Computing Slant Ranges
Slant range is very important for calculating weapons effects against airborne or submerged targets, as well as ranges for sensor systems, because the targets are not on the same plane as the weapon/sensor itself.
Slant Range = SQRT (RangeGround2 + RangeHeight2)
RangeGround and RangeHeight can be in any unit measurement: feet; yards, rods, meters, etc as long as both ranges are in the same measurement format; e.g. both are in feet.
A destroyer is 4,000 yards from a submarine which is at 500 feet. What is the slant range line of sight for the destroyer's bow-mounted sonar to the submarine?
First, we convert 500 feet to yards – 166.6 yards, and then begin the math:
(4,000 yards2 + 166.6 yards2) = 16,027,756
SQRT(16,027,756) = 4,003.47 yards.
Thus, the LOS distance for the destroyer's sonar to the submarine is 4,003.47 yards.