FOAIE DE CALCULE TRNSFORMAREA UNGHIURILOR 1 din gms in grd din grd. in rad. din rad in grad din grd in gms din gms in zecimi de gms din zecimi de gms in gms din gms in gms din gms in Mm din gms in Mm poz POZITIV -33.030 -33.05000 -0.57683 -33.030 1 -71.373 -71.62167 -1.25003 2 35.260 35.43333 0.61843 2 2- 1 139.374 -148.453 68.290 211.147 139.62333 -148.755 68.483 211.245 2.43689 -2.59626 1.19526 3.68692

c= 4353.3 c + = 4353.3 lg c= 3.638819

-1983.0 1983.0

-4297.3 4297.3

2126.0 2126.0

8377.4 8377.4

-8925.3 8925.3 148.5

4109.0 4109.0 211.1

FUNCTII TRIGONOMETRICE 1 NR./FCT. unghiuri in RAD SIN COS TG CTG COSEC sin + lgsin cos + lgcos tg + lgtg ctg + lgctg cosec + lgcosec cosM= cosM + = lgcosM= M in rad.= M in grade= M in gms= M in Mm= -33.050 -0.57683 -0.54537 0.83819 -0.65065 -1.53693 -1.83362 0.54537 9.73669 0.83819 9.92335 0.65065 9.81335 1.53693 0.18665 1.83362 0.26331 -0.90008 0.90008 9.95428 2.69074 154.16825 154.101 9250.1 1 -71.622 -1.25003 -0.94900 0.31529 -3.00991 -0.33224 -1.05375 0.94900 9.97726 0.31529 9.49871 3.00991 0.47855 0.33224 9.52145 1.05375 0.02274 lgtgD= lgtgD-tf= tgD= D in rad.= D in grade= D in gms= D in gzm= cosD= secD= secD + = lgsecD= 1 35.433 0.61843 0.57976 0.81479 0.71154 1.40540 1.72487 0.57976 9.76324 0.81479 9.91105 0.71154 9.85220 1.40540 0.14780 1.72487 0.23676 0.31180 0.31180 2.05024 1.11700 63.99925 64.000 64.0 0.43838 2.28111 2.28111 0.35815 2 139.623 2.43689 0.64781 -0.76180 -0.85036 -1.17597 1.54366 0.64781 9.81145 0.76180 9.88184 0.85036 9.92961 1.17597 0.07039 1.54366 0.18855 -148.755 -2.59626 -0.51870 -0.85496 0.60670 1.64827 -1.92790 0.51870 9.71492 0.85496 9.93194 0.60670 9.78297 1.64827 0.21703 1.92790 0.28508 2- 1 M 68.483 1.19526 0.93031 0.36677 -0.900077 2.53648 0.39425 1.07491 0.93031 9.96863 0.36677 0.90008 9.56440 9.95428 2.53648 0.40423 0.39425 9.59577 1.07491 0.03137 D1 1.32497 0.96994 D2 1.50443 0.99780

3.98570 15.04487

0.96994 9.98674

0.99780 9.99904

3.98570 15.04487 0.60050 1.17739

lgctg v1= 10.33720 lgctg v2= 10.94063 lgctg v1-tf.= 0.33720 lgctg v2-tf.= 0.94063 ctg v1= 2.17369 ctg v2= 8.72234 tg v1= 0.46005 tg v2= 0.11465 v1 in rad.= 0.43118 v2 in rad.= 0.11415 v1 in grade= 24.70470 v2 in grade= 6.54030 v1 gms= 24.423 v2 gms= 6.324 v1 gms= 24.423 v2 gms= -6.324 VERIFICARE 31.245 31.147

ctgD1= 0.25090 ctgD2= 0.06647 lgcos v1= 19.91009 lgcos v2= tgD1= 3.98570 tgD2= 15.04487 lgcos v1-tf= 9.91009 lgcos v2-tf D1 in rad= 1.32497 D2 in rad= 1.50443 cos v1= 0.81300 cos v2= D1 in grad= 75.91541 D2 in grad= 86.19727 v1 rad= 0.62152 v2 rad= D1 in dms= 75.549 D2 in dms= 86.118 v1 grad= 35.61024 v2 grad= D1 in dzm= 75.9 D2 in dzm= 86.2 v1 dms= 35.366 v2 dms= D1'+' dzm= 75.9 D2'+' dzm= 86.2 v1 dms= -35.366 v2 dms= 360-D1= 284.1 360-D2= 273.8 D1+180= 255.9 D2+180= 266.2 180-D1= 104.1 180-D2= 93.8 D1= 284.1 D2= 273.8 1 in rad.= -1.250 2 in rad.= 2.437 v1 in rad.= 0.431 v2 in rad.= -0.114 v1 in rad.= -0.819 v2 in rad.= 2.323 v1 in grd= 24.7047 v1 in grd.= -46.917 v2 in grd.= 133.083 v2 in grd= 6.540297 v1 in gms= -46.550 v2 in gms= 133.050 in grd.= 148.755 v1 in grd= -46.917 v2 in grd= 133.083 180 v1 in gms= -46.550 v2 in gms= 133.050 180.000

1.Calculul distantei ortodromice (M) dist.lox.m 3.Calculul lga= 19.49994 lgb= 29.76634 lgtgD= 10.31180 lgm= lga-tf.= 9.49994 lgb-tf.= 9.76634 lgtgD-tf.= 0.31180 lgm-tf.= a= 0.31618 b= 0.58390 2.05024 m= 0.3161816

FUNCTII LOGARITMICE

LATITUDINI CRESCANDE c=7915.70447lg{tg(45+ /2)[(1-esin /1+esin )la put(e/2) 1 2 = -33.050 35.433 in rad.= -0.57683 0.61843 7915.70447 7915.70447 e= 0.0818191986 0.0818191986 45+ /2= 0.49698 1.09461 tg(45+ /2)= 0.54239 1.93885 1-esin = 1.04462 0.95256 1+esin = 0.95538 1.04744 (1-esin /1+esin )= 1.09341 0.90943 (1-esin /1+esin )la put.e/2= 1.00366 0.99612 tg(45+ /2)(1-esin /1+esin )la put(e/2)= 0.54438 1.93133 lgtg(45+ /2)(1-esin /1+esin )la put(e/2)= -0.26410 0.28586 c= -2090.54548 2262.75936 0.45452 c1 c2

19.91009 9.91009 0.81300 0.62152 35.61024 35.366 35.366

20.06063 0.06063 1.14982

lgn= 9.953721 lgn-tf.= 9.95372 n= 0.89892

4.Calculul drumului final D2 lgm= 20.00948 lgn= 9.98027 lgm-tf.= 0.00948 lgn-tf.= 9.98027 m= 1.02206 n= 0.95560

19.91009 9.91009

REZOLVARE PROBLEME NAVIGATIE ORTODROMICA 6.Calculul coordonatelor punctelor interm 1= 33 03.0 S 1= 071 37.3 W Valparaiso Z Z1 Z2 Z3 2= 35 26.0 N 2= 139 37.4 E Yokohama z -80 -90 -100 1.Calculul distantei ortodromice (M) cosM=sin 1sin 2+cos 1cos 2cos z= v- z 33.050 43.050 53.050 2= 35 26.0 lgsin 1= 9.73669 lgcos 1= 9.92335 lgtg v= 9.85503 9.85503 9.85503 - 1= -33 03.0 lgsin 2= 9.76324 lgcos 2= 9.91105 lgcos z= 9.92318 9.86354 9.77863 = 68 29.0 lg a= 9.49994 lgcos = 9.93194 lgtg z= 9.77822 9.71857 9.63366 = 4109 Mm a= 0.31618 lg b= 9.76634 z= -30.581 -27.368 -23.166 2= -139 37.4 b= 0.58390 - 1= -071 37.3 a= -0.31618 v= -35.366 = -148 45.3 +b= -0.58390 M= 154 10.1 v= -046.550 = 8925.3 Mm cosM= -0.90008 M= 9250.1 Mm Z10 Z11 Z12 = 211.15 lgcos M= 9.95428 -170 -180 170 2.Calculul distantei loxodromice (m) tgD= / c m= secD 123.050 133.050 143.050 c2= 2262.76 lg = 3.95062 lg = 3.61374 9.85503 9.85503 9.85503 - c1= -2090.55 +colog c= 6.36118 lgsecD= 0.35815 9.73708 9.83446 9.90282 c= 4353.30 lgtgD= 0.31180 lgm= 3.97188 9.59211 9.68949 9.75786 lg c= 3.63882 D= 64 00.0 m= 9373.1 Mm 21.212 26.041 29.477 colog c= 6.36118 D= 64 0 m= 9373.1 Diferenta dintre distanta loxodromica si distanta ortodromica C=m-M -M= 9250.1 C= 123.0 Mm 3.Calculul drumului initial D1 4.Calculul drumului final D2 ctgD1=tg 2cos 1cosec -sin 1ctg ctgD2=-tg 1cos 2cosec +sin 2ctg lgtg 2= 9.85220 lgsin 1= 9.73669 lgtg 1= 9.81335 lgsin 2= 9.76324 lgcos 1= 9.92335 lgctg = 0.21703 lgcos 2= 9.91105 lgctg = 0.21703 lgcosec = 0.28508 lgn= 9.95372 lgcosec = 0.28508 lgn= 9.98027 lgm= 0.06063 n= 0.89892 lgm= 0.00948 n= 0.95560 m= 1.14982 m= 1.02206PUNCT DE PLECARE PUNCT DE SOSIRE

m= 1.14982 D1= 284 1 +n= 0.89892 D2= 273 8 ctgD1= 0.25090 D1= 75 54.9 D2= 86 5.Calculul coordonatelor vertexului a.Latitudinea vertexului cos v1=cos 1sinD1 cos v2=cos 2sinD2 lgcos 1= 9.92335 lgcos 2= 9.91105 lgsinD1= 9.98674 lgsinD2= 9.99904 lgcos v1= 9.91009 lgcos v2= 9.91009 v1= -35 36.6 v2= 35 36.6 b.Longitudinea vertexului ctg v1=sin 1tgD1 ctg v2=sin 2tgD2 lgsin 1= 9.73669 lgsin 2= 9.76324 lgtgD1= 0.60050 lgtgD2= 1.17739 lgctg v1= 0.33720 lgctg v2= 0.94063 v1= 024 42.3 v2= -006 32.4 1= -071 37.3 v1= 024 42.3 v1= -046 55.0

11.8

m= +n= ctgD2=

-1.02206 -0.95560 0.06647

Verificare v1= 024 v2= 006 = 148 = 180 v1= 024 v2= 006 = 031

42.3 32.4 45.3 00.0 42.3 32.4 14.7

+

+ v2= 133 05.0

tg z=tg vcos z Z4 Z5 -110 -120 63.050 73.050 9.85503 9.85503 9.65581 9.46387 9.51084 9.31891 -17.578 -11.463

Z6 -130 83.050 9.85503 9.08074 8.93577 -04.558

Z7 -140 93.050 9.85503 8.73065 8.58568 02.124

Z8 -150 103.050 9.85503 9.35481 9.20984 09.125

Z9 -160 113.050 9.85503 9.59336 9.44839 15.411

Z13 160 153.050 9.85503 9.95020 9.80524 32.338

Z14 150 163.050 9.85503 9.98079 9.83582 34.252

Z15 140 173.050 9.85503 9.99683 9.85186 35.247

N S

E W

Punct de plecare 1= -33.030 Punct de sosire 2= 35.260 1.Calculul distantei ortodromice (M) 2= 35.26 -' 1= -33.03 = 68.29 = 4109.0 Mm

1= -71.373 2= 139.374 cosM=sin 1sin 2+cos 1cos 2cos lgsin 1= 9.73669 lgcos 1= 9.92335 lgsin 2= 9.76324 lgcos 2= 9.91105 lg a= 9.49994 lgcos = 9.93194 a= 0.31618 lg b= 9.76634 b= 0.58390 2= 139.37 -7630.749 a= -0.31618 1= -71.37 7630.749 +'b= -0.58390 = -148.45 211.15 cosM= -0.90008 M= 154.101 = 8925.3 Mm lgcos M= 9.95428 M= 9250.1 Mm 2.Calculul distantei loxodromice (m) tgD= / c m= secD c2= 2262.8 lg = 3.95062 -80.2 lg = 3.61374 - c1= -2090.5 +colog c= 6.36118 lgsecD= 0.35815 c= 4353.3 lgtgD= 0.31180 lgm= 3.97188 lg c= 3.63882 D= 64.000 m= 9373.1 colog c= 6.36118 D= 64.0 m= 9373.08 Diferenta dintre distanta loxodromica si distanta ortodromica C=m-M M= 9250.09 C= 123.0 3.Calculul drumului initial D1 4.Calculul drumului final D2 ctgD1=tg 2cos 1cosec -sin 1ctg ctgD2=-tg 1cos 2cosec +sin 2ctg lgtg 2= 9.85220 lgsin 1= 9.73669 lgtg 1= 9.81335 lgsin 2= 9.76324 lgcos 1= 9.92335 lgctg = 0.21703 lgcos 2= 9.91105 lgctg = 0.21703 lgcosec = 0.28508 lgn= 9.95372 lgcosec = 0.28508 lgn= 9.98027 lgm= 0.06063 n= 0.89892 lgm= 0.00948 n= 0.95560 m= 1.14982 m= 1.02206 m= 1.14982 m= n= 0.89892 D1= 75 54.9 n= ctgD1= 0.25090 D1= 284.1 ctgD2= 5.Calculul coordonatelor vertexului a.Latitudinea vertexului cos v1=cos 1sinD1 cos v2=cos 2sinD2 lgcos 1= 9.92335 lgcos 2= 9.91105 lgsinD1= 9.98674 lgsinD2= 9.99904 lgcos v1= 9.91009 lgcos v2= 9.91009 v1= -35.366 v2= 35.366 b.Longitudinea vertexului ctg v1=sin 1tgD1 ctg v2=sin 2tgD2 lgsin 1= 9.73669 lgsin 2= 9.76324 lgtgD1= 0.60050 lgtgD2= 1.17739 lgctg v1= 0.33720 lgctg v2= 0.94063 v1= 24.423 v2= -6.324 1= v1= v1= -71.373 24.423 -46.550 139.374 -6.324 133.050 tg z=tg vcos -100 53.050 9.85503 9.77863 9.63366 23.166 -23.166 -110 63.050 9.85503 9.65581 9.51084 17.578 -17.578 z -120 73.050 9.85503 9.46387 9.31891 11.463 -11.463 -130 83.050 9.85503 9.08074 8.93577 4.558 -4.558 -140 93.050 9.85503 8.73065 8.58568 2.124 2.124 -150 103.050 9.85503 9.35481 9.20984 9.125 9.125 -160 113.050 9.85503 9.59336 9.44839 15.411 15.411 -170 123.050 9.85503 9.73708 9.59211 21.212 21.212 -180 133.050 9.85503 9.83446 9.68949 26.041 26.041 170 143.050 9.85503 9.90282 9.75786 29.477 29.477 -1.02206 -0.95560 0.06647 D2=

D2= 273.8 86 11.8

Verificare v1= v2= = = v1= v2= =

24.423 6.324 148.453 180.000 24.423 6.324 31.147

TRUE

+

+

v2=

FALSE

6.Calculul punctelor intermediare Z z= v- z lgtg v= lgcos z= lgtg z= z= v= v= z-poz -80 33.050 9.85503 9.92318 9.77822 30.581 -30.581 -35.366 -46.550 33.050 -90 43.050 9.85503 9.86354 9.71857 27.368 -27.368

43.050

53.050

63.050

73.050

83.050

93.050

103.050

113.050

123.050

133.050

143.050

9.864 0.000 9.864

160 153.050 9.85503 9.95020 9.80524 32.338 32.338

150 163.050 9.85503 9.98079 9.83582 34.252 34.252

140 173.050 9.85503 9.99683 9.85186 35.247 35.247

153.050

163.050

173.050

0

0

L1 Z1, Z1,

-71.373 -71.373 180 -81.373 -91.373 Z1' -81.373 -91.373 -101.373 Z2 -80 -90 -100 Z3 -80 -90 -100 Z4, 180 -80 -90 -100 Z6 -80 -90 -100 Z in rad. -1.39626 -1.5708 -1.74533 v in gms= -46.550 -46.550 -46.550 v in rad.= -0.81886 -0.81886 -0.81886 z in rad. 0.577408 0.751941 0.926474 z in grd. 33.083 43.083 53.083 z in gms. 33.050 43.050 53.050 v in gms.= -35.366 v in rad.= 0.62152 0.62152 0.62152 v in rad.+ = 0.62152 0.62152 0.62152 tg v= 0.71620 0.71620 0.71620 lgtg v= -0.14497 -0.14497 -0.14497 lgtg v + = 9.85503 9.85503 9.85503 cos z= 0.83788 0.73036 0.60066 cos z + = 0.83788 0.73036 0.60066 lgcos z= -0.07682 -0.13646 -0.22137 lgcos z + = 9.92318 9.86354 9.77863 lgtg z= 19.77822 19.71857 19.63366 lgtg z tf.= 9.77822 9.71857 9.63366 0.60009 0.52309 0.43019 0.54049 0.48195 0.40626 30.96754 27.61348 23.27692 30.581 27.368 23.166

-111.373 -110 -110 -110 -110 -110 -1.91986 -46.550 -0.81886 1.101007 63.083 63.050 0.62152 0.62152 0.71620 -0.14497 9.85503 0.45270 0.45270 -0.34419 9.65581 19.51084 9.51084 0.32422 0.31353 17.96388 17.578

-121.373 -131.373 -141.373 -151.373 -161.373 -171.373 -181.373 -191.373 -201.373 -120 -130 -140 -150 -160 -170 -180 -190 -200 -120 -130 -140 -150 -160 -170 -180 170 160 -120 -130 -140 -150 -160 -170 -180 -120 -130 -140 -150 -160 -170 -180 170 160 -120 -130 -140 -150 -160 -170 -180 170 160 -2.0944 -2.26893 -2.44346 -2.61799 -2.79253 -2.96706 -3.14159 -3.31613 -3.49066 -46.550 -46.550 -46.550 -46.550 -46.550 -46.550 -46.550 -46.550 -46.550 -0.81886 -0.81886 -0.81886 -0.81886 -0.81886 -0.81886 -0.81886 -0.81886 -0.81886 1.27554 1.450073 1.624605 1.799138 1.973671 2.148204 2.322737 2.49727 2.671803 73.083 83.083 93.083 103.083 113.083 123.083 133.083 143.083 153.083 73.050 83.050 93.050 103.050 113.050 123.050 133.050 143.050 153.050 0.62152 0.62152 0.71620 -0.14497 9.85503 0.29099 0.29099 -0.53613 9.46387 19.31891 9.31891 0.20840 0.20546 11.77216 11.463 0.62152 0.62152 0.71620 -0.14497 9.85503 0.12043 0.12043 -0.91926 9.08074 18.93577 8.93577 0.08625 0.08604 4.92970 4.558 0.62152 0.62152 0.71620 -0.14497 9.85503 -0.05378 0.05378 -1.26935 8.73065 18.58568 8.58568 0.03852 0.03850 2.20591 2.124 0.62152 0.62152 0.71620 -0.14497 9.85503 -0.22636 0.22636 -0.64519 9.35481 19.20984 9.20984 0.16212 0.16072 9.20874 9.125 0.62152 0.62152 0.71620 -0.14497 9.85503 -0.39206 0.39206 -0.40664 9.59336 19.44839 9.44839 0.28080 0.27375 15.68457 15.411 0.62152 0.62152 0.71620 -0.14497 9.85503 -0.54585 0.54585 -0.26292 9.73708 19.59211 9.59211 0.39094 0.37267 21.35255 21.212 0.62152 0.62152 0.71620 -0.14497 9.85503 -0.68306 0.68306 -0.16554 9.83446 19.68949 9.68949 0.48921 0.45498 26.06815 26.041 0.62152 0.62152 0.71620 -0.14497 9.85503 -0.79951 0.79951 -0.09718 9.90282 19.75786 9.75786 0.57261 0.52003 29.79575 29.477 0.62152 0.62152 0.71620 -0.14497 9.85503 -0.89166 0.89166 -0.04980 9.95020 19.80524 9.80524 0.63861 0.56833 32.56269 32.338

-211.373 -210 150

-221.373 -220 140

-231.373 -230 130 130

-241.373 -240 120 120

-251.373 -250 110 110

-261.373 -260 100 100

150 140 150 140 -3.66519 -3.83972 -46.550 -46.550 -0.81886 -0.81886 2.846336 3.020869 163.083 173.083 163.050 173.050 0.62152 0.62152 0.71620 -0.14497 9.85503 -0.95673 0.95673 -0.01921 9.98079 19.83582 9.83582 0.68521 0.60073 34.41926 34.252 0.62152 0.62152 0.71620 -0.14497 9.85503 -0.99272 0.99272 -0.00317 9.99683 19.85186 9.85186 0.71099 #VALUE! 0.61806 #VALUE! 35.41234 #VALUE! 35.247

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!