Geodesic Lines vs Rhumb Lines

Let's start with a couple of simple definitions.

Geodesic Lines

These are the classic shortest distance, along the ellipsoid surface, between any two geodetic positions on the ellipsoid, in which the bearing of the line changes as you move along the geodesic from one point to the other.

TPC uses the equations by Thaddeus Vincenty in his 'Direct and Inverse Solutions of Geodesics on the Ellipsoid with application of nested equations', Published in 1975.  These are the classic, iterative solutions to computing a geodesic foresight (Direct) and inversing the geodesic distance and end point directions (Inverse) between two geodetic positions.

In spherical geometry, we have 'great-circles' which pass through the center of the sphere. You might be tempted to think of geodesics as 'great-ellipses' that pass through the center of the ellipsoid. In some cases you would be right, but not always. Geodesics are not defined or computed uniformly everywhere on a spheroid. The good thing is that TPC understands these issues and always computes the correct geodesic given your geodetic positions.

Rhumb Lines

Also called loxodromes, these are lines of constant direction along the ellipsoid surface between any two geodetic positions on the ellipsoid. Originally developed to aid in navigation (it's easier to set a compass heading and follow it), they are now used in the Public Land Survey System because of the prescription to run true lines (all East-West lines must be perpendicular to the meridian an any point along the line).

TPC computes rhumb lines by computing a 'small circle' at the given latitude.  If a rhumb line is not exactly due East-West, TPC computes the mean latitude of the line and uses it to compute the small circle. Using the radius of the small circle, TPC then computes offsets and intersections to the latitudinal arc of the line.

Some COGO routines, like 'Offset to a line', include a [x] Latitude Arc option. Turn this on to compute on the rhumb line instead of the geodesic line.

Geodetic Editions

The personal edition is not a geodetic edition. It will not include the geodetic distance types, but will include at least some of the coordinate distance types.