About eleven years ago, I published in these pages a pocket calculator algorithm for a sextant line of position calculation.
As it turns out, this same algorithm can be used to calculate the Intercept, (Great Circle distance in Nautical Miles) from the departure to the
destination location, as well as the Azimuth (initial compass course to be steered). Some of the variables must be redefined, but the calculation is the same.
Ho = 90 degrees. Substitute the observed sextant altitude Ho with the value 90. If you are at that location, the “star” must be at the Zenith!
DEC = Substitute the Declination of the heavenly body with the latitude of the destination. (Positive for N, negative for S). Declination is the same as latitude.
GHA = Substitute the Greenwich Hour Angle of the heavenly body with the degrees west of Greenwich of the destination. (GHA is always positive, always to the W, from 0 to 360 degrees. GHA is the same as longitude only for W longitudes. So if your destination longitude is 10 degrees E, your GHA is 350 degrees. If the destination longitude is 10 degrees W, the GHA is 10 degrees.
Lat = The Latitude of the departure point (Positive for N, negative for S)
Lon = The Longitude of the departure point (Positive for E, negative for W)
LHA = GHA + LON (Add or subtract 360 degrees if LHA is outside the range -360 to 360 .
Cos DEC x Cos LHA = C
Sin DEC = S
Hc = INVsin ( S x Sin Lat + C x Cos Lat )
Intercept = Ho – Hc Make sure Ho and Hc are in units of minutes (‘) of arc. One minute of arc = 1 nautical mile.
X = ( S x Cos Lat – C x Sin Lat ) / Cos Hc
If X is greater than +1 or less than -1 (due to truncation error), just reset it to +1 or -1.
A = INVcos ( X )
If LHA > 180 degrees, then Azimuth Z = A
Otherwise, Z = 360- A
Throughout the GC track, the compass heading will change continuously, so in practice, this calculation will have to be repeated frequently so the vessel’s course can be readjusted.