Is it possible to calculate 3D geodesic length of a line?

Question

I have LIDAR coverage for a route which crosses multiple UTM zones. I want to calculate the length of this route as accurately as possible correcting for projection error, elevation, and curvature of the earth. I have figured out the first two parts but the curvature issue has stumped me. By modeling the Earth in AutoCAD using UTM WGS 84 parameters I've come up with a length multiplier of 1.000457002 to account for curvature but I'm not sure if that is correct, or if that can be multiplied with a 3D length to get the proper answer.

All thoughts are appreciated.

Thank you,

-Lee

DanPatterson_Retired · Answer

It would be an interesting comparison to extract an elevation profile from a seamless DEM between two points at some distance and compare that to planar and geodesic length assuming flat terrain.  A line of latitude or longitude (over 3, 6 ... degrees) would standardize the calculations from coordinates.

LeeDavis1 · Answer

It is a unique problem. I am in the engineering business and these differences in length correlate to differences in material quantities, so we are talking about millions of dollars. Our data gets very detailed over long stretches of terrain.

Thanks,

DanPatterson_Retired · Answer

It would be an interesting exercise.  I doubt that most people have lines with sufficiently dense vertices to accommodate such calculations over long distances while accounting for the possible range in elevation errors over those same differences.