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NAVIGATION FORMULAS

SAILINGS:

4 PLANE SAILING – DISTANCE ALONG RHUMB LINE = D’LAT * SEC COURSE

TAN COURSE= DEPARTURE¸ D’ LAT.

5 PARALLEL SAILING – DEPARTURE= D’ LONG. * COS LAT.

6 MID LAT SAILING – DEPARTURE = D’LONG * TRUE MID LAT.

TAN COURSE= DEP¸ D’ LAT, DISTANCE= D’LAT * SEC COURSE (NOTE) –

DISTANCE MUST BE 600 MILES LESS AND LATITUDE BELOW 60 DEGREES.

7 MERCATOR SAILING – TAN COURSE = D’ LONG ¸M, DISTANCE = D’LAT * SEC

COURSE.

8 GREAT CIRCLE FORMULAS:

COS DISTANCE= (COS L1* COS L2 * COS DLO. ) + ( SIN L1 * SIN L2) - MINUS SIGN IF

GREAT CIRCLE CROSSES THE EQUATOR.

COS IC = SIN L2- (COS DIST * SIN L1)¸SIN DIST. * COS L1)

COS FC= SIN L1- (COS DIST * SIN L2)¸ SIN DIST * COS L2 OR

SIN IC= SIN DLO * COS L2 * CSC DIST.

SIN FC= SIN DLO * COS L1 CSC DIST.

COS LAT. VERTEX = COS L1 * SIN IC

SIN DLOV= COS IC * CSC LAT V

SIN LX = SIN LV * COS DISTANCE OF Vx

SIN DLOVx = SEC Lx * SIN DISTANCE OF Vx (FROM THE VERTEX)

COS DLOVx= TAN Lx * COT LV

TAN Lx= COS DLOVx * TAN LV

SIN Dv= COS L1 * SIN DLOv (NOTE) : THE COURSE OF THE GREAT CIRCLE WHEN

CROSSING THE EQUATOR IS EQUAL TO THE CO- LATITUDE OF THE VERTEX

COMPOSITE GREAT CIRCLE SAILING :

4 TO FIND THE LONGITUDE AT THE LIMITING LATITUDE OR PARALLEL.:

5 COS P1 = TAN L1/ TAN LV

6 TO FIND LONGITUDE WHEN LEAVING MAX. LAT.

7 COS P2= TAN L2/ TAN LV

8 TO FIND INITIAL COURSE IC - SIN ANGLE A= COS LV/ COS L1

2

9 TO FIND FINAL COURSE= FC - SIN ANGLE B = COS LV/ COS L2

10 TO FIND TOTAL DISTANCE AV1 – COS DIST. AV1= SIN L1/ SIN LV

11 COS VB2 = SIN L2 / SIN LV,

12 P3 = DLO- (P1 + P2)

13 COS V1 V2 = P3 * 60 * COS LV (PARALLEL SAILING )

14 HAVERSINE FORMULAS:

15 HAV A= ( HAV a- ( HAV b-c)/ SIN B SIN C )

16 SINE LAW:

SIN A/ SIN a= SIN B/ SIN b = SIN C/ SIN c

RIGHT ANGLE SPHERICAL TRIANGLE :

SINE MIDDLE PART = PRODUCT OF COSINES OF OPPOSITE PARTS

= TAN OF ADJACENT PARTS

COMPUTATION OF SUNRISE OR SUNSET :

4 COS HA = TAN LAT * TAN DEC

5 COS Z = SEC LAT * SIN DEC (NOTE) LAT. AND DEC SAME NAME -HA IS OVER 90

DEGREES OR 6 HOURS AND VALUE MUST BE SUBTRACTED FROM 12 HRS (180

DEG)

6 DECLINATION AND LATITUDE –OPPOSITE NAME TO LAT – HA WILL BE LESS THAN

6 HRS.

7 * FINDING LOCAL HOUR ANGLE AT THE PRIME VERTICAL:

8 COS LHA = COT LAT * TAN DEC – WHEN THE BODY CROSSES THE PRIME

VERTICAL.

9 COS PX= COS PZ * COS X

10 SIN ALT= COSEC LAT SIN DEC.

11 * FINDING GYRO ERROR (AMPLITUDE METHOD)- SIN AMPL= SINDEC *SEC LAT

12 * FINDING AZIMUTH – SIN Z= SIN t * COS DEC * SEC HO.

13 CONSTRUCTING MERCATOR CHART- LENGTH OF LATITUDE SCALE SHOULD

EQUAL DMP * LENGTH OF 1’ LONGITUDE

COMPASS ERROR;

CORRECTING THE COMPASS------- EASTERLY VARIATION AND DEVIATION +

(from compass to true) -- WESTERLY VARIATION AND DEVIATION

--

FORMULAS TO CONVERT SOLAR TIME INTO SIDEREAL TIME:- CONVERSION

FACTOR

= 24 HRS-00 MIN.-00 SEC./ 23 HRS- 56 MIN- 04 SEC.

FROM SIDEREAL TIME TO SOLAR TIME :

3

COVERSION FACTOR:

23 HRS.- 56 MIN- 04 SEC / 24 HRS –OO MIN –OO SEC.

RIGHT ASCENSION OF A STAR = 360 DEGREES – SHA

END; COMPILER: C/M RICARDO T. COLOYAN TEL * 26130-57

PLEASE FEEL FREE TO CONTACT OR SEEK ASSISTANCE IF YOU HAVE PROBLEMS IN

GREAT CIRCLE SAILING OR COMPOSITE SAILING, WHICH IS PRESENTLY USED IN OCEAN

NAVIGATION. SOLUTIONS ON COMPUTING THE POINTS OR LATITUDES OF POINTS ALONG

THE GREAT CIRCLE TRACK WITH ITS COMPUTED DISTANCE AND COURSE COULD BE

EASILY SOLVE ( EXAMPLE: FROM KOBE, JAPAN TO CALIFORNIA , USA.)