Home/Aerospace Engineering/Figure of Merit (Rotor Hover Efficiency)

Formula & Calculator

Figure of Merit (Rotor Hover Efficiency)

Ratio of ideal (momentum theory) induced hover power to actual measured power, quantifying rotor hover efficiency.

RotorcraftAircraft DesignEfficiency

Figure of Merit (Rotor Hover Efficiency) Calculator

FM = Pideal / Pactual
Solve for FM, Pideal, or Pactual
FM Pideal, Pactual
W
W
Solve for:
Result
Copied!
Figure of Merit vs. Ideal Power FM(Pideal) = Pideal / Pactual
FM(Pideal) for fixed Pactual Computed point
All values positive • FM typically 0.6–0.8 for efficient rotors
FM = P_ideal / P_actual
Figure of Merit (Rotor Hover Efficiency)

Variables

SymbolQuantityUnit
FMFigure of merit
P_idealIdeal induced powerW
P_actualActual measured powerW

What it means

The figure of merit is a measure of how efficiently a rotor converts power into thrust in hover, accounting for losses due to non‑uniform inflow, tip losses, and profile drag. An ideal rotor would have FM=1, but practical values are 0.6‑0.8. FM is used to compare rotor designs and to estimate actual power requirements. It is a key performance metric in helicopter design. Understanding FM is essential for optimising rotor efficiency and for predicting hover performance.

Worked example

Figure of Merit – Two Examples

Real‑World
Scenario: P_ideal = 180,000 W, P_actual = 230,000 W. Find FM.
ParameterValue
P_ideal180,000 W
P_actual230,000 W
1FM = P_ideal/P_actual = 180000/230000 = 0.7826 (78.3%)
Result 0.783 ✓ Good
Scenario: P_ideal = 220,000, P_actual = 270,000. Find FM.
ParameterValue
P_ideal220,000
P_actual270,000
1FM = 220000/270000 = 0.8148 (81.5%)
Result 0.815 ✓ Excellent
Key insight: Figure of Merit measures rotor hover efficiency – typical values 0.7–0.85.

Common mistakes

  • Figure of merit (rotor hover efficiency): FM = P_ideal / P_actual.
  • P_ideal: Ideal power for hovering (from momentum theory).
  • P_actual: Actual power required.
  • FM < 1; typical 0.7‑0.8 for good rotors.
  • Indicates aerodynamic efficiency of rotor.

Applications

Figure of merit, FM = P_ideal / P_actual, is a measure of rotor hover efficiency, comparing ideal (minimum) power to actual required power. A high FM (e.g., 0.75‑0.85) indicates an efficient rotor. Engineers use FM to assess blade design, tip shape, and twist, and to optimise rotor performance. By maximising FM, aerospace engineers can reduce hover power requirements, improve payload capacity, and extend mission endurance for helicopters and eVTOL aircraft.

  • Rotor blade design and optimisation
  • Performance evaluation of different rotor configurations
  • Hover power prediction and test correlation
  • Design of efficient rotors for UAVs and air taxis
  • Energy efficiency improvements for electric rotorcraft