State-Plane Grid-to-Ground Distance
The grid scale factor the COGO and slope tiles say they skip: elevation factor EF = R/(R+h) with R = 20,906,000 ft, combined factor CF = grid-scale-factor x EF, and ground = grid / CF. A 10,000 ft grid distance at a 0.9999 scale factor and 5,280 ft ellipsoid height is 10,003.53 ft on the ground. Enter the ellipsoid height h = orthometric elevation H + geoid height N (N ~ -30 m in the US), not the elevation alone. Per the NGS State Plane Coordinate System; the published control governs.
Formula and source
elevation factor EF = R/(R+h), R = 20,906,000 ft (NGS mean earth radius); combined factor CF = grid_scale_factor x EF; ground = grid / CF (grid = ground x CF).
NGS / NOAA State Plane Coordinate System grid-to-ground reduction, by name; first-principles.
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