DANI Lucrare G.M.

STAN Daniel Loredan MTC an III gr IIIN 3

I. Date initialeSe considera reteaua de nivelment geometric de ordin superior, formata din reperii de nivelment A, B, C, D si data prin:

1 Cota provizorie si gravitatea absoluta in punctul A 0.00002*N0.00006

HA= 1052.711 m 0.0001*N

gA= 977862.97 mgal 0.0003

2 Coordonatele geodezice aproximative, diferentele de nivel si gravitate rezultate in urma masuratorilor de nivelment geometric si de gravimetrie,efectuate intre reperii de ordin inferior situati pe liniile de nivelment A-B, A-C, A-D, B-C, C-D

Nr. Coord. geodezice Coord. planimetricepunct B L

[gg.mmss] [gg.mmss] [m] [m]A 45.3827 25.0223 460123.721 503061.796

AB1 45.3845 24.5926 460644.218 499263.913AB2 45.3751 24.5630 458979.031 495452.365AB3 45.3911 24.5330 461452.392 491557.739AB4 45.3726 24.5033 458217.737 487719.860AB5 45.3926 24.4732 461930.624 483809.374AB6 45.3712 24.4435 457805.570 479964.861AB7 45.3929 24.4134 462048.041 476060.724AB8 45.3809 24.3835 459594.706 472175.238AB9 45.3921 24.3533 461835.836 468245.619AB10 45.3718 24.3233 458060.179 464327.614AB11 45.3901 24.2933 461262.836 460449.161AB12 45.3739 24.2632 458757.701 456513.176

B 45.3809 24.1910 459757.368 446948.653A 45.3827 25.0223 460123.721 503061.796

AC1 45.4004 25.0041 463082.698 500887.286AC2 45.4051 24.5739 464534.112 496949.312AC3 45.4313 24.5705 468917.594 496216.353AC4 45.4323 24.5304 469231.591 491006.177AC5 45.4616 24.5317 474571.179 491294.723AC6 45.4602 24.4838 474150.371 485266.962AC7 45.4912 24.4920 480013.060 486187.343AC8 45.4848 24.4424 479289.713 479796.565AC9 45.5203 24.4509 485305.787 480786.564AC10 45.5142 24.4019 484680.079 474530.349AC11 45.5446 24.4047 490357.292 475157.020AC12 45.5444 24.3621 490321.199 469425.354AC13 45.5722 24.3617 495198.774 469363.357AC14 45.5722 24.3242 495223.451 464734.465

C 46.0350 24.2724 507243.329 457969.697A 45.3827 25.0223 460123.721 503061.796

AD1 45.4024 25.0250 463701.049 503678.627AD2 45.4221 25.0128 467311.664 501903.125AD3 45.4419 25.0330 470955.313 504538.887AD4 45.4617 25.0050 474596.061 501080.054AD5 45.4815 25.0353 478240.321 505030.096AD6 45.5013 25.0030 481880.661 500647.271AD7 45.5211 25.0358 485525.107 505132.000AD8 45.5410 25.0026 489196.253 500560.306AD9 45.5608 25.0346 492840.538 504867.482

AD10 45.5807 25.0040 496511.966 500860.989AD11 46.0005 25.0311 500155.709 504108.797AD12 46.0206 25.0112 503889.597 501547.928

D 46.0908 25.0159 516916.529 502552.970B 45.38086 24.19096 459757.367548828 446948.653350078

BC1 45.3959 24.2016 463140.825 448405.955BC2 45.4204 24.1937 467006.244 447594.431BC3 45.4341 24.2213 469973.007 450992.110BC4 45.4559 24.2026 474251.304 448714.154BC5 45.4729 24.2352 476994.364 453185.412BC6 45.4951 24.2134 481400.700 450240.677BC7 45.5120 24.2510 484112.374 454921.610BC8 45.5340 24.2303 488454.388 452215.746BC9 45.5516 24.2610 491387.965 456267.262BC10 45.5729 24.2452 495505.547 454617.041

C 46.0350 24.2724 507243.329 457969.697C 46.03496 24.27236 507243.328601616 457969.697101031

CD1 46.0357 24.3024 507434.196 461838.883CD2 46.0512 24.3302 509729.232 465246.940CD3 46.0422 24.3623 508162.888 469556.611CD4 46.0621 24.3848 511821.644 472688.168CD5 46.0501 24.4220 509333.574 477231.016CD6 46.0715 24.4441 513459.523 480272.995CD7 46.0556 24.4813 511007.937 484817.717CD8 46.0756 24.5041 514705.166 488003.134CD9 46.0705 24.5403 513123.902 492336.356

D 46.0908 25.0159 516916.529 502552.970

II. Compensarea reţelei libere de nivelment geometrica. Compensarea reţelei libere de nivelment geometric cu diferenţe de nivel măsurate

Calculul diferenţelor de nivel măsurate şi al distanţelor

TronsonA

AB1 520.497 -3797.883 3833.38362918394AB2 -1665.187 -3811.548 4159.41692169856AB3 2473.361 -3894.626 4613.63451132299AB4 -3234.655 -3837.879 5019.19389363242AB5 3712.887 -3910.486 5392.34922616634AB6 -4125.053 -3844.513 5638.82453580102 68294.4984394306AB7 4242.470 -3904.138 5765.48737712466AB8 -2453.335 -3885.485 4595.19839950692AB9 2241.130 -3929.620 4523.77907470858AB10 -3775.658 -3918.005 5441.17188075692AB11 3202.657 -3878.453 5029.85214327809AB12 -2505.135 -3935.985 4665.58460777078

B 999.667 -9564.522 9616.62223847938A

AC1 2958.977 -2174.510 3672.06175235424AC2 1451.414 -3937.974 4196.93260645187AC3 4383.483 -732.959 4444.33881903616AC4 313.997 -5210.177 5219.62971734898AC5 5339.588 288.546 5347.3783529826AC6 -420.809 -6027.761 6042.43173851819AC7 5862.689 920.381 5934.49483150379 88416.4030212036AC8 -723.347 -6390.778 6431.58445901348AC9 6016.074 989.999 6096.98668128275

ΔX[m]

ΔY[m]

D[m]

Dij[m]

AC10 -625.708 -6256.215 6287.42648180844AC11 5677.214 626.671 5711.69594652858AC12 -36.093 -5731.666 5731.77934362691AC13 4877.575 -61.997 4877.96911287649AC14 24.677 -4628.892 4628.95804219507

C 12019.877 -6764.768 13792.735135676A

AD1 3577.328 616.831 3630.117771302AD2 3610.615 -1775.502 4023.54928335032AD3 3643.649 2635.762 4497.04575001208AD4 3640.748 -3458.834 5021.81023053988AD5 3644.261 3950.042 5374.33427624122AD6 3640.340 -4382.825 5697.47541960858 73437.1500553364AD7 3644.445 4484.728 5778.82097623487AD8 3671.146 -4571.694 5863.25003711026AD9 3644.284 4307.176 5642.03662138312

AD10 3671.428 -4006.493 5434.2774431794AD11 3643.744 3247.808 4881.09871119875AD12 3733.887 -2560.869 4527.68882617733

D 13026.932 1005.042 13065.6447089986B

BC1 3383.457 1457.302 3683.95322641811BC2 3865.419 -811.524 3949.68848845314BC3 2966.763 3397.680 4510.64436295377BC4 4278.297 -2277.957 4846.94828325588BC5 2743.060 4471.258 5245.61937149696 59707.6021181515BC6 4406.337 -2944.735 5299.74229903732BC7 2711.674 4680.934 5409.65013587807BC8 4342.014 -2705.865 5116.1300938806BC9 2933.576 4051.516 5002.0650795255BC10 4117.582 -1650.221 4435.95713885215

C 11737.782 3352.656 12207.2036384C

CD1 190.867 3869.186 3873.89097751687CD2 2295.036 3408.056 4108.77596461377CD3 -1566.344 4309.672 4585.48829471374CD4 3658.756 3131.556 4815.92563471517CD5 -2488.070 4542.848 5179.5715549655 53244.3447480246CD6 4125.949 3041.979 5126.11847782771CD7 -2451.585 4544.722 5163.79393414303CD8 3697.229 3185.418 4880.20338099985CD9 -1581.264 4333.222 4612.72221433655

D 3792.627 10216.614 10897.8543141924

Calculul diferenţelor de nivel măsurate şi al distanţelor

Tronson

AB 141.4849 68294.4984AC 198.4704 88416.4030AD 105.3535 73437.1501BC 57.0210 59707.6021CD -93.0728 53244.3447

Calculul cotelor provizorii

Punct Formule de calcul Observaţii

A 1052.7110 HAo initial

δhijo[m]

Dijo[m]

Cota provizorie[m]

B 1194.1959 HBo= Hao+δhABoC 1251.1814 HCo= Hao+δhACoD 1158.0645 HDo= Hao+δhADo

Calculul neînchiderilor

Triunghi FormuleNeînchideri

[m] [mm]n(ABC) δhAB + δhBC - δhAC 0.0355 35.5000000000132n(ACD) δhAC + δhCD - δhAD 0.0441 44.099999999986

total - 0.0796 79.5999999999992

Sistemul ecuaţiilor de condiţie

Nr. Tronson Pondere xA xB

1 A-B 0.015 -1 12 A-C 0.011 -1 03 A-D 0.014 -1 04 B-C 0.017 0 -15 C-D 0.019 0 06 ecuaţie fictivă 1.502 1 1

Matricea coeficienţilor

A

-1 1 0 0-1 0 1 0-1 0 0 10 -1 1 00 0 -1 11 1 1 1

Matricea ponderilor

P

0.0146425 0 0 00 0.0113101 0 00 0 0.0136171 00 0 0 0.01674830 0 0 00 0 0 0

-0.01464247 -0.01131012 -0.01361709 00.01464247 0 0 -0.01674829

0 0.01131012 0 0.016748290 0 0.01361709 0

N

1.54155559 1.48734345 1.49067580 1.488368831.48734345 1.53337667 1.48523763 1.501985921.49067580 1.48523763 1.54882566 1.483204581.48836883 1.50198592 1.48320458 1.53438434

Rezolvarea sistemului normal de ecuaţii N*X+L=0

calculate din punctul A

Produsul AT*P

AT*P

Matricea sistemului normal (produsul AT*P*A)

Nr.Coeficienţi

xA xB xC xD1 1.54155559243616 1.48734345195419 1.49067580128667 1.488368833672632 1.48734345195419 1.53337667377676 1.48523763378129 1.501985919837413 1.49067580128667 1.48523763378129 1.54882566178128 1.483204582500424 1.48836883367263 1.50198591983741 1.48320458250042 1.5343843433392

Rezolvare prin schema Gauss

Nr. xA xB xC xD1 1.541555592 1.487343452 1.490675801 1.4883688342 -1 -0.964832835 -0.966994514 -0.9654979953 1.533376674 1.485237634 1.5019859204 0.0983388749938874 0.0469846749460652 0.06595879910459495 -1 -0.477783327793669 -0.6707296489683746 1.54882566178128 1.483204582500427 0.0849018450709678 0.01244607063499568 -1 -0.1465936414525769 1.5343843433392

10 0.051302181627167511 -1

12 1.04121404787833 -0.065951376621559 -0.0124964506539861 -1

Calculul corecţiilor

Nr. CorecţiaValoare calculată corecţie

[m] [m]1 vAB = -xA + xB + lAB 0.0000 -0.02033852 vAC = -xA + xC + lAC 0.0000 -0.00261983 vAD = -xA + xD + lAD 0.0000 0.02404604 vBC = -xB + xC + lBC -0.0355 -0.01778135 vCD = -xC + xD + lCD -0.0441 -0.0174342

Calculul estimatorilor de precizie

m = 5 numărul de măsurători

n = 4 numărul de necunoscuted = 1 defectul de rang

so = 0.0035364 eroarea unităţii de pondere [m]

Altitudinile compensate (definitive) ale punctelor noi

PunctCote provizorii Cote compensate 1

[m] [mm] [m]A 1052.7110 -0.27191769 1052.7107B 1194.1959 -20.61044503 1194.1753C 1251.1814 -2.89174112 1251.1785D 1158.0645 23.77410384 1158.0883

Termen liberl

Diferenţexi

Compensarea a III. Date iniţiale

Se consideră reţeaua de nivelment geometric de ordin superior, formată din reperii de nivelment A, B, C, D şi dată prin:

1. Cota provizorie şi gravitatea absolută în punctul A

HA = 1052.711 mgA = 977862.97 mgal

2. Coordonatele geodezice aproximative, diferenţele de nivel şi gravitate rezultate în urma măsurătorilor de nivelment geometric şi de gravimetrie,efectuate între reperii de ordin inferior situaţi pe liniile de nivelment A-B, A-C, A-D, B-C, C-D

Coordonate geodezice aproximative Coordonate planimetriceB L X0 Y0

[gg.mmss] [gg.mmss] [m] [m]A 45.3827 25.0223 460123.721 503061.796

AB1 45.3845 24.5926 460644.218 499263.913

AB2 45.3751 24.5630 458979.031 495452.365

AB3 45.3911 24.5330 461452.392 491557.739

AB4 45.3726 24.5033 458217.737 487719.860

AB5 45.3926 24.4732 461930.624 483809.374

AB6 45.3712 24.4435 457805.570 479964.861

AB7 45.3929 24.4134 462048.041 476060.724

AB8 45.3809 24.3835 459594.706 472175.238

AB9 45.3921 24.3533 461835.836 468245.619

AB10 45.3718 24.3233 458060.179 464327.614

AB11 45.3901 24.2933 461262.836 460449.161

AB12 45.3739 24.2632 458757.701 456513.176

B 45.3809 24.1910 459757.368 446948.653

A 45.3827 25.0223 460123.721 503061.796

AC1 45.4004 25.0041 463082.698 500887.286

AC2 45.4051 24.5739 464534.112 496949.312

AC3 45.4313 24.5705 468917.594 496216.353

AC4 45.4323 24.5304 469231.591 491006.177

AC5 45.4616 24.5317 474571.179 491294.723

AC6 45.4602 24.4838 474150.371 485266.962

AC7 45.4912 24.4920 480013.060 486187.343

AC8 45.4848 24.4424 479289.713 479796.565

AC9 45.5203 24.4509 485305.787 480786.564

AC10 45.5142 24.4019 484680.079 474530.349

AC11 45.5446 24.4047 490357.292 475157.020

AC12 45.5444 24.3621 490321.199 469425.354

AC13 45.5722 24.3617 495198.774 469363.357

AC14 45.5722 24.3242 495223.451 464734.465

C 46.0350 24.2724 507243.329 457969.697

A 45.3827 25.0223 460123.721 503061.796

AD1 45.4024 25.0250 463701.049 503678.627

AD2 45.4221 25.0128 467311.664 501903.125

AD3 45.4419 25.0330 470955.313 504538.887

AD4 45.4617 25.0050 474596.061 501080.054

AD5 45.4815 25.0353 478240.321 505030.096

AD6 45.5013 25.0030 481880.661 500647.271

AD7 45.5211 25.0358 485525.107 505132.000

Nr. pct.

AD8 45.5410 25.0026 489196.253 500560.306

II. Compensarea reţelei libere de nivelment geometric

b. Compensarea reţelei libere de nivelment geometric folosind sistemul de altitudini ortometrice sferoidice

Calculul corecţiilor ortometrice pe tronsoane

K Bmin Bmax Valoare BmK1 45.5807 46.0908 0.0232563701 45.83571

K2 45.4729 45.5807 0.0242086885 45.52676

K3 45.3712 45.4729 0.0240093228 45.42201

TronsonLatitudine Coeficient

Bi K

De la La [gg.mmss] [min] -A AB1 45.3827 0.2867 0.0240093228

AB1 AB2 45.3844 -1.5667 0.0240093228AB2 AB3 45.3750 2.6667 0.0240093228AB3 AB4 45.3910 -3.0833 0.0240093228AB4 AB5 45.3725 3.3333 0.0240093228AB5 AB6 45.3925 -3.5667 0.0240093228AB6 AB7 45.3711 3.6167 0.0240093228AB7 AB8 45.3928 -2.0000 0.0240093228AB8 AB9 45.3808 1.8667 0.0240093228AB9 AB10 45.3920 -3.3833 0.0240093228AB10 AB11 45.3717 3.0500 0.0240093228AB11 AB12 45.3900 -2.7000 0.0240093228AB12 B 45.3738 1.1667 0.0240093228

B - 45.3808 0.0000A AC1 45.3827 2.9367 0.0240093228

AC1 AC2 45.4003 0.7833 0.0240093228AC2 AC3 45.4050 4.3667 0.0240093228AC3 AC4 45.4312 0.1667 0.0240093228AC4 AC5 45.4322 4.8833 0.0240093228AC5 AC6 45.4615 -0.2333 0.0240093228AC6 AC7 45.4601 5.1667 0.0232563701AC7 AC8 45.4911 -1.0667 0.0242086885AC8 AC9 45.4847 5.9167 0.0242086885AC9 AC10 45.5202 -1.0167 0.0242086885AC10 AC11 45.5141 5.0667 0.0242086885AC11 AC12 45.5445 -0.0333 0.0242086885AC12 AC13 45.5443 4.6333 0.0242086885AC13 AC14 45.5721 0.0000 0.0242086885AC14 C 45.5721 77.1333 0.0232563701

C - 46.0349 0.0000A AD1 45.3827 3.2700 0.0240093228

AD1 AD2 45.4023 3.2833 0.0240093228AD2 AD3 45.4220 3.3000 0.0240093228AD3 AD4 45.4418 3.3000 0.0240093228AD4 AD5 45.4616 3.3000 0.0240093228AD5 AD6 45.4814 3.3000 0.0242086885AD6 AD7 45.5012 3.3000 0.0242086885AD7 AD8 45.5210 3.3167 0.0242086885AD8 AD9 45.5409 3.3000 0.0242086885

Diferenţa delatitudine

ΔB'= Bj - Bi

AD9 AD10 45.5607 3.3167 0.0242086885AD10 AD11 45.5806 69.9667 0.0232563701AD11 AD12 46.0004 3.3500 0.0232563701AD12 D 46.0205 11.7000 0.0232563701

D - 46.0907 0.0000B BC1 45.38082 2.5000 0.0240093228

BC1 BC2 45.3958 4.0833 0.0240093228BC2 BC3 45.4203 2.2833 0.0240093228BC3 BC4 45.4340 3.6333 0.0240093228BC4 BC5 45.4558 2.8333 0.0240093228BC5 BC6 45.4728 3.7000 0.0242086885BC6 BC7 45.4950 2.8167 0.0242086885BC7 BC8 45.5119 3.6667 0.0242086885BC8 BC9 45.5339 2.9333 0.0242086885BC9 BC10 45.5515 3.5500 0.0242086885BC10 C 45.5728 77.0167 0.0232563701

C - 46.0349 0.0000C CD1 46.0349 0.1200 0.0232563701

CD1 CD2 46.0356 2.5833 0.0232563701CD2 CD3 46.0511 -1.5000 0.0232563701CD3 CD4 46.0421 3.3167 0.0232563701CD4 CD5 46.0620 -2.0000 0.0232563701CD5 CD6 46.0500 3.5667 0.0232563701CD6 CD7 46.0714 -2.6500 0.0232563701CD7 CD8 46.0555 3.3333 0.0232563701CD8 CD9 46.0755 -0.8500 0.0232563701CD9 D 46.0704 3.3833 0.0232563701

D - 46.0907 0.0000 0.0232563701

Diferenţe de nivel măsurate şi corectate

Nr. Tronsonδho δors δho + δors[m] [mm] [m]

1 A-B 141.4823 0.0087 141.49102 A-C 198.4674 -3.4509 195.01653 A-D 105.3509 -4.0664 101.28454 B-C 57.0188 -3.9596 53.05925 C-D -93.0748 -0.3256 -93.4004

Cote provizorii

Punct Relaţii de calcul Observaţii

A 1052.7110 HAo iniţialB 1194.1933 HBo = HAo + δhABoC 1251.1784 HCo = HAo + δhACoD 1158.0619 HDo = HAo + δhADo


Triunghi Relaţii de calcul

n(ABC) δhAB + δhBC - δhAC 0.0337 33.7000n(ACD) δhAC + δhCD - δhAD 0.0417 41.7000

total 0.0754 75.4000

Cota provizorie[m]

calculate din punctul A, fără a se ţine cont de corecţiile ortometrice

Neînchideri[m]

Neînchideri[mm]

Sistemul de ecuaţii

Nr. Tronson Pondere xA xB

1 A-B 0.0146387 -1 1

2 A-C 0.0113116 -1 0

3 A-D 0.0136234 -1 0

4 B-C 0.0124977 0 -1

5 C-D 0.0187813 0 0

6 ecuaţie fictivă 1.4170526 1 1

Matricea ponderilor

P

0.0146 0 0 00 0.0113 0 00 0 0.0136 00 0 0 0.01250 0 0 00 0 0 0

Matricea coeficienţilor

A

-1 1 0 0-1 0 1 0-1 0 0 10 -1 1 00 0 -1 1

1 1 1 1

Produsul AT*P

AT*P

-0.01463869 -0.01131161 -0.01362338 00.01463869 0 0 -0.01249768

0 0.01131161 0 0.012497680 0 0.01362338 0

Matricea sistemului normal (produsul AT*P*A)

N

1.45662630 1.40241393 1.40574101 1.403429241.40241393 1.44418899 1.40455494 1.417052621.40574101 1.40455494 1.45964318 1.398271351.40342924 1.41705262 1.39827135 1.44945727

Determinantul sistemului

D 0.000517359189

Minori

111.44418899 1.40455494 1.41705262

0.00739860973034551.40455494 1.45964318 1.398271351.41705262 1.39827135 1.44945727

131.40241393 1.44418899 1.41705262

-0.0027700624122864

13 1.40574101 1.40455494 1.39827135 -0.00277006241228641.40342924 1.41705262 1.44945727

211.40241393 1.40574101 1.40342924

0.00205087083072951.40455494 1.45964318 1.398271351.41705262 1.39827135 1.44945727

231.45662630 1.40241393 1.40342924

0.0030374311.40574101 1.40455494 1.398271351.40342924 1.41705262 1.44945727

311.40241393 1.40574101 1.40342924

-0.0027700621.44418899 1.40455494 1.417052621.41705262 1.39827135 1.44945727

331.45662630 1.40241393 1.40342924

0.0069985041.40241393 1.44418899 1.417052621.40342924 1.41705262 1.44945727

411.40241393 1.40574101 1.40342924

0.0024864031.44418899 1.40455494 1.417052621.40455494 1.45964318 1.39827135

431.45662630 1.40241393 1.40342924

0.0010997381.40241393 1.44418899 1.417052621.40574101 1.40455494 1.39827135

Rezolvarea sistemului normal de ecuaţii

Nr.Coeficienţi

xA xB xC xD1 1.45662630352075 1.4024139288315 1.40574100645747 1.403429238646972 1.4024139288315 1.4441889871625 1.40455494209852 1.417052619364173 1.40574100645747 1.40455494209852 1.4596431790825 1.398271349818194 1.40342923864697 1.41705261936417 1.39827134981819 1.44945726962736


Nr. xA xB xC xD1 1.4566263 1.4024139 1.4057410 1.40342922 -1 -0.9627822 -0.9650663 -0.96347933 1.4441890 1.4045549 1.41705264 0.0939698 0.0511325 0.06585595 -1 -0.5441375 -0.70081986 1.4596432 1.39827137 0.0751868 0.00803448 -1 -0.106859067866639 1.4494573

10 0.050270611 -112 0.0017328 -0.0154607 -0.0058693 0.0195972


Nr. Corecţia

[m] [m]

1 vAB = -xA + xB + lAB -0.00000867 -0.0172020942 vAC = -xA + xC + lAC 0.00345095 -0.0041511133 vAD = -xA + xD + lAD 0.00406643 0.0219308214 vBC = -xB + xC + lBC -0.02974040 -0.0201490355 vCD = -xC + xD + lCD -0.04137442 -0.015907973


m = numărul de măsurători 5n = numărul de necunoscute 4d = defectul de rang 1

so = eroarea unităţii de pondere [m] 0.0032331

Nr. Punct Abatere standard

[m] [mm]

1 A 0.0122263 12.2263378

2 B 0.0154364 15.4363717

3 C 0.0118912 11.89115264 D 0.0144198 14.4198314

Altitudini compensate (definitive) ale punctelor noi în sistemul de altitudini ortometrice-sferoidice

Punct Cote provizorii Cote compensate

[m] [mm] [m]

A 1052.7110 1.7328 1052.7127B 1194.1933 -15.4607 1194.1778C 1251.1784 -5.8693 1251.1725D 1158.0619 19.5972 1158.0815

Verificarea compensării

Tronsonδhijo δhors Corecţie δhcomp

[m] [m] [mm] [m]

AB 141.4823 0.0087 -17.20209442 141.4651AC 198.4674 -3.4509 -4.15111341 198.4598AD 105.3509 -4.0664 21.93082106 105.3688BC 57.0188 -3.9596 -20.14903501 56.9947CD -93.0748 -0.3256 -15.90797278 -93.0910

Termen liber l

Valoare calculată corecţie

Diferenţe

Se considera reteaua de nivelment geometric de ordin superior, formata din reperii de nivelment A, B, C, D si data prin:

0.00003*N0.000090.002*N

0.006

Coordonatele geodezice aproximative, diferentele de nivel si gravitate rezultate in urma masuratorilor de nivelment geometric si de gravimetrie,

δh δg

[m] [mgal]0.0000 0.0000

10.2040 -2.38611.0625 -2.64610.2436 -2.39610.7133 -2.53610.8947 -2.59611.0437 -2.63610.2360 -2.39610.2731 -2.40611.0804 -2.64610.1123 -2.35610.8587 -2.58610.7265 -2.54614.0361 -3.5360.0000 0.000013.0976 -3.256013.3607 -3.336012.5206 -3.086013.0842 -3.246012.5681 -3.096012.4617 -3.066012.5180 -3.076012.8190 -3.166013.0795 -3.246012.8397 -3.176013.1501 -3.266013.3646 -3.336012.7030 -3.136012.4400 -3.0560

18.4636 -4.86600.0000 0.00007.9059 -1.69608.5029 -1.87608.2126 -1.78608.4411 -1.85607.9823 -1.71608.4173 -1.84607.7618 -1.65607.9126 -1.69608.0166 -1.7260

7.6569 -1.62608.0150 -1.72607.7383 -1.6460

8.7902 -1.96600.0000 0.00005.4426 -0.95605.7226 -1.04605.5127 -0.97605.3499 -0.92605.5222 -0.98605.2374 -0.89605.3775 -0.93605.0359 -0.83605.1464 -0.86605.2564 -0.9060

3.4174 -0.35600.0000 0.0000-8.0477 3.0940-8.1280 3.1140-8.1093 3.1040-8.2153 3.1440-8.3673 3.1840-8.1090 3.1040-8.2284 3.1440-7.8926 3.0440-7.7370 2.9940

-20.2382 6.7440

0.000010.204011.062510.243610.713310.894711.0437 141.484910.236010.273111.080410.112310.858710.726514.03610.000013.097613.360712.520613.084212.568112.461712.5180 198.470412.819013.0795

δh[m]

δhij[m]

12.839713.150113.364612.703012.440018.46360.00007.90598.50298.21268.44117.98238.4173 105.35357.76187.91268.01667.65698.01507.73838.79020.00005.44265.72265.51275.34995.5222 57.02105.23745.37755.03595.14645.25643.41740.0000-8.0477-8.1280-8.1093-8.2153-8.3673 -93.0728-8.1090-8.2284-7.8926-7.7370

-20.2382

xC xD s

0 0 0.0000 0.00001 0 0.0000 0.00000 1 0.0000 0.00001 0 -0.0355 -0.0355000000000132-1 1 -0.0441 -0.0440999999999861 1 0.0000 4.0000

Matricea coeficienţilor transpusă

-1 -1 -1AT 1 0 0

0 1 0

0 0 1

0 00 00 00 0

0.0187813 00 1.5019859

0 1.501985920 1.50198592

-0.01878134 1.501985920.01878134 1.50198592

Matricea inversă a sistemului normal calculată din minorii matricei N

14.2929840816767 -4.10468640693616 -5.26225555703402-4.10468640693616 19.8910201780289 -3.9110354865698-5.26225555703402 -3.9110354865698 12.1971916825201-4.75959581704672 -11.7088519838631 -2.85745433825655

l[m]

N-1

Elementele matricei inverse

L N-10.000000000 14.292984082 -4.104686407 -5.262255557 -4.7595958170.000594564 -4.104686407 19.891020178 -3.911035487 -11.7088519840.000233693 -5.262255557 -3.911035487 12.197191683 -2.857454338-0.000828257 -4.759595817 -11.708851984 -2.857454338 19.492348440

L S Control QA QB0.0000000 6.0079437 6.007943679 1 00.0000000 -3.8973253 -3.897325344 -0.648695386 00.0005946 6.0085382 6.008538244 0 10.0005946 0.2118769 0.21187691319954 -0.964832834606829 1-0.0060461 -2.1545591 -2.15455905116578 9.81130641027571 -10.16891844717730.0002337 6.0081774 6.008177372 0 0-0.0000504 0.0972975 0.0972975356869728 -0.506013471760134 -0.4777833277936690.0005934 -1.1460003 -1.14600025011993 5.95998203969734 5.62747873611345-0.0008283 6.0071154 6.007115422 0 0-0.0012197 0.0500825 0.0500825182340791 -0.244177649078036 -0.600689651121770.0237741 -0.9762259 -0.97622589616262 4.75959581704669 11.7088519838632

-0.0000326 -0.0000326 -1.00003262107834 14.2929840816767 19.8910201780289

Valoare calculată corecţiePondere

[pvv]

[mm] [m2] [mm2]-20.3385273 0.014642-2.6198234 0.01131024.0460215 0.013617 0.000025012 25.012081829-17.7812961 0.016748-17.4341550 0.018781

PunctAbatere standard Abatere standard

[m] [mm]A 0.0133697 13.3696912B 0.0007929 0.7929237C 0.0010126 1.0125815D 0.0008010 0.8009914


Tronsonδhijo Corecţia δhijcomp δhijcalc

[m] [mm] [m] [m]AB 141.4849 -20.33852734 141.4646 141.4646AC 198.4704 -2.61982343 198.4678 198.4678AD 105.3535 24.04602152 105.3775 105.3775BC 57.0210 -17.78129609 57.0032 57.0032

CD -93.0728 -17.43415504 -93.0902 -93.0902

Termenliber

2. Coordonatele geodezice aproximative, diferenţele de nivel şi gravitate rezultate în urma măsurătorilor de nivelment geometric şi de gravimetrie,

δh δgCoordonate geodezice aproximative

B[m] [mgal] [gg.mmss]

0.0000 0.000 AD9 45.5608

10.2040 -2.386 AD10 45.5807

11.0625 -2.646 AD11 46.0005

10.2436 -2.396 AD12 46.0206

10.7133 -2.536 D 46.0908

10.8947 -2.596 B 45.38086

11.0437 -2.636 BC1 45.3959

10.2360 -2.396 BC2 45.4204

10.2731 -2.406 BC3 45.4341

11.0804 -2.646 BC4 45.4559

10.1123 -2.356 BC5 45.4729

10.8587 -2.586 BC6 45.4951

10.7265 -2.546 BC7 45.5120

14.0361 -3.536 BC8 45.5340

0.0000 0.000 BC9 45.5516

13.0976 -3.256 BC10 45.5729

13.3607 -3.336 C 46.0350

12.5206 -3.086 C 46.03496

13.0842 -3.246 CD1 46.0357

12.5681 -3.096 CD2 46.0512

12.4617 -3.066 CD3 46.0422

12.5180 -3.076 CD4 46.0621

12.8190 -3.166 CD5 46.0501

13.0795 -3.246 CD6 46.0715

12.8397 -3.176 CD7 46.0556

13.1501 -3.266 CD8 46.0756

13.3646 -3.336 CD9 46.0705

12.7030 -3.136 D 46.0908

12.4400 -3.05618.4636 -4.8660.0000 0.0007.9059 -1.6968.5029 -1.8768.2126 -1.7868.4411 -1.8567.9823 -1.7168.4173 -1.8467.7618 -1.656

Nr. pct.

7.9126 -1.696

f'= 0.0053q'= 3437.7468

Hi δho

[m] [m] [m] [mm] [m]1052.7110 1057.8130 10.2040 -0.0073 10.19671062.9150 1068.4463 11.0625 0.0402 11.10271073.9775 1079.0993 10.2436 -0.0691 10.17451084.2211 1089.5778 10.7133 0.0807 10.79401094.9344 1100.3818 10.8947 -0.0881 10.80661105.8291 1111.3510 11.0437 0.0952 11.13891116.8728 1121.9908 10.2360 -0.0974 10.13861127.1088 1132.2454 10.2731 0.0544 10.32751137.3819 1142.9221 11.0804 -0.0512 11.02921148.4623 1153.5185 10.1123 0.0937 10.20601158.5746 1164.0039 10.8587 -0.0852 10.77351169.4333 1174.7966 10.7265 0.0762 10.80271180.1598 1187.1779 14.0361 -0.0333 14.00281194.1959 0.00871194.1959 1200.7447 13.0976 -0.0847 13.01291207.2935 1213.9738 13.3607 -0.0228 13.33791220.6542 1226.9145 12.5206 -0.1286 12.39201233.1748 1239.7169 13.0842 -0.0050 13.07921246.2590 1252.5431 12.5681 -0.1469 12.42121258.8271 1265.0580 12.4617 0.0071 12.46881271.2888 1277.5478 12.5180 -0.1535 12.36451283.8068 1290.2163 12.8190 0.0333 12.85231296.6258 1303.1656 13.0795 -0.1867 12.89281309.7053 1316.1252 12.8397 0.0324 12.87211322.5450 1329.1201 13.1501 -0.1630 12.98711335.6951 1342.3774 13.3646 0.0011 13.36571349.0597 1355.4112 12.7030 -0.1520 12.55101361.7627 1367.9827 12.4400 0.0000 12.44001374.2027 1383.4345 18.4636 -2.4817 15.98191392.6663 -3.45091392.6663 1396.6193 7.9059 -0.1096 7.79631400.5722 1404.8237 8.5029 -0.1107 8.39221409.0751 1413.1814 8.2126 -0.1120 8.10061417.2877 1421.5083 8.4411 -0.1126 8.32851425.7288 1429.7200 7.9823 -0.1133 7.86901433.7111 1437.9198 8.4173 -0.1149 8.30241442.1284 1446.0093 7.7618 -0.1155 7.64631449.8902 1453.8465 7.9126 -0.1167 7.79591457.8028 1461.8111 8.0166 -0.1168 7.8998

Altitudineprovizorie

Altitudinemedie

Diferenţemăsurate

Corecţieortometrică

Diferenţecorectate

Hm = (Hi+Hj)/2

δors= -K*ΔB*Hm

δh= δho+δors

1465.8194 1469.6479 7.6569 -0.1180 7.53891473.4763 1477.4838 8.0150 -2.4041 5.61091481.4913 1485.3605 7.7383 -0.1157 7.62261489.2296 1493.6247 8.7902 -0.4064 8.38381498.0198 -4.06641498.0198 1500.7411 5.4426 -0.0901 5.35251503.4624 1506.3237 5.7226 -0.1477 5.57491509.1850 1511.9414 5.5127 -0.0829 5.42981514.6977 1517.3727 5.3499 -0.1324 5.21751520.0476 1522.8087 5.5222 -0.1036 5.41861525.5698 1528.1885 5.2374 -0.1369 5.10051530.8072 1533.4960 5.3775 -0.1046 5.27291536.1847 1538.7027 5.0359 -0.1366 4.89931541.2206 1543.7938 5.1464 -0.1096 5.03681546.3670 1548.9952 5.2564 -0.1331 5.12331551.6234 1553.3321 3.4174 -2.7822 0.63521555.0408 -3.95961555.0408 1551.0170 -8.0477 -0.0043 -8.05201546.9931 1542.9291 -8.1280 -0.0927 -8.22071538.8651 1534.8105 -8.1093 0.0535 -8.05581530.7558 1526.6482 -8.2153 -0.1178 -8.33311522.5405 1518.3569 -8.3673 0.0706 -8.29671514.1732 1510.1187 -8.1090 -0.1253 -8.23431506.0642 1501.9500 -8.2284 0.0926 -8.13581497.8358 1493.8895 -7.8926 -0.1158 -8.00841489.9432 1486.0747 -7.7370 0.0294 -7.70761482.2062 1472.0871 -20.2382 -0.1158 -20.35401461.9680 -0.3256

D[m] [km]

68312.1211 68.312188404.7225 88.404773403.2191 73.403280014.8683 80.014953244.5369 53.2445

Observaţii

iniţial

calculate din punctul A, fără a se ţine cont de corecţiile ortometrice

xC xD s Relaţii de calcul

0 0 -0.000008669 -0.00000867

1 0 0.003450946 0.00345095

0 1 0.004066429 0.00406643

1 0 -0.029740400 -0.02974040

-1 1 -0.041374424 -0.04137442

1 1 0.000000000 4.00000000

0 00 00 00 0

0.0188 00 1.4171

Matricea coeficienţilor transpusă

AT

-1 -1 -11 0 00 1 00 0 1

0 1.417052620 1.41705262

-0.01878127 1.417052620.01878127 1.41705262


N-1

14.30072159 -3.96411405 -5.35423448-3.96411405 22.79584155 -5.87102859-5.35423448 -5.87102859 13.52736088-4.80595054 -12.78427639 -2.12567528

121.40241393 1.40455494 1.417052621.40574101 1.45964318 1.398271351.40342924 1.39827135 1.44945727

141.40241393 1.44418899 1.40455494

l[m]

lAB=-δOR

lAC=-δOR

lAD=-δOR

lBC=-nABC-δ

lCD=-nACD-δ

14 1.40574101 1.40455494 1.459643181.40342924 1.41705262 1.39827135

221.45662630 1.40574101 1.403429241.40574101 1.45964318 1.398271351.40342924 1.39827135 1.44945727

241.45662630 1.40241393 1.405741011.40574101 1.40455494 1.459643181.40342924 1.41705262 1.39827135

321.45662630 1.40574101 1.403429241.40241393 1.40455494 1.417052621.40342924 1.39827135 1.44945727

341.45662630 1.40241393 1.405741011.40241393 1.44418899 1.404554941.40342924 1.41705262 1.39827135

421.45662630 1.40574101 1.403429241.40241393 1.40455494 1.417052621.40574101 1.45964318 1.39827135

441.45662630 1.40241393 1.405741011.40241393 1.44418899 1.404554941.40574101 1.40455494 1.45964318

Elementele matricei inverse

L N-1-0.000094307 14.300721591 -3.964114048 -5.354234484 -4.8059505350.000371559 -3.964114048 22.795841554 -5.871028590 -12.7842763920.000444414 -5.354234484 -5.871028590 13.527360876 -2.125675278-0.000721666 -4.805950535 -12.784276392 -2.125675278 19.892324729

L S Control QA QB-0.0000943 5.6681162 5.6681162 1 00.0000647 -3.8912631 -3.8912631 -0.6865179 00.0003716 5.6685820 5.6685820 0 10.0004624 0.2114205 0.2114205 -0.9627822 1-0.0049203 -2.2498776 -2.2498776 10.2456592 -10.64172020.0004444 5.6686549 5.6686549 0 00.0002838 0.0835050 0.0835050 -0.4411804 -0.5441375

-0.00377515163323 -1.11063421949987 -1.11063421949986 5.86779387801752 7.23714444824088-0.0007217 5.6674888 5.6674888 0 0-0.0009852 0.0492855 0.0492855 -0.2415982 -0.64267380.0195972 -0.9804028 -0.9804028 4.8059505 12.7842764-0.0095241 75.4256357 -0.0095241 14.3007216 22.7958416

Termenliber

Pondere [pvv]

[mm]

-17.2020944 0.0146387 0.0000209057 20.90570519-4.1511134 0.011311621.9308211 0.0136234-20.1490350 0.0124977-15.9079728 0.0187813

δhcalc

[m]

141.4651198.4598105.368856.9947-93.0910

0 0 1-1 0 11 -1 1

0 1 1

-4.75959581704672-11.7088519838631-2.8574543382565519.4923484398262

Soluţii

X Necunoscuta-0.00027192 xA [m]-0.02061045 xB [m]-0.00289174 xC [m]0.02377410 xD [m]

QC QD0 00 00 00 00 01 01 0

-11.7783070457906 00 1

-0.146593641452576 12.85745433825656 -19.4923484398262

12.1971916825201 19.4923484398262

Coordonate geodezice aproximative Coordonate planimetriceδh δg

L X0 Y0[gg.mmss] [m] [m] [m] [mgal]25.0346 492840.538 504867.482 8.0166 -1.72625.0040 496511.966 500860.989 7.6569 -1.62625.0311 500155.709 504108.797 8.0150 -1.72625.0112 503889.597 501547.928 7.7383 -1.64625.0159 516916.529 502552.970 8.7902 -1.96624.19096 459757.367548828 446948.653350078 0.0000 0.00024.2016 463140.825 448405.955 5.4426 -0.95624.1937 467006.244 447594.431 5.7226 -1.04624.2213 469973.007 450992.110 5.5127 -0.97624.2026 474251.304 448714.154 5.3499 -0.92624.2352 476994.364 453185.412 5.5222 -0.98624.2134 481400.700 450240.677 5.2374 -0.89624.2510 484112.374 454921.610 5.3775 -0.93624.2303 488454.388 452215.746 5.0359 -0.83624.2610 491387.965 456267.262 5.1464 -0.86624.2452 495505.547 454617.041 5.2564 -0.90624.2724 507243.329 457969.697 3.4174 -0.35624.27236 507243.328601616 457969.697101031 0.0000 0.00024.3024 507434.196 461838.883 -8.0477 3.09424.3302 509729.232 465246.940 -8.1280 3.11424.3623 508162.888 469556.611 -8.1093 3.10424.3848 511821.644 472688.168 -8.2153 3.14424.4220 509333.574 477231.016 -8.3673 3.18424.4441 513459.523 480272.995 -8.1090 3.10424.4813 511007.937 484817.717 -8.2284 3.14424.5041 514705.166 488003.134 -7.8926 3.04424.5403 513123.902 492336.356 -7.7370 2.99425.0159 516916.529 502552.970 -20.2382 6.744

Latitudine Latitudine medie

B Bm

[gg] [mm] [ss] [secunde] [gg.mmss]45 38 27 164307 45.383645 38 44 164324 45.379745 37 50 164270 45.383045 39 10 164350 45.381845 37 25 164245 45.382545 39 25 164365 45.381845 37 11 164231 45.382045 39 28 164368 45.386845 38 8 164288 45.386445 39 20 164360 45.381945 37 17 164237 45.380945 39 0 164340 45.381945 37 38 164258 45.377345 38 8 164288 45.381845 38 27 164307 45.391545 40 3 164403 45.402745 40 50 164450 45.418145 43 12 164592 45.431745 43 22 164602 45.446945 46 15 164775 45.460845 46 1 164761 45.475645 49 11 164951 45.487945 48 47 164927 45.502545 52 2 165122 45.517245 51 41 165101 45.529345 54 45 165285 45.544445 54 43 165283 45.558245 57 21 165441 45.572145 57 21 165441 45.803546 3 49 165829 45.708845 38 27 164307 45.392545 40 23 164423 45.412245 42 20 164540 45.431945 44 18 164658 45.451745 46 16 164776 45.471545 48 14 164894 45.491345 50 12 165012 45.511145 52 10 165130 45.531045 54 9 165249 45.5508

45 56 7 165367 45.570745 58 6 165486 45.790546 0 4 165604 46.010546 2 5 165725 46.055646 9 7 166147 45.735845 38 8 164288 45.388345 39 58 164398 45.408145 42 3 164523 45.427245 43 40 164620 45.444945 45 58 164758 45.464345 47 28 164848 45.483945 49 50 164990 45.503545 51 19 165079 45.522945 53 39 165219 45.542745 55 15 165315 45.562245 57 28 165448 45.803946 3 49 165829 46.034946 3 49 165829 46.035346 3 56 165836 46.043446 5 11 165911 46.046646 4 21 165861 46.052146 6 20 165980 46.056046 5 0 165900 46.060746 7 14 166034 46.063546 5 55 165955 46.065546 7 55 166075 46.073046 7 4 166024 46.080646 9 7 166147 46.0907

Relaţii de calcul

0 0 1-1 0 11 -1 10 1 1

Vectorul AT*P*L

-4.80595054

L

-0.00009431-12.78427639 0.00037156-2.12567528 0.0004444119.89232473 -0.00072167

0.0020508708307295

0.0024864026732296

lAB=-δORAB

lAC=-δORAC

lAD=-δORAD

lBC=-nABC-δORBC

lCD=-nACD-δORCD

0.0024864026732296

0.0117936381079861

-0.006614063

0.003037431

0.001099738

-0.006614063

0.010291477

Soluţii

X Necunoscuta0.00173277 xA [m]-0.01546065 xB [m]-0.00586929 xC [m]0.01959716 xD [m]

QC QD0 00 00 00 00 01 01 0

-13.3002131969197 00 1

-0.1068591 12.1256753 -19.8923247

13.5273609 19.8923247

I. Date iniţiale

Se consideră reţeaua de nivelment geometric de ordin superior, formată din reperii de nivelment A, B, C, D şi dată prin:

1. Cota provizorie şi gravitatea absolută în punctul A

HA = 1052.711 m

gA = 977862.97 mgal

2. Coordonatele geodezice aproximative, diferenţele de nivel şi gravitate rezultate în urma măsurătorilor de nivelment geometric şi de gravimetrie,efectuate între reperii de ordin inferior situaţi pe liniile de nivelment A-B, A-C, A-D, B-C, C-D

Coordonate geodezice aproximative Coordonate planimetriceδh δg

B L X0 Y0

[gg.mmss] [gg.mmss] [m] [m] [m] [mgal]

A 45.3827 25.0223 460123.721 503061.796 0.0000 0.0000

AB1 45.3845 24.5926 460644.218 499263.913 10.2040 -2.386AB2 45.3751 24.5630 458979.031 495452.365 11.0625 -2.646AB3 45.3911 24.5330 461452.392 491557.739 10.2436 -2.396AB4 45.3726 24.5033 458217.737 487719.860 10.7133 -2.536

AB5 45.3926 24.4732 461930.624 483809.374 10.8947 -2.596

AB6 45.3712 24.4435 457805.570 479964.861 11.0437 -2.636AB7 45.3929 24.4134 462048.041 476060.724 10.2360 -2.396AB8 45.3809 24.3835 459594.706 472175.238 10.2731 -2.406AB9 45.3921 24.3533 461835.836 468245.619 11.0804 -2.646AB10 45.3718 24.3233 458060.179 464327.614 10.1123 -2.356AB11 45.3901 24.2933 461262.836 460449.161 10.8587 -2.586AB12 45.3739 24.2632 458757.701 456513.176 10.7265 -2.546

B 45.3809 24.1910 459757.368 446948.653 14.0361 -3.536

A 45.3827 25.0223 460123.721 503061.796 0.0000 0.0000

AC1 45.4004 25.0041 463082.698 500887.286 13.0976 -3.2560

AC2 45.4051 24.5739 464534.112 496949.312 13.3607 -3.3360

AC3 45.4313 24.5705 468917.594 496216.353 12.5206 -3.0860

AC4 45.4323 24.5304 469231.591 491006.177 13.0842 -3.2460

AC5 45.4616 24.5317 474571.179 491294.723 12.5681 -3.0960

AC6 45.4602 24.4838 474150.371 485266.962 12.4617 -3.0660

AC7 45.4912 24.4920 480013.060 486187.343 12.5180 -3.0760

AC8 45.4848 24.4424 479289.713 479796.565 12.8190 -3.1660

AC9 45.5203 24.4509 485305.787 480786.564 13.0795 -3.2460

AC10 45.5142 24.4019 484680.079 474530.349 12.8397 -3.1760

AC11 45.5446 24.4047 490357.292 475157.020 13.1501 -3.2660

AC12 45.5444 24.3621 490321.199 469425.354 13.3646 -3.3360

AC13 45.5722 24.3617 495198.774 469363.357 12.7030 -3.1360

AC14 45.5722 24.3242 495223.451 464734.465 12.4400 -3.0560

C 46.0350 24.2724 507243.329 457969.697 18.4636 -4.8660

A 45.3827 25.0223 460123.721 503061.796 0.0000 0.0000

AD1 45.4024 25.0250 463701.049 503678.627 7.9059 -1.6960

AD2 45.4221 25.0128 467311.664 501903.125 8.5029 -1.8760

AD3 45.4419 25.0330 470955.313 504538.887 8.2126 -1.7860

AD4 45.4617 25.0050 474596.061 501080.054 8.4411 -1.8560

AD5 45.4815 25.0353 478240.321 505030.096 7.9823 -1.7160

Nr. pct.

AD6 45.5013 25.0030 481880.661 500647.271 8.4173 -1.8460

AD7 45.5211 25.0358 485525.107 505132.000 7.7618 -1.6560

AD8 45.5410 25.0026 489196.253 500560.306 7.9126 -1.6960

II. Compensarea reţelei libere de nivelment geometric

c. Compensarea reţelei libere de nivelment geometric folosind sistemul de altitudini normale

Calculul corecţiilor normale pe tronsoane

γ45 = 980617.600 mgal

Tronson Gravitatea

H δho g

De la La [m] [m] [m] [mgal] [mgal]

A AB1 1052.7110 1057.8130 10.2040 977862.9700 977861.7770AB1 AB2 1062.9150 1068.4463 11.0625 977860.5840 977859.2610AB2 AB3 1073.9775 1079.0993 10.2436 977857.9380 977856.7400AB3 AB4 1084.2211 1089.5778 10.7133 977855.5420 977854.2740AB4 AB5 1094.9344 1100.3818 10.8947 977853.0060 977851.7080AB5 AB6 1105.8291 1111.3510 11.0437 977850.4100 977849.0920AB6 AB7 1116.8728 1121.9908 10.2360 977847.7740 977846.5760AB7 AB8 1127.1088 1132.2454 10.2731 977845.3780 977844.1750AB8 AB9 1137.3819 1142.9221 11.0804 977842.9720 977841.6490AB9 AB10 1148.4623 1153.5185 10.1123 977840.3260 977839.1480AB10 AB11 1158.5746 1164.0039 10.8587 977837.9700 977836.6770AB11 AB12 1169.4333 1174.7966 10.7265 977835.3840 977834.1110AB12 B 1180.1598 1187.1779 14.0361 977832.8380 977831.0700

B - 1194.1959 - - 977829.3020 -A AC1 1052.7110 1059.2598 13.0976 977862.9700 977861.3420

AC1 AC2 1065.8086 1072.4890 13.3607 977859.7140 977858.0460AC2 AC3 1079.1693 1085.4296 12.5206 977856.3780 977854.8350AC3 AC4 1091.6899 1098.2320 13.0842 977853.2920 977851.6690AC4 AC5 1104.7741 1111.0582 12.5681 977850.0460 977848.4980AC5 AC6 1117.3422 1123.5731 12.4617 977846.9500 977845.4170AC6 AC7 1129.8039 1136.0629 12.5180 977843.8840 977842.3460AC7 AC8 1142.3219 1148.7314 12.8190 977840.8080 977839.2250AC8 AC9 1155.1409 1161.6807 13.0795 977837.6420 977836.0190AC9 AC10 1168.2204 1174.6403 12.8397 977834.3960 977832.8080

AC10 AC11 1181.0601 1187.6352 13.1501 977831.2200 977829.5870AC11 AC12 1194.2102 1200.8925 13.3646 977827.9540 977826.2860AC12 AC13 1207.5748 1213.9263 12.7030 977824.6180 977823.0500AC13 AC14 1220.2778 1226.4978 12.4400 977821.4820 977819.9540AC14 C 1232.7178 1241.9496 18.4636 977818.4260 977815.9930

C - 1251.1814 - - 977813.5600 -A AD1 1052.7110 1056.6640 7.9059 977862.9700 977862.1220

AD1 AD2 1060.6169 1064.8684 8.5029 977861.2740 977860.3360AD2 AD3 1069.1198 1073.2261 8.2126 977859.3980 977858.5050AD3 AD4 1077.3324 1081.5530 8.4411 977857.6120 977856.6840

Altitudiniprovizorii

Altitudinimedii

Diferenţe măsurate

Gravitateamedie

Hm= (Hi+Hj)/2

gm= (gi+gj)/2

AD4 AD5 1085.7735 1089.7647 7.9823 977855.7560 977854.8980AD5 AD6 1093.7558 1097.9645 8.4173 977854.0400 977853.1170AD6 AD7 1102.1731 1106.0540 7.7618 977852.1940 977851.3660AD7 AD8 1109.9349 1113.8912 7.9126 977850.5380 977849.6900AD8 AD9 1117.8475 1121.8558 8.0166 977848.8420 977847.9790AD9 AD10 1125.8641 1129.6926 7.6569 977847.1160 977846.3030

AD10 AD11 1133.5210 1137.5285 8.0150 977845.4900 977844.6270AD11 AD12 1141.5360 1145.4052 7.7383 977843.7640 977842.9410AD12 D 1149.2743 1153.6694 8.7902 977842.1180 977841.1350

D - 1158.0645 - - 977840.1520 -B BC1 1194.1959 1196.9172 5.4426 977829.3020 977828.8240

BC1 BC2 1199.6385 1202.4998 5.7226 977828.3460 977827.8230BC2 BC3 1205.3611 1208.1175 5.5127 977827.3000 977826.8120BC3 BC4 1210.8738 1213.5488 5.3499 977826.3240 977825.8610BC4 BC5 1216.2237 1218.9848 5.5222 977825.3980 977824.9050BC5 BC6 1221.7459 1224.3646 5.2374 977824.4120 977823.9640BC6 BC7 1226.9833 1229.6721 5.3775 977823.5160 977823.0480BC7 BC8 1232.3608 1234.8788 5.0359 977822.5800 977822.1620BC8 BC9 1237.3967 1239.9699 5.1464 977821.7440 977821.3110BC9 BC10 1242.5431 1245.1713 5.2564 977820.8780 977820.4250BC10 C 1247.7995 1249.5082 3.4174 977819.9720 977819.7940

C - 1251.2169 - - 977819.6160 -C CD1 1251.1814 1247.1576 -8.0477 977813.5600 977815.1070

CD1 CD2 1243.1337 1239.0697 -8.1280 977816.6540 977818.2110CD2 CD3 1235.0057 1230.9511 -8.1093 977819.7680 977821.3200CD3 CD4 1226.8964 1222.7888 -8.2153 977822.8720 977824.4440CD4 CD5 1218.6811 1214.4975 -8.3673 977826.0160 977827.6080CD5 CD6 1210.3138 1206.2593 -8.1090 977829.2000 977830.7520CD6 CD7 1202.2048 1198.0906 -8.2284 977832.3040 977833.8760CD7 CD8 1193.9764 1190.0301 -7.8926 977835.4480 977836.9700CD8 CD9 1186.0838 1182.2153 -7.7370 977838.4920 977839.9890CD9 D 1178.3468 1168.2277 -20.2382 977841.4860 977844.8580

D - 1158.1086 - - 977848.2300 -

Diferenţe de nivel măsurate şi corectate

Nr. Tronson

1 A-B 141.4849 0.0922 141.4850 68218.13222 A-C 198.4704 -47.0977 198.4233 88481.91993 A-D 105.3535 -54.1277 105.2994 73603.80174 B-C 57.0210 -49.6947 56.9713 59705.87615 C-D -93.0728 -9.7612 -93.0826 53243.2257

Cote provizorii

Punct Relaţii de calcul Observaţii

A 1052.7110 HAo iniţial

B 1194.1959

δho[m]

δnorm[mm]

δho + δnorm[m]

D[m]

Cota provizorie[m]

HBo = HAo + δhABo

calculate din punctul A, fără a se ţine cont de

corecţiile normale

C 1251.1814

D 1158.0645


Triunghi Formule

n(ABC) δhAB + δhBC - δhAC 0.0355 35.5000

n(ACD) δhAC + δhCD - δhAD 0.0441 44.1000total - 0.0796 79.6000

Sistemul de ecuaţii

Nr. Tronson Pondere xA xB xC xD

1 A-B 0.0146589 -1 1 0 02 A-C 0.0113017 -1 0 1 03 A-D 0.0135863 -1 0 0 14 B-C 0.0167488 0 -1 1 05 C-D 0.0187817 0 0 -1 16 ecuaţie fictivă 1.5015472 1 1 1 1

Matricea ponderilor

0.0147 0 0 0 0 00 0.0113 0 0 0 00 0 0.0136 0 0 0

P 0 0 0 0.0167 0 00 0 0 0 0.0188 00 0 0 0 0 1.5015

Matricea coeficienţilor A

-1 1 0 0

-1 0 1 0 Matricea coeficienţilor transpusă AT

-1 0 0 1A 0 -1 1 0 AT

0 0 -1 11 1 1 1

Matricea ponderilor P

P 0.0146589 0 0 0 0 00 0.0113017 0 0 0 00 0 0.0135863 0 0 00 0 0 0.0167488 0 00 0 0 0 0.0187817 00 0 0 0 0 1.5015472

HCo = HAo + δhACo

HDo = HAo + δhADo

Neînchideri[m]

Neînchideri[mm]

Produsul AT*P

AT*P -0.01465886 -0.01130174 -0.01358625 0 0 1.501547200.01465886 0 0 -0.01674877 0 1.50154720

0 0.01130174 0 0.01674877 -0.01878173 1.501547200 0 0.01358625 0 0.01878173 1.50154720

Matricea sistemului normal (produsul AT*P*A) Matricea inversă a sistemului normal calculată din minorii matricei N

N 1.54109406 1.48688835 1.49024546 1.48796095 N-11.48688835 1.53295483 1.48479843 1.501547201.49024546 1.48479843 1.54837945 1.482765471.48796095 1.50154720 1.48276547 1.53391519

Vectorul AT*P*L

Determinantul sistemului L -0.00126633

D 0.000659495942 -0.00023910

0.00141497

0.00009045

Minori

11 1.53295483 1.48479843 1.50154720 0.00943201843271.48479843 1.54837945 1.482765471.50154720 1.48276547 1.53391519

12 1.48688835 1.48479843 1.50154720 0.00269932352621.49024546 1.54837945 1.482765471.48796095 1.48276547 1.53391519

13 1.48688835 1.53295483 1.50154720 -0.00347297131321.49024546 1.48479843 1.482765471.48796095 1.50154720 1.53391519

14 1.48688835 1.53295483 1.48479843 0.00314992086121.49024546 1.48479843 1.548379451.48796095 1.50154720 1.48276547

21 1.48688835 1.49024546 1.48796095 0.00269932352621.48479843 1.54837945 1.482765471.50154720 1.48276547 1.53391519

22 1.54109406 1.49024546 1.48796095 0.01311281731251.49024546 1.54837945 1.482765471.48796095 1.48276547 1.53391519

23 1.54109406 1.48688835 1.48796095 0.0025799171.49024546 1.48479843 1.482765471.48796095 1.50154720 1.53391519

24 1.54109406 1.48688835 1.49024546 -0.0077237741.49024546 1.48479843 1.548379451.48796095 1.50154720 1.48276547


Nr. Coeficienţi

xA xB xC xD L

1 1.54109406 1.48688835 1.49024546 1.48796095 -0.0012663282 1.48688835 1.53295483 1.48479843 1.50154720 -0.0002390953 1.49024546 1.48479843 1.54837945 1.48276547 0.0014149724 1.48796095 1.50154720 1.48276547 1.53391519 0.000090450


Nr. xA xB xC xD L

1 1.5410941 1.4868883 1.4902455 1.4879609 -0.001266332 -1.0000000 -0.96482647 -0.96700487 -0.96552247 0.000821713 1.5329548 1.4847984 1.5015472 -0.000239104 0.09836560 0.04697017 0.06592309 0.000982695 -1.00000000 -0.47750602 -0.67018443 -0.009990196 1.5483795 1.4827655 0.001414977 0.08487630 0.01242132 0.002170288 -1.00000000 -0.14634612 -0.025569879 1.5339152 0.0000904510 0.05125701 0.0003369211 -1.00000000 -0.0065731912 0.02501562 0.00616549 -0.02460791 -0.00657319 -0.00006857

xA xB xC xD


Nr. Corecţia Termen liber l Pondere

[m] [m] [mm]

1 vAB = -xA + xB + lAB -0.00009223 -0.018942363 -18.9423627 0.01465892 vAC = -xA + xC + lAC 0.04709775 -0.002525786 -2.5257856 0.01130173 vAD = -xA + xD + lAD 0.05412771 0.022538898 22.5388981 0.01358634 vBC = -xB + xC + lBC 0.01419467 -0.016578735 -16.5787353 0.01674885 vCD = -xC + xD + lCD -0.03433882 -0.016304099 -16.3040986 0.0187817


m = numărul de măsurători 5 Punct

n = numărul de necunoscute 4 [m]

d = defectul de rang 1 A 0.0124941

so = eroarea unităţii de pondere [m] 0.0033038 B 0.0147317

C 0.0115394

D 0.0145926

Altitudini compensate (definitive) ale punctelor noi în sistemul de altitudini normale

Punct Cote provizorii Diferenţe Cote compensate

Termenliber

Valoare calculatăcorecţie

Abatere standard

[m] [mm] [m]

A 1052.7110 25.0156 1052.7360B 1194.1959 6.1655 1194.2021C 1251.1814 -24.6079 1251.1568D 1158.0645 -6.5732 1158.0579


Tronson δhijo δhnorm Corecţia δhcomp δhcalc

[m] [mm] [mm] [m] [m]

AB 141.4849 0.0922 -18.94236266 141.4660 141.4660AC 198.4704 -47.0977 -2.52578563 198.4208 198.4208AD 105.3535 -54.1277 22.53889805 105.3219 105.3219BC 57.0210 -49.6947 -16.57873532 56.9547 56.9547CD -93.0728 -9.7612 -16.30409856 -93.0989 -93.0989

2. Coordonatele geodezice aproximative, diferenţele de nivel şi gravitate rezultate în urma măsurătorilor de nivelment geometric şi de gravimetrie,

Coordonate planimetriceδh δg

B L X0 Y0

[gg.mmss] [gg.mmss] [m] [m] [m] [mgal]

AD9 45.5608 25.0346 492840.538 504867.482 8.0166 -1.7260

AD10 45.5807 25.0040 496511.966 500860.989 7.6569 -1.6260

AD11 46.0005 25.0311 500155.709 504108.797 8.0150 -1.7260

AD12 46.0206 25.0112 503889.597 501547.928 7.7383 -1.6460

D 46.0908 25.0159 516916.529 502552.970 8.7902 -1.9660

B 45.38086 24.19096 459757.367549 446948.65335 0.0000 0.0000

BC1 45.3959 24.2016 463140.825 448405.955 5.4426 -0.9560

BC2 45.4204 24.1937 467006.244 447594.431 5.7226 -1.0460

BC3 45.4341 24.2213 469973.007 450992.110 5.5127 -0.9760

BC4 45.4559 24.2026 474251.304 448714.154 5.3499 -0.9260

BC5 45.4729 24.2352 476994.364 453185.412 5.5222 -0.9860

BC6 45.4951 24.2134 481400.700 450240.677 5.2374 -0.8960

BC7 45.5120 24.2510 484112.374 454921.610 5.3775 -0.9360

BC8 45.5340 24.2303 488454.388 452215.746 5.0359 -0.8360

BC9 45.5516 24.2610 491387.965 456267.262 5.1464 -0.8660

BC10 45.5729 24.2452 495505.547 454617.041 5.2564 -0.9060

C 46.0350 24.2724 507243.329 457969.697 3.4174 -0.3560

C 46.03496 24.27236 507243.328602 457969.697101 0.0000 0.0000

CD1 46.0357 24.3024 507434.196 461838.883 -8.0477 3.0940

CD2 46.0512 24.3302 509729.232 465246.940 -8.1280 3.1140

CD3 46.0422 24.3623 508162.888 469556.611 -8.1093 3.1040

CD4 46.0621 24.3848 511821.644 472688.168 -8.2153 3.1440

CD5 46.0501 24.4220 509333.574 477231.016 -8.3673 3.1840

CD6 46.0715 24.4441 513459.523 480272.995 -8.1090 3.1040

CD7 46.0556 24.4813 511007.937 484817.717 -8.2284 3.1440

CD8 46.0756 24.5041 514705.166 488003.134 -7.8926 3.0440

CD9 46.0705 24.5403 513123.902 492336.356 -7.7370 2.9940

D 46.0908 25.0159 516916.529 502552.970 -20.2382 6.7440

Nr. pct.

Coordonate geodezice aproximative

δg (gm-γm)/γ45 δors

[mgal] [mgal] [mgal] - [mm] [mm] [mm] [m]

-2.3860 980292.7334 980291.1589 -0.0024774 -0.0252794 -0.6056 -0.6309 9.5731-2.6460 980289.5844 980287.8775 -0.0024766 -0.0273976 1.5148 1.4874 12.5499-2.3960 980286.1705 980284.5900 -0.0024758 -0.0253615 -2.2661 -2.2914 7.9522-2.5360 980283.0094 980281.3563 -0.0024751 -0.0265160 3.0025 2.9760 13.6893-2.5960 980279.7032 980278.0222 -0.0024743 -0.0269564 -3.4647 -3.4917 7.4030-2.6360 980276.3411 980274.6371 -0.0024735 -0.0273165 3.9067 3.8794 14.9231-2.3960 980272.9331 980271.3536 -0.0024727 -0.0253106 -4.0316 -4.0569 6.1791-2.4060 980269.7742 980268.1891 -0.0024719 -0.0253943 2.3753 2.3499 12.6230-2.6460 980266.6039 980264.8942 -0.0024711 -0.0273812 -2.1575 -2.1849 8.8955-2.3560 980263.1845 980261.6242 -0.0024704 -0.0249810 3.7193 3.6943 13.8066-2.5860 980260.0639 980258.3884 -0.0024696 -0.0268164 -3.1423 -3.1691 7.6896-2.5460 980256.7129 980255.0578 -0.0024688 -0.0264816 2.5244 2.4979 13.2244-3.5360 980253.4027 980251.2369 -0.0024680 -0.0346411 -0.9331 -0.9677 13.0684

- 980249.0711 - - - - - --3.2560 980292.7334 980290.7124 -0.0024774 -0.0324478 -2.8038 -2.8363 10.2613-3.3360 980288.6915 980286.6299 -0.0024766 -0.0330889 -1.3230 -1.3561 12.0046-3.0860 980284.5684 980282.6364 -0.0024758 -0.0309984 -4.0444 -4.0754 8.4452-3.2460 980280.7045 980278.6856 -0.0024750 -0.0323832 -0.2881 -0.3205 12.7637-3.0960 980276.6667 980274.7275 -0.0024742 -0.0310958 -5.0412 -5.0723 7.4958-3.0660 980272.7882 980270.8654 -0.0024734 -0.0308226 0.4125 0.3816 12.8433-3.0760 980268.9425 980267.0110 -0.0024726 -0.0309519 -5.6586 -5.6896 6.8284-3.1660 980265.0795 980263.1015 -0.0024718 -0.0316858 0.7226 0.6909 13.5099-3.2460 980261.1235 980259.1054 -0.0024710 -0.0323192 -5.9359 -5.9682 7.1113-3.1760 980257.0872 980255.1060 -0.0024702 -0.0317163 0.6462 0.6145 13.4542-3.2660 980253.1249 980251.0958 -0.0024694 -0.0324725 -5.7237 -5.7562 7.3939-3.3360 980249.0667 980247.0046 -0.0024686 -0.0329914 0.0629 0.0299 13.3945-3.1360 980244.9424 980242.9823 -0.0024678 -0.0313480 -5.0217 -5.0530 7.6500-3.0560 980241.0223 980239.1028 -0.0024670 -0.0306890 0.0000 -0.0307 12.4093-4.8660 980237.1833 980234.3344 -0.0024661 -0.0455338 -12.6110 -12.6566 5.8070

- 980231.4854 - - - - - --1.6960 980292.7334 980291.5135 -0.0024774 -0.0195862 -3.3521 -3.3717 4.5342-1.8760 980290.2936 980288.9816 -0.0024766 -0.0210587 -3.2705 -3.2916 5.2113-1.7860 980287.6696 980286.4024 -0.0024759 -0.0203335 -3.3238 -3.3441 4.8685-1.8560 980285.1352 980283.8328 -0.0024751 -0.0208928 -3.3491 -3.3700 5.0711

Diferenţe de gravitate

Gravitateanormală

Gravitatea normală

medie

Termen decalcul

Corecţia datoratăgravităţii

Corecţieortometrică

Corecţia normală

Diferenţe de nivel

corectate

γ=γ45-

0,3086*Hi

γm= (γi+γj)/2

δn = δho*(gm-

γm)/γ45

δnorm= δors+δn

δho + δhnorm

-1.7160 980282.5303 980281.2986 -0.0024744 -0.0197511 -3.3740 -3.3937 4.5886-1.8460 980280.0670 980278.7682 -0.0024736 -0.0208210 -3.3988 -3.4196 4.9977-1.6560 980277.4694 980276.2717 -0.0024728 -0.0191937 -3.4233 -3.4425 4.3193-1.6960 980275.0741 980273.8532 -0.0024721 -0.0195606 -3.4763 -3.4959 4.4167-1.7260 980272.6323 980271.3953 -0.0024713 -0.0198116 -3.4713 -3.4911 4.5255-1.6260 980270.1583 980268.9769 -0.0024706 -0.0189168 -3.5246 -3.5435 4.1134-1.7260 980267.7954 980266.5587 -0.0024698 -0.0197955 -3.5188 -3.5386 4.4764-1.6460 980265.3220 980264.1280 -0.0024690 -0.0191062 -3.6311 -3.6502 4.0881-1.9660 980262.9340 980261.5776 -0.0024683 -0.0216967 -12.7535 -12.7752 -3.9850

- 980260.2213 - - - - - --0.9560 980249.0711 980248.2314 -0.0024672 -0.0134281 -3.4465 -3.4600 1.9826-1.0460 980247.3916 980246.5086 -0.0024665 -0.0141147 -3.9344 -3.9485 1.7741-0.9760 980245.6256 980244.7750 -0.0024658 -0.0135930 -3.0685 -3.0821 2.4306-0.9260 980243.9243 980243.0989 -0.0024650 -0.0131876 -4.3847 -4.3979 0.9520-0.9860 980242.2734 980241.4213 -0.0024643 -0.0136082 -2.8722 -2.8858 2.6364-0.8960 980240.5692 980239.7611 -0.0024635 -0.0129026 -4.5513 -4.5642 0.6732-0.9360 980238.9530 980238.1232 -0.0024628 -0.0132438 -2.8647 -2.8779 2.4996-0.8360 980237.2935 980236.5164 -0.0024621 -0.0123988 -4.5250 -4.5374 0.4985-0.8660 980235.7394 980234.9453 -0.0024613 -0.0126670 -3.1154 -3.1281 2.0183-0.9060 980234.1512 980233.3401 -0.0024606 -0.0129339 -4.3339 -4.3468 0.9096-0.3560 980232.5291 980232.0018 -0.0024599 -0.0084064 -12.4577 -12.4661 -9.0487

- 980231.4745 - - - - - -3.0940 980231.4854 980232.7272 -0.0024654 0.0198408 -0.2284 -0.2085 -8.25623.1140 980233.9689 980235.2231 -0.0024648 0.0200338 -2.4311 -2.4111 -10.53913.1040 980236.4772 980237.7285 -0.0024642 0.0199827 1.6103 1.6303 -6.47903.1440 980238.9798 980240.2474 -0.0024636 0.0202388 -3.8076 -3.7874 -12.00273.1840 980241.5150 980242.8061 -0.0024629 0.0206081 2.5427 2.5633 -5.80403.1040 980244.0972 980245.3484 -0.0024623 0.0199670 -4.2307 -4.2107 -12.31973.1440 980246.5996 980247.8692 -0.0024617 0.0202559 2.4776 2.4979 -5.73053.0440 980249.1389 980250.3567 -0.0024611 0.0194244 -3.7387 -3.7193 -11.61192.9940 980251.5745 980252.7684 -0.0024605 0.0190366 1.5787 1.5977 -6.13936.7440 980253.9622 980257.0849 -0.0024599 0.0497841 -3.7633 -3.7135 -23.9517

- 980260.2077 - - - - - -

s Relaţii de calcul

-0.00009223 -0.00009223 l.AB = -δnormAB0.04709775 0.04709775 l.AC = -δnormAC0.05412771 0.05412771 l.AD = -δnormAD0.01419467 0.01419467l.BC = -n(ABC) – δnormBC-0.03433882 -0.03433882l.CD = -n(ACD) – δnormCD

0 4.00000000 X

Matricea coeficienţilor transpusă AT

-1 -1 -1 0 0 11 0 0 -1 0 10 1 0 1 -1 10 0 1 0 1 1

l[m]


14.30185970 -4.09301006 -5.26609960 -4.77625511-4.09301006 19.88309022 -3.91195353 -11.71163170-5.26609960 -3.91195353 12.19969127 -2.85514321-4.77625511 -11.71163170 -2.85514321 19.50952495

31 1.48688835 1.49024546 1.48796095 -0.0034729711.53295483 1.48479843 1.501547201.50154720 1.48276547 1.53391519

32 1.54109406 1.49024546 1.48796095 0.0025799171.48688835 1.48479843 1.501547201.48796095 1.48276547 1.53391519

33 1.54109406 1.48688835 1.48796095 0.0080456471.48688835 1.53295483 1.501547201.48796095 1.50154720 1.53391519

34 1.54109406 1.48688835 1.49024546 0.0018829551.48688835 1.53295483 1.484798431.48796095 1.50154720 1.48276547

41 1.48688835 1.49024546 1.48796095 0.0031499211.53295483 1.48479843 1.501547201.48479843 1.54837945 1.48276547

42 1.54109406 1.49024546 1.48796095 -0.0077237741.48688835 1.48479843 1.501547201.49024546 1.54837945 1.48276547

43 1.54109406 1.48688835 1.48796095 0.0018829551.48688835 1.53295483 1.501547201.49024546 1.48479843 1.48276547

44 1.54109406 1.48688835 1.49024546 0.0128664531.48688835 1.53295483 1.484798431.49024546 1.48479843 1.54837945

Elementele matricei inverse Soluţii

N-1 X Necunoscuta

14.30185970 -4.09301006 -5.26609960 -4.77625511 0.02501562 xA [m]-4.09301006 19.88309022 -3.91195353 -11.71163170 0.00616549 xB [m]-5.26609960 -3.91195353 12.19969127 -2.85514321 -0.02460791 xC [m]-4.77625511 -11.71163170 -2.85514321 19.50952495 -0.00657319 xD [m]

S Control QA QB QC QD

6.0049225 6.0049225 1 0 0 0-3.8965321 -3.8965321 -0.64888966 0.00000000 0.00000000 0.000000006.0059497 6.0059497 0 1 0 00.2122415 0.2122415 -0.96482647 1.00000000 0.00000000 0.00000000-2.1576806 -2.1576806 9.80857612 -10.16615569 0.00000000 0.000000006.0076038 6.0076038 0 0 1 00.0994679 0.0994679 -0.50629442 -0.47750602 1.00000000 0.00000000-1.1719160 -1.1719160 5.96508598 5.62590535 -11.78185215 0.000000006.0062793 6.0062793 0 0 0 10.0515939 0.0515939 -0.24481658 -0.60030327 -0.14634612 1.00000000-1.0065732 -1.0065732 4.77625511 11.71163170 2.85514321 -19.50952495-0.0000686 -0.0000686 14.3018597 19.8830902 12.1996913 19.5095250

[pvv]

0.0000218298 21.82983735

[mm]

12.4941440

14.7316772

11.5394384

14.5926310

N= 3 0.0000033

0.0006

II. Date iniţiale

Se dă reţeaua de nivelment trigonometric dezvoltată din punctul A şi formată din punctele A, A1, A2, A3, dată prin: - coordonatele geodezice aproximative B, L; - distanţele zenitale măsurate şi lungimile laturilor; - înălţimea instrumentului şi a semnalului, în fiecare punct al reţelei.

Datele reţelei de nivelment trigonometric

Punct B B L

[grade] [minute] [secunde] [gg.mmss] [grade] [minute]

A 45 38 28.36 45.382836 25 2A1 45 38 28.36 45.382836 25 0A2 45 39 58.36 45.395836 25 0A3 45 39 57.36 45.395736 25 2

Măsurători în reţeaua de nivelment trigonometric

A A1 98.3914867 2624.0476A A2 99.7187767 3838.3746A A3 98.8122467 2756.8216A1 A2 101.0545667 2783.9786A1 A3 100.2116367 3804.5006A1 A 101.4710267 2624.0476A2 A3 99.1222267 2640.5016A2 A 100.2107167 3838.3746A2 A1 98.8323167 2783.9786A3 A 101.0602867 2756.8216A3 A1 99.7171067 3804.5006A3 A2 100.7569467 2640.5016

Compensarea reţelei de nivelment trigonometric

Parametrii elipsoidului Krasovski

a = 6378245.000 m semiaxa maref = 1/298,3 = 0.003352330 - turtirea geometricăb = a*(1-f) = 6356863.018773 m semiaxa mică

e = 0.081813334017 - prima excentricitatec = a^2/b = 6399698.901783 m raza de curbură polară

Calculul razelor medii

Tronson Unghi zenital W

Zi Rm

Punctstaţie

Punctvizat

Unghi zenitalZo

DistanţaDijo

Raza medie de curbură

(Gauss)

Raza elipsei meridiane

Raza primului vertical

M N

De la La [g] [m] [m] [m] -A A1 98.3915 6375286.696 6363115.536 6387481.136 0.998554025A1 A 101.4710 6375286.696 6363115.536 6387481.136 0.998554025A A2 99.7188 6375295.020 6363127.999 6387485.306 0.998553373A2 A 100.2107 6375295.020 6363127.999 6387485.306 0.998553373A A3 98.8122 6375294.928 6363127.860 6387485.260 0.998553381A3 A 101.0603 6375294.928 6363127.860 6387485.260 0.998553381A1 A2 101.0546 6375295.020 6363127.999 6387485.306 0.998553373A2 A1 98.8323 6375295.020 6363127.999 6387485.306 0.998553373A1 A3 100.2116 6375294.928 6363127.860 6387485.260 0.998553381A3 A1 99.7171 6375294.928 6363127.860 6387485.260 0.998553381A2 A3 99.1222 6375303.253 6363140.324 6387489.430 0.998552729A3 A2 100.7569 6375303.253 6363140.324 6387489.430 0.998552729

Diferenţe de nivel calculate

Tronson ctgZo HI HS

De la La [g] - [m] [m] [m]A A1 98.3915 0.0252718 2624.0476 1.5841 4.8044A1 A 101.4710 -0.0231109 2624.0476 1.5741 5.0444A A2 99.7188 0.0044175 3838.3746 1.5841 4.3944A2 A 100.2107 -0.0033099 3838.3746 1.5041 5.0444A A3 98.8122 0.0186594 2756.8216 1.5841 4.7244A3 A 101.0603 -0.0166565 2756.8216 1.5541 5.0444A1 A2 101.0546 -0.0165666 2783.9786 1.5741 4.3944A2 A1 98.8323 0.0183440 2783.9786 1.5041 4.8044A1 A3 100.2116 -0.0033244 3804.5006 1.5741 4.7244A3 A1 99.7171 0.0044437 3804.5006 1.5541 4.8044A2 A3 99.1222 0.0137889 2640.5016 1.5041 4.7244A3 A2 100.7569 -0.0118907 2640.5016 1.5541 4.3944

Diferenţe de nivel medii aproximative

Tronson

De la La [m]A A1 63.6044A A2 15.1954A A3 48.8547A1 A2 -48.3552A1 A3 -14.7269A2 A3 33.7135

Altitudini provizorii

Punct Observaţii[m]

A 1050.4890 cota punctului A în sistemul de altitudini normaleA1 1114.0934A2 1065.6844A3 1099.3437

Unghi zenital Zo

DistanţaDijo

δhm =

(δhij+δhji)/2

Cota provizorie

calculate din punctul A, conform diferenţelor medii aproximative

Calculul distanţelor reduse pe elipsoid

Tronson Dijo Dij' Rm

De la La [m] [m] [m]A A1 2624.0476 2622.8314 6375286.696A A2 3838.3746 3837.7076 6375295.020A A3 2756.8216 2755.9240 6375294.928A1 A2 2783.9786 2783.0819 6375295.020A1 A3 3804.5006 3803.8117 6375294.928A2 A3 2640.5016 2639.8388 6375303.253

Diferenţe de nivel provizorii şi distanţele reduse la cota medie

Tronson Direcţia

De la La De la La [m] [m] [m]

A A1A A1 63.0942 2622.3862 6375286.696A1 A -64.1145 2622.3862 6375286.696

A A2A A2 14.1456 3837.0708 6375295.020A2 A -16.2451 3837.0708 6375295.020

A A3A A3 48.3002 2755.4594 6375294.928A3 A -49.4093 2755.4594 6375294.928

A1 A2A1 A2 -48.9414 2782.6062 6375295.020A2 A1 47.7690 2782.6062 6375295.020

A1 A3A1 A3 -15.7980 3803.1515 6375294.928A3 A1 13.6558 3803.1515 6375294.928

A2 A3A2 A3 33.1893 2639.3907 6375303.253A3 A2 -34.2376 2639.3907 6375303.253

Calculul coeficienţilor sistemului liniar de corecţii

ρcc = 636619.7723676 coeficient de transformare radiani-secunde cc

Ko = 0.13 coeficient de refracţie aproximativ

Tronson pij tij tij*100 aij bij

De la La - [m/cc] [cm/cc] [cc/cm] [cc]

A A1 0.0003813 0.0041219 0.41219 2.42609 130.93238A1 A 0.0003813 0.0041214 0.41214 2.42634 130.93238A A2 0.0002606 0.0060274 0.60274 1.65910 191.57977A2 A 0.0002606 0.0060273 0.60273 1.65911 191.57977A A3 0.0003629 0.0043298 0.43298 2.30959 137.57638A3 A 0.0003629 0.0043295 0.43295 2.30975 137.57638A1 A2 0.0003594 0.0043721 0.43721 2.28723 138.93178A2 A1 0.0003594 0.0043724 0.43724 2.28708 138.93178A1 A3 0.0002629 0.0059740 0.59740 1.67391 189.88623A3 A1 0.0002629 0.0059741 0.59741 1.67389 189.88623A2 A3 0.0003789 0.0041467 0.41467 2.41154 131.78105A3 A2 0.0003789 0.0041465 0.41465 2.41165 131.78105

Sistemul liniar al ecuaţiilor de corecţie

Tronsonp dx1 dx2 dx3 dy*100

De la La

A A1 0.00038 -2.42609 0 0 -130.93238

δhij = Dij'' = Raza medieRm

A1 A 0.00038 2.42634 0 0 -130.93238A A2 0.00026 0 -1.65910 0 -191.57977A2 A 0.00026 0 1.65911 0 -191.57977A A3 0.00036 0 0 -2.30959 -137.57638A3 A 0.00036 0 0 2.30959 -137.57638A1 A2 0.00036 2.28723 -2.28723 0 -138.93178A2 A1 0.00036 -2.28708 2.28708 0 -138.93178A1 A3 0.00026 1.67391 0 -1.67391 -189.88623A3 A1 0.00026 -1.67389 0 1.67389 -189.88623A2 A3 0.00038 0 2.41154 -2.41154 -131.78105A3 A2 0.00038 0 -2.41165 2.41165 -131.78105

Număr de ecuaţii: 12

Număr de necunoscute: 4

Sistemul normal al ecuaţiilor de corecţie (conform metodei celor mai mici pătrate)

Matricea coeficienţilor A Expresia matriceală a sistemuluiMatricea ponderilor P Sistemul normalizatVectorul necunoscutelor X Matricea normalăVectorul termenilor liberi L Soluţiile sistemuluiMatricea normală N Vectorul corecţiilor

Ecuaţie dx1 dx2 dx3 dy l s

1 0.00972276 -0.00375984 -0.00147349 -0.00002047 0.05140167 0.055870632 -0.00375984 0.00960152 -0.00440692 0.00001224 -0.01096653 -0.009519543 -0.00147349 -0.00440692 0.00975214 -0.00000514 -0.01237667 -0.008510074 -0.00002047 0.00001224 -0.00000514 91.93737992 6.62143850 98.55880505

Rezolvarea sistemului normal prin schema Gauss

Nr. dy*100 l s

1 0.00972276 -0.00375984 -0.00147349 -0.00002047 0.05140167 0.055870632 -1 0.3867053913 0.151550202791 0.002105138522712 -5.286737176804 -5.7463764442183 0.00960152 -0.00440692 0.00001224 -0.01096653 -0.009519544 0.00814757 -0.00497673 0.00000433 0.00891077 0.012085945 -1 0.610823574547 -0.00053120621545 -1.093672268001 -1.483379899676 0.00975214 -0.00000514 -0.01237667 -0.008510077 0.00648893 -0.00000560 0.00085617 0.007339518 -1 0.000863007715214 -0.131943633752 -1.1310806260379 91.93737992 6.62143850 98.5588050510 91.93737987 6.62154272 98.5589225811 -1 -0.072022312642 -1.07202231264212 -5.76098939 -1.17426626 -0.13200579 -0.07202231 -0.75850434 -7.40800131


Nr. Corecţia Pondere

[cc] [cc]

1 A A1 vij = - aij*dx1 – bij*dy + lij -20.04174 3.36497 0.000382 A1 A vij = aij*dx1 – bij*dy + lij -0.55188 -5.09995 0.000383 A A2 vij = - aij*dx2 – bij*dy + lij -8.44312 5.35490 0.00026

dx1[cm]

dx2[cm]

dx3[cm]

Termenliber

Valoare calculată corecţie

4 A2 A vij = aij*dx2 – bij*dy + lij -6.77302 7.02500 0.000265 A A3 vij = - aij*dx3 – bij*dy + lij -14.25224 -4.34367 0.000366 A3 A vij = aij*dx3 – bij*dy + lij -3.15032 6.75825 0.000367 A1 A2 vij = aij*dx1 – aij*dx2 – bij*dy + lij 4.30522 1.13472 0.000368 A2 A1 vij = - aij*dx1 + aij*dx2 – bij*dy + lij -31.27393 -8.09187 0.000369 A1 A3 vij = aij*dx1 – aij*dx3 – bij*dy + lij -9.52590 -5.49322 0.0002610 A3 A1 vij = - aij*dx1 + aij*dx3 – bij*dy + lij -18.90335 4.41598 0.0002611 A2 A3 vij = aij*dx2 – aij*dx3 – bij*dy + lij -2.39763 7.09354 0.0003812 A3 A2 vij = - aij*dx2 + aij*dx3 – bij*dy + lij -21.61011 -12.11893 0.00038

Calculul abaterii standard a necunoscutelor

Eroarea unităţii de pondere = 0.14567 cm SQRT([pvv]/(m-n+d))Numărul de măsurători (ecuaţii) = 12 - m

Numărul de necunoscute = 4 - nDefectul de rang = 0 - d

s1 = -69.22227 cm abaterea standard pentru dx1s2 = -77.34217 cm abaterea standard pentru dx2s3 = -71.51718 cm abaterea standard pentru dx3s4 = -0.60083 - abaterea standard pentru dy

Altitudinile compensate (definitive) ale punctelor noi

Punctdx

[m] [cm] [m]

A 1050.4890 1050.4890A1 1114.0934 -5.761 1114.0358A2 1065.6844 -1.174 1065.6726A3 1099.3437 -0.132 1099.3424

Valoarea compensată a coeficientului de refracţie

Ko 0.13dy*100 -0.0720223

K 0.0579777


Tronson Direcţia Dij''

De la La De la La [m] - [m]

A A1A A1 63.09423 2.4261 2622.3862A1 A -64.11452 2.4263 2622.3862

A A2A A2 14.14562 1.6591 3837.0708A2 A -16.24510 1.6591 3837.0708

A A3A A3 48.30020 2.3096 2755.4594A3 A -49.40926 2.3098 2755.4594

A1 A2A1 A2 -48.94139 2.2872 2782.6062A2 A1 47.76896 2.2871 2782.6062

A1 A3A1 A3 -15.79796 1.6739 3803.1515A3 A1 13.65579 1.6739 3803.1515

A2 A3A2 A3 33.18932 2.4115 2639.3907A3 A2 -34.23758 2.4117 2639.3907

Cota provizorie

Cota compensată

δhij = aij =

Tronson Corecţie δhijcomp ΔH = Hj - Hi

De la La [g] [cc] [g] [m] [m]

A A1 98.39149 3.36497 98.39182 63.60438A1 A 101.47103 -5.09995 101.47052 -63.60438A A2 99.71878 5.35490 99.71931 15.19536A2 A 100.21072 7.02500 100.21142 -15.19536A A3 98.81225 -4.34367 98.81181 48.85473A3 A 101.06029 6.75825 101.06096 -48.85473A1 A2 101.05457 1.13472 101.05468 -48.40902A2 A1 98.83232 -8.09187 98.83151 48.40902A1 A3 100.21164 -5.49322 100.21109 -14.74965A3 A1 99.71711 4.41598 99.71755 14.74965A2 A3 99.12223 7.09354 99.12294 33.65937A3 A2 100.75695 -12.11893 100.75573 -33.65937

Matricea coeficienţilor A Vectorul termenilor liberi L

A

-2.42609 0.00000 0.00000 -130.93238

L

2.42634 0.00000 0.00000 -130.932380.00000 -1.65910 0.00000 -191.579770.00000 1.65911 0.00000 -191.579770.00000 0.00000 -2.30959 -137.576380.00000 0.00000 2.30959 -137.576382.28723 -2.28723 0.00000 -138.93178-2.28708 2.28708 0.00000 -138.931781.67391 0.00000 -1.67391 -189.88623-1.67389 0.00000 1.67389 -189.886230.00000 2.41154 -2.41154 -131.781050.00000 -2.41165 2.41165 -131.78105

Matricea coeficienţilor transpusă AT

AT

-2.42608601197 2.4263395247 0 0 0 00 0 -1.659097234915 1.65911143390831 0 00 0 0 0 -2.309590158554 2.309590158554

-130.932378137 -130.9323781 -191.5797707384 -191.579770738364 -137.5763765483 -137.5763765483

Matricea ponderilor P

P

0.00038 0 0 0 0 00 0.00038 0 0 0 00 0 0.00026 0 0 00 0 0 0.00026 0 00 0 0 0 0.00036 00 0 0 0 0 0.000360 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

Unghi zenitalZ

Unghi zenitalcompensat

Zcomp

Produsul AT*P

AT*P

-0.00092514444 0.0009252411 0 0 0 00 0 -0.000432386405 0.000432390105817 0 00 0 0 0 -0.00083818696 0.00083818696

-0.04992871715 -0.049928717 -0.049928651957 -0.04992865195725 -0.049928652682 -0.049928652682

Matricea sistemului normal (produsul AT*P*A) Matricea inversă a sistemului normal calculată din minorii matricei N

N

0.0097228 -0.0037598 -0.0014735 -0.0000205

N-1-0.0037598 0.0096015 -0.0044069 0.0000122-0.0014735 -0.0044069 0.0097521 -0.0000051-0.0000205 0.0000122 -0.0000051 91.9373799

Determinantul matricei sistemului

D 0.00004726

Minori

110.00960152 -0.00440692 0.00001224

0.00682308045714131

-0.00440692 0.00975214 -0.000005140.00001224 -0.00000514 91.93737992

12-0.00375984 -0.00440692 0.00001224

-0.0039680231641232

-0.00147349 0.00975214 -0.00000514-0.00002047 -0.00000514 91.93737992

13-0.00375984 0.00960152 0.00001224

0.00282404346877133

-0.00147349 -0.00440692 -0.00000514-0.00002047 0.00001224 91.93737992

14-0.00375984 0.00960152 -0.00440692

-1.1485328576E-0934

-0.00147349 -0.00440692 0.00975214-0.00002047 0.00001224 -0.00000514

21-0.00375984 -0.00147349 -0.00002047

-0.0039680231641241

-0.00440692 0.00975214 -0.000005140.00001224 -0.00000514 91.93737992

220.00972276 -0.00147349 -0.00002047

0.0085176828993242

-0.00147349 0.00975214 -0.00000514-0.00002047 -0.00000514 91.93737992

230.00972276 -0.00375984 -0.00002047

-0.0044543

-0.00147349 -0.00440692 -0.00000514-0.00002047 0.00001224 91.93737992

240.00972276 -0.00375984 -0.00147349

0.00000000044

-0.00147349 -0.00440692 0.00975214-0.00002047 0.00001224 -0.00000514


Coeficienţi Elementele matricei inverse

xA xB xC xD L N-1

0.0097228 -0.0037598 -0.0014735 -0.0000205 0.0514017 144.376845759 83.963639581-0.0037598 0.0096015 -0.0044069 0.0000122 -0.0109665 83.963639581 180.234748499-0.0014735 -0.0044069 0.0097521 -0.0000051 -0.0123767 59.756951551 94.133101633-0.0000205 0.0000122 -0.0000051 91.9373799 6.6214385 0.000024303 -0.000000044

Vectorul corecţiilor A*X + L

V

3.36497

A*X

23.40671-5.09995 -4.548067.30312 15.746245.07676 11.84978-4.03879 10.213456.45337 9.603693.82053 -0.48469

-10.77751 20.49641-5.27226 4.253644.19502 23.098374.58009 6.97773-9.60536 12.00475

Vectorul corecţiilor transpus VT

VT 3.36497 -5.09995 7.30312 5.07676 -4.03879 6.45337

Produsul VT*P

VT*P 0.00128 -0.00194 0.00190 0.00132 -0.00147 0.00234

Produsul VT*P*V

VT*P*V 0.15772

Termenliber

L Hi Hs

[secunde] [gg.mmss] [m] [m]

21.64 25.022164 1.5841 5.044420.64 25.002064 1.5741 4.804419.64 25.001964 1.5041 4.394421.64 25.022164 1.5541 4.7244

sinBm Bi Bj Bm

- [secunde] [secunde] [secunde] [grade]0.657073877 164308.360 164308.360 164308.360 45.6412110.657073877 164308.360 164308.360 164308.360 45.6412110.657221878 164308.360 164398.360 164353.360 45.6537110.657221878 164398.360 164308.360 164353.360 45.6537110.657220234 164308.360 164397.360 164352.860 45.6535720.657220234 164397.360 164308.360 164352.860 45.6535720.657221878 164308.360 164398.360 164353.360 45.6537110.657221878 164398.360 164308.360 164353.360 45.6537110.657220234 164308.360 164397.360 164352.860 45.6535720.657220234 164397.360 164308.360 164352.860 45.6535720.657368209 164398.360 164397.360 164397.860 45.6660720.657368209 164397.360 164398.360 164397.860 45.666072

[m]63.0942-64.114514.1456-16.245148.3002-49.4093-48.941447.7690-15.798013.655833.1893-34.2376

δhij

Hi Hj Dij'

[m] [m] [m] [g]

1050.4890 1114.0934 2622.8314 98.39151114.0934 1050.4890 2622.8314 101.47101050.4890 1065.6844 3837.7076 99.71881065.6844 1050.4890 3837.7076 100.21071050.4890 1099.3437 2755.9240 98.81221099.3437 1050.4890 2755.9240 101.06031114.0934 1065.6844 2783.0819 101.05461065.6844 1114.0934 2783.0819 98.83231114.0934 1099.3437 3803.8117 100.21161099.3437 1114.0934 3803.8117 99.71711065.6844 1099.3437 2639.8388 99.12221099.3437 1065.6844 2639.8388 100.7569

lij

[cc]

-20.04174-0.55188-8.44312-6.77302

-14.25224-3.150324.30522

-31.27393-9.52590

-18.90335-2.39763

-21.61011

l Sumă

-20.04174 -153.40020

Unghi zenital Zo

-0.55188 -129.05792-8.44312 -201.68199-6.77302 -196.69368

-14.25224 -154.13821-3.15032 -138.417114.30522 -134.62656

-31.27393 -170.20570-9.52590 -199.41213

-18.90335 -208.78958-2.39763 -134.17868

-21.61011 -153.39116

A*X + L = PN*X + AT*P*L = 0N = AT*P*AX = -(N-1)*(AT*P*L)V = A*X + L

Control

Control Q1 Q2 Q3 Qk

0.05587063 1 0 0 0-5.746376444218 -102.85147548553 0 0 0

-0.00951954 0 1 0 00.01208594 0.38670539 1 0 0

-1.48337989967 -47.462684843166 -122.7360308761 0 0-0.00851007 0 0 1 00.00733951 0.38775897 0.61082357 1 0

-1.131080626037 -59.756951530352 -94.13310163321 -154.10849475 098.55880505 0 0 0 198.55892258 0.00223436 -0.00000406 0.00086301 1

-1.072022312642 -2.430303325E-05 4.416873732E-08 -9.386908E-06 -0.01087697-0.7585043 144.3768458 180.2347485 154.1084948 0.0108770

[pvv]

0.169759

0.169759

Hi Hj Dij'

[m] [m] [m] [m] [g]

1050.4890 1114.0934 2622.8314 6375286.6955 98.391821114.0934 1050.4890 2622.8314 6375286.6955 101.470521050.4890 1065.6844 3837.7076 6375295.0201 99.719311065.6844 1050.4890 3837.7076 6375295.0201 100.211421050.4890 1099.3437 2755.9240 6375294.9276 98.811811099.3437 1050.4890 2755.9240 6375294.9276 101.060961114.0934 1065.6844 2783.0819 6375295.0201 101.054681065.6844 1114.0934 2783.0819 6375295.0201 98.831511114.0934 1099.3437 3803.8117 6375294.9276 100.211091099.3437 1114.0934 3803.8117 6375294.9276 99.717551065.6844 1099.3437 2639.8388 6375303.2527 99.122941099.3437 1065.6844 2639.8388 6375303.2527 100.75573

Raza medieRm

Unghi zenital

compensatZcomp

Vectorul termenilor liberi L

-20.04174-0.55188-8.44312-6.77302

-14.25224-3.150324.30522

-31.27393-9.52590

-18.90335-2.39763

-21.61011

2.287226617595 -2.2870847448551 1.6739084424032 -1.6738938882 0 0-2.287226617595 2.2870847448551 0 0 2.41153674 -2.41165427

0 0 -1.673908442403 1.6738938882 -2.41153674 2.41165427-138.9317768601 -138.93177686007 -189.8862292724 -189.88622927 -131.781047 -131.781047

0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

0.00036 0 0 0 0 00 0.00036 0 0 0 00 0 0.00026 0 0 00 0 0 0.00026 0 00 0 0 0 0.00038 00 0 0 0 0 0.00038

0.000821972801 -0.0008219218152 0.0004401371998 -0.0004401334 0 0-0.000821972801 0.0008219218152 0 0 0.00091367 -0.00091372

0 0 -0.0004401372 0.0004401334 -0.00091367 0.00091372-0.049928651957 -0.0499286519572 -0.049928652682 -0.0499286527 -0.04992859 -0.04992859

Matricea inversă a sistemului normal calculată din minorii matricei N Vectorul AT*P*L

144.376845759 83.963639581 59.756951551 0.000024303

L

0.051401783.963639581 180.234748499 94.133101633 -0.000000044 -0.010966559.756951551 94.133101633 154.108494761 0.000009387 -0.01237670.000024303 -0.000000044 0.000009387 0.010876969 6.6214385

-0.00375984 -0.00147349 -0.00002047 0.002820.00960152 -0.00440692 0.000012240.00001224 -0.00000514 91.93737992

0.00972276 -0.00147349 -0.00002047 -0.00445-0.00375984 -0.00440692 0.00001224-0.00002047 -0.00000514 91.93737992

0.00972276 -0.00375984 -0.00002047 0.00728-0.00375984 0.00960152 0.00001224-0.00002047 0.00001224 91.93737992

0.00972276 -0.00375984 -0.00147349 0.000000000-0.00375984 0.00960152 -0.00440692-0.00002047 0.00001224 -0.00000514

-0.00375984 -0.00147349 -0.00002047 0.000000.00960152 -0.00440692 0.00001224-0.00440692 0.00975214 -0.00000514

0.00972276 -0.00147349 -0.00002047 0.00000-0.00375984 -0.00440692 0.00001224-0.00147349 0.00975214 -0.00000514

0.00972276 -0.00375984 -0.00002047 0.00000-0.00375984 0.00960152 0.00001224-0.00147349 -0.00440692 -0.00000514

0.00972276 -0.00375984 -0.00147349 0.00000-0.00375984 0.00960152 -0.00440692-0.00147349 -0.00440692 0.00975214

Soluţii

X Necunoscuta

59.756951551 0.000024303 -5.76098939 dx1 [cm]94.133101633 -0.000000044 -1.17426626 dx2 [cm]

154.108494761 0.000009387 -0.13200579 dx3 [cm]0.000009387 0.010876969 -0.07202231 dy*100

3.82053 -10.77751 -5.27226 4.19502 4.58009 -9.60536

0.00137 -0.00387 -0.00139 0.00110 0.00174 -0.00364

DANI Lucrare G.M.

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Transcript of DANI Lucrare G.M.