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If we assume that the altitude is held constant, the great circle distance is correct. However if the radius of the circle is not constant how can the distance be calculated? In my case the altitude changes linearly from point1 to point2.

What is the correct way then, to calculate the distance between two Lat Long points with different altitudes?

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    You may get more error by treating the coordinates as spherical and including Z change than by using spheroidal computations and ignoring Z. The US Geodetic Survey has both 2D and 3D algorithms posted for both geodetic problems – Vince Dec 24 '16 at 1:44
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    First you should ask yourself how you are travelling. Are on flying or on he ground ? – radouxju Dec 24 '16 at 13:06
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    That is a good question to ask. As I didn't want to get into orbital dynamics, I use a simple interpolation for the altitude and an existing great circle distance. The interpolation reduces to using the average altitude for the great circle calculation. And that worked perfectly well for my application. – esdanol Aug 21 '18 at 17:10