calcul ortodroma.xlsx

7/23/2019 calcul ortodroma.xlsx

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FOAIE DE CALCULE

TRNSFORMAREA UNGHIURILOR

φ1 λ1 φ2 λ2 Δλ φ2-φ1

-6.080 155.400 41.440 -124.120 80.080 47.520

d! "#$ ! "%d -6.1&&&& 155.66667 41.7&&&& -124.20000 80.1&& 47.867

d! "%d. ! %'d. -0.10705 2.716(0 0.728&8 -2.16770 1.&(85( 0.8&54&d! %'d ! "%'d

d! "%d ! "#$ -6.080

d! "#$ ! )*+# d* "#$

d! )*+# d* "#$ ! "#$

d! "#$ ! "#$

d! "#$ ! M# -&68.0 (&40.0 2504.0 -7452.0 4808.0 2872.0

d! "#$ ! M# ,) &68.0 (&40.0 2504.0 7452.0 4808.0 2872.0

O/ITI 80.1

FUNCTII TRIGONOMETRICE

φ1 λ1 φ1 λ2 Δλ φ2-φ1

NR.FCT. -6.1&& 155.667 41.7&& -124.200 80.1&& 47.867

!"3% ! RAD -0.10705 2.716(0 0.728&8 -2.16770 1.&(85( 0.8&54&

SIN -0.10684 0.41204 0.66566 -0.82708 0.(8521 0.7415(

COS 0.((428 -0.(1116 0.74625 -0.56208 0.171&6 0.67086

TG -0.10746 -0.45222 0.8(201 1.47146 5.74(4( 1.1054&

CTG -(.&05(( -2.211&2 1.12106 0.67(60 0.17&(& 0.(046&

COSEC -(.&5(57 2.426(2 1.50226 -1.20(07 1.01501 1.&4846

$! 0.10684 0.41204 0.66566 0.82708 0.(8521 0.7415(

"$! (.02874 (.614(4 (.82&26 (.(1755 (.((&5& (.87016

+$ 0.((428 0.(1116 0.74625 0.56208 0.171&6 0.67086

"+$ (.((751 (.(5(60 (.87288 (.74(80 (.2&&(0 (.8266&" 0.10746 0.45222 0.8(201 1.47146 5.74(4( 1.1054&

"" (.0&124 (.655&5 (.(50&7 0.16775 0.75(6& 0.04&5&

+" (.&05(( 2.211&2 1.12106 0.67(60 0.17&(& 0.(046&

"+" 0.(6876 0.&4465 0.04(6& (.8&225 (.240&7 (.(5647

+$*+ (.&5(57 2.426(2 1.50226 1.20(07 1.01501 1.&4846

"+$*+ 0.(7126 0.&8506 0.17674 0.08245 0.00647 0.12(84

+$M 0.05602 ""D 0.18(05 +"D1 0.(1880 +"D2

+$M 0.05602 ""D- 0.18(05 "D1 1.088&7 "D2

"+$M 8.748&5 "D 1.54542 D1 ! %'d 0.8276( D2 ! %'d

M ! %'d. 1.51475 D ! %'d. 0.((648 D1 ! "%'d 47.42&0( 2 ! "%'d

M ! "%'d*86.7885& D ! "%'d*57.0(40( D1 ! d#$ 47.254 2 ! d#$M ! "#$ 86.47& D ! "#$ 57.056 D1 ! d)# 47.4 2 ! d)#

M ! M# 5207.& D ! ")# 57.1 D199 d)# 47.4 299 d)#

+$D 0.54&26 &60-D1 &12.6 &60-D2

$*+D 1.84074 D1180 227.4 D2180

$*+D 1.84074 180-D1 1&2.6 180-D2

"$*+D 0.264(( D1 47.4 D2

λ1 ! %'d. 2.717 2 ! %'d.



"+"Δλ:1 (.06552 "+"Δλ:2 10.52841 λ:1 ! %'d. -1.455 2 ! %'d.

"+"Δλ:1-. (.06552 +"Δλ:2-. 0.52841 λ:1 ! %'d. 1.262 2 ! %'d.

+"Δλ:1 0.11628 +"Δλ:2 &.&7606 λ:1 ! "%d. 72.2(( 2 ! "%d.

"Δλ:1 8.5((61 "Δλ:2 0.2(620 λ:1 ! "#$ 72.180 2 ! "#$

Δλ:1 ! %'d. 1.4550& λ:2 ! %'d. 0.287(7 λ:1 ! "%d 72.2(( :2 ! "%d

Δλ:1 ! "%'d* 8&.&6718 2 ! "%'d* 16.4((48 λ:1 ! "#$ 72.180 2 ! "#$

Δλ:1 "#$ 8&.220 Δλ:2 "#$ 16.&00Δλ:1 "#$ -8&.220 Δλ:2 "#$ 16.&00

1.Calculul distantei ortodromic

ERIFICARE ((.867 "' 18.85200 ";

((.520 "'-. 8.85200 ";-.

' 0.07112 ;

0.071121



FUNCTII LOGARITMICE

Δφ+ &111.1

Δφ+ &111.1

Δλ "Δφ+ &.4(2(1(

-27(.520

-27(.867

-4.8845(

27(.5

M D1 D2

0.8276( 1.&7612

0.7&6&7 0.(8111

0.056021

1.088&7 5.07171

0.7&6&7 0.(8111

(.86710 (.((172

0.05602

8.748&51.088&7 5.07171

0.0&678 0.70515

0.1(717 "+$φ:1 1(.8646 "+$φ:2 1(.8646

5.07171 "+$φ:1- (.86460 "+$φ:2- (.86460

1.&7612 +$φ:1 0.7&215 +$φ:2 0.7&215

78.845(4 φ:1 %'d 0.74(&2 φ:2 %'d 0.74(&2

78.508 φ:1 "%'d 42.(&266 :2 "%'d 42.(&26678.8 φ:1 d#$ 42.560 :2 d#$ 42.560

78.8 φ:1 d#$ -42.560 :2 d#$ 42.560

281.2

258.8

101.2

78.8

-2.168



0.288

-1.880 Δλ:1 ! "%d 8&.&6718

-107.701 Δλ:2 ! "%d 16.4((48

-107.420 Δλ ! "%d. 80.1&&&&

-107.701 180

-107.420 180.000

(M) d$.<.# 3.Calculul drumului initial D1 4.Calculul drumul

2(.1042( ""D 10.18(05 "# 1(.(54&5 "! 18.26(11 "# 18.(105(

(.1042( ""D-. 0.18(05 "#-. (.(54&5 "!-. 8.26(11 "#-. 8.(105(

0.12714 1.54542 # 0.(0022 ! 0.01858 # 0.081&(



LATITUDINI CRESCANDE

φ+7(15.70447"=">45φ2?@>1-*$!φ1*$!φ?' ,>*2?B

φ1 φ2

φ -6.1&& 41.7&&

φ ! %'d. -0.10705 0.728&8

7(15.70447 7(15.70447

* 45φ20.7&187 1.14(5(

">45φ2? 0.8(8&0 2.2&204

1-*$!φ 1.00874 0.(4554

1*$!φ 0.((126 1.05446

>1-*$!φ1*$!φ? 1.01764 0.8(670

>1-*$!φ1*$!φ?' ,.*21.00072 0.((555

">45φ2?>1-*$!φ1*$!φ?' ,>*2? 0.8(8(4 2.22211

"">45φ2?>1-*$!φ1*$!φ?' ,>*2? -0.04627 0.&4677

φ+ -&66.245(5 2744.8(2&1

0.75405

φ+1 φ+2



i fnal D2

"! 1(.06&6& 1(.86460

"!-. (.06&6& (.86460

! 0.11578



RE/OLARE ROLEME NAIGATIE ORTODROMICA

UNCT DE LECARE φ1 06 08.0 S λ1 155 40.0 E ','%'$

UNCT DE SOSIRE φ2 41 44.0 N λ2 124 12.0 3'#'1.Calculul distantei ortodromice (M) cosM=sinφ1sinφ2+cosφ1cosφ2cosΔλ

φ2 41 44.0 "$!φ1 (.02874 "+$φ1 (.((751

-φ1 -06 08.0 "$!φ2 (.82&26 "+$φ2 (.87288

Δφ 47 52.0 " ' 8.85200 "+$Δλ (.2&&(0Δφ 2872 M# ' 0.07112 " ; (.1042(

λ2 -124 12.0 ; 0.12714

-λ1 155 40.0 ' -0.07112

Δλ 080 08.0 ; 0.12714 M 86 47.&

Δλ 4808 M# +$M 0.05602 M 5207.& M#

Δλ -27(.52 "+$ M 8.748&5

2.Calculul distantei loxodromice (m) tD=Δλ!Δφc m=ΔφsecD

φ+2 2744.8( "Δλ &.681(6 "Δφ &.45818

-φ+1 -&66.25 +"Δφ+ 6.50708 lgsecD= 0.264((

Δφ+ &111.14 lgtgD= 0.18(05 lgm= &.72&18

"Δφ+ &.4(2(2 D= 57 05.6 m= 5286.6 M#

"Δφ+ 6.50708 D= 57 1 m= 5286.6D*%*!' d!%* d$'!' <d%#+' $ d$'!' %d%#+' C=m-M -M= 5207.&

C= 7(.& M#

3.Calculul drumului initial D1 4.Calculul drumului final D2

+"D1"φ2+$φ1+$*+Δλ-$!φ1+"Δλ +"D2-"φ1+$φ2+$*+Δλ$!φ2+"Δλ

""φ2 (.(50&7 "$!φ1 (.02874 ""φ1 (.0&124 "$!φ2 (.82&26

"+$φ1 (.((751 "+"Δλ (.240&7 "+$φ2 (.87288 "+"Δλ (.240&7

+$*+Δλ 0.00647 "! 8.26(11 "+$*+Δλ 0.00647 "! (.06&6&

"# (.(54&5 ! 0.01858 "# 8.(105( ! 0.11578

# 0.(0022 # 0.081&(

# 0.(0022 D1 47 4 # -0.081&(

! -0.01858 D2 78 8 ! 0.11578+"D1 0.(1880 D1 47 25.4 D2 78 50.8 "D2 0.1(717

".Calculul coordonatelor #ertexului

'.L'd!*' :*%*<

+$φ:1+$φ1$!D1 +$φ:2+$φ2$!D2

"+$φ1 (.((751 "+$φ2 (.87288

"$!D1 (.86710 "$!D2 (.((172

"+$φ:1 (.86460 "+$φ:2 (.86460

φ:1 -42 56.0 φ:2 42 56.0

;.L!"d!*' :*%*<

+"Δλ:1$!φ1"D1 +"Δλ:2$!φ2"D2 *%+'%*

"$!φ1 (.02874 "$!φ2 (.82&26 Δλ:1 08& 22.0

""D1 0.0&678 ""D2 0.70515 Δλ:2 016 &0.0+"Δλ:1 (.06552 "+"Δλ:2 0.52841 Δλ 080 08.0

Δλ:1 -08& 22.0 Δλ:2 016 &0.0 180 00.0

λ1 155 40.0 Δλ:1 08& 22.0

Δλ:1 -08& 22.0 Δλ:2 016 &0.0

λ:1 072 18.0 λ:2 -107 42.0 Δλ 0(( 52.0



6.Calculul coordonatelor punctelor interm"φ)"φ:+$Δλ)

/ $1 $2 $3 $4 $" $% $& $'

λ) 160 170 180 -170 -160 -150 -140 -1&0Δλ)λ:-λ) -87.420 -(7.420 -107.420 -117.420 -127.420 -1&7.420 -147.420 -157.420

""φ: (.(686& (.(686& (.(686& (.(686& (.(686& (.(686& (.(686& (.(686&

"+$Δλ) 8.60&&( (.1270( (.482(& (.667&1 (.78642 (.86(02 (.(26(( (.(6624

""φ) 8.57202 (.0(572 (.45157 (.6&5(5 (.75505 (.8&765 (.8(56& (.(&487φ) 2.'3 &.%3 1".4&% 23.232 2*.3'2 34.31* 3'.1' 4.432

φ: -42.560

λ: 072.180



N E

S



!+ d* ,*+'%* φ1 -6.080 λ1 155.400

!+ d* $$%* φ2 41.440 λ2 -124.120

1.Calculul distantei ortodromice (M) cosM=sinφ1sinφ2+cosφ1cosφ2

φ2 41.44 "$!φ1 (.02874 "+$φ1

-9φ1 -6.08 "$!φ2 (.82&26 "+$φ2

Δφ 47.52 " ' 8.85200 "+$ΔλΔφ 2872.0 M# ' 0.07112 " ;

;

λ2 -124.12 82&.87(4 ' -0.07112

λ1 155.40 82&.87(4 9; 0.12714

Δλ 80.08 -27(.52 +$M 0.05602 M 86.47&

Δλ 4808.0 M# "+$ M 8.748&5 M 5207.&

2.Calculul distantei loxodromice (m) tD=Δλ!Δφc m=Δφsec

φ+2 2744.( "Δλ &.681(6 -80.2 "Δφ &.45818

-φ+1 -&66.2 +"Δφ+ 6.50708 "$*+D 0.264((

Δφ+ &111.1 ""D 0.18(05 "# &.72&18

"Δφ+ &.4(2(2 D 57.056 # 5286.6

+"Δφ+6.50708 D 57.1 #D*%*!' d!%* d$'!' <d%#+' $ d$'!' %d%#+' C#-M M

C

3.Calculul drumului initial D1 4.Calculul drumului fnal D2

+"D1"φ2+$φ1+$*+Δλ-$!φ1+"Δλ +"D2-"φ1+$φ2+$*+Δλ$!φ2+

""φ2 (.(50&7 "$!φ1 (.02874 ""φ1 (.0&124 "$!φ2

"+$φ1 (.((751 "+"Δλ (.240&7 "+$φ2 (.87288 "+"Δλ

"+$*+Δλ 0.00647 "! 8.26(11 "+$*+Δλ 0.00647 "!

"# (.(54&5 ! 0.01858 "# 8.(105( !

# 0.(0022 # 0.081&(

# 0.(0022 # -0.081&(

! -0.01858 D1 47 25.4 ! 0.11578+"D1 0.(1880 D1 47.4 +"D2 0.1(717 D2

".Calculul coordonatelor #ertexului D2 78

'.L'd!*' :*%*<

+$φ:1+$φ1$!D1 +$φ:2+$φ2$!D2

"+$φ1 (.((751 "+$φ2 (.87288

"$!D1 (.86710 "$!D2 (.((172

"+$φ:1 (.86460 "+$φ:2 (.86460

φ:1 -42.560 φ:2 42.560

;.L!"d!*' :*%*<

+"Δλ:1$!φ1"D1 +"Δλ:2$!φ2"D2 *%+'%*

"$!φ1 (.02874 "$!φ2 (.82&26 Δλ:1 8&.220

""D1 0.0&678 ""D2 0.70515 Δλ:2 16.&00"+"Δλ:1 (.06552 "+"Δλ:2 0.52841 Δλ 80.080

Δλ:1 -8&.220 Δλ:2 16.&00 180.000

λ1 155.400 -124.120 Δλ:1 8&.220

Δλ:1 -8&.220 16.&00 Δλ:2 16.&00

λ:1 72.180 λ:2 -107.420 Δλ ((.520



%.Calculul unctelor intermediare "φ)"φ:+$Δλ)

/ 160 170 180 -170 -160 -150 -140

Δλ)λ:-λ) -87.420 -(7.420 -107.420 -117.420 -127.420 -1&7.420 -147.420

""φ: (.(686& (.(686& (.(686& (.(686& (.(686& (.(686& (.(686&

"+$Δλ) 8.60&&( (.1270( (.482(& (.667&1 (.78642 (.86(02 (.(26((

""φ) 8.57202 (.0(572 (.45157 (.6&5(5 (.75505 (.8&765 (.8(56&φ) 2.08& 7.06& 15.476 2&.2&2 2(.&82 &4.&1( &8.108

-2.08& 7.06& 15.476 2&.2&2 2(.&82 &4.&1( &8.108

φ: -42.560

λ: 72.180

Δλ)-,) 87.420 (7.420 107.420 117.420 127.420 1&7.420 147.420



cosΔλ

(.((751

(.87288

(.2&&(0(.1042(

0.12714

M#

D

5286.5(5207.&1

7(.&

"Δλ

(.82&26

(.240&7

(.06&6&

0.11578

78.8

50.8

1.000

0.000



-1&0

-157.420

(.(686&

(.(6624

(.(&48740.4&2

40.4&2

157.420

(.127

0.000

(.127



0 0

L1 155.4 155.4

/1ΔλJ180 145.4 1&5.4

/1ΔλK180 165.4 175.4

/19 165.4 175.4 185.4 1(5.4 205.4 215.4 225.4 2&5.4

/2 160 170 180 1(0 200 210 220 2&0

/& 160 170 180 -170 -160 -150 -140 -1&0

/4ΔλJ180 160 170 180

/5ΔλK180 160 170 180 -170 -160 -150 -140 -1&0

/6 160 170 180 -170 -160 -150 -140 -1&0

/ ! %'d. 2.7(2527 2.(6706 &.1415(& &.&16126 &.4(065( &.6651(1 &.8&(724 4.014257

λ: ! "#$ 72.180 72.180 72.180 72.180 72.180 72.180 72.180 72.180λ: ! %'d. 1.261864 1.261864 1.261864 1.261864 1.261864 1.261864 1.261864 1.261864

Δλ) ! %'d. -1.5&066 -1.7052 -1.87(7& -2.05426 -2.2287( -2.40&&& -2.57786 -2.752&(

Δλ) ! "%d. -87.701 -(7.701 -107.701 -117.701 -127.701 -1&7.701 -147.701 -157.701

Δλ) ! "#$. -87.420 -(7.420 -107.420 -117.420 -127.420 -1&7.420 -147.420 -157.420

φ: ! "#$. -42.560

φ: ! %'d. 0.74(&2 0.74(&2 0.74(&2 0.74(&2 0.74(&2 0.74(&2 0.74(&2 0.74(&2

φ: ! %'d. 0.74(&2 0.74(&2 0.74(&2 0.74(&2 0.74(&2 0.74(&2 0.74(&2 0.74(&2

"φ: 0.(&0&2 0.(&0&2 0.(&0&2 0.(&0&2 0.(&0&2 0.(&0&2 0.(&0&2 0.(&0&2

""φ: -0.0&1&7 -0.0&1&7 -0.0&1&7 -0.0&1&7 -0.0&1&7 -0.0&1&7 -0.0&1&7 -0.0&1&7

""φ: (.(686& (.(686& (.(686& (.(686& (.(686& (.(686& (.(686& (.(686&

+$Δλ) 0.04012 -0.1&400 -0.&0404 -0.46485 -0.6115& -0.7&(64 -0.84527 -0.(2521

+$Δλ) 0.04012 0.1&400 0.&0404 0.46485 0.6115& 0.7&(64 0.84527 0.(2521"+$Δλ) -1.&(661 -0.872(1 -0.51707 -0.&&26( -0.21&58 -0.1&0(8 -0.07&01 -0.0&&76

"+$Δλ) 8.60&&( (.1270( (.482(& (.667&1 (.78642 (.86(02 (.(26(( (.(6624

""φ) 18.57202 1(.0(572 1(.45157 1(.6&5(5 1(.75505 1(.8&765 1(.8(56& 1(.(&487

""φ) . 8.57202 (.0(572 (.45157 (.6&5(5 (.75505 (.8&765 (.8(56& (.(&487

0.0&7&& 0.12466 0.28286 0.4&246 0.568(2 0.68810 0.786&7 0.86074

0.0&7&1 0.12402 0.27566 0.40817 0.51725 0.6026( 0.666&7 0.71070

2.1&76( 7.10574 15.7(&88 2&.&8652 2(.6&652 &4.5&18& &8.18040 40.72004

2.08& 7.06& 15.476 2&.2&2 2(.&82 &4.&1( &8.108 40.4&2



245.4 255.4 265.4 275.4 285.4 2(5.4 &05.4 &15.4 &25.4

240 250 260 270 280 2(0 &00 &10 &20

-120 -110 -100 -(0 -80 -70 -60 -50 -40

-120 -110 -100 -(0 -80 -70 -60 -50 -40

ALUE ALUE ALUE ALUE ALUE ALUE ALUE ALUE ALUE





&&5.4 &45.4

&&0 &40

-&0 -20

-&0 -20

ALUE ALUE

ALUE ALUE

ALUE ALUE

calcul ortodroma.xlsx

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