Ideal hover power is T times √(DL / 2ρ)
Disk loading DL = T/A, induced velocity vi = √(DL / (2ρ)), and ideal power Pi = T vi. Shaft power is Pi / FM. A 20 kN thrust on a 20-metre disk (10 m radius) at sea level, with FM = 0.70, needs on the order of a hundred-plus kilowatts of shaft power — the exact figure is in the calculator. Given an available shaft power P, the minimum density that can still hover is ρmin = (T / (2A)) (T / (P FM))², which this page converts to a pressure altitude in the U.S. Standard Atmosphere, 1976.
That ceiling only knows about induced power and ISA density. It does not lapse the engine, add profile or tail-rotor power, or include ground effect, retreating-blade stall, or tip Mach. A HOGE chart in the flight manual always wins. Related tools: rotor tip speed, propeller static thrust, and drone flight time for a battery-powered multirotor.
Sources
- Momentum / actuator-disk theory (Gessow and Myers; Leishman, Principles of Helicopter Aerodynamics).
- Hover figure of merit.
- U.S. Standard Atmosphere, 1976, for the density-to-altitude inversion.
Frequently asked questions
Is this a hover-out-of-ground-effect ceiling?
No. It is an induced-power ceiling at the figure of merit you type, in a standard atmosphere, with no engine lapse and no profile power. Use the flight-manual HOGE chart for a real number.
What figure of merit is typical?
Well-designed helicopter rotors often sit around 0.6–0.8 in hover. 0.70 is a round default.
Does ground effect change the answer?
Yes, in the real helicopter — in ground effect you need less power. This page is the out-of-ground-effect ideal disk.