Spectra Precision Survey Pro v4.5 Recon and Nomad User Manual - Manual (Page 235)

GPS Overview
225
• Stereographic
The Stereographic projection results from projecting an ellipsoid onto
a plane. Directions are true from the center point and distortions in
scale, area and shape increase uniformly away from the central point.
The stereographic projection is azimuthal.
Because the scale is distorted somewhat uniformly in all directions,
stereographic map projections are a good representation of a
surveyor’s typical flat earth ground coordinate system. For this
reason, the stereographic map projection is used by the Ground - TDS
Localization
mode algorithm to convert (lat,lng) into local ground level
coordinates. For more information on localization, see Page 271.
Scale Factors
When converting distances on a map to distances on the ground, you
must correct for two different scale distortions. First, the effects of the
map projection distortion must be corrected with the mapping plane
scale factor. Second, the geometric effect of your height above the
reference surface (ellipsoid height) must be corrected with the
ellipsoid scale factor. Generally, these two scale factors are multiplied
together into the combined scale factor.
Mapping Plane Scale Factor
This scale factor accounts for the distortions caused by the mapping
plane equations as they fit a curved surface onto a flat plane. It is a
function of the mapping plane equations and its exact value depends
on your location on the map. Although the scale factor is computed
with differential equations of the map projection, one can visualize it
in a geometric sense. Consider the following diagrams:
• Universal Transverse Mercator Projection
The scale factor at the central meridian (CM) is 0.9996. The scale
factor is 1.0 approximately 170-km east and west of the CM. The
scale factor is less than one between the CM and the point of
tangency. The scale factor is greater than one beyond the point of
tangency. Therefore, at the central meridian, a geodetic distance of
100m scales into a mapping plane distance of 99.96m.