Spectra Precision Survey Pro CE v3.60 GPS User Manual - Manual (Page 18)

GPS User’s Manual
14
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)
2
1
2 2
) sin 1 (
φ
e
a
R
−
=
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:
k
cf
= k
elip
* k
map
dist
grid
= dist
ground
* k
cf
Vertical Coordinate Systems
GPS measurements provide ellipsoid heights. Most
survey projects require orthometric elevations. To
convert heights into elevations, you need to correct
for the difference between the surface of the
reference ellipsoid and the level surface representing
the gravity field.
The procedure to convert heights (h) to elevations (H)
involves the use of a geoid model. The geoid is a
theoretical surface that approximates mean sea
level. If one knows the separation between the reference ellipsoid
and the geoid, called the geoid undulation (N), then one can
determine orthometric elevations from ellipsoidal heights.
R +h
Radius of
Ellipsoid, R
Ellipsoid
Height, h
Distance on
Ground
Distance on
Ellipsoid
Terrain
Geoid
Ellipsoid
H
N
h
h=H+N
Fig. 5: Ellipsoid Scale Factor
Fig. 6: The Height Equation