as orthometric height or Mean Sea Level height.
Elevation is labeled "H".
2-4 General
An ELLIPSOID is defined as "a surface whose
plane sections (cross sections) are ellipses or circles, or
the solid enclosed by such a surface." It can be more
easily identified as a sphere which is flattened, or
squashed, on the sides or the top and bottom. In
geodesy, we use an ellipsoid that is flattened on the top
and bottom; this is referred to as an oblate ellipsoid.
The terms ellipsoid and spheroid are considered
interchangeable; this text will use the term ellipsoid
unless the mathematical figure of a spheroid is
necessary. See Figure 2-3.
SPHERE
ELLIPSOID
Figure 2-3 Ellipsoid
2-5 Defining Parameters of an Ellipsoid
a. An ellipsoid is generally defined in terms of three
parameters, or dimensions, which provide the size and
ellipticity of the ellipsoid. Tables A-1a and A-1b list
the defining parameters for 42 ellipsoids.
1. Semi-major Axis: The semi-major axis of an
ellipsoid is the distance along the equatorial plane of
an ellipsoid from the center of that plane to its edge; or
the equatorial radius. It is referred to as the long
radius of an ellipsoid or one-half of the largest
diameter. The semi-major axis is labeled "a". See
Figure 2-4.
2. Semi-minor Axis: The semi-minor axis of an
ellipsoid is the distance in a meridional plane from the
center of the plane to its closest edge; or the polar
radius. It can also be referred to as the short radius of
the ellipsoid or one-half of the shortest diameter. The
semi-minor axis is labeled "b". See Figure 2-4.
3. Flattening: The flattening of an ellipsoid is the
ratio of the difference between the equatorial and polar
radii (semi-major and semi-minor axis) to the
equatorial radius (semi-major axis) and is labeled "f".
It is more commonly expressed as the inverse of
flattening (1/f). Flattening can also be called
ellipticity.
Figure 2-4 Defining Parameters
b. There are other defining parameters for ellipsoids
which are discussed in detail in DMA TM 8358.1 and
DMA TR 8350.2. These parameters include earth
gravity information, angular velocity, and eccentricity;
an understanding of these parameters is not necessary
for artillery surveyors and will not be discussed in this
text.
c. Computing Ellipsoid Parameters
DRAFT
2-2
Section II
ELLIPSOIDS