Short Distance Sailing Formulae

Short Distance Sailing.

Short distance sailing is a term which is applied to sailing along a rhumb-line for distances less than 600 nautical miles.  From the formulae derived in the book Astro Navigation Demystified, the following are used extensively in short distance sailing:

To Calculate Departure when the course is not known:  dep.= d.long cos(mean lat)

To Calculate Departure when the course is Known:  Dep  = Dist x Sin(course)

To Calculate Distance when departure and course are known:

Dist  =  Dep /Sin (course)

To Calculate Dlat when the distance and course are known:

DLat = Dist x Cos(course)

To Calculate Course to Steer(the rhumb line course between two points)

Tan(course) =   Dep / D.Lat

To calculate Dlong (difference in longitude corresponding to the departure):

DLong.  =  Dep. x Sec(Mean.Lat)  or Dlong =  Dep  / Cos(Mean.Lat)

Example.  At 0900 GMT, a life raft is reported to be in position 30^o 56’.4 S, 0^o 25’.6 E.  A rescue ship reports that its ETA at the vicinity is 2130 GMT.  The rescue ship’s navigator calculates that wind and ocean currents will cause the life raft to drift in direction 345^o at 3 knots.  Calculate the expected position of the life raft when the rescue ship is due to arrive.

 Solution:

Dist. = 37.5 nautical miles

Dep. = 37.5 Sin(345) = 9’.7 West

Dlat  = 37.5 Cos(345) = 36’.2N

New Lat  = 30^o 20’.2S.

M.lat  = 30^o 38’.3S.

DLong. = 9.7 Sec(30.64) = 11’.27W.

New Long = 0^o 14’.33E

Therefore, New Pos.   = 30^o 20’.2S.  0^o 14’.33E  

Click here for on exercise in this topic.

A fuller explanation of the application of spherical trigonometry in astro navigation is given in the book ‘Astro Navigation Demystified’.

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