Spectra Precision Survey Pro CE v3.60 GPS User Manual - Manual (Page 16)

GPS User’s Manual
12
Lambert projections are used for about half of the State Plane
Coordinate System zones in the USA.
• 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 TDS
localization algorithm to convert (lat,lng) into local ground level
coordinates. For more information on localization, see page 35.
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: