When sailing from point 1 (L1, LO1) to point 2 (L2, LO2) t = DLO = difference in longitude (degrees) R = length of the perpendicular K = distance from the equator to the perpendicular as measured along the meridian of point one D = distance from point 1 to point 2 (degrees) C = course angle at point 1 csc R = csc t * sec L2 ( R is less than 90 degrees ) csc K = csc L2 / sec R (note 1) sec D = sec R * sec ( K-L1 ) csc C = csc R / csc D (note 2)
Turning the equations over and converting to the sine cosine format, we get a set of formulas usable on a calculator.
sin R = sin t * cos L2 ( R is less than 90 degrees ) sin K = sin L2 / cos R (note 1)(note 3) cos D = cos R * cos (K-L1) sin C = sin R / sin D (note 2) (note 1) If t is greater than 90 degrees then K is greater than 90 degrees. (note 2) If L1 is greater than K then C is greater than 90 degrees. (note 3) If only the course angle is required, Tan C = tan R / sin (K-L1) If L1 is greater than K, C will be a negative angle and the correct answer will be C+180 degrees.
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