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 30o 56’.4 S, 0o 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 345o at 3 knots. Calculate the expected position of the life raft when the rescue ship is due to arrive.
Dist. = 37.5 nautical miles
Dep. = 37.5 Sin(345) = 9’.7 West
Dlat = 37.5 Cos(345) = 36’.2N
New Lat = 30o 20’.2S.
M.lat = 30o 38’.3S.
DLong. = 9.7 Sec(30.64) = 11’.27W.
New Long = 0o 14’.33E
Therefore, New Pos. = 30o 20’.2S. 0o 14’.33E
A fuller explanation of the application of spherical trigonometry in astro navigation is given in the book ‘Astro Navigation Demystified’.
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