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Derivation and Limitations of the Elevation Factor for Reducing Lines to the Ellipsoid

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This article explores the derivation and use of the elevation factor (R/(R + h)) in the reduction of long lines to the ellipsoid reference surface. It is shown that the formula for the reduction of a level distance (LD) is the degenerate form of the formula for the reduction of a long line to the ellipsoid. This degenerate formula is similar to the popular elevation factor used to reduce ground distances to the ellipsoid in the use of state plane coordinates. The article continues with a study of the factors involved with the use of spherical mean radius of the Earth instead of the Radius of Curvature in the Normal Section for the reduction of long lines. The article concludes with the development of a "Worst-Case" Tipping Point Formula for use in determining when the Radius of Curvature in the Normal Section should be used in the elevation factor in the reduction of a LD.
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Keywords: ELEVATION FACTOR; GEODETIC REDUCTIONS; LEVEL DISTANCE; SPHERICAL RADIUS

Document Type: Review Article

Publication date: November 1, 2017

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