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RAUN RAZLIKE ZEMLJOPISNIH KOORDINATA,SREDNJE ZEMLJOPISNE IRINE I RAZMAKA

Stipe Gali2012

JEDINICE ZA MJERENJE KUTEVA

PUNI KRUG:1. KUTNA MJERA 0 - 3602. LUNA MJERA 2R3. SATNA MJERA 24h

PRETVARANJE STUPNJEVA : 3602 SR ; 15360

24 SSh

PRETVARANJE RADIJANA: RS 180 ;

Rh 12

PRETVARANJE SATI: hhS 1524360 ; hhR 1224

2

1. PRIMJERNeka se kut = 203 17 49 pretvori u lunu i satnu mjeru

smhSh 27.11331355312963.13152969444.203

154917203

15

radSSR 548201039.31802969444.203141592654.3

1803602

2. PRIMJERNeka se luk u satnoj mjeri od 7h 37m 54s pretvori u kutnu i lunu mjeru

3028114475.114631666667.71554377151524360 smhhhS

radhhR 997965662.112631666667.7141592654.3

12242

3. PRIMJER = 254 30 54 pretvori u stupnjeve

515.254254515.0609.30

9.30254min309.06054stupnjevi

ute

4. PRIMJER = 025.123794 pretvori u 0.123794 60 7.42764 025 7.427640.42764 60 25.6584025.123794 025 0725.66

5. PRIMJER358 sati pretvori u dane

dana91666667.1424358 6. PRIMJER903.5 sati pretvori u dane/sate/minute

mhd 30153730605.0155.15

5.152464583333.03764583333.3764583333.37245.903

7. PRIMJERIzraunajte 1 luka velike krunice za Bessel elipsoid pod uvjetom da se izjednai povrinaelipsoida sa povrinom kugle.a = 6377397.155b = 6356078.963

abr 44 2 abr 2

136.6366729963.6356078155.6377397 abrr20

r260360 006433.18526036021 r

8. PRIMJERIzraunajte 1 luka velike krunice za WGS 84 pod uvjetom da se izjednai povrina elipsoida sapovrinom kugle.a = 6378137b = 6356078.963

abr 44 2 abr 2

429.6367098963.63560786378137 abrr20

r260360 113857.18526036021 r

9.PRIMJERIzraunajte 1 luka velike krunice za Bessel elipsoid ako se volumen elipsoida izjednai savolumenom kugle.volumen elipsoida = 4/3a2bvolumen kugle = 4/3r3

32 34

34 rba

3 2 bar 3 2 963.6356078155.6377397 r

158.6370283r040257.185360360

21 r

10 PRIMJEROpseg Elipse

...5642

531342

312112)(4

62422

2 eeeaeaEL

gdje je:

2,eEeE potpuni eliptiki integral druge vrste

Nepotpuni I. vrste:

22 sin1 ed

Nepotpuni II. vrste: de 22 sin1potpuni eliptiki integral druge vrste:

2

0

22 sin12,

deeEeEpriblina formula:

215875.185236060/91.400078625.1 babaL 11. PRIMJERNautike tablice br.6, daju nam jednu minutu luka velike krunice + 1 luka paralele (Besselovelipsoid)meridijan 1= 1852.009 - 9.434 cos2 + 0.020 cos4

paralela 1= 1856.686 cos - 1.576 cos3 + 0.002 cos5vidi NT6.12.PRIMJERPretvori 5.6 km u NM.ako je:

mNM 18521 mkm 10001

slijedi da je:kmNM 852.11 NMkm 852.1

11 ;

NMkm 023758.3852.16.56.5

13. PRIMJERPretvorite 5 stopa u metre.

mcmftmcmft

524.14.15253048.048.301

14. PRIMJERPretvorite 5 metara u stope.

ftm 3048.011

ftm 40419948.163048.055

15. PRIMJERPretvorite 20 ina u centimetre.

cmin 54.21 cmcmin 8.5054.22020

16. PRIMJERPretvorite 80 centimetara u ine

cmin 54.21 cmcm 54.2

11

incm 49606299.3154.28080

NAVIGACIJA IVJEBE

1. PRIMJER1= 2808.5N 12 2= 2205,0N------------------- 2= 2205,0N =? -1= 2808.5N

------------------- =0603.5S

---------------------------------------------------------------------------------------------------------------------2.PRIMJER1= 1030.0N 12 2= 0520,0S------------------- 2= 0520,0S =? -1= 1030.0N

------------------- =1550.0S

---------------------------------------------------------------------------------------------------------------------3.PRIMJER1= 09141.3E 12 2= 06821,5E------------------- 2= 06821,5E =? -1= 09141.3E

------------------- =02319.8W

---------------------------------------------------------------------------------------------------------------------4.PRIMJER1= 17000.0E 12 2= 16000,0W------------------- 2= 16000,0W =? -1= 17000.0E

------------------- =33000.0W - 360 =03000.0E

5. PRIMJERN0.20211 E7.050221 N0.1510 E8.54170

-------------------------------------------------------------------?2 ; ?2

12 12

+NNN

0.35310.15100.2021

2

1

+WE

EE

5.591663605.001938.541707.05022

2

1

---------------------------------------------------------------------------------------------------------------------6.PRIMJER

N8.29141 E5.140281 N2.11122 E8.170052

-------------------------------------------------------------------?S ; ? ; ?

221 S 12 12N8.29141 N2.11122 E8.170052

+ N2.11122 - N8.29141 - E5.140281 2/0.41262 NS S6.1802 W7.56022

NS 5.2013---------------------------------------------------------------------------------------------------------------------7. PRIMJER

N0.15361 W0.140021 N0.15362 E0.050072

-------------------------------------------------------------------?S ; ? ; ? ; ?R

N0.15361 N0.15362 E0.050072 + N0.15362 - N0.15361 - W0.140021

2/0.30722 NS 0.0000 E0.19009NS 0.1536 600.19009 E

559

Razmak (R) moemo dobiti na etiri naina:1 nain:(pomou formule)

SR cos 8025338.4500.1536cos559 2. nain:(pomou logaritamskih tablica)

SR cosSR coslogloglog 74741.247559log NT

+ 09343.01090657.9480.1536coslog NT 8.4504765398.209343.074741.2log NTR

3. nain:(grafiki)

0.451R

4. nain(tablino, NT 4)

8.450R

8. PRIMJERNMR 5.341

NS 0.4045-----------------------------

?a.) raunski:

SR cos ;S

R cos = 4.4008008606728493.4880.4045cos

5.341

b.) tablino:

5.341R360800814333333.8606.488

9. PRIMJERE0.02008 = 482

NS `0.4051------------------------------

?Ra.) raunski:

SR cosNMR 2999535068.298`0.4051cos`482

b.) tablino:

10. PRIMJER

W

NP 3.310201.2340

1

11

W

NP 3.310209.1940

2

22

--------------------------------------------------------------?S ; ? ; ? ; ?R ; ?PK ; ?D

221 S 12 12

N1.23401 N9.19402 W3.310202 + N9.19402 - N1.23401 - W3.310201

2/3.40802 NS S2.0300 0.00000NS 5.2140

R

Scos SR cos = NM05.2140cos0.00000

180PK Vidi sliku

DK Pcos

PKD cos

= 180cos2.3 = NM2.3

11. PRIMJER

E

SP 0.000503.1200

1

11

E

NP 0.000500.3000

2

22

-----------------------------------------------------------------?S ; ? ; ? ; ?R ; ?PK ; ?D

221 S 12 12

S3.12001 N0.30002 E0.000502 + N0.30002 - S3.12001 - E0.000501

2/7.17002 NS N3.4200 0.00000NS 510800

R

Scos SR cos = NM0510800cos0.00000

000PK Vidi sliku

DK Pcos

PKD cos

= 000cos3.42 = NM3.42

12. PRIMJER

W

NP 0.200010.3045

1

11

W

NP 0.210020.3045

2

22

-----------------------------------------------------------------?S ; ? ; ? ; ?R ; ?PK ; ?D

221 S 12 12

N0.30451 N0.30452 W0.210022 + N0.30452 - N0.30451 - W0.200011

2/0.00912 NS 0.0000 600.01001 WNS 0.3045 W61

R

Scos SR cos = NMN 75546512.420.3045cos61

270PK Vidi slikuNMD 8.42 Vidi sliku

13. PRIMJER

W

NP 0.300003.2150

1

11

E

NP 0.510003.2150

2

22

-----------------------------------------------------------------?S ; ? ; ? ; ?R ; ?PK ; ?D

221 S 12 12

N3.21501 N3.21502 E0.510002 + N3.21502 - N3.21501 - W0.300001

2/6.421002 NS 0.0000 600.21001 ENS 3.2150 E81

R


090PK Vidi slikuNMD 7.51 Vidi sliku

14. PRIMJER

E

NP 1.550155.3443

1

11

E

NP 3.590150.5043

2

22

-----------------------------------------------------------------?S ; ? ; ? ; ?R ; ?PK ; ?D

a.) raunski:

221 S 12 12

N5.34431 N0.50432 E3.590152 + N0.50432 - N5.34431 - E1.550151

2/5.24872 NS N5.1500 000 04.2 E NS 154243 N5.15 E2.4

R

Scos SR cos = NMN 036250987.3154243cos2.4

LRtgK =

3.03625098715.5 N = 19588716.0 08316935.011 011.1L PK K

cos LK D cos LD K

= 08316935.11cos5.15 = NM79458198.15 NM8.15

b.) tablino:3,03 0,19548387115, 5

RtgK 11.06091476P LK K

15, 5cos cos11.06091476L

D K

NMD 79338153,15 NM8.15

15. PRIMJER

W

NP 0.320505.3443

1

11

W

NP 0.300491.2143

2

22

-----------------------------------------------------------------?S ; ? ; ? ; ?R ; ?PK ; ?D

a.) raunski:

221 S 12 12

N5.34431 N1.21432 W0.300492 + N1.21432 - N5.34431 - W0.320501

2/6.55862 NS S4.1300 600.02001 ENS 8.2743 S4.13 E62

R


LRtgK = S4.13

00051374.45 = 358247294.3 073.41781697LK

6.1064.073180PK

cos LK D cos LD K

= 41781697.73cos4.13 = NM95323456.46 NM47

b.) tablino:45 3.35820895513.4L

RtgK 73,41763806LK

6.1065823619.10641763806.73180PK13.4 46.9527422 47cos cos73,41763806L

D NMK

16. PRIMJER

E

SP 0.210200.3034

1

11

E

SP 0.010200.5234

2

22

-----------------------------------------------------------------?S ; ? ; ? ; ?R ; ?PK ; ?D

a.) raunski:

221 S 12 12

S0.30341 S0.52342 E0.010202 + S0.52342 - S0.30341 - E0.210201

2/0.22692 SS S0.2200 W0.20000SS 0.4134 S22 W20

R

Scos SR cos = NMS 44619206.160.4134cos20

LRtgK = 0.22

44619206.16

= 747554184.0 36.78010597 036,8LK

180 036.8 216.8PK

cos LK D cos LD K

= 78010597.36cos

0.22 = NM46774897.27 NM5.27

17. PRIMJER

U tx = 0815 vlastiti brod se naao na

W

SP 0.510430.1120

1

11

,

a u tx = 1220 na poziciji

W

SP 0.590430.0919

2

22

. Odredite:------------------------------------------------------------------------------

?S ; ? ; ? ; ?R ; ?PK ; ?D ; b = ?a.) raunski:

221 S 12 12

S0.11201 S0.09192 W0.590432 + S0.09192 - S0.11201 - W0.510431

2/0.20392 SS N0.0201 W0.08000SS 0.4019 N62 W08

R

Scos SR cos = NMS 533331996.70.4019cos08

LRtgK = 0.62

533331996.7

= 121505354.0 927784311.06K

1.3539.06360PK

cos LK D cos LD K

= 927784311.06cos0.62 = NM45599323.62 NM5.62

2 1220Xt - 1 0815Xt

0405Xt

D v t 62,45599323 15,29534528 15,30405D NMv vt

18. PRIMJER

U poziciji

E

NP 8.230169.2843

1

11

smjera se drugi brod p=177, d=3.9. ?2 P---------------------------------------------------------------------------------------------------------------------

cosK D cos cos177 3.9 3.894655186 3.9K D

N9.28431 N9.28431 + S9.0300 + N0.25432

N0.25432 2/9.53862 NSNS 572643

RtgK 3.894655186 177 0.204110229R tgK tg

S

R cos 3.0281149452.0572643cos

204110229.0

E8.230161 + E3.00000

E1.240162

Tablino: Ako nam su nam poznati p i D, onda vrijednosti , R, moemo izvaditi iz NT br.3.

9.39.3 S ima negativan predznak jer jevrijednost p =177 u SE kvadrantu.

25.0R

19. PRIMJER

U poziciji

E

NP 8.550151.3143

1

11

smjera se drugi brod p=351, d=3.4. ?2 P---------------------------------------------------------------------------------------------------------------------

cosK D cos cos351 3.4 3.358140358 3.4K D

N1.31431 N1.31431 + N4.0300 + N5.34432

N5.34432 2/6.05872 NSNS 8.3243

RtgK 3.358140358 351 0.531877181R tgK tg

S

R cos 7.073381249.08.3243cos

531877181.0

E8.550151 + W7.00000

E1.550152

Tablino: Ako nam su nam poznati p i D, onda vrijednosti , R, moemo izvaditi iz NT br.3.

4.34.3 N ima pozitivan predznak jer jevrijednost p =351 u NW kvadrantu.

56.0R

20. PRIMJERU tx=0800 vlastiti brod se naao na poziciji

E

NP 5.270147.1844

1

11

i istovremeno je snimionepoznati brod u p=173, d=6.8.U tx=0845 vlastiti brod se naao na poziciji

E

NP 1.400147.1044

2

22

i istovremeno se nepoznatibrod naao na p=289, d=11.3.a.) Kolika je brzina i kurs vlastitog broda.b.) Kolika je brzina i kurs nepoznatog broda.

sinR D K 828711535.0173sin8.6 R

cosD K 749313831.6173cos8.6

12 2 21 SN`7.18441 N`7.18441

+ S`7.0600 + N`0.12442 N`0.12442 2/`7.30802 NS

NS 211544

S

R cos =1.1570452191.2E

121 014 27.5 E

+ 000 01.2 E 2 014 28.7E

---------------------------------------------------------------------------------------------------------------------6843599.10R 678920145.3 2 44 14.4 N

NS 331244 90565557.14 E2.250142 ---------------------------------------------------------------------------------------------------------------------

Za nepoznati brod:4.2 5.3 NS 2.1344

508335226.2R

LRtgK 46.26440908 46.3LK ; 7.3133.46360PK

cos LK D 2, 4 3, 471562417 3,5cos cos 46,26440908LD NMK

tvD 3,471562417 4.628749889 4.60845 0800

Dv vt

Za vlastiti brod:8 6.12 NS 7.1444

026171713.9R

LRtgK 48.44905904 048.4LK ; 180 048.4 131.6PK

cos LK D cos LD K

12,06116809 12.1D NM

tvD 12.06116809 16,08155746 16.10845 0800

Dv vt

21. PRIMJERSa pozicije polaska

E

NP 8.110650.5607

1

11

brod je u toku dana plovio u sljedeim kursovima iprevalio ove daljine: Kp=117 D=44.8NM ; Kp=090 D=19.4NM ; Kp=311 D=42NM;Kp=262 D=15.9NM. Izraunajte koordinate pozicije dolaska ?2 P

N0.56071 N0.56071 + N0.0500 N0.01082

N0.01082 2/0.57152 NSNS 5.5807

S

R cos = N

E5.5807cos

82.11 = E9.11

E8.110651 + E9.11000

E7.230652 Rjeenje:

E

NP 7.230650.0108

2

22

22. PRIMJER

W

NP 6.000306.0030

1

11

Kp = 300 ; D = 120NMKp = 044 ; D = 062NMKp = 180 ; vB = 12 v ; t = 0640---------------------------------------------------------------------------------------------------------------------

?2 PtvD B = mhv 400612 = NM80

N6.00301 N6.00301 + N6.2400 N2.25302

N2.25302 2/8.25602 NSNS 9.1230

S

R cos = N

W9.1230cos

8.60 = W4.70 = W4.10001

W6.000301 + W4.10001

W0.110312 Rjeenje:

W

NP 0.110312.2530

2

22

23. PRIMJERSa pozicije polaska

W

SP 8.190390.2414

1

11

brod je u toku dana plovio u sljedeim kursovima iprevalio ove daljine: Kp=026 D=24.4NM ; Kp=000 D=109.3NM ; Kp=315 D=44NM;Kp=272 D=9.6NM. Izraunajte koordinate pozicije dolaska ?2 P

Rjeenje:

W

SP 6.500393.4111

2

22

24. PRIMJER

W

NP 0.280410.4456

1

11

Kp = 330 ; vB = 12 v ; t = 02-20-00Kp = 168 ; D = 47NMKp = 180 ; D = 26NMKp = 258 ; vB = 12 v ; t = 05-20-00Kp = 090 ; D = 3.2NM---------------------------------------------------------------------------------------------------------------------Izraunajte koordinate pozicije dolaska ?2 P

Rjeenje:

W

NP 4.220439.4255

2

22

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