Normal heights are heights above sea level, one of several types of height which are all computed slightly differently. Alternatives are: orthometric heights and dynamic heights.
The normal height of a point is computed from geopotential numbers by dividing the point's geopotential number, i.e. its geopotential difference with that of sea level, by the average, normal gravity computed along the plumbline of the point. (More precisely, along the ellipsoidal normal, averaging over the height range from 0 — the ellipsoid — to ; the procedure is thus recursive.
Normal heights are thus dependent upon the reference ellipsoid chosen. The Soviet Union and many other Eastern European countries have chosen a height system based on normal heights, determined by geodetic precise levelling. Normal gravity values are easy to compute and "hypothesis-free", i.e., one does not have to know, as one would for computing orthometric heights, the density of the Earth's crust around the plumbline.
Normal heights figure prominently in the theory of the Earth's gravity field developed by the school of M.S. Molodenskii. The reference surface that normal heights are measured from is called the quasi-geoid, a representation of "mean sea level" similar to the geoid and close to it, but lacking the physical interpretation of an equipotential surface.
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