If the rhumb line heading and the great-circle heading are found, and the smaller value subtracted from the larger value the result is called the great-circle correction angle (Theta sub c) which I will call GCC for great circle correction.
DLO = difference in longitude Lm = mean latitude = ((L1+L2)/2) Ld = (L2-L1) = latitude difference tan GCC = tan (( DLO ) / 2 ) * sin Lm / cos ( Ld / 2 ) A second approximation can be made, giving; GCC = ( DLO / 2 ) * sin Lm (round off to integer value)
If the great circle path is divided into N parts so that we have a sequence of chords or legs to approximate the great-circle then the heading correction ( Hc ) to be applied to the initial rhumb line heading will be as follows.
Hc = ( GCC * (N-1)) / N
Considering that the angles will be small integer values, we can set N = GCC producing the following.
Hc = GCC - 1
Dividing the distance to the final great-circle destination by N we get the distance for each leg.
( The rhumb line distance divided by N can be used as an aproximation)Dividing the length of each leg by the cruising speed gives the time it should take to travel the leg.
When N is set equal to GCC and there are no errors due to round off or drift, the course change at the end of each leg should be 2 degrees. At the end of each leg the whole computation is repeated to find the new heading.
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