With an ellipsoid height for a point derived by GPS of 1467.4 ft and a geoid separation of -23.8 ft, what is the orthometric elevation for the point?

With an ellipsoid height for a point derived by GPS of 1467.4 ft and a geoid separation of -23.8 ft, what is the orthometric elevation for the point?

• A. 1491.2 ft
• B. 1700.0 ft
• C. 1420.5 ft
• D. 1467.4 ft

Answer: (A)

Orthometric height is obtained by subtracting the geoid separation (geoid undulation) from the ellipsoidal height: H = h − N. Here, the ellipsoidal height is 1467.4 ft and the geoid separation is −23.8 ft. Subtracting a negative value adds: H = 1467.4 − (−23.8) = 1491.2 ft. Because the geoid separation is negative, the orthometric height ends up larger than the ellipsoidal height. So the orthometric elevation is 1491.2 ft. The other numbers would require different N values (for example, H = 1700 would need N = −232.6 ft; H = 1420.5 would need N = 46.9 ft; H = 1467.4 would need N = 0), which contradicts the given geoid separation.

Orthometric height is obtained by subtracting the geoid separation (geoid undulation) from the ellipsoidal height: H = h − N. Here, the ellipsoidal height is 1467.4 ft and the geoid separation is −23.8 ft. Subtracting a negative value adds: H = 1467.4 − (−23.8) = 1491.2 ft. Because the geoid separation is negative, the orthometric height ends up larger than the ellipsoidal height. So the orthometric elevation is 1491.2 ft. The other numbers would require different N values (for example, H = 1700 would need N = −232.6 ft; H = 1420.5 would need N = 46.9 ft; H = 1467.4 would need N = 0), which contradicts the given geoid separation.