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COMPENSAREA DRUMUIRII SPRIJINITE LA CAPETE PE PUNCTE DE COORDONATE CUNOSCUTE

ȘI LATURI CU ORIENTĂRI CUNOSCUTE Se dau:

1. Inventar de coordonate puncte vechi;

2. Măsurători de teren: lungimi înclinate măsurate dus întors, unghiuri zenitale în cele două poziții ale lunetei, direcții orizontale în cele două poziții ale lunetei;

3. Schița drumuirii.

Se cere:

1. Completarea și prelucrarea carnetului de teren;

2. Calculul și compensarea drumuirii sprijinite la capete pe puncte de coordonate cunoscute și laturi cu orientări cunoscute;

3. Calculul coordonatelor punctelor radiate;

4. Să se prezinte la scara 1:1000 punctele de drumuire și punctele radiate;

5. Să se întocmească profilul topografic prin punctele de drumuire, scara lungimilor 1:1000, scara înălțimilor 1:100.

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1. INVENTAR DE COORDONATE PUNCTE VECHI:

Nr. punct X [m] Y [m] H [m] 1 1244,388 7913,383 150,432 2 1137,484 7954,687 150,500 3 1372,142 8185,265 150,196 4 1509,047 8167,262 150,450

2. MĂSURĂTORI DE TEREN: PS PV L [m] Z (poziția I) Z (poziția II) Dir. (poziția I) Dir. (poziția II)

1 2 253 55 72 53 55 62 11 128,563 100 24 47 299 75 31 159 63 36 359 63 50 2 253 55 66 53 55 85

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1 128,567 99 75 39 300 24 74 71 42 70 271 42 74 12 61,897 100 38 36 299 61 73 218 74 00 18 73 78 1 71 42 85 271 42 99

111 st. el. 17,312 98 58 41 152 43 70 112 c. apa. 15,430 99 91 75 253 97 50 113 st. el. 10,866 101 10 74 355 74 42

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11 61,894 99 61 02 300 39 03 217 95 54 17 95 59 13 31,341 100 51 80 299 48 25 382 88 70 182 88 74 11 217 95 49 17 95 32

121 c. can 15,658 95 93 55 283 13 28 122 c gaz 6,439 94 98 21 89 96 72

13 12 31,348 99 49 23 300 50 62 67 26 06 267 26 20 14 83,511 99 79 19 300 20 66 378 32 80 178 33 00 13 67 26 15 267 26 48

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13 83,503 100 20 43 299 79 78 172 29 60 372 29 77 3 42,026 99 05 93 300 94 28 344 19 30 144 19 63 13 172 29 73 372 29 87

141 lampadar 18,208 97 25 45 194 55 04 142 hidrant 24,261 98 02 38 318 77 84 143 gaigar 24,807 97 94 92 17 03 72

144 c. telefon 21,221 96 23 59 107 09 38

3 14 42,019 100 95 30 299 04 58 183 01 84 383 02 08 4 296 87 06 96 87 26 14 183 01 77 383 01 66

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3. SCHIȚA DRUMUIRII:

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1) Calculul distanțelor orizontale: D → = L → · cosα → = 128,563 · cos (−0 24 63 ) = 128,563 · 0,999993 = 128,562 D → = L → · cosα → = 61,897 · cos (−0 38 66 ) = 61,897 · 0,999982 = 61,896 D → = L → · cosα → = 31,341 · cos (−0 51 23 ) = 31,341 · 0,999968 = 31,340 D → = L → · cosα → = 83,511 · cos (0 20 53 ) = 83,511 · 0,999995 = 83,511 D → = L → · cosα → = 42,26 · cos (0 94 32 ) = 42,26 · 0,999890 = 42,26 2) Calculul orientărilor și distanțelor laturilor de sprijin:

θ = arctan∆푌∆푋 = arctan

7954,687− 7913,3831137,484− 1244,388 = arctan

41,304−106,904 = arctan (−0,386) =

= −23 , 4720 = −23 47 20 = 200 −23 47 20 = 176 52 80

θ = arctan ∆푌∆푋 = arctan

8167,262− 8185,2651509,047− 1372,142 = arctan

−18,003136,905 = arctan (−0,132) =

= −8 , 3531 = 400 − 8 35 51 = 391 64 49

D = ∆푋 + ∆푌 = (−106,904) + (41,304) = 11428.465 + 1706,020 = = 13134,485 = 114,606

D = ∆푋 + ∆푌 = (136,905) + (−18,003) = 18742.979 + 324,080 = = 19067,059 = 138,084 3) Calculul unghiului de frângere ω: 휑 = 푑푖푟 → − 푑푖푟 → = 253 55 67 − 159 63 39 = 93 92 28 휔 = 400 − 휑 = 400 − 93 92 28 = 306 07 72 휔 = 푑푖푟 → − 푑푖푟 → = 218 73 79 − 71 42 72 = 147 31 07 휔 = 푑푖푟 → − 푑푖푟 → = 382 88 89 − 217 95 75 = 164 93 14

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휑 = 푑푖푟 → − 푑푖푟 → = 67 26 13 − 378 32 81 + 400 = −311 06 68 + 400 = = 88 93 32 휔 = 400 −휑 = 400 − 88 93 32 = 311 06 68 휔 = 푑푖푟 → − 푑푖푟 → = 344 19 41 − 172 29 69 = 171 89 72 휔 = 푑푖푟 → − 푑푖푟 → = 296 87 28 − 183 01 96 = 113 85 32 4) Calculul orientărilor provizorii sau transmiterea orientărilor: θ → = θ + 휔 − 400 = 176 52 80 + 306 07 72 − 400 = 82 60 52 θ → = θ → + 휔 = (θ → ± 200 ) + 휔 = 82 60 52 + 200 + 147 31 07 = = 429 91 59 − 400 = 29 91 59 θ → = θ → + 휔 = (θ → ± 200 ) + 휔 = 29 91 59 + 200 + 164 93 14 = = 394 84 73 θ → = θ → + 휔 = (θ → ± 200 ) + 휔 = 394 84 73 − 200 + 311 06 68 = = 505 91 41 − 400 = 105 91 41 θ → = θ → + 휔 = (θ → ± 200 ) + 휔 = 105 91 41 + 200 + 171 89 72 = = 477 81 13 − 400 = 77 81 13 θ → = θ → + 휔 = (θ → ± 200 ) + 휔 = 77 81 13 + 200 + 113 85 32 = = 391 66 45 5) Calculul corecțiilor pentru orientări: e = V − V = θ

→− θ = 391 66 45 − 391 64 49 = 1 96

c = −e = −1 96

q =cn =

−1 966 = −0 , 326 = −32 , 6

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6) Compensarea orientărilor: θ → = θ → + 1 · q = 82 60 52 −33 = 82 60 19 θ → = θ → + 2 · q = 29 91 59 −65 = 29 90 94 θ → = θ → + 3 · q = 394 84 73 −98 = 394 83 75 θ → = θ → + 4 · q = 105 91 41 − 1 30 = 105 90 11 θ → = θ → + 5 · q = 77 81 13 − 1 63 = 77 79 50 θ → = θ → + 6 · q = 391 66 45 − 1 96 = 391 64 49 = θ 7) Calculul creșterilor de coordonate provizorii: δ → = L → · cosθ → = 128,563 · cos 82 60 19 = 128,563 · 0,269900 = 34,699 δ

→= L → · sinθ → = 128,563 · sin 82 60 19 = 128,563 · 0,962889 = 123,792

δ → = D → · tan α → = 128,562 · tan(−00 24 63 ) = 128,562 · (−0,003868) = −0,497 δ → = L → · cos θ → = 61,897 · cos 29 90 94 = 61,897 · 0,891652 = 55,191 δ

→= L → · sin θ → = 61,897 · sin 29 90 94 = 61,897 · 0,452722 = 28,022

δ → = D → · tan α → = 61,896 · tan (−00 38 66 ) = 61,896 · (0,006073) = −0,376 δ → = L → · cos θ → = 31,341 · cos 394 83 75 = 31,341 · 0,996714 = 31,238 δ

→= L → · sin θ → = 31,341 · sin 394 83 75 = 31,341 · (−0,081004) = −2,539

δ → = D → · tan α → = 31,340 · tan (−0 51 23 ) = 31,340 · (−0,008048) = −0,252 δ → = L → · cos θ → = 83,511 · cos 105 90 11 = 83,511 · (−0,092561) = −7,730 δ

→= L → · sin θ → = 83,511 · sin 105 90 11 = 83,511 · 0,995707 = 83,153

δ → = D → · tan α → = 83,511 · tan 0 20 53 = 83,511 · 0,003225 = 0,269

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δ → = L → · cosθ → = 42,26 · cos 77 79 50 = 42,26 · 0,341766 = 14,443 δ

→= L → · sinθ → = 42,26 · sin 77 79 50 = 42,26 · 0,939785 = 39,715

δ → = D → · tan α → = 42,26 · tan 0 94 32 = 42,26 · 0,014816 = 0,626 8) Calculul corecțiilor pentru creșterile de coordonate: e = V − V = δ − (x − x ) = = δ → + δ → + δ → + δ → + δ → − (x − x ) = = 34,699 + 55,191 + 31,238− 7,730 + 14,443− (1372,142− 1244,388) = = 127,841− 127,754 = 0,087 e = V − V = δ − (y − y ) = = δ

→+ δ

→+ δ

→+ δ

→+ δ

→− (y − y ) =

= 123,792 + 28,022− 2,539 + 83,153 + 39,715− (8185,265− 7913,383) = = 272,143− 271,882 = 0,261 e = V − V = δ − (H − H ) = = δ → + δ → + δ → + δ → + δ → − (H − H ) = = −0,497− 0,376− 0,252 + 0,269 + 0,626− (150,196− 150,432) = = −0,23 + 0,236 = 0,006 D → = D → + D → + D → + D → + D → = = 128,562 + 61,896 + 31,340 + 83,511 + 42,26 = 347,569

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e , = e + e = 0,087 + 0,261 = 0,007569 + 0,068121 = 0,07569 ≈ 0,275

T , = ±30 cm e , < T , e = 0,006

T = ±0,2 D [ ] = ±0,2 0,347569 ≈ ±0,2 · 0,590 = ±0,118

e < T c = −e = −0,087 c = −e = −0,261 c = −e = −0,006

K =c∑D =

−0,087347,569 = −0,000250

K =c∑D =

−0,261347,569 = −0,000751

K =c∑D =

−0,006347,569 = −0,000017

9) Compensarea creșterilor de coordonate: δ → = δ → + K · D → = 34,699− 0,032 = 34,667 K · D → = (−0,000250) · 128,562 = −0,032 δ

→= δ

→+ K · D → = 123,792− 0,097 = 123,695

K · D → = (−0,000751) · 128,562 = −0,097 δ → = δ → + K · D → = −0,497 − 0,002 = −0,499 K · D → = (−0,000017) · 128,562 = −0,002

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δ → = δ → + K · D → = 55,191− 0,016 = 55,175 K · D → = (−0,000250) · 61,896 = −0,016 δ

→= δ

→+ K · D → = 28,022− 0,047 = 27,975

K · D → = (−0,000751) · 61,896 = −0,047 δ → = δ → + K · D → = −0,376− 0,001 = −0,377 K · D → = (−0,000017) · 61,896 = −0,001 δ → = δ → + K · D → = 31,238− 0,008 = 31,230 K · D → = (−0,000250) · 31,340 = −0,008 δ

→= δ

→+ K · D → = −2,539− 0,024 = −2,563

K · D → = (−0,000751) · 31,340 = −0,024 δ → = δ → + K · D → = −0,252− 0,001 = −0,253 K · D → = (−0,000017) · 31,340 = −0,001 δ → = δ → + K · D → = −7,730− 0,021 = −7,751 K · D → = (−0,000250) · 83,511 = −0,021 δ

→= δ

→+ K · D → = 83,153− 0,062 = 83,091

K · D → = (−0,000751) · 83,511 = −0,062 δ → = δ → + K · D → = 0,269− 0,001 = 0,268 K · D → = (−0,000017) · 83,511 = −0,001 δ → = δ → + K · D → = 14,443− 0,010 = 14,433 K · D → = (−0,000250) · 42,26 = −0,010 δ

→= δ

→+ K · D → = 39,715− 0,031 = 39,684

K · D → = (−0,000751) · 42,26 = −0,031 δ → = δ → + K · D → = 0,626− 0,001 = 0,625 K · D → = (−0,000017) · 42,26 = −0,001

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10) Calculul coordonatelor absolute: x = x + δ → = 1244,388 + 34,667 = 1279,055 y = y + δ

→= 7913,383 + 123,695 = 8037,078

H = H + δ → = 150,432− 0,499 = 149,933 x = x + δ → = 1279,055 + 55,175 = 1334,230 y = y + δ

→= 8037,078 + 27,975 = 8065,053

H = H + δ → = 149,933− 0,377 = 149,556 x = x + δ → = 1334,230 + 31,230 = 1365,460 y = y + δ

→= 8065,053− 2,563 = 8062,490

H = H + δ → = 149,556− 0,253 = 149,303 x = x + δ → = 1365,460− 7,751 = 1357,709 y = y + δ

→= 8062,490 + 83,091 = 8145,581

H = H + δ → = 149,303 + 0,268 = 149,571 x = x + δ → = 1357,709 + 14,433 = 1372,142 y = y + δ

→= 8145,581 + 39,684 = 8185,265

H = H + δ → = 149,571 + 0,625 = 150,196

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11) Calculul coordonatelor absolute ale punctelor radiate: x = x + δ → = 1279,055 + 14,560 = 1293,615 y = y + δ

→= 8037,078− 9,365 = 8027,713

H = H + δ → = 149,933 + 0,433 = 150,366 δ → = L → · cosθ → = 17,312 · cos 363 61 17 = 17,312 · 0,841044 = 14,560 δ

→= L → · sinθ → = 17,312 · sin 363 61 17 = 17,312 · (−0,540967) = −9,365

δ → = D → · tanα → = 17,308 · tan 1 41 59 = 17,308 · 0,022244 = 0,385 D → = L → · cosα → = 17,312 · cos 1 41 59 = 17,312 · 0,999753 = 17,308 ω = dir → − dir → = 152 43 70 − 71 42 72 = 81 00 98 θ → = (θ → ± 200 ) + ω = 282 60 19 + 81 00 98 = 363 61 17 x = x + δ → = 1279,055 + 8,031 = 1287,086 y = y + δ

→= 8037,078 + 13,175 = 8050,253

H = H + δ → = 149,933 + 0,020 = 149,953 δ → = L → · cosθ → = 15,430 · cos 65 14 97 = 15,430 · 0,520492 = 8,031 δ

→= L → · sinθ → = 15,430 · sin 65 14 97 = 15,430 · 0,853867 = 13,175

δ → = D → · tanα → = 15,430 · tan 0 08 25 = 15,430 · 0,001296 = 0,020 D → = L → · cosα → = 15,430 · cos 0 08 25 = 15,430 · 0,999999 = 15,430 ω = dir → − dir → = 253 97 50 − 71 42 72 = 182 54 78 θ → = (θ → ± 200 ) + ω = 282 60 19 + 182 54 78 −= = 465 14 97 − 400 = 65 14 97

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x = x + δ → = 1279,055− 9,432 = 1269,623 y = y + δ

→= 8037,078 + 5,396 = 8042,474

H = H + δ → = 149,933− 0,189 = 149,744 δ → = L → · cosθ → = 10,866 · cos 166 91 89 = 10,866 · (−0,867999) = −9,432 δ

→= L → · sinθ → = 10,866 · sin 166 91 89 = 10,866 · 0,496565 = 5,396

δ → = D → · tanα → = 10,864 · tan(−1 10 74 ) = 10,864 · (−0,017397) = −0,189 D → = L → · cosα → = 10,866 · cos(−1 10 74 ) = 10,866 · 0,999849 = 10,864 ω = dir → − dir → = 355 74 42 − 71 42 72 = 284 31 70 θ → = (θ → ± 200 ) + ω = 282 60 19 + 284 31 70 − 400 = = 566 91 89 − 400 = 166 91 89 x = x + δ → = 1334,230− 1,207 = 1333,023 y = y + δ

→= 8065,053− 15,611 = 8049,442

H = H + δ → = 149,556 + 0,999 = 150,555 δ → = L → · cosθ → = 15,658 · cos 295 08 57 = 15,658 · (−0,077117) = −1,207 δ

→= L → · sinθ → = 15,658 · sin 295 08 57 = 15,658 · (−0,997022) = −15.611

δ → = D → · tanα → = 15,626 · tan 4 06 45 = 15,626 · 0,063932 = 0,999 D → = L → · cosα → = 15,658 · cos4 06 45 = 15,658 · 0,997963 = 15,626 ω = dir → − dir → = 283 13 38 − 217 95 75 = 65 17 63 θ → = (θ → ± 200 ) + ω = 229 90 94 + 65 17 63 = 295 08 57

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x = x + δ → = 1334,230− 0,194 = 1334,036 y = y + δ

→= 8065,053 + 6,436 = 8071,489

H = H + δ → = 149,556 + 0,507 = 150,063 δ → = L → · cosθ → = 6,439 · cos 101 91 91 = 6,439 · (−0,030141) = −0,194 δ

→= L → · sinθ → = 6,439 · sin 101 91 91 = 6,439 · 0,999546 = 6,436

δ → = D → · tanα → = 6,419 · tan 5 01 79 = 6,419 · 0,078985 = 0,507 D → = L → · cosα → = 6,439 · cos5 01 79 = 6,439 · 0,996895 = 6,419 ω = dir → − dir → = 89 96 72 − 217 95 75 + 400 = =−127 99 03 + 400 = 272 00 97 θ → = (θ → ± 200 ) + ω = 229 90 94 + 272 00 97 − 400 = = 501 91 91 − 400 = 101 91 91 x = x + δ → = 1357,709 + 7,793 = 1365,502 y = y + δ

→= 8145,581− 16,456 = 8129,125

H = H + δ → = 149,571 + 0,785 = 150,356 δ → = L → · cosθ → = 18,208 · cos 328 15 46 = 18,208 · 0,427975 = 7,793 δ

→= L → · sinθ → = 18,208 · sin 328 15 46 = 18,208 · (−0,903790) = −16,456

δ → = D → · tanα → = 18,191 · tan 2 74 55 = 18,191 · 0,043153 = 0,785 D → = L → · cosα → = 18,208 · cos2 74 55 = 18,208 · 0,999070 = 18,191 ω = dir → − dir → = 194 55 04 − 172 29 69 = 22 25 35 θ → = (θ → ± 200 ) + ω = 305 90 11 + 22 25 35 = 328 15 46

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x = x + δ → = 1357,709 + 16,501 = 1374,210 y = y + δ

→= 8145,581 + 17,785 = 8163,366

H = H + δ → = 149,571 + 0,753 = 150,324 δ → = L → · cosθ → = 24,261 · cos 52 38 26 = 24,261 · 0,680154 = 16,501 δ

→= L → · sinθ → = 24,261 · sin 52 38 26 = 24,261 · 0,733070 = 17,785

δ → = D → · tanα → = 24,249 · tan 1 97 62 = 24,249 · 0,031052 = 0,753 D → = L → · cosα → = 24,261 · cos1 97 62 = 24,261 · 0,999518 = 24,249 ω = dir → − dir → = 318 77 84 − 172 29 69 = 146 48 15 θ → = (θ → ± 200 ) + ω = 305 90 11 + 146 48 15 − 400 = = 452 38 26 − 400 = 52 38 26 x = x + δ → = 1357,709− 17,717 = 1339,992 y = y + δ

→= 8145,581 + 17,364 = 8162,945

H = H + δ → = 149,571 + 0,799 = 150,370 δ → = L → · cosθ → = 24,807 · cos 150 64 14 = 24,807 · (−0,714195) = −17,717 δ

→= L → · sinθ → = 24,807 · sin 150 64 14 = 24,807 · 0,699947 = 17,364

δ → = D → · tanα → = 24,794 · tan2 05 08 = 24,794 · 0,032225 = 0,799 D → = L → · cosα → = 24,807 · cos2 05 08 = 24,807 · 0,999481 = 24,794 ω = dir → − dir → = 17 03 72 − 172 29 69 + 400 = =−155 25 97 + 400 = 244 74 03 θ → = (θ → ± 200 ) + ω = 305 90 11 + 244 74 03 − 400 = = 550 64 14 − 400 = 150 64 14

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x = x + δ → = 1357,709− 17,030 = 1340,679 y = y + δ

→= 8145,581− 12,661 = 8132,920

H = H + δ → = 149,571 + 1,253 = 150,824 δ → = D → · cosθ → = 21,221 · cos 240 69 80 = 21,221 · (−0,802524) = −17,030 δ

→= D → · sin θ → = 21,221 · sin 240 69 80 = 21,221 · (−0,596620) = −12,661

δ → = D → · tanα → = 21,184 · tan3 76 41 = 21,184 · 0,059195 = 1,253 D → = L → · cosα → = 21,221 · cos3 76 41 = 21,221 · 0,998253 = 21,184 ω = dir → − dir → = 107 09 38 − 172 29 69 + 400 = = −65 20 31 + 400 = 334 79 69 θ → = (θ → ± 200 ) + ω = 305 90 11 + 334 79 69 − 400 = = 640 69 80 − 400 = 240 69 80