Spectra Precision Survey Pro v4.6 Ranger User Manual - Manual (Page 228)

User’s Manual – GPS Mode
218
• TDS Localization Stereographic Projection
The scale factor at the start location (usually the first GPS base
station in a project) is calculated for ground distances at the base
height. The scale factor increases more or less uniformly in all
directions as you move away from the base. The scale factor does not
change appreciable within the range of RTK GPS, so this map
projection is an excellent way to model simple flat earth ground level
coordinate systems.
Ellipsoid Scale Factor
This scale factor accounts for the height of the ground above the
reference surface (the ellipsoid). This scale factor is defined
geometrically: Consider the following diagram:
dist
ground
/(R+h) = dist
elip
/R
dist
elip
/dist
ground
= R/(R+h)
k
elip
= R/ (R+h)
Combined Scale Factor
Generally, the two scale factors are multiplied together into a
combined scale factor. The combined scale factor is then applied to
grid distances to get ground distances:
Fig. 5: Ellipsoid Scale Factor
The effect of height above the ellipsoid on scale.
R+h
Radius of
Ellipsoid, R
Ellipsoid
Height, h
Distance on
Ground
Distance on
Ellipsoid