In many cases, the three defining parameters
discussed in paragraphs 2-5;a;1,2, and 3 above will not
be available. The user can compute the third
parameter from two known parameters using the
formulas below.
1. To compute the semi-minor axis (b) use the
formula b=a(1-f).
Example: GRS-80 ellipsoid
Step 1: determine f. 1/f = 298.257222101 so
f = 1/298.257222101
f = 0.00335281068118
Step 2: determine b. b=a(1-f)
b = 6378137 ( 1 - 0.00335281068118 )
b = 6356752.31414
* NIMA published value for b is 6356752.3141.
2. To compute flattening (1/f) use the formula
f=(a-b)/a.
Example: GRS-80 ellipsoid
Step 1: determine f. f = ( a - b ) / a
f = (6378137 - 6356752.3141) / 6378137
f = 0.00335281068751
Step 2: determine 1/f.
Flattening = 1 / 0.00335281068751
1/f = 298.257221538
* NIMA published value for 1/f is 298.257222101.
3. These computations may provide a quantity that
is slightly different than the accepted NIMA
parameters. This is generally due to rounding and is
considered insignificant for many geodetic applications
and for all artillery survey applications.
2-6 Reference Ellipsoid
a. The oblate ellipsoid is used in geodesy because it is
a regularly shaped mathematical figure. Unlike the
geoid, there is no undulation. If the geoid were
regularly shaped, there would be no need for an
ellipsoid, we would simply compute surveys referenced
strictly to the geoid itself. Since that is not the case, an
ellipsoid is defined and then fixed to a specific location
(usually located on the surface of the geoid) and
orientation which makes it closely resemble the surface
of the geoid; this is accomplished by establishing a
Horizontal Datum which is discussed in detail in
Section 3 of this chapter. Once an ellipsoid is fixed by
a specific datum it is referred to as a Reference
Ellipsoid.
b. Reference ellipsoids can be either local in extent or
global. If the ellipsoid resembles only a small region
of the geoid, and it is fixed to a point on the surface of
the earth, it is local. If the ellipsoid is fixed to the
center of mass of the earth and is designed to resemble
the geoid as a whole, then it can be considered global
and is considered an Earth-centered Earth-fixed
(ECEF) ellipsoid. See Figures 2-5 and 2-6.
Figure 2-5 Local Reference Ellipsoid
DRAFT
2-3
ELLIPSOID
GEOID
GEOID
ELLIPSOID
N
Ellipsoid
Geoid