Accuracy of Elevation Reduction Factor

摘要

When using state plane coordinates or performing other geodetic computations, the ratio rl(r + h) is the elevation factor commonly used to reduce a horizontal distance to its sea-level or ellipsoidal equivalent. In most cases, an approximation is used for the Earth's radius while the value of the elevation is usually much better known. This is as it should be, but the question examined in this paper is, What is an acceptable approximation for the Earth's radius and how accurately must the elevation be known to assure sufficient precision in the answer? An equation that can be used to answer these questions is derived using concepts of error propagation.