0 0 0 -0.10207

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0.353667 1.544267 0 0 0 2.897934

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 3

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.638643 -0.39158 0.247064

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1.638643 0.608421 3.247064

0 0.111855 0.460926 0 0.314822 0.217716 0 0.314822 0.451771 0 0.31504 0.451162 0 0.271139 0.343721 0 0.417746 0.296226 0 0.407865 0.153334 4.998629

0 0.446303 -0.21799 0 -0.24627 0.684317 0 0.875912 -0.22037 0 -0.24624 1.122847 0 0.791848 -0.24256 0 -0.22859 0.840493 0 1.046509 -0.23824 4.548008 Verif

1 1.78075 0.103095 1 0.192642 2.150918 1 2.437002 0.107493 1 0.192472 2.794533 1 2.312558 0.171167 1 0.12508 2.38476 1 2.685152 0.370176 28.09739 28.09739

Schema Gauss Doolittlea] a] 3 b] 0 c] 0 d] 0 e] 0 f] 0 g] 0 h] 0 i] w] 6 s] 8.90955231 R1 R2 Verificare

11

-1 b[ k1 $ (2.00)

0 3 0 3 -1 2.018454962

0 0 0 0 0 3 0 0 3 -1 2.0050623

0 0 0 0 0 0 0 0 0 0 3 0 0 0 3 -1 2.0059495

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 3 -1 1.9940852

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 3

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

c[

k2

d[

k3

0.0904477 0.0301492 0.3444676 0 0.3444676 0.1148225 0.0944894 0 0 0.0944894 0.0314965 0.1110493 0 0 0 0.1110493 0.0370164 0.1104014 0 0 0 0 0.1104014 0.0368005 0.0655672 0 0 0 0 0 0.0655672

-2 6 0 6 -2 6 0 0 6 -2 6 0 0 0 6 -2 6 0 0 0 0 6 -2 6 0 0 0 0 0 6

-2.9698508 8.65553241 0 8.65553241 -2.8851775 8.90551064 0 0 8.90551064 -2.9685035 8.88895073 0 0 0 8.88895073 -2.9629836 9.1104014 0 0 0 0 9.1104014 -3.0368005 8.93443282 0 0 0 0 0 8.93443282

R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15 R16 R17 R18 R19 R20 R21 R22 R23 R24 R25 R26 R27 R28 R29 R30 R31 R32

-2.97

-2.885

-2.969

-2.963

[e

k4

-3.037

[f

k5

12

[g

k6

-1 2.0035128

0 3 0 0 0 0 0 0 3 -1 2.00546822

0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 -1 1.98676344

0.0218557 0.1020661 0 0 0 0 0 0 0.1020661 0.034022 0.2470644 0 0 0 0 0 0 0 0.2470644 0.0823548 4.9986292 0.0027269 0.0395526 0.0029761 0.0041106 0.0040628 -0.001433 0.0034725 0.0203469

-2 6 0 0 0 0 0 0 6 -2 6 0 0 0 0 0 0 0 6 -2 -0.11048 0.180895 0.688935 0.188979 0.222099 -0.2208 0.131134 0.204132 -0.49413

-2.9781443 8.8979339 0 0 0 0 0 0 8.8979339 -2.965978 9.24706441 0 0 0 0 0 0 0 9.24706441 -3.0823548 4.88814978 0.26861613 0.99385013 0.280492 0.32903716 -0.335267 0.19526852 0.3027258 -0.7615402

R33 R34 R35 R36 R37 R38 R39 R40 R41 R42 R43 R44 R45 R46 R47 R48 R49 R50 R51 R52 R53 R54 R55 R56 R57 R58 R59 R60 R61

-2.978

-2.966

[h

k7

-3.082

[i

k8

13

k9

4.9199476 -1 -0.160726

[v v]

0.790763 -0.16073 -12 -12 -12 -12 -12 -12 -12 -12 -0.1271 -96.1271

6.1613323 -1.2523166

R62 R63

-1.161

14

Calculul coreciilork1 2.0048 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 k2 2.0185 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 k3 2.005 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 k4 2.006 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 k5 1.99 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 k6 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 k7 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 k8 1.99 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0.638643 -0.39158 -0.64633 0.544267 0.52071 -0.58628 -0.56128 0.671686 0.56109 -0.67214 -0.56109 0.466601 0.334448 -0.67892 k9 -0.16073 0.43768 -0.52813 2.0752 -1.92 2.0048 2.0185 2.0722 1.9093 2.0051 1.9149 2.0801 2.0059 2.0961 1.8979 1.9941 1.9039 -2.102 2.0035 2.0872 1.9093 2.0055 1.9016 2.0929 1.9868 2.0894 1.9238 4.3064 3.6863 4.0194 4.0742 4.2941 3.6456 4.0203 3.6668 4.3266 4.0238 4.3938 3.6021 3.9764 3.6247 4.4186 4.0141 4.3564 3.6454 4.0219 3.6160 4.3804 3.9472 4.3656 3.7011 96.1271 6 6 6 6 6 6 6 6 -0.11 -12.0291 -12.1107 -12.0304 -12.0357 -11.9645 -12.0211 -12.0328 -11.9206 0.0178 vi vv w kw

-96.1271

15

Compensarea unghiurilorTriunghi 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 unghi masurat 73.7355 69.0669 57.1982 200.001 58.5179 79.4529 62.0298 200.001 60.3452 67.4485 72.2069 200.001 70.2261 67.4485 62.326 200.001 70.2156 67.4391 62.3459 200.001 64.3212 69.4373 66.2421 200.001 68.2605 63.4712 68.2689 200.001 59.9432 63.8177 76.2397 200.001 vi -0.0002 -0.0002 -0.0002 -0.0006 -0.0002 -0.0002 -0.0002 -0.0006 -0.0002 -0.0002 -0.0002 -0.0006 -0.0002 -0.0002 -0.0002 -0.0006 -0.0002 -0.0002 -0.0002 -0.0006 -0.0002 -0.0002 -0.0002 -0.0006 -0.0002 -0.0002 -0.0002 -0.0006 -0.0002 -0.0002 -0.0002 -0.0006 unghi compensat 73.7353 69.0667 57.1980 200.0000 58.5177 79.4527 62.0296 200.0000 60.3450 67.4483 72.2067 200.0000 70.2259 67.4483 62.3258 200.0000 70.2154 67.4389 62.3457 200.0000 64.3210 69.4371 66.2419 200.0000 68.2603 63.4710 68.2687 200.0000 59.9430 63.8175 76.2395 200.0000 sin 0.92 0.88 0.78 0.8 0.95 0.83 0.81 0.87 0.91 0.89 0.87 0.83 0.89 0.87 0.83 0.85 0.89 0.86 0.88 0.84 0.88 0.81 0.84 0.93

2

3

4

5

6

7

8

16

Calculul distantelor

D A-B

2260.4478

DA B =

( X B X A ) 2 + (YB YA ) 2

D B-1 2341.8410 1. in triunghiiul AB1 avem:

D AB D D = A1 = B 1 = K 1 sin 2 sin 3 sin 1>>

DB 1 =

D A B *sin 1 sin 2

D 1-2 2684.4034 2. in triungiul B12 avem:

D B 1 D D = B 2 = 2 1 = K 2 sin 6 sin 4 sin 5>>

D1 2 =

DB 1 *sin 5 sin 6

D 2-3 2789.3840 3. in triunghiul 123 avem:

D D D1 2 = 2 3 = 13 = K 3 sin 8 sin 9 sin 7>>

D2 3 =

D1 2 *sin 9 sin 8


D23 D D = 2 4 = 3 4 = K 4 sin 12 sin 10 sin 11>>

D3 4 =

D2 3 *sin 11 sin 12 D3 4 * s in15 s in14


D 3 4 D D = 4 5 = 35 = K 5 sin 14 sin 15 sin 13>>

D4 5 =


D4 5 D D 6 = 4 6 = 5 >> = K 7 sin 18 sin 16 sin 17 D5 6 D D = 5C = 6 C = K8 sin 20 sin 19 sin 21>>

D5 6 =

D4 5 *sin 17 sin 18

D 6-C 3000.2143 7. in triunghiul 56C avem:

Verificare

D6 C =D6 C D D = 6 D = C D = K8 sin 24 sin 22 sin 23>>

D5 6 *sin 21 sin 20

D C-D 2715.4942 8. in triunghiul 6CD avem:

DC D =

D6 C *sin 23 sin 24

17

Calculul orientarilor AB B1 12 23 34 45 56 6C CD 26.4736 169.2756 27.7933 167.4483 37.6742 167.4588 31.7798 163.5195 23.4625 cos 0.914774515 0.885783347 0.906204471 0.872099197 0.829945956 0.872179883 0.877967499 0.840259978 0.932851182 sin 0.40396483 0.46409898 0.42283975 0.48932912 0.5578438 0.48918529 0.47872024 0.5421837 0.36026195

Calculul Coordonatelor definitive X1=XB+DB-1*Cos B-1 Y1=YB+DB-1*Sin B-1 X2=X1+D1-2*Cos 1-2 Y2=Y1+D1-2*Sin 1-2 X3=X2+D2-3*Cos 2-3 Y3=Y2+D2-3*Sin 2-3 X4=X3+D3-4*Cos 3-4 Y4=Y3+D3-4*Sin 3-4 X5=X4+D4-5*Cos 4-5 Y5=Y4+D4-5*Sin 4-5 X6=X5+D5-6*Cos 5-6 Y6=Y5+D5-6*Sin 5-6 XC=X6+D6-C*Cos 6-CYC=Y6+D6-C*Sin 6-CP1 P2 P3 P4 P5 P6 Verif C x y x y x y x y x y x y x y 584706 395564.1 587138.6 396699.2 584706 398064.1 587138.6 399699.2 584705 401064.1 587223.7 402437.4 584702.7 404064.1

18

INCADRAREA RETELEI GEODEZICE PRIN INTERSECTIE MULTIPLA COMBINATAIncadrarea punctelor P1 si P2

z + l AB = V AB Scrierea1ecuatiilor de erori : c x + d y z + l AP 1 P1 2 AP 1 = V AP 1 AP 1 P1 A a AP 1 x P1 + b AP 1 y P1 z1 + l AP 1 = V AP1 z1 + l AD = V AD

a x + d y z + l = V C P1 P1 C P1 P1 3 C P1 C P1 C cC P2 x P 2 + d C P2 y P 2 z 3 + lC P2 = VC P2 zz3 ++ llC B == VV B 4 B C CB C

z 2 + l B C = VB C B a B P1 x P1 + bB P1 y P1 z 2 + l B P1 = VB P1 z 23 ++ l B C == VBA C A AA

D c D P2 x P 2 + d D P2 y P 2 z 4 + l D P2 = VD P2 = A aP1A xP1 + bP1A yP1 z5 +z 4lP+1Al D AV=P1VD A P1 aP1B xP1 + d P1B yP1 z5 + lP1B = VP1B a x + d y z + l = V cP12D xPP12 + d PP12D yPP21 z65 + lPP21BD = VPP21BD P B B P2 cP 2C xP 2 + d P 2C yP 2 z6 + lP 2C = VP 2C P1: a x +b y +c x +d cP 2D xP 2 + d P 2 D yP 2 z6 + lP 2D = VP 2DP1 P 2 P1 P1 P 2 P1 P1 P 2 P2

P1 P 2

5 +l P1P 2 =VP1P 2 z

P 2 : a P 2 P1 P 2 +bP 2 P1 P 2 +c P 2 P1 P1 +d P 2 P1 6 +l P 2 P1 =VP 2 P1 x y x z

19

Schita retelei de triangulaie necesare ridicarii

P2 B

P4

P6

D

P1

P3

P5

C

Schita retelei de triangulatie

Ca etape de rezolvare a interseciei multiple se parcurg:1.

determinarea coordonatelor provizorii a punctului P0

2. calculul coeficienilor de direcie 3. calculul termenilor liberi 4. calculul coeficienilor ecuaiilor normale 5. rezolvarea sistemului normal de ecuaii determinarea valorilor cele mai probabile ale coordonatelor Coordonatele punctelor78.3444 119.5394 x 584713 586780 584703 587236 51.8708 106.9342 52.2477 109.4143 26.4736 23.4625 223.463 y 393564.1 394477.3 404064.1 405042.4 275.7102 314.0482 tg AP1 tg BP1 tg DP2 tg CP2 sinus 0.044368 -0.04954 0.039142 -0.06997 cosinus 0.99902 0.99877 0.99923 0.99755

A B C D

Unghiuri masurate= = = = AB CD DC

2.82547914 3.15517069 2.49250613 4.45787365

YS1= XS1= YS2= XS2=

397077.833 585956.093 400641.929 585470.406

Calculul coeficientilor de directietg ctg 0.4416 2.2645 26.4736 2.8255 0.3539 78.3444 9.3388 0.1071 93.2090 1073.3989 -0.0009 100.0593 23.1909 0.0431 97.2566 -3.1552 -0.3169 119.5394 0.4416 2.2645 226.4736 0.3862 2.5894 223.4624 2.4925 0.4012 275.7102 6.2233 0.1607 289.8571 23.1909 0.0431 297.2566 0.3862 2.5894 23.4624 1073.3989 -0.0009 sin q cos q 0.4040 0.9148 0.9427 0.3336 0.9943 0.1065 D=x/cos q D=y/sin q D=sqrt(x+y) 2260.4478 2260.4478 2260.4478 3727.2772 3727.2772 3727.2772 7118.2616 7118.2616 7118.2616 10499.9930 10499.9930 10499.9930 10574.9486 10574.9486 10574.9486 2728.0512 2728.0512 2728.0512 2260.4478 2260.4478 2260.4478 2715.4942 2715.4942 2715.4942 4741.4220 4741.4220 4741.4220 8066.7364 8066.7364 8066.7364 10574.9486 10574.9486 10574.9486 2715.4942 2715.4942 2715.4942 10499.9930 10499.9930 a b -1.1377 2.5763 -1.6101 0.5699 -0.8893 0.0952 Control a/b=-tg b/a=-ctg -0.4416 -2.2645 -2.8255 -0.3539 -9.3388 -0.1071 Numar viza

Punct A B A S1 A S2 A C B D B S1 B A D C D S2 D S1 D B C D C A

X 584712.52 586780.32 2067.80 584712.52 585956.09 1243.58 584712.52 585470.41 757.89 584712.52 584702.73 -9.78 586780.32 587235.89 455.57 586780.32 585956.09 -824.22 586780.32 584712.52 -2067.80 587235.89 584702.73 -2533.15 587235.89 585470.41 -1765.48 587235.89 585956.09 -1279.79 587235.89 586780.32 -455.57 584702.73 587235.89 2533.15 584702.73 584712.52

Y 393564.13 394477.27 913.14 393564.13 397077.83 3513.70 393564.13 400641.93 7077.80 393564.13 404064.12 10499.99 394477.27 405042.40 10565.13 394477.27 397077.83 2600.56 394477.27 393564.13 -913.14 405042.40 404064.12 -978.28 405042.40 400641.93 -4400.47 405042.40 397077.83 -7964.57 405042.40 394477.27 -10565.13 404064.12 405042.40 978.28 404064.12 393564.13

1

2

3

1.0000 0.0009 0.9991 0.0431 0.9533 0.3021 0.4040 0.9148 0.3603 0.9329 0.9281 0.3724 0.9873 0.1587 0.9991 0.0431 0.3603 0.9329 1.0000 0.0009

-0.6063 -0.0006 -0.6014 0.0259 -2.2246 -0.7050

1073.3989 0.0009 -23.1909 -0.0431 3.1552 0.3169 6 4

5

1.1377 -2.5763

-0.4416 -2.2645 7

0.8446 -2.1870

-0.3862 -2.5894 8

1.2461 -0.4999

-2.4925 -0.4012 9

0.7792 -0.1252

-6.2233 -0.1607 10

0.6014 -0.0259 -0.8446 2.1870

-23.1909 -0.0431 -0.3862 -2.5894 11

12

0.6063 0.0006

1073.3989 0.0009

13

C S2 S1 D S1 S2 S1 A S1 B S2 D S2 C S2 A S2 S1

9.78 584702.73 585470.41 767.67 585956.09 587235.89 1279.79 585956.09 585470.41 -485.69 585956.09 584712.52 -1243.58 585956.09 586780.32 824.22 585470.41 587235.89 1765.48 585470.41 584702.73 -767.67 585470.41 584712.52 -757.89 585470.41 585956.09 485.69

-10499.99 404064.12 400641.93 -3422.19 397077.83 405042.40 7964.57 397077.83 400641.93 3564.10 397077.83 393564.13 -3513.70 397077.83 394477.27 -2600.56 400641.93 405042.40 4400.47 400641.93 404064.12 3422.19 400641.93 393564.13 -7077.80 400641.93 397077.83 -3564.10

300.0593 -4.4579 -0.2243 314.0482 6.2233 0.1607 89.8571 -7.3383 -0.1363 108.6222 2.8255 0.3539 278.3444 -3.1552 -0.3169 319.5394 2.4925 0.4012 75.7102 -4.4579 -0.2243 114.0482 9.3388 0.1071 293.2090 -7.3383 -0.1363 308.6222 0.9758 0.2189 0.9873 0.1587 0.9908 0.1350 0.9427 0.3336 0.9533 0.3021 0.9281 0.3724 0.9758 0.2189 0.9943 0.1065 0.9908 0.1350

10499.9930 3507.2348 3507.2348 3507.2348 8066.7364 8066.7364 8066.7364 3597.0373 3597.0373 3597.0373 3727.2772 3727.2772 3727.2772 2728.0512 2728.0512 2728.0512 4741.4220 4741.4220 4741.4220 3507.2348 3507.2348 3507.2348 7118.2616 7118.2616 7118.2616 3597.0373 3597.0373 3597.0373 1.7711 0.3973 -0.7792 0.1252 -1.7536 -0.2390 4.4579 0.2243 -6.2233 -0.1607 7.3383 0.1363 16

14

15

1.6101 -0.5699

-2.8255 -0.3539 17

2.2246 0.7050 -1.2461 0.4999 -1.7711 -0.3973

3.1552 0.3169 -2.4925 -0.4012 4.4579 0.2243

18

19

20

0.8893 -0.0952

-9.3388 -0.1071 21

1.7536 0.2390

7.3383 0.1363

22

Calculul termenilor liberiPunct Statie Viza Numar viza S1 a b c S2 d l

A

B S1 S2 C

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

-1.610134

0.5699 0.8892639 0.095222

-1.5000 0.5000 2.5000 -1.5000 0.0000 1.0000 3.0000 2.0000 0.0000 1.0000 2.0000 3.0000 1.0000 0.0000 2.0000 1.0000 -3.0000 0.0000 4.0000 -4.0000 -1.0000 2.0000 0.0000 -2.0000 -1.0000 -4.0000 3.0000 0.0000

[ ] B [ ] D C S2 S1 B D A S2 D S2 A B 1.2461272 0.7791962 -0.125 -0.49995 D S1 A -2.224551 -0.705

[ ] C [ ] P1 -0.779196 -1.753638 1.6101338 2.2245512 0.1252 -0.239 -0.57 0.705 1.7536377 0.238972

1.7711466

0.397308

[ ] D P2 C A S1 [ ] 19 20 21 22 1.7536377 0.239 1.2461272 1.7711466 0.8892639 1.7536377 0.49995 0.397308 0.095222 0.238972

Punct Statie B S1 S2

Viza

Numar viza 1 2 3

ic26.4736 78.3444 93.2090

ri14.3210 66.1920 81.0568

zi = ic-ri12.1526 12.1524 12.1522

z m={zi}/n12.15245

im=zm+ri26.4735 78.3445 93.2092

li=-(mc)0.0002 0.0001 0.0003

A

C [ ] B [ ] D C S2 S1 B [ ] C D A S2 [ ] D P1 S2 A B [ ] D P2 C A S1 [ ] D S1 A

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

100.0593 97.2566 119.5394 226.4736 223.4624 275.7102 289.8571 297.2566 23.4624 300.0593 314.0482 89.8571 108.6222 278.3444 319.5394

87.9067 87.0045 109.2875 216.2216 210.2093 297.7418 290.6241 291.7035 13.1057 289.7025 303.6910 71.6981 90.4624 260.1849 301.3802

12.1526 48.6098 10.2521 10.2519 10.2520 13.2531 -22.0316 -0.7669 5.5531 10.3567 10.3568 10.3572 18.1590 18.1598 18.1595 18.1592

100.0592 97.2567 119.5397 226.4738 223.4625 310.9950 303.8773 304.9567 23.4626 300.0594 314.0479 89.8575 18.1594 108.6218 278.3443 319.5396

10.2522

13.25

10.3569

19 20 21 22

75.7102 114.0482 293.2090 308.6222

55.1611 93.4992 272.6597 288.0736

20.5491 20.5490 20.5493 20.5486 20.5489

75.7100 114.0481 293.2086 308.6225

0.0001 0.0000 0.0001 0.0003 0.0002 0.0000 0.0001 0.0002 0.0003 0.0001 0.0000 0.0002 0.0001 0.0003 0.0000 0.0004 0.0004 0.0001 0.0002 0.0000 0.0002 0.0001 0.0004 0.0003 0.0000

PunctA B S1 S2 C B D S1

x584712.515 586780.315 585956.093 585470.406 584702.733 586780.315 587235.887 585956.093

y393564.130 394477.271 397077.833 400641.929 404064.118 394477.271 405042.402 397077.833

x2067.800 1243.578 757.891 -9.782 455.572 -824.222

y913.141 3513.703 7077.800 10499.988 10565.131 2600.562

ic26.4736 78.3444 93.2090 100.0593 97.2566 119.5394

ri12.1523 14.3210 66.1920 81.0568 87.9067 10.2522 87.0045 109.2875

A D C S2 S1 B C D A S2 S1 D S2 A B S2 D C A S1

584712.515 587235.887 584702.733 585470.406 585956.093 586780.315 584702.733 587235.887 584712.515 585470.406 585956.093 587235.887 585470.406 584712.515 586780.315 585470.406 587235.887 584702.733 584712.515 585956.093

393564.130 405042.402 404064.118 400641.929 397077.833 394477.271 404064.118 405042.402 393564.130 400641.929 397077.833 405042.402 400641.929 393564.130 394477.271 400641.929 405042.402 404064.118 393564.130 397077.833

2067.800 2533.154 767.673 485.687 824.222 2533.154 9.782 767.673 1279.794 -485.687 1243.578 824.222 1765.481 -767.673 -757.891 485.687

-913.141

226.4736

216.2216 13.2532

-978.284 -4400.473 -7964.569 10565.131 978.284 10499.988 -3422.189 7964.569 3564.097 -3513.703 -2600.562 4400.473 3422.189 -7077.800 -3564.097

223.4624 310.9953 303.8774 304.9565 23.4624 300.0593 314.0482 89.8571 108.6222 278.3444 319.5394 75.7102 114.0482 293.2090 308.6222

210.2093 297.7418 290.6241 291.7035 10.3569 13.1057 289.7025 303.6910 18.1594 71.6981 90.4624 260.1849 301.3802 20.5489 55.1611 93.4992 272.6597 288.0736

Tabel de coeficientiNumar crt. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 a 0 1.61013376 0 0 0 2.22455117 0 0 0 0.77919622 0 0 0 0 0.77919622 1.75363774 1.61013376 2.22455117 0 0 0 1.75363774 b 0 0.569862199 0 0 0 0.705049389 0 0 0 0.125205867 0 0 0 0 0.125205867 0.238971902 0.569862199 0.705049389 0 0 0 0.238971902 c 0 0 0.88926389 0 0 0 0 0 1.2461272 0 0 0 0 1.77114664 0 1.75363774 0 0 -1.2461272 1.77114664 0.88926389 1.75363774 d 0 0 0.09522238 0 0 0 0 0 -0.4999495 0 0 0 0 0.3973075 0 0.2389719 0 0 0.4999495 -0.3973075 -0.0952224 -0.2389719 l -1.5000 0.5000 2.5000 -1.5000 1.0000 3.0000 2.0000 1.0000 2.0000 3.0000 1.0000 2.0000 1.0000 -3.0000 4.0000 -4.0000 -1.0000 2.0000 -2.0000 -1.0000 -4.0000 3.0000 s -1.5000 -0.5403 1.7060 -1.5000 1.0000 0.0704 2.0000 1.0000 2.7462 3.6540 1.0000 2.0000 1.0000 -0.8315 3.3460 -4.0000 0.0403 4.9296 -2.7462 -3.1685 -3.2060 3.0000 19.37185606 aa 0 2.592530712 0 0 0 4.948627908 0 0 0 0.607146747 0 0 0 0 0.607146747 3.075245328 2.592530712 4.948627908 0 0 0 ab 0 0.91755436 0 0 0 1.56841844 0 0 0 0.09755994 0 0 0 0 0.09755994 0.41907015 0.91755436 1.56841844 0 0 0 0.41907015 1.94474857 ac 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.0752453 0 0 0 0 0 3.0752453 6.1504907 ad 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.41907 0 0 0 0 0 0.41907 0.83814 al 0 -0.8050669 0 0 0 -6.6736535 0 0 0 2.33758866 0 0 0 0 -3.1167849 7.01455097 -1.6101338 4.44910234 0 0 0 5.26091322 6.85651617

as 0 0.8699 0 0 0 -0.157 0 0 0 2.8472 0 0 0 0 -2.607 7.0146 0.0648 10.966 0 0 0 5.2609 24.26

bb 0 0.3247 0 0 0 0.4971 0 0 0 0.0157 0 0 0 0 0.0157 0.0571 0.3247 0.4971 0 0 0 0.0571 1.7892

bc 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.41907 0 0 0 0 0 0.41907 0.83814

bd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.05711 0 0 0 0 0 0.05711 0.11422

bl 0 0.28493 0 0 0 -2.1151 0 0 0 -0.3756 0 0 0 0 0.50082 0.95589 0.56986 1.4101 0 0 0 0.71692 1.94775

bs 0 -0.30788 0 0 0 -0.04964 0 0 0 -0.4575 0 0 0 0 0.41894 0.955888 -0.02295 3.475612 0 0 0 0.716916 4.72939

cc 0 0 0.7908 0 0 0 0 0 1.5528 0 0 0 0 3.137 0 3.0752 0 0 1.5528 3.137 0.7908 3.0752 17.112

cd 0 0 -0.0847 0 0 0 0 0 -0.623 0 0 0 0 0.70369 0 0.41907 0 0 -0.623 0.70369 -0.0847 0.41907 0.83016

cl 0 0 2.22316 0 0 0 0 0 2.49225 0 0 0 0 5.31344 0 7.01455 0 0 2.49225 1.77115 3.55706 5.26091 16.6135

cs 0 0 -1.517 0 0 0 0 0 3.42209 0 0 0 0 -1.4728 0 -7.0146 0 0 3.42209 5.6118 -2.8509 -5.2609 -5.6603

dd 0 0 0.00907 0 0 0 0 0 0.24995 0 0 0 0 0.15785 0 0.05711 0 0 0.24995 0.15785 0.00907 0.05711 0.94796

dl 0 0 0.23806 0 0 0 0 0 -0.9999 0 0 0 0 -1.1919 0 -0.9559 0 0 -0.9999 0.39731 0.38089 -0.7169 -3.8483 Verificare

ds 0 0 0.16245 0 0 0 0 0 1.37295 0 0 0 0 0.33038 0 0.95589 0 0 1.37295 1.25885 0.30528 0.71692 3.02251 129.649

ll 2.25 0.25 6.25 2.25 1 9 4 1 4 9 1 4 1 9 16 16 1 4 4 1 16 9 121

ls 2.25 0.27014 4.2649 2.25 1 0.2112 4 1 5.49236 10.962 1 4 1 2.49464 13.384 16 0.04027 9.8592 5.49236 3.16845 12.8238 9 109.343

ss 2.25 0.291893 2.910294 2.25 1 0.004956 4 1 7.541492 13.35165 1 4 1 0.691469 11.19578 16 0.001622 24.30096 7.541492 10.0391 10.27817 9 129.6489

Schema Gauss Doolittlea] 19.3718561 1 3.34576291 b] 1.94474857 0.10039041 1.78924329 19.3718561 21.1610994 1 -3.4393334 c] -6.1504907 -0.3174962 -0.8381403 -6.1252657 -6.963406 -0.3290664 17.1116581 19.3718561 21.1610994 57.6446135 1 [d k3 -1.332443 d] -0.8381403 -0.0432659 -0.1142151 -44.948787 -45.063002 -2.1295208 0.83016298 142.1557 3.26994028 146.255803 2.53719809 0.94795526 19.3718561 21.1610994 57.6446135 99.1255242 1 -2.9365092 l 6.856516167 0.353942139 1.947753089 5.494538122 7.442291211 0.351696813 -16.613464 -17.3771077 -19.7994572 -53.7900288 -0.93313192 -3.84827083 -2.36801499 -128.130254 -156.73647 -291.08301 -2.93650916 121 19.37185606 21.16109935 57.64461348 99.12552416 318.3030931 s 21.1844899 1.09357048 2.78464095 1.77834773 4.56298868 0.21563098 1.32835706 5.62422888 32.2931606 36.5890324 0.63473463 2.90031558 0.76642549 208.982036 230.420393 443.069171 4.46977884

[a [b k1

[c

k2

k4

[V V]

Tabelul coordonatelor finale cu corectiile aplicateXS1 YS1 XS2 YS2 585956.089 397077.829 585470.405 400641.926

VERIFICAREA NIVELITICA A RETELEIVerificarea nivelitic se realizeaz prin nivelment trigonometric la distane mari,aplicnd corecia de sfericitate i refracie

D

H = D tg = D ctg Z

S

Z D hp0A

ip0

HA

N

Ho p

HB = HA + hAB unde: hAB = D*ctg.Z+i-S+C , unde: i nalimea aparatului S nalimea semnalului C corecia de sfericitate i refracieD2 2R

C = (1 k )

unde : k coeficientul de refracie ( k=0,14) R = 6378,975 km (raza medie n punctul central de proiecie) D lungimea vizei

(R =

M *N

)

Calculul cotelor reteleiNr. Punct A P1 P2 P3 P4 P5 P6 C

X 584712.515 584705.951 587138.57 584705.95 587138.567 584705.011 587223.684 584702.733

Y 393564.130 395564.117 396699.189 398064.116 399699.187 401064.112 402437.443 404064.118

z 305.369 304.023 304.235 306.125 306.362 306.333 307.321 304.325

dx -6.564 2432.6 -2433 2432.6 -2434 2518.7 -2521

dy 1999.99 1135.07 1364.93 1635.07 1364.92 1373.33 1626.68

dz -1.346 0.212 1.89 0.237 -0.029 0.988 -2.996

D 2000 2684.4 2789.38 2931.06 2790.2 2868.75 3000.21

i 1.321 1.302 1.362 1.232 1.333 1.325 1.213

S 4.2 3.6 5 3.2 4.3 4.3 5.1

C 0.269636 0.485752 0.524488 0.579118 0.524795 0.554761 0.606768

() 0.00063 0.00075 0.00179 0.00055 0.00086 0.00119 9.5E-05

j 0.0402 0.048 0.1142 0.0353 0.0551 0.0756 0.006

z' 99.96 99.952 99.886 99.965 99.945 99.924 99.994

z 99.962 99.954 99.888 99.967 99.947 99.926 99.996

punct statie vizat A P1 P2 P3 P4 P5 P6 [] P1 P2 P3 P4 P5 P6 C

D

Z

i

s

C

Dh'

corectie

Dh

H 305.369 304.2421 304.7481 306.9436 307.5016 307.7782 309.0804 306.413 304.325

punct A P1 P2 P3 P4 P5 P6 C

1999.99818 2684.40342 2789.38397 2931.05507 2790.20001 2868.75455 3000.21127 19064.0065

99.9618 99.954 99.8878 99.9667 99.9469 99.9264 99.996

1.321 1.302 1.362 1.232 1.333 1.325 1.213

4.2 3.6 5 3.2 4.3 4.3 5.1

0.26964 0.48575 0.52449 0.57912 0.52479 0.55476 0.60677 Wh= Ch= T=

-1.4088 0.12767 1.80237 0.14492 -0.1167 0.89788 -3.0903 -2.6869 0.00014 0.87325

0.2818832 0.3783445 0.3931406 0.413108 0.3932556 0.4043272 0.422855 2.686914

-1.12695 0.506011 2.195509 0.558026 0.276599 1.302203 -2.6674

Tabelul cotelor finaleA C P1 P2 P3 P4 P5 P6 305.369 306.413 304.242051 304.748063 306.943572 307.501598 307.778197 309.080399

CUPRINS

STABILIREA REELEI DE RIDICARE...................................................................................................2 LANT DE TRIUNGHIURI.........................................................................................................................2 Rezolvarea retelei din punct de vedere planimetric ............................................................................3 Compensarea Unghiurilor ...................................................................................................................3 Stabilirea numrului ecuaiilor de condiie..........................................................................................3 Conditia de baza:.................................................................................................................................4 Stabilirea conditiilor geometrice:.........................................................................................................4 Sistemul ecuatiilor de erori:.................................................................................................................5 Tabelul coeficientilor ecuatiilor normale:............................................................................................7 Schema Gauss Doolittle.....................................................................................................................11 Calculul coreciilor .........................................................................................................................15 Calculul distantelor............................................................................................................................17 Calculul orientarilor...........................................................................................................................18 INCADRAREA RETELEI GEODEZICE PRIN INTERSECTIE MULTIPLA COMBINATA..............19 Schita retelei de triangulatie..............................................................................................................20 Coordonatele punctelor......................................................................................................................21 Calculul coeficientilor de directie......................................................................................................22 Calculul termenilor liberi ..................................................................................................................23 Tabel de coeficienti............................................................................................................................27 Schema Gauss Doolittle.....................................................................................................................29 Tabelul coordonatelor finale cu corectiile aplicate............................................................................29 VERIFICAREA NIVELITICA A RETELEI............................................................................................30 Calculul cotelor retelei.......................................................................................................................31 Tabelul cotelor finale.........................................................................................................................32

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