Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution ( spheroid) respectively. Other terms used are ellipticity, or oblateness. The usual notation for flattening is and its definition in terms of the semi-axes and of the resulting ellipse or ellipsoid is
The compression factor is in each case; for the ellipse, this is also its aspect ratio.
There are three variants: the flattening [1] sometimes called the first flattening, [2] as well as two other "flattenings" and each sometimes called the second flattening, [3] sometimes only given a symbol, [4] or sometimes called the second flattening and third flattening, respectively. [5]
In the following, is the larger dimension (e.g. semimajor axis), whereas is the smaller (semiminor axis). All flattenings are zero for a circle (a = b).
(First) flattening | Fundamental. Geodetic reference ellipsoids are specified by giving | ||
---|---|---|---|
Second flattening | Rarely used. | ||
Third flattening | Used in geodetic calculations as a small expansion parameter. [6] |
The flattenings can be related to each-other:
The flattenings are related to other parameters of the ellipse. For example,
where is the eccentricity.
Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution ( spheroid) respectively. Other terms used are ellipticity, or oblateness. The usual notation for flattening is and its definition in terms of the semi-axes and of the resulting ellipse or ellipsoid is
The compression factor is in each case; for the ellipse, this is also its aspect ratio.
There are three variants: the flattening [1] sometimes called the first flattening, [2] as well as two other "flattenings" and each sometimes called the second flattening, [3] sometimes only given a symbol, [4] or sometimes called the second flattening and third flattening, respectively. [5]
In the following, is the larger dimension (e.g. semimajor axis), whereas is the smaller (semiminor axis). All flattenings are zero for a circle (a = b).
(First) flattening | Fundamental. Geodetic reference ellipsoids are specified by giving | ||
---|---|---|---|
Second flattening | Rarely used. | ||
Third flattening | Used in geodetic calculations as a small expansion parameter. [6] |
The flattenings can be related to each-other:
The flattenings are related to other parameters of the ellipse. For example,
where is the eccentricity.