Rotor Hover Power Calculator (Momentum Theory)
A hovering helicopter or drone pushes air down to hold itself up. Momentum theory gives the speed of that air and the ideal power; dividing by the figure of merit gives a realistic power.
Standards:
- NGSS HS-PS3-1
- AP1 Unit 3
- IB A.3
Our alignment; not reviewed by the standards bodies.
The equation
Worked example
- Given
- Mass (kg): 2700 kg
- Rotor radius R (m): 5.1 m
- Figure of merit FM (0–1, typical 0.6–0.8): 0.75
- Altitude, standard atmosphere (m, 0–6000): 0 m
- Answer
- Thrust needed T: 26.48 kN
- Disk loading T/A: 324 N/m²
- Induced velocity v_i: 11.50 m/s
- Ideal power: 304.5 kW
- Estimated real power: 406.0 kW
- Check
- The induced velocity matches Leishman’s momentum-theory result v_i = √(T / 2ρA) (Principles of Helicopter Aerodynamics, ch. 2), and the example uses the same generic 2,700 kg helicopter as the Aero track; the build checks both.
Assumptions
Single ideal rotor in hover, out of ground effect, uniform inflow, U.S. Standard Atmosphere 1976.
Go deeper
Sources
- J. G. Leishman, Principles of Helicopter Aerodynamics, 2nd ed., Cambridge University Press, 2006.
- NOAA, NASA, USAF, U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, 1976.