- Understanding the radar horizon

The formula for the distance to the radar horizon is

The radius of the earth at the equator is 6378155 m.

1. The formula for the radar horizon uses the square root of the earth radius. This would indicate the radar horizon is longer than the visual horizon by a factor of the square root of 4/3, or 1.155.
2. (2·(4/3)·6378155·50)^0.5 = 29162 m = 29 km.
3. The radar horizon for the 50 m radar to 0 height is 29162 m. The radar horizon for the 10 m target to 0 height is 13042 m. The horizon limitation is 29161 + 13042 = 42204 m = 42 km.
4. h = 100000² / (2·((4/3)·6378155)) = 588 m
5. The radar horizon for 10000 feet altitude is 123 nmi. The radar horizon for 20000 feet altitude is 174 nmi. Add the two to get the horizon limitation of 297 nmi.