Distances as measured on a Grid, the Ellipsoid, the Geoid and on the Ground
You should be aware that there are significant changes when converting distances from a UTM map to the equivalent ground distance when using NAD27 versus using NAD83, as mentioned below:
Basis upon which the Great Circle Distance Calculation is Derived (recalling how to determine the length of a circle).
False Origin
Surfaces, Orientations and Coincidences
Illustrations of different map projections
The UTM Projection-based coordinate system