Formulas

Question 1

Plane Sailing Formulas

Answer 1

Dep = D’Long x Cos M Lat
Tan Course = Dep / D’Lat
Distance = D’Lat / Cos Course

Question 2

Mercator Sailing Formulas

Answer 2

Tan Course = D’Long / DMP
Distance = D’Lat / Cos Course

Question 3

Calculated Zenith Distance Formula

Answer 3

Cos CZD = (Cos LHA x Cos Lat x Cos Dec) +- (Sin Lat x Sin Dec)
+ = Lat & Dec SAME
- = Lat & Dec DIFFERENT

Question 4

Great Circle - DISTANCE

Answer 4

Cos AB = (Cos P x Sin PA x Sin PB) + (Cos PA x Cos PB)

Question 5

Great Circle - INITIAL COURSE

Answer 5

Cos A = (Cos PB - (Cos PA x Cos AB)) / (Sin PA x Sin AB)

Question 6

Great Circle - FINAL COURSE

Answer 6

Cos B = (Cos PA - (Cos PB x Cos AB)) / (Sin PB x Sin AB)

Question 7

Azimuth Formulas

Answer 7

A = Tan Lat / Tan LHA - named opposite to Lat unless LHA between 90 - 270 degrees
B = Tan Dec / Sin LHA - named same as Dec
C = A +- B (+ = SAME, - = DIFF) - named larger value of A or B or same
Tan Azi = 1 / (C x Cos Lat) - named N/S on C, named W if LHA 0 - 180 degrees, E if LHA 180 - 360 degrees

Question 8

Amplitude Formula

Answer 8

Sin Amp = Sin Dec / Cos Lat

Question 9

Napier’s Rules

Answer 9

Sin Mid Part = Cos Opposite x Cos Opposite
Sin Mid Part = Tan Adjacent x Tan Adjacent

Question 10

Napier’s Rules - OPPOSITE

Answer 10

Sin = Cos
Cos = Sin
Tan = 1 / Tan

Question 11

Sextant Altitude to True Altitude

Answer 11

Sextant Altitude
Index Error (+ = OFF ARC, - = ON ARC)
Observed Altitude
Dip (from Height of Eye)
Apparent Altitude
Total Correction
Extra Correction (specific planets)
True Altitude

Question 12

Meridian Passage Formulas

Answer 12

Lat = TZD + Dec (if Dec & DR Lat SAME)
Lat = TZD - Dec (if Dec & DR Lat DIFFERENT)