INZENJERSKA-GEODEZIJA-3

Zdadatak 1

Zadatak 2

kontroliše se vertikalnost stubaopažanjima sa datih tačaka A i b. Opaža se do plan opažanja je dat u TABLI 2, A NAJVJEROVATNIJE KOORDINATE TAČAKA osn standard mjerenja ugla 3'' i dužine 3+2ppm koja se veličina odstupanja može sigurno odrediti vertikalnost se provjerava samo mjerenjem pravaca sa stanice 1 koja se veličina odstupanja može otkriti ovim planom opažanja

A

plan opažnja B D C G

Duzina Direk.ugao 50 90 35.3553390593 45 35.3553390593 45 35.3553390593 45

B

A D C G

50 35.3553390593 35.3553390593 35.3553390593

Y 100 150 125

X 100 100 125

A B D

σp= σd= σ0= ρ=

A=

270 315 315 315

3 3+2ppm 1 206264.806247096 YD 0 -4.1252961249 0 0 0 -4.1252961249 0 0 -0.7071067812 0 0

XD 0 4.1252961249 0 0 0 -4.1252961249 0 0 -0.7071067812 0 0

YC 0 0 -4.1252961249 0 0 0 -4.1252961249 0 0 -0.7071067812 0

0.7071067812 0 0

-0.7071067812 0 0

0 0.7071067812 0

N=

3.8878457304 2.1510571E-016 0 4.510281038E-016 3.8878457304 0 0 0 3.8878457304 0 0 4.5102810E-016 0 0 0 0 0 0 -0.4583662361 0.4583662361 -0.4583662361 -0.4583662361 -0.4583662361 -0.4583662361

Ql=

8.3192051431 0.226931619 0.226931619 0.226931619 -1.44070535E-015 3.356514883E-016 3.356514883E-016 3.356514883E-016 0 0 0 1.3870765421 1.3870765421 1.3870765421

0.226931619 8.760687881 0.00619025 0.00619025 3.3565149E-016 3.3565149E-016 7.9361849E-016 7.9361849E-016 2.2204460E-016 1.1102230E-016 1.1102230E-016 -1.4627500037 0.0378367308 0.0378367308

0.226931619 0.00619025 8.760687881 0.00619025 3.3565149E-016 7.9361849E-016 3.3565149E-016 7.9361849E-016 1.1102230E-016 2.2204460E-016 1.1102230E-016 0.0378367308 -1.4627500037 0.0378367308

Qv=

0.6807948569 -0.226931619 -0.226931619 -0.226931619 1.440705351E-015 -3.35651488E-016 -3.35651488E-016 -3.35651488E-016 0 0 0 -1.3870765421 -1.3870765421 -1.3870765421

-0.226931619 0.239312119 -0.00619025 -0.00619025 -3.356515E-016 -3.356515E-016 -7.936185E-016 -7.936185E-016 -2.220446E-016 -1.110223E-016 -1.110223E-016 1.4627500037 -0.0378367308 -0.0378367308

-0.226931619 -0.00619025 0.239312119 -0.00619025 -3.356515E-016 -7.936185E-016 -3.356515E-016 -7.936185E-016 -1.110223E-016 -2.220446E-016 -1.110223E-016 -0.0378367308 1.4627500037 -0.0378367308

Kyy 0.4884817028 0.4884817028 0.4884817028

Kxx Kyx 0.4884817028 4.2834378E-017 0.4884817028 4.2834378E-017 0.4884817028 4.2834378E-017

datih tačaka A i b. Opaža se donja D,srednjac, i gornja G tačka na stubu. TNIJE KOORDINATE TAČAKA osnovne mreže i približne koordinate tačaka na objektu su date u tabeli 2

ravaca sa stanice 1 planom opažanja

B -1 -0.7071067812 -0.7071067812 -0.7071067812

A -6.12574E-017 -0.7071067812 -0.7071067812 -0.7071067812

b -2.52705E-016 -4.1252961249 -4.1252961249 -4.1252961249

a 4.1252961 4.1252961 4.1252961 4.1252961

Pip 0.1111111 0.1111111 0.1111111 0.1111111

1 0.7071067812 0.7071067812 0.7071067812

1.837723E-016 -0.7071067812 -0.7071067812 -0.7071067812

7.581150E-016 -4.1252961249 -4.1252961249 -4.1252961249

-4.125296 -4.125296 -4.125296 -4.125296

0.1111111 0.1111111 0.1111111 0.1111111

XC YG XG 0 0 0 0 0 0 4.1252961249 0 0 0 -4.1252961249 4.1252961249 0 0 0 0 0 0 -4.1252961249 0 0 0 -4.1252961249 -4.1252961249 0 0 0 -0.7071067812 0 0 0 -0.7071067812 -0.7071067812

Z1 1 1 1 1 0 0 0 0 0 0 0

Z2 0 0 0 0 1 1 1 1 0 0 0

ABP ADP ACP AGP BAP BDP BCP BGP ADD ACD AGD

0 0 0 -0.7071067812 0 0 0 0.7071067812 -0.7071067812

0 0 0

0 0 0

BDD BCD BGD

0 0 2.151057E-016 3.8878457304 0 0 0.4583662361 -0.4583662361

0 0 0 0 3.8878457304 4.510281E-016 -0.4583662361 -0.4583662361

0 0 0 0 2.151057E-016 3.8878457304 0.4583662361 -0.4583662361

-0.458366 0.4583662 -0.458366 0.4583662 -0.458366 0.4583662 0.4444444 0

-0.458366 -0.458366 -0.458366 -0.458366 -0.458366 -0.458366 0 0.4444444

0.226931619 0.00619025 0.00619025 8.760687881 3.356515E-016 7.936185E-016 7.936185E-016 3.356515E-016 1.110223E-016 1.110223E-016 2.220446E-016 0.0378367308 0.0378367308 -1.4627500037

1.440705E-015 -3.35651E-016 -3.35651E-016 -3.35651E-016 8.3192051431 0.226931619 0.226931619 0.226931619 -1.3870765421 -1.3870765421 -1.3870765421 4.440892E-016 4.440892E-016 4.440892E-016

-3.35651E-016 -3.35651E-016 1.917044E-016 1.917044E-016 0.226931619 8.760687881 0.00619025 0.00619025 1.4627500037 -0.0378367308 -0.0378367308 -4.44089E-016 -2.22045E-016 -2.22045E-016

-3.4E-016 1.92E-016 -3.4E-016 1.92E-016 0.2269316 0.0061903 8.7606879 0.0061903 -0.037837 1.46275 -0.037837 -2.2E-016 -4.4E-016 -2.2E-016

-3.4E-016 1.92E-016 1.92E-016 -3.4E-016 0.2269316 0.0061903 0.0061903 8.7606879 -0.037837 -0.037837 1.46275 -2.2E-016 -2.2E-016 -4.4E-016

-5.6E-016 2.22E-016 8.33E-017 8.33E-017 -1.387077 1.46275 -0.037837 -0.037837 0.4884817 0.2312699 0.2312699 -2.2E-016 -1.4E-016 -1.4E-016

-0.226931619 -0.00619025 -0.00619025 0.239312119 -3.35651E-016 -7.93618E-016 -7.93618E-016 -3.35651E-016 -1.11022E-016 -1.11022E-016 -2.22045E-016 -0.0378367308 -0.0378367308 1.4627500037

-1.44071E-015 3.356515E-016 3.356515E-016 3.356515E-016 0.6807948569 -0.226931619 -0.226931619 -0.226931619 1.3870765421 1.3870765421 1.3870765421 -4.44089E-016 -4.44089E-016 -4.44089E-016

3.356515E-016 3.356515E-016 -1.91704E-016 -1.91704E-016 -0.226931619 0.239312119 -0.00619025 -0.00619025 -1.4627500037 0.0378367308 0.0378367308 4.440892E-016 2.220446E-016 2.220446E-016

3.36E-016 -1.9E-016 3.36E-016 -1.9E-016 -0.226932 -0.00619 0.2393121 -0.00619 0.0378367 -1.46275 0.0378367 2.22E-016 4.44E-016 2.22E-016

3.36E-016 -1.9E-016 -1.9E-016 3.36E-016 -0.226932 -0.00619 -0.00619 0.2393121 0.0378367 0.0378367 -1.46275 2.22E-016 2.22E-016 4.44E-016

5.55E-016 -2.2E-016 -8.3E-017 -8.3E-017 1.3870765 -1.46275 0.0378367 0.0378367 8.9407824 -0.23127 -0.23127 2.22E-016 1.39E-016 1.39E-016

χ² 5.9914645 Z λ1 λ2 θ A B 3.979096E-016 0.4884817028 0.4884817028 84.490611 1.7107661 1.7107661 8.566876E-017 0.4884817028 0.4884817028 0 1.7107661 1.7107661 8.566876E-017 0.4884817028 0.4884817028 0 1.7107661 1.7107661

su date u tabeli 2

Pid 0.1040583 0.1060528 0.1060528 0.1060528 0.1040583 0.1060528 0.1060528 0.1060528

P=

0.1111111111 0 0 0 0 0.1111111 0 0 0 0 0.1111111111 0 0 0 0 0.1111111 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

Qx=

0.4884817028 -1.28503E-016 0.231269851 -9.99469E-017 0.231269851 -9.99469E-017 0.9808112289 0.9808112289

-1.43E-017 0.4884817 0 0.2312699 0 0.2312699 -0.9808112 0.9808112

0.231269851 -9.99469E-017 0.4884817028 -1.28503E-016 0.231269851 -9.99469E-017 0.9808112289 0.9808112289

0 0.2312699 -1.4E-017 0.4884817 0 0.2312699 -0.980811 0.9808112

-5.6E-016 8.33E-017 2.22E-016 8.33E-017 -1.387077 -0.037837 1.46275 -0.037837 0.2312699 0.4884817 0.2312699 -1.4E-016 -2.2E-016 -1.4E-016

-5.6E-016 8.33E-017 8.33E-017 2.22E-016 -1.387077 -0.037837 -0.037837 1.46275 0.2312699 0.2312699 0.4884817 -1.4E-016 -1.4E-016 -2.2E-016

1.3870765421 -1.4627500037 0.0378367308 0.0378367308 0 -2.22045E-016 -7.28584E-017 -7.28584E-017 -1.11022E-016 -5.55112E-017 -5.55112E-017 0.4884817028 0.231269851 0.231269851

1.3870765 0.0378367 -1.46275 0.0378367 0 -7.29E-017 -2.22E-016 -7.29E-017 -5.55E-017 -1.11E-016 -5.55E-017 0.2312699 0.4884817 0.2312699

1.3870765421 0.0378367308 0.0378367308 -1.4627500037 0 -7.28584E-017 -7.28584E-017 -2.22045E-016 -5.55112E-017 -5.55112E-017 -1.11022E-016 0.231269851 0.231269851 0.4884817028

1 2 3 4 5 6 7 8 9 10 11 12 13 14

5.55E-016 -8.3E-017 -2.2E-016 -8.3E-017 1.3870765 0.0378367 -1.46275 0.0378367 -0.23127 8.9407824 -0.23127 1.39E-016 2.22E-016 1.39E-016

5.55E-016 -8.3E-017 -8.3E-017 -2.2E-016 1.3870765 0.0378367 0.0378367 -1.46275 -0.23127 -0.23127 8.9407824 1.39E-016 1.39E-016 2.22E-016

-1.3870765421 1.4627500037 -0.0378367308 -0.0378367308 0 2.220446E-016 7.285839E-017 7.285839E-017 1.110223E-016 5.551115E-017 5.551115E-017 8.9407823659 -0.231269851 -0.231269851

-1.3870765 -0.0378367 1.46275 -0.0378367 0 7.286E-017 2.220E-016 7.286E-017 5.551E-017 1.110E-016 5.551E-017 -0.2312699 8.9407824 -0.2312699

-1.3870765421 -0.0378367308 -0.0378367308 1.4627500037 0 7.285839E-017 7.285839E-017 2.220446E-016 5.551115E-017 5.551115E-017 1.110223E-016 -0.231269851 -0.231269851 8.9407823659

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.1111111111 0 0 0 0 0 0 0 0.1111111111 0 0 0 0 0 0 0 0.1111111 0 0 0 0 0 0 0 0.1111111 0 0 0 0 0 0 0 0.106053 0 0 0 0 0 0 0 0.106053 0 0 0 0 0 0 0 0.106052815

0 0 0

0 0 0

0.231269851 -9.99469E-017 0.231269851 -9.99469E-017 0.4884817028 -1.28503E-016 0.9808112289 0.9808112289

0 0.231269851 0 0.231269851 -1.4278E-017 0.4884817028 -0.980811229 0.9808112289

Qli 8.319205143 8.760687881 8.760687881 8.760687881 8.319205143 8.760687881 8.760687881 8.760687881 0.488481703 0.488481703 0.488481703 0.488481703 0.488481703 0.488481703

σl=σo*√Qli 2.8843032336 2.9598459218 2.9598459218 2.9598459218 2.8843032336 2.9598459218 2.9598459218 2.9598459218 0.6989146606 0.6989146606 0.6989146606 0.6989146606 0.6989146606 0.6989146606

Qvi 0.680794857 0.239312119 0.239312119 0.239312119 0.680794857 0.239312119 0.239312119 0.239312119 8.940782366 8.940782366 8.940782366 8.940782366 8.940782366 8.940782366

σv=σo*√Qvi 0.8251029371 0.4891953791 0.4891953791 0.4891953791 0.8251029371 0.4891953791 0.4891953791 0.4891953791 2.9901141058 2.9901141058 2.9901141058 2.9901141058 2.9901141058 2.9901141058

0 0 0

0.9808112 -0.980811 0.9808112 -0.980811 0.9808112 -0.980811 8.3192051 -1.4E-015

0 0 0

0.9808112 0.9808112 0.9808112 0.9808112 0.9808112 0.9808112 1.44E-015 8.3192051

0 0 0

0 0 0

0 0 0

1 2 3 4 5 6 7 8

Qxi 0.48848 0.48848 0.48848 0.48848 0.48848 0.48848 8.31921 8.31921

σx=σo*√Qxi 0.698914661 0.698914661 0.698914661 0.698914661 0.698914661 0.698914661 2.884303234 2.884303234

5=5*σl 14.42152 14.79923 14.79923 14.79923 14.42152 14.79923 14.79923 14.79923 3.494573 3.494573 3.494573 3.494573 3.494573 3.494573

√λo 2.80158522 Gii 30.55893493 51.54232447 51.54232447 51.54232447 30.55893493 51.54232447 51.54232447 51.54232447 8.834742053 8.834742053 8.834742053 8.834742053 8.834742053 8.834742053

ri=Pi*Qvi 0.075644 0.02659 0.02659 0.02659 0.075644 0.02659 0.02659 0.02659 0.948195 0.948195 0.948195 0.948195 0.948195 0.948195

6

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11

0.11111 0.11111 0.11111 0.11111 0.11111 0.11111 0.11111 0.11111 0.10605 0.10605 0.10605

0.106053 0 0 0 0.106053 0 0 0 0.106053

7=7*σl 20.19012 20.71892 20.71892 20.71892 20.19012 20.71892 20.71892 20.71892 4.892403 4.892403 4.892403 4.892403 4.892403 4.892403

12 13 14

0.10605 0.10605 0.10605

a) OD T T T T

I PLAN OPAZANJA DO M.VELICINA 1 DUZINA 2 DUZINA 3 DUZINA 5 DUZINA 1-T-2 UGAO

ρ= 206264.8062 Δ= 30 σpol/ob= 10 σob= 3.333333333 σd1= 0.415578501 σd2= 0.342524008 σα=√σd1²+σd2² 0.53854265 σo= 1

KOORDINATE TACA 1 2 3 5 T priblizne

A=

N=

YT 0.7404321748 0.8429222096 -0.1614483022 -0.9813382906 0.1390839864

0.2690045154 -0.0014017831

b)

OD T T T T T T

Ql=

II PLAN OPAZANJA DO M.VELICINA 1 PRAVAC 2 PRAVAC 3 PRAVAC 5 PRAVAC 1 DUZINA 2 DUZINA

0.1008410101 0.0461406937 -0.020565974 0.0204830821 0.1102594751 0.4612129191

0.0461406937 0.0650155175 0.0514386302 -0.0022282422 -0.2764997336 0.01177655

σ 0.41558 0.34252 0.52114 0.45589 3.33333 3.33333

-0.020566 0.0204830821 0.051439 -0.0022282422 0.121562 0.0484365387 0.048437 0.1500678398 -0.26038 0.5563870913 -0.524513 -0.1745069213

Qv=

0.0718644802 -0.046140694 0.0205659739 -0.020483082 -0.110259475 -0.461212919

-0.0461406937 0.0523071783 -0.0514386302 0.0022282422 0.2764997336 -0.01177655

Kxx=

3.8058547883 0.1093453533 0.1093453533 3.901595895 Kyy Kxx 3.805854788 3.901595895

T

0.020566 -0.0204830821 -0.051439 0.0022282422 0.150029 -0.0484365387 -0.048437 0.057768658 0.26038 -0.5563870913 0.524513 0.1745069213

Kyx Z 0.10935 0.2387299408

c) Kontrola geometrije Za duzine: k²= 3.703703704 σci= 2.72165527 σcs= 2.72165527 σε= 1.924500897 Za pravce: k² σci 0.0575684968 2.7216552698 0.0391075653 2.7216552698 0.0905303626 2.7216552698 0.0692788326 2.7216552698

σcs 2.7216552698 2.7216552698 2.7216552698 2.7216552698

σε 0.239934 0.197756 0.300883 0.263209

Zakljucak: Potrebno je izvrsiti centrisanje istrumenta I signala sa tacnoscu od 2.72 mm, duz

KOORDINATE TACAKA Y[m] 3705 3238 5143 6410 4930

XT 0.67213108 -0.5380355 -0.9868812 0.19228926 -0.005696

X[m] 4028 6220 6442 4850 5140

Duzina 1654.439 2007.303 1319.308 1508.145

Direk.ugao 227.768243 302.550003 9.29097085 101.086413

a -0.092312 -0.086616 0.025241 0.134215

b 0.0837969685 -0.0552870179 -0.1542921657 0.0262988762

T1D T2D T3D T5D 1T2u

0.09 0 0 0 0

0 0.09 0 0 0

0 0 0.09 0 0

0 0 0 0.09 0

σyT= σxT= σpolT=

1.928103162 2.51738087 3.17092861

P=

5.7902038771 0 0 0 0 0

Qx=

3.8058547883 0.1093453533 0.0739154473

-0.0014018 0.15780554

A=

N=

0.11025948 -0.2764997 -0.2603803 0.55638709 3.95794206 0.98278939

P=

Qx=

YT 0.08379697 -0.05528702 -0.15429217 0.02629888 0.74043217 0.84292221

XT -0.092312 -0.086616 0.025241 0.134215 0.672131 -0.538035

3.717582 0.0330232 0.033023 6.33720644

Z 1 1 1 1 0 0

T1p T2p T3p T5p T1d T2d

0.27098186 0.002643 -0.427606 0.00264335 0.269018 -0.534071 -0.42760567 -0.534071 22.80718

0.46121292 0.01177655 -0.52451264 -0.17450692 0.98278939 3.73438908

1 2 3 4 5 6

0.10084 0.06502 0.12156 0.15007 3.95794 3.73439

σl 0.31755474 0.25498141 0.34865775 0.38738591 1.98945773 1.93245675

-0.1102595 0.27649973 0.26038025 -0.5563871 7.15316905 -0.9827894

-0.46121292 -0.01177655 0.52451264 0.17450692 -0.98278939 7.37672204

1 2 3 4 5 6

λ1 λ2 θ 3.9730903 3.7343604 33.1783

0.07186 0.05231 0.15003 0.05777 7.15317 7.37672

σv 0.26807551 0.22870763 0.38733559 0.24035111 2.6745409 2.71601216

ri 0.4161099921 0.4458402354 0.5524071526 0.2779524224 0.6437852144 0.6639049832 3

χ² 5.99146 A B Odnos 4.879 4.7301467 0.96949

u od 2.72 mm, duzine je potrebno mjeriti sa tacnoscu 1.92 mm a uglove sa tacnoscu 0.2".

A 0.672131 -0.53804 -0.98688 0.192289

B 0.740432 0.842922 -0.161448 -0.981338

Za ocjenu koord tacake T mogu se koristiti 2 plana opazanj Sa tacke T bice vrseno obiljezavanje tacaka na objektu toko Odrediti sve kriterijume kvaliteta mreze (uraditi proracun t

0 0 0 0 3.447941

0 0 0 8.5235 0 0 0 3.682006 0 0 0 4.811474 0 0 0 0 0 0

0.109345 0.073915 3.901596 0.093413 0.093413 0.047419

√λo

σyT= σxT= σpolT=

0 0 0 0 0.09 0

1.95086 1.97525 2.77623

0 0 0 0 0 0.09

1 2 3 4 5 6

5.7902 8.5235 3.68201 4.81147 0.09 0.09

5 1.587774 1.274907 1.743289 1.93693 9.947289 9.662284

2.80159 Gii 1.804899 1.43716 1.964409 2.422588 11.6389 11.46119

7 2.222883 1.78487 2.440604 2.711701 13.9262 13.5272

koristiti 2 plana opazanja.Koord koje definisu datum mreze su 1,2,3,5 I priblizne koord tacke T. e tacaka na objektu tokom izgradnje, dozvoljeno odstupanje obiljezene tacke od projektovane vrijednosti koord mreze (uraditi proracun tacnosti) za drugi plan opazanja. Koji od 2 plana opazanja daje bolju srednju gresku poloz

koord tacke T. d projektovane vrijednosti koord je Δ=30 mm. a daje bolju srednju gresku polozaja tacke T?

OD R1 R2 R3 R4

A=

DO R2 R3 R4 R1

D[m] 100 100 100 100

Δh[m] 2 5 2 5

BR.STANICA 4 6 4 4

Pi 0.25 0.16667 0.25 0.25

R1 -1 0 0 1

R2 1 -1 0 0

R3 0 1 -1 0

R4 0 0 1 -1

R1R2 R2R3 R3R4 R4R1

N=

Radimo minimalni trag zato sto nemam poznate visine repera, tj. datum ni 0.5 -0.25 0 -0.25 1 -0.25 0.416667 -0.166667 0 1 0 -0.166667 0.416667 -0.25 1 -0.25 0 -0.25 0.5 1 1 1 1 1 0

Ql=

3.111111 -1.333333 -0.888889 -0.8888888889 -1.333333 4 -1.333333 -1.3333333333 -0.888889 -1.333333 3.111111 -0.8888888889 -0.888889 -1.333333 -0.888889 3.1111111111

1 2 3 4

Qv=

0.888889 1.333333 0.888889 0.8888888889 1.333333 2 1.333333 1.3333333333 0.888889 1.333333 0.888889 0.8888888889 0.888889 1.333333 0.888889 0.8888888889

1 2 3 4

2) Proracun tacnosti a) Proracunati standardna odstupanja za centrcinje istrumenta I signala (broj girusa 3) n= 3 Δ= 20 mm D= 150 m σpol/ob= 6.66667 σob= 2.22222 ρ= 206265 σp= 3.05577 k²= 3.11259 σci= 1.81444 σcs= 1.81444 σε= 3.05577

b) Standardno odstupanje aritmeticke sredine σas=σp/√n=

1.76425

c) Dozvoljena razlika 2C σkl=σp*√2= σ2c=σkl*√2= tp= w2c=tp*σ2c=

4.32152 6.11155 1.95996 11.9784

σo=

0.3

Nivelmanske strane: R1-R2, R3-R4 i R4-R1 su na terenu jednolikog pa repera R3. Visinska razlika početne i zadnje stepenice je 5 m. Standar kvaliteta mreže.

nagli pad terena

P=

0.25 0 0 0

0 0.166667 0 0

0 0 0.25 0

0 0 0 0.25

isine repera, tj. datum nije klasicno definisan. 1.277778 -0.166667 -0.833333 -0.277778 0.25 -0.166667 1.5 -0.5 -0.833333 0.25 Qx= -0.833333 -0.5 1.5 -0.166667 0.25 -0.277778 -0.833333 -0.166667 1.277778 0.25 0.25 0.25 0.25 0.25 3.47E-018 σl 3.111111 0.52915 4 0.6 3.111111 0.52915 3.111111 0.52915

0.888889 2 0.888889 0.888889

ala (broj girusa 3)

σv 0.28284 0.42426 0.28284 0.28284

ri 0.222222 0.333333 0.222222 0.222222 1

√λo= 5 2.645751 3 2.645751 2.645751

2.80159 Gii 7 3.565836 3.704052 3.565836 4.2 3.565836 3.704052 3.565836 3.704052

-R1 su na terenu jednolikog pada, a na nivelmanskoj strani R2-R3 se nalaze stepenice, neposredno ispred adnje stepenice je 5 m. Standard mjerenja visinske razlike po stanici je 0.3 mm. Proračunati kriterijume kvaliteta mreže. Visina letve je 3 m.

30 T= Δ=T/2= 15 σpol/ob= 5 k²= 8.33333 σodmj= 2.88675 σo= 3

A=

N=

Qx=

priblizno=

3

Tacke objekta Br. Y X A 70 70 B 80 70 C 80 80 D 70 80 Tacke postojece mreze Br. Y X 1 100 100 2 95.865 47.78 3 45.656 48.382

YA XA YB XB YC XC -0.707107 -0.70710678 0 0 0 0 0 0 -0.5547 -0.83205 0 0 0 0 0 0 -0.707107 -0.707107 0 0 0 0 0 0 -0.758532 0.651636265 0 0 0 0 0 0 -0.5811 0.813845 0 0 0 0 0 0 -0.441748 0.897139 0 0 0 0 0 0 0.747731 0.664001533 0 0 0 0 0 0 0.8463 0.532707 0 0 0 0 0 0 0.735701 0.677306 0 0 0 0 0 0

1.634472 0.502207976 0 0 0 0 0.502208 1.365527858 0 0 0 0 0 0 1.36157 0.439458 0 0 0 0 0.43946 1.638428 0 0 0 0 0 0 1.236397 0.601986 0 0 0 0 0.601986 1.763603 0 0 0 0 0 0 0 0 0 0 0 0

0.689764 -0.25367827 0 0 -0.253678 0.825614243 0 0 0 0 0.80405 -0.215662 0 0 -0.2157 0.668186

0 0 0 0

0 0 0 0

Qx=

Ql=

Qv=

Kxx=

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0.970011 -0.331102 -0.331102 0.680039 0 0 0 0

0.504011 0 0 0 -0.029635 0 0 0.51091804 0 0 0 -0.200213 0 0 0.49392 0 0 0 0 0 0 0.536983 0 0 -0.029635 0 0 0 0.998229 0 0 -0.20021325 0 0 0 0.91804 0 0 -0.0218 0 0 0 0 0 0 0.152888 0 0 -0.499105 0 0 0 -0.029821 0 0 -0.45803434 0 0 0 -0.187503 0 0 -0.4995 0 0 0 0 0 0 -0.474613 0 0

0.495989 0 0 0 0.029635 0 0 0.48908196 0 0 0 0.200213 0 0 0.50608 0 0 0 0 0 0 0.463017 0 0 0.029635 0 0 0 0.001771 0 0 0.200213247 0 0 0 0.08196 0 0 0.02179 0 0 0 0 0 0 -0.152888 0 0 0.499105 0 0 0 0.029821 0 0 0.458034335 0 0 0 0.187503 0 0 0.49949 0 0 0 0 0 0 0.474613 0 0

2.069291 -0.7610348 0 0 0 0 -0.761035 2.476842728 0 0 0 0 0 0 2.41216 -0.646986 0 0 0 0 -0.647 2.004557 0 0 0 0 0 0 2.910032 -0.993306 0 0 0 0 -0.993306 2.040117 0 0 0 0 0 0

Kxx=

0 T A B C D

0

0

0

Kyy Kxx Kyx Z 2.069291 2.476842728 -0.761 1.575689 2.412156 2.004557108 -0.647 1.35665 2.910032 2.040117439 -0.9933 2.168728 2.270628 2.142276007 -0.6719 1.349853

0

0

λ1 3.060911 2.886682 3.559439 2.881378

λ2 1.485222 1.530031 1.390711 1.531525

Plan opazanja duzina A B 1 C D A B 2 C D A B 3 C D

D 42.42641 36.05551 28.28427 36.05551 34.09878 27.3025 35.91416 41.31739 32.55715 40.58138 46.68199 39.90399

YD XD 0 0 0 0 0 0 -0.83205 -0.5547002 0 0 0 0 0 0 -0.626008 0.779816945 0 0 0 0 0 0 0.610064 0.792351882

1A 1B 1C 1D 2A 2B 2C 2D 3A 3B 3C 3D

Direk.ugao 225 213.6900675 225 236.3099325 310.6650832 324.4733 333.7845483 321.2438182 48.39422874 57.81143471 47.36650598 37.5941551

A 0.707107 0.83205 0.707107 0.5547 -0.651636 -0.813845 -0.897139 -0.779817 -0.664002 -0.532707 -0.677306 -0.792352

B 0.707107 0.5547 0.707107 0.83205 0.758532 0.581082 0.441748 0.626008 -0.747731 -0.846299 -0.735701 -0.610064

Pi 1

P=

1 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 1.456372 0.456752742 0.456753 1.543628281

0 0 0 0

0 0 0 0

1 2 3 4

σpol Qxi σx 0.689763514 2.49156 3.69302 0.825614243 2.7259 0.804051881 2.690068 3.64007 0.668185703 2.452279

A B

0 0 0 0 0.756876 -0.2239562 -0.223956 0.714092002

5 6 7 8

0.970010657 0.680039146 0.756875868 0.714092002

2.954674 3.85363 2.473935 2.609958 3.6385 2.535119

C D

0 0 -0.499105 0 0 0 0 0 0 -0.45803434 0 0 -0.021785 0 0 0 -0.499488 0 0 0.15288814 0 0 0 -0.474613 0 0 -0.029821 0 0 0 0 0 0 -0.18750342 0 0 0.999062 0 0 0 -0.021501 0 0 0.949516382 0 0 0 0.156717 0 0 0.49776 0 0 0 0 0 0 0.571042342 0 0 -0.021501 0 0 0 0.507015 0 0 0.156717066 0 0 0 0.513501

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

0 0 0.499105 0 0 0 0 0 0 0.458034335 0 0 0.021785 0 0 0 0.499488 0 0 -0.15288814 0 0 0 0.474613 0 0 0.029821 0 0 0 0 0 0 0.187503423 0 0 0.000938 0 0 0 0.021501 0 0 0.050483618 0 0 0 -0.156717 0 0 0.50224 0 0 0 0 0 0 0.428957658 0 0 0.021501 0 0 0 0.492985 0 0 -0.15671707 0 0 0 0.486499

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

Elipsa gresaka

0 0 0 0 0 0 0 0 0 0 0 0 2.270628 -0.67186861

-0.671869 2.142276007 θ 127.505 143.7422 146.824 137.7281

A 4.282445494 4.158779935 4.618035413 4.154958095

B 2.983062 3.027726 2.886589 3.029204

Odnos χ² 0.696579016 5.99146 0.728032373 0.625068523 0.729057729

0 0 0 1 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 0 1 0

Qlii 0.504011 0.510918 0.493923 0.536983 0.998229 0.91804 0.999062 0.949516 0.49776 0.571042 0.507015 0.513501

σl 2.129811 2.144356 2.108389 2.198373 2.997343 2.874432 2.998593 2.923294 2.116563 2.26702 2.13615 2.149769

Qvii 0.495989 0.489082 0.506077 0.463017 0.001771 0.08196 0.000938 0.050484 0.50224 0.428958 0.492985 0.486499

σv 2.112795 2.098032 2.134173 2.041361 0.126237 0.858862 0.091869 0.674057 2.126067 1.964846 2.106387 2.092485

rii 0.495989 0.489082 0.506077 0.463017 0.001771 0.08196 0.000938 0.050484 0.50224 0.428958 0.492985 0.486499 4

5 10.64906 10.72178 10.54195 10.99187 14.98671 14.37216 14.99297 14.61647 10.58282 11.3351 10.68075 10.74885

√λo 2.80159 Gii 11.93408 12.01806 11.81454 12.35169 199.7381 29.35777 274.4579 37.40674 11.85958 12.8327 11.97039 12.04992

7 14.90868 15.01049 14.75872 15.38861 20.9814 20.12102 20.99015 20.46306 14.81594 15.86914 14.95305 15.04838

0 0 0 0 0 0 0 0 0 0 0 1

Tacka 1 2 3 4 A

X 4000 3000 4000 6400 4000

Y 1000 2400 6000 2400 2400

Plan opazanih duzina 1-A 2-A 3-A 4-A

D 1400 1000 3600 2400

σd= 3mm+2ppm 5 σo=

A=

YA XA 1 6.125742E-017 0 1 -1 -1.83772E-016 1.225148E-016 -1

1-A 2-A 3-A 4-A

N=

0.9834550966 3.934024E-017 3.934024E-017 1.4109138725

Ql=

1.0168232423 1.506496E-017 -1.0168232423 1.095110E-016

1.506496E-017 0.7087604846 -1.01899E-016 -0.7087604846

-1.0168232423 -1.01899E-016 1.0168232423 -2.26773E-017

1.095110E-016 -0.7087604846 -2.26773E-017 0.7087604846

Qv=

0.3287767577 -1.50650E-017 1.0168232423 -1.09511E-016

-1.50650E-017 0.2912395154 1.018986E-016 0.7087604846

1.0168232423 1.018986E-016 3.1447767577 2.267730E-017

-1.09511E-016 0.7087604846 2.267730E-017 1.7248395154

Kxx=

5.0841162115 -1.41759E-016 -1.41759E-016 3.5438024231

A

Qx=

Kyy Kxx Kyx Z 5.084116212 3.543802423 -1.4176E-016 1.540313788

Za duzinu d1-A sracunati dozvoljeno odstupanje vises

σd=

5.8

tp= wd=

2.575829396 21.12808262

Direk.ugao A B 90 -6.12574E-017 -1 0 -1 0 270 1.836970E-016 1 180 1 -1.2E-016

P=

0.7431629013 0 0 0

0 1 0 0

σd 5.8 5 10.2 7.8

Pi 0.743163 1 0.240292 0.410914

0 0 0 0 0.240292 0 0 0.410914

A 1.01682324 -2.83519E-017 σy σx σpol -2.835E-017 0.7087604846 5.041883 4.209396 6.568074

1 2 3 4

Qlii 1.0168232423 0.7087604846 1.0168232423 0.7087604846

σl 5.041883 4.209396 5.041883 4.209396

1 2 3 4

Qvii 0.3287767577 0.2912395154 3.1447767577 1.7248395154

σv 2.866953 2.698331 8.866759 6.566657

λ1 λ2 5.0841162 3.543802423

θ 90

rii 0.244335 0.29124 0.755665 0.70876 2

5 25.20941 21.04698 25.20941 21.04698

√λo 2.80159 Gii 32.87299 25.95665 32.87299 25.95665

A B Odnos χ² 5.51918 4.60788 0.83489 5.99146

ljeno odstupanje visestrukog mjerenja u jednom smjeru

7 35.29318 29.46577 35.29318 29.46577

Br tacke 1 2 3 T

Y 1593.745 2047.2 2500.655 2047.205

ρ= σo= σd=

206264.8062 1 3

A=

YT -6.01864E-006 -0.3034751944 -6.01891E-006 0.9999999999 7.356446E-006 -0.9999999999

X 2047.2 2726.87 2047.2 2047.194

XT -0.4548688004 -2.23250E-006 0.4548788316 -1.32316E-005 -1 -1.32319E-005

D Direk.ugao 453.46000004 270.0007581 679.67600002 359.9995785 453.45000004 89.99924187

Z 1 1 1 0 0 0

T1p T2p T3p T1d T2d T3d

N=

0.3333333333 -8.47033E-021 -0.366135601 -8.89385E-021 0.3333333333 -8.08023E-006 -0.3661356014 -8.08023E-006 2.280458192

Ql=

1.1530965793 0.3549314544 -0.0883391221 0.5847798015 1.3645977973 -0.5847436896

0.3549314544 0.512908951 0.3549331888 -0.5205689476 -5.73577E-006 0.5205689476

-0.088339122 0.584779801 0.3549331888 -0.52056895 1.1531474386 0.584756585 0.5847565846 3.642337442 -1.364645099 5.2314E-005 -0.584792698 -3.64233744

Qv=

0.7090540509 -0.3549314544 0.0883391221 -0.5847798015 -1.3645977973 0.5847436896

-0.3549314544 0.3159657916 -0.3549331888 0.5205689476 5.735767E-006 -0.5205689476

0.0883391221 -0.5847798 -0.354933189 0.520568948 0.7090853251 -0.58475658 -0.584756585 5.357662558 1.3646450988 -5.231E-005 0.584792698 3.642337441

Kxx=

3.6423374423 1.417571E-005 1.417571E-005 3.0000000003

Tacka T

Kyy 3.642337442

Kxx 3

Kyx Z 1.4176E-005 0.64233744

Kontrola geometrije: Za duzine: Za pravce: 3 σd= k² σci σcs k²= 3 0.620716877 2.449489743 2.44948974 σci= 2.449489743 0.276291581 2.449489743 2.44948974 σcs= 2.449489743 0.620744255 2.449489743 2.44948974 σε= 1.732050808

1

Dozvoljena razlika mjerenja duzine u jednom smjer σd= tp= w=

2

Dozvoljena razlika mjerenja duzine naprijed-nazad σd= tp= σΔd= w=

3

3 1.95996441 5.87989323

3 1.95996441 4.24264069 8.31542475

Dozvoljena razlika redukovanih pravaca: σαred tp 1.92984488 1.95996441 1.287536207 1.929887439

4

Dozvoljena razlika nezatvaranja figure: σαred σugla 1.92984488 2.7292128 1.287536207 1.82085117 1.929887439 2.72927299

5

Dozvoljena razlika 2C:

σkl σ2c 1.92984488 2.7292128 1.287536207 1.82085117 1.929887439 2.72927299

6

Dozvoljeno odstupanje aritmeticke sredine: σas 0.4548688 0.303475194 0.454878832

b a A B σp Pi -6.01864E-006 -0.454869 -1.32316E-005 1 1.364606 0.537013 -0.3034751944 -2.2E-006 -1 7.36E-006 0.910426 1.206455 -6.01891E-006 0.454879 -1.32319E-005 -1 1.364636 0.53699 0.111111 0.111111 0.111111

P=

Qx=

1.3645977973 -5.73577E-006 -1.3646450988 5.231374E-005 3.0000000001 2.707672E-005

-1.3645977973 5.735767E-006 1.3646450988 -5.23137E-005 5.9999999999 -2.70767E-005

0.537013 0 0 1.2064549063 0 0 0 0 0 0 0 0

0 0 0.53699 0 0 0

0 0 0 0 0 0 0 0 0 0.111111 0 0 0 0.111111 0 0 0 0.111111

3.642337 1.417571E-005 0.58479 σy σx σz 1.42E-005 3.0000000003 1.29E-005 1.908491 1.732051 0.729656 0.58479 1.290570E-005 0.532398

-0.584744 0.520569 -0.584793 -3.642337 2.71E-005 3.642337

0.584744 -0.520569 0.584793 3.642337 -2.7E-005 5.357663

1 2 3 4 5 6

Qlii 1.153097 0.512909 1.153147 3.642337 3 3.642337

σl 1.073823 0.716177 1.073847 1.908491 1.732051 1.908491

1 2 3 4 5 6

Qvii 0.709054 0.315966 0.709085 5.357663 6 5.357663

σv 0.842053 0.562108 0.842072 2.314663 2.44949 2.314663

rii 0.380772 0.381198 0.380772 0.595296 0.666667 0.595296 3

λ1 3.642337443

λ2 3

: σε 0.787855873 0.525634456 0.787873248

a duzine u jednom smjeru:

ja duzine naprijed-nazad:

edukovanih pravaca: wred 3.782427279 2.523525141 3.782510693

ezatvaranja figure: tp wugla 1.959964409 5.34916 3.5688 5.34928

razlika 2C:

θ 89.99873554

A 4.6715

B Odnos χ² 4.23962 0.90755 5.99146

tp w2c 1.959964409 5.34916 3.5688 5.34928

e aritmeticke sredine:

σpol 2.577273 √λo= 5 5.369117 3.580883 5.369235 9.542454 8.660254 9.542454

2.80159 Gii 6.195537 4.131167 6.195674 10.89328 10.29368 10.89328

7 7.516763 5.013236 7.516929 13.35944 12.12436 13.35944

w=5 wii 20.32808 20.29132 20.32808 8.497963 6.25 8.497963

RS2 RS2 RS8 RS7 RS1 RS6 RS5 RS6 RS5 RS2 RS3 RS4 R1 R2 R3

RS1 RS8 RS7 RS1 RS6 RS5 RS2 RS7 RS8 RS3 RS4 RS5 RS3 RS1 RS5

σhob= nmax= σΔh= σo=

0.4 4 0.565685 0.282843

N=

0.25 0 0 0 0 -0.25 0 0 0

2 4 2 4 2 2 2 4 4 2 2 2 4 4 4

0 0.25 0 -0.25 0 0 0 0 0

Pi 0.5 0.25 0.5 0.25 0.5 0.5 0.5 0.25 0.25 0.5 0.5 0.5 0.25 0.25 0.25

0 0 0.25 0 0 0 0 -0.25 0

A=

R1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0

P=

0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 -0.25 0 1.5 -0.5 0 0 0 -0.5

0 0 0 -0.5 1.75 -0.5 0 -0.5 0

N=

0 0 1

0 0 1

0 0 1

-0.25 0 1

0 -0.25 1

Qx=

4.3599568 -1.0125234 -0.7967637 -0.6488871 -0.2435011 -1.0125234 4.091771 -0.8195508 0.4554074 -0.290828 -0.7967637 -0.8195508 3.8379267 -0.4559144 -0.2959272 -0.6488871 0.4554074 -0.4559144 0.8190438 0.0728084 -0.2435011 -0.290828 -0.2959272 0.0728084 0.6008938 0.7235932 -0.6488871 -0.4331274 -0.2852507 0.1201353 0.0543238 -0.6433098 -0.2066912 -0.2796735 0.0030132 -0.4331274 -0.4559144 0.2015631 -0.0922781 0.0677092 -0.651118 -0.1112407 -0.2618263 0.2523957 -0.027582 -0.7279246 -0.191553 -0.4367924 0.1720834 -0.0553089 -0.6240285 -0.3733712 -0.3328963 -0.0097348 0.0485872 0.0909091 0.0909091 0.0909091 0.0909091 0.0909091

Ql=

1.2743208 0.4697634 0.2857143 0.5188431 -0.4662577 0.4697634 1.6862401 -0.5714286 -0.6450482 0.1472393 0.2857143 -0.5714286 1.4285714 -0.5714286 5.551E-017 0.5188431 -0.6450482 -0.5714286 1.7353199 -0.6134969 -0.4662577 0.1472393 -5.55E-017 -0.6134969 1.2269939 -0.4399649 -0.1016652 -0.2857143 -0.0525855 -0.4662577 -0.3680982 -0.5153374 1.388E-017 0.1472393 -0.2944785 -0.0525855 0.4978089 0.5714286 -1.121823 -0.6134969 0.1016652 1.1709027 -0.5714286 -0.4978089 -0.1472393 0.1226994 0.1717791 -5.55E-017 -0.0490798 0.0981595 0.1226994 0.1717791 2.776E-017 -0.0490798 0.0981595 0.1226994 0.1717791 2.776E-017 -0.0490798 0.0981595 6.106E-016 2.220E-016 4.441E-016 -5.55E-017 -8.88E-016 0 0 0 0 0 0 0 0 0 0

Qv=

0.7256792 -0.4697634 -0.2857143 -0.5188431 0.4662577 -0.4697634 2.3137599 0.5714286 0.6450482 -0.1472393 -0.2857143 0.5714286 0.5714286 0.5714286 -5.55E-017 -0.5188431 0.6450482 0.5714286 2.2646801 0.6134969 0.4662577 -0.1472393 5.551E-017 0.6134969 0.7730061 0.4399649 0.1016652 0.2857143 0.0525855 0.4662577 0.3680982 0.5153374 -1.39E-017 -0.1472393 0.2944785 0.0525855 -0.4978089 -0.5714286 1.121823 0.6134969 -0.1016652 -1.1709027 0.5714286 0.4978089 0.1472393

Qv= -0.1226994 -0.1717791 5.551E-017 0.0490798 -0.0981595 -0.1226994 -0.1717791 -2.78E-017 0.0490798 -0.0981595 -0.1226994 -0.1717791 -2.78E-017 0.0490798 -0.0981595 -6.11E-016 -2.22E-016 -4.44E-016 5.551E-017 8.882E-016 0 0 0 0 0 0 0 0 0 0

Dozvol

Dozvoljena razlika

D

R2 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0

R3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1

RS1 1 0 0 1 -1 0 0 0 0 0 0 0 0 1 0

RS2 -1 -1 0 0 0 0 1 0 0 -1 0 0 0 0 0

RS3 0 0 0 0 0 0 0 0 0 1 -1 0 1 0 0

RS4 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0

RS5 0 0 0 0 0 1 -1 0 -1 0 0 1 0 0 1

0 0.25 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0.5 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0.25 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0.5 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0.5 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0.5 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0.25 0 0 0 0 0 0 0

-0.25 0 0 0 -0.5 1.25 -0.5 0 0

0 0 0 0 0 -0.5 1 -0.5 0

0 0 -0.25 0 -0.5 0 -0.5 2 -0.5

0 0 0 -0.5 0 0 0 -0.5 1.25

0 0 0 -0.25 0 0 0 0 -0.25

0 0 0 0 -0.25 0 0 -0.25 0

1 1 1 1 1 1 1 1 1

0 0 1

0 0 1

0 -0.25 1

-0.25 0 1

1 -0.5 1

-0.5 1 1

1 1 0

0.7235932 0.054324 -0.4331274 -0.651118 -0.7279246 -0.6240285 -0.6488871 -0.64331 -0.4559144 -0.1112407 -0.191553 -0.3733712 -0.4331274 -0.206691 0.20156308 -0.2618263 -0.4367924 -0.3328963 -0.2852507 -0.279673 -0.0922781 0.2523957 0.1720834 -0.0097348 0.1201353 0.003013 0.0677092 -0.027582 -0.0553089 0.0485872 1.0872296 0.41796 -0.069491 -0.2874816 -0.3642882 -0.2603921 0.4179602 1.196544 0.15694512 -0.1837449 -0.3096312 -0.2057351 -0.069491 0.156945 0.56519944 0.1018101 -0.0731561 0.03074 -0.2874816 -0.183745 0.10181007 0.9127415 0.2189322 0.037114 -0.3642882 -0.309631 -0.0731561 0.2189322 1.2604428 0.5071961 -0.2603921 -0.205735 0.03074004 0.037114 0.5071961 1.1825208 0.0909091 0.090909 0.09090909 0.0909091 0.0909091 0.0909091

0.0909090909 0.0909090909 0.0909090909 0.0909090909 0.0909090909 0.0909090909 0.0909090909 0.0909090909 0.0909090909 0.0909090909 0.0909090909 -1.26162E-018

-0.4399649 -0.368098 -0.0525855 0.1016652 0.1226994 0.1226994 -0.1016652 -0.515337 0.49780894 1.1709027 0.1717791 0.1717791 -0.2857143 -3E-017 0.57142857 -0.5714286 -2.78E-017 5.551E-017 -0.0525855 0.147239 -1.121823 -0.4978089 -0.0490798 -0.0490798 -0.4662577 -0.294479 -0.6134969 -0.1472393 0.0981595 0.0981595 1.2743208 -0.368098 0.51884312 -0.4697634 0.1226994 0.1226994 -0.3680982 1.030675 0.14723926 0.5153374 -0.3435583 -0.3435583 0.5188431 0.147239 1.73531989 0.6450482 -0.0490798 -0.0490798 -0.4697634 0.515337 0.6450482 1.6862401 -0.1717791 -0.1717791 0.1226994 -0.343558 -0.0490798 -0.1717791 1.4478528 -0.5521472 0.1226994 -0.343558 -0.0490798 -0.1717791 -0.5521472 1.4478528 0.1226994 -0.343558 -0.0490798 -0.1717791 -0.5521472 -0.5521472 4.441E-016 -2E-016 9.437E-016 5.551E-017 0 7.216E-016 0 0 0 0 -1.11E-016 1.110E-016 0 0 0 0 -5.55E-017 5.551E-017

0.1226993865 0.1717791411 0 -0.0490797546 0.0981595092 0.1226993865 -0.3435582822 -0.0490797546 -0.1717791411 -0.5521472393 -0.5521472393 1.4478527607 -5.55112E-016 0 0

0.4399649 0.368098 0.05258545 -0.1016652 -0.1226994 -0.1226994 0.1016652 0.515337 -0.4978089 -1.1709027 -0.1717791 -0.1717791 0.2857143 2.78E-017 -0.5714286 0.5714286 2.776E-017 -5.55E-017 0.0525855 -0.147239 1.12182296 0.4978089 0.0490798 0.0490798 0.4662577 0.294479 0.61349693 0.1472393 -0.0981595 -0.0981595 0.7256792 0.368098 -0.5188431 0.4697634 -0.1226994 -0.1226994 0.3680982 0.969325 -0.1472393 -0.5153374 0.3435583 0.3435583 -0.5188431 -0.147239 2.26468011 -0.6450482 0.0490798 0.0490798 0.4697634 -0.515337 -0.6450482 2.3137599 0.1717791 0.1717791

-0.1226993865 -0.1717791411 0 0.0490797546 -0.0981595092 -0.1226993865 0.3435582822 0.0490797546 0.1717791411

-0.1226994 0.343558 0.04907975 -0.1226994 0.343558 0.04907975 -0.1226994 0.343558 0.04907975 -4.44E-016 1.67E-016 -9.44E-016 0 0 0 0 0 0

0.1717791 0.1717791 0.1717791 -5.55E-017 0 0

0.5521472 0.5521472 0.5521472 0 1.110E-016 5.551E-017

0.5521472 0.5521472 0.5521472 -7.22E-016 -1.11E-016 -5.55E-017

0.5521472393 0.5521472393 0.5521472393 5.551115E-016 0 0

Aritmeticka sredina napred-nazad: σhob 0.4

nmax 4

σΔh σo 0.565685 0.282843

Dozvoljeno odstupanje visinske razlike napred-nazad: σst 0.2828427

σΔΔ̄h 0.8

σΔΔ̲h tp w 1.131371 1.959964 2.217446599

Dozvoljena razlika visinskih razlika dobijena promjenom visine instrumenta: σd 1.6

wd1 wd2 2.217447 3.135943

Dozvoljena razlika citanja letve na stanici: σl 0.2828427

σd 0.4

wd 0.783986

RS6 0 0 0 0 1 -1 0 -1 0 0 0 0 0 0 0

RS7 0 0 1 -1 0 0 0 1 0 0 0 0 0 0 0

RS8 0 1 -1 0 0 0 0 0 1 0 0 0 0 0 0

RS2 RS2 RS8 RS7 RS1 RS6 RS5 RS6 RS5 RS2 RS3 RS4 R1 R2 R3

RS1 RS8 RS7 RS1 RS6 RS5 RS2 RS7 RS8 RS3 RS4 RS5 RS3 RS1 RS5

0 0 0 0 0 0 0 0 0.25 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0.5 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0.5 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0.5 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0.25 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0.25 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.25

2.775558E-016 2.775558E-016 0 0 -5.55112E-017 -5.55112E-017 -1.66533E-016 5.551115E-017 1.110223E-016 -5.55112E-016 5.551115E-016 1.665335E-016 4 -1.11022E-016 0

-2.77556E-016 -2.77556E-016 0 0 5.551115E-017 5.551115E-017 1.665335E-016 -5.55112E-017 -1.11022E-016

1.110223E-016 2.775558E-017 2.775558E-017 0 0 5.551115E-017 -5.55112E-017 1.387779E-017 -2.77556E-017 -3.33067E-016 3.330669E-016 8.326673E-017 1.165734E-015 4 -1.66533E-016

-1.11022E-016 -2.77556E-017 -2.77556E-017 0 0 -5.55112E-017 5.551115E-017 -1.38778E-017 2.775558E-017

-5.55112E-017 0 5.551115E-017 -1.11022E-016 1.110223E-016 0 -5.55112E-017 0 0 0 -8.32667E-017 1.110223E-016 7.216450E-016 5.551115E-017 4

5.551115E-017 0 -5.55112E-017 1.110223E-016 -1.11022E-016 0 5.551115E-017 0 0

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

Qlii 1.274321 1.68624 1.428571 1.73532 1.226994 1.274321 1.030675 1.73532 1.68624 1.447853 1.447853 1.447853 4 4 4

σl 0.31929 0.36729 0.33806 0.37259 0.3133 0.31929 0.28715 0.37259 0.36729 0.34034 0.34034 0.34034 0.56569 0.56569 0.56569

1 2 3 4 5 6 7 8 9

Qvii 0.725679 2.31376 0.571429 2.26468 0.773006 0.725679 0.969325 2.26468 2.31376

σv 0.24094 0.43023 0.21381 0.42565 0.24868 0.24094 0.27847 0.42565 0.43023

umenta:

5.551115E-016 -5.55112E-016 -1.66533E-016 0 1.110223E-016 0

3.330669E-016 -3.33067E-016 -8.32667E-017 -1.16573E-015 0 1.665335E-016

0 8.326673E-017 -1.11022E-016 -7.21645E-016 -5.55112E-017 0

10 11 12 13 14 15

0.552147 0.21017 0.552147 0.21017 0.552147 0.21017 0 0 0 0 0 0

1. za potebe vertikalnog osmatranja inženjerskog objekta, razvijena je kontrolna nivelmanska mreža. skica KNM sa oznakama repera ... plan mjerenja ... preciznog geometrijskog nivelmanasa brojem stanica. veličina pomjeranja koju geometrjskim merenjima u mreži treba otkriti je 3mm

visinska razlika sa rs8-rs7 je 5m i određuje se nivelanjem niz stepenice dužina takvog put nivelanja je 100m. za datu geometriju mreže, plan opažanja i zahtjevanu veličinu pomjeranja, uraditi kompletan proračun tačnosti mreže (visine svih repera su nepoznate).

2. za visinsku razliku r1-rs3, planiranu projektom potrebno je proračunati - standardno odstupanje aritmetičke sredine - standardno odstupanje nivelanja u jednom smijeru (planirano je nivelanje naprijed nazad - dozvoljenu razliku visinske razlike određenih sa promjenom visine instrumenta - dozvoljeno nezatvaranje nivelmanskog poligona rs2-rs3-rs4-rs5

rii 0.36284 0.57844 0.285714 0.56617 0.386503 0.36284 0.484663 0.56617 0.57844 0.276074 0.276074 0.276074 0 0 0 5

√λo= 5 1.596447 1.836431 1.690309 1.862965 1.566521 1.596447 1.43574 1.862965 1.836431 1.701677 1.701677 1.701677 2.828427 2.828427 2.828427

2.80159 Gii 1.860401 2.08377 2.096514 2.106228 1.80255 1.860401 1.609697 2.106228 2.08377 2.132806 2.132806 2.132806 #DIV/0! #DIV/0! #DIV/0!

7 2.235025 2.571004 2.366432 2.608151 2.193129 2.235025 2.010036 2.608151 2.571004 2.382348 2.382348 2.382348 3.959798 3.959798 3.959798

na je kontrolna

anica. otkriti je 3mm

penice dužina takvog puta

mjeranja, uraditi nate).

ačunati

nivelanje naprijed nazad) ne instrumenta

T 1 2 3 T

Y 3820.311 4000 4347.851 4000

ρo=

206264.8062

A=

YT 2.109520E-016 -1.3726645166 -3.63089E-017 1 0 -1

X 6000 6150.266 6000 6000

σɛα= σɛd= σci= σcs= σo=

1 2+3 2 2 1

XT -1.1478989045 0 0.5929688466 1.837723E-016 -1 -6.12574E-017

Z 1 1 1 0 0 0

T-1p T-2p T-3p T-1d T-2d T-3d

T-1 T-2 T-3

Pi 0.159472 0.117139 0.41555 0.120619 0.121903 0.110023

N=

0.4513568306 -1.86571E-017 -0.160793 -1.86571E-017 0.4781477849 0.06335 -0.1607932072 0.0633504132 0.692162

Ql=

4.8744293873 0.9397038604 0.2709368734 0.6551200292 2.6443665874 -0.6551200292

0.9397038604 4.5913377706 0.751573464 -2.7506239745 0.1080670236 2.7506239745

0.270937 0.751573 2.090612 0.523964 -1.045269 -0.523964

0.65512 -2.750624 0.523964 2.418116 0.07534 -2.418116

2.644367 0.108067 -1.045269 0.07534 2.119423 -0.07534

Qv=

1.3962581923 -0.9397038604 -0.2709368734 -0.6551200292 -2.6443665874 0.6551200292

-0.9397038604 3.9454937296 -0.751573464 2.7506239745 -0.1080670236 -2.7506239745

-0.270937 -0.751573 0.315836 -0.523964 1.045269 0.523964

-0.65512 2.750624 -0.523964 5.872477 -0.07534 2.418116

-2.644367 -0.108067 1.045269 -0.07534 6.083796 0.07534

Kxx=

2.4181158395 -0.0753395561 0.568638 -0.0753395561 2.1194232514 -0.211483 0.5686378353 -0.211482959 1.596203

Z

λ1

Tacka

Kyy

Kxx

Kyx

Qx=

T

2.4181158395 2.1194232514 -0.07534 0.334547 2.436043

D Direk.ugao b a A 179.689 270 2.10952E-016 -1.147899 1.83772E-016 150.266 0 -1.372664517 0 -1 347.851 90 -3.63089E-017 0.592969 -6.12323E-017

P=

B 1 0 -1

σp² 6.270688 8.536832 2.406448

0.15947215 0 0 0 0 0 0 0.1171394797 0 0 0 0 0 0 0.41555 0 0 0 0 0 0 0.1206186303 0 0 0 0 0 0 0.12190337 0 0 0 0 0 0 0.110023

2.418116 -0.07533956 0.5686378353 σy σx σz σpol -0.07534 2.11942325 -0.211482959 1.55503 1.455823908 1.2634092 2.13015 0.568638 -0.21148296 1.5962028217 √λo= Qlii σl rii 5 -0.65512 1 4.8744293873 2.207811 0.22266429 11.03905 2.750624 2 4.5913377706 2.142741 0.46217308 10.7137 -0.523964 3 2.0906119698 1.445895 0.13124581 7.229474 -2.418116 4 2.4181158395 1.555029 0.70833018 7.775146 -0.07534 5 2.1194232514 1.455824 0.74163517 7.27912 2.418116 6 2.4181158395 1.555029 0.73395147 7.775146 3 Qvii σv 0.65512 1 1.3962581923 1.181634 -2.750624 2 3.9454937296 1.986327 0.523964 3 0.3158362422 0.561993 2.418116 4 5.872477391 2.423319 0.07534 5 6.0837955854 2.466535 6.670887 6 6.6708870243 2.582806

λ2

θ

A

B

Odnos

χ²

2.101496 103.384608 3.8204010883 3.548386 0.9287992237 5.9914645

σd² 8.290593 8.203219 9.089003

2.80159 Gii 14.86744 12.04065 11.99636 9.584705 9.317531 9.858896

7 15.45468 14.99919 10.12126 10.8852 10.19077 10.8852