Item 1552

OTHER: Aerodynamics - General - Figure of Merit

Notes:

A measure of the efficiency of a hovering Helicopter.

FM = Ideal power required to hover / Actual power required to hover. [Source ~ PHA p.46]

The Induced Power divided by the Actual Power. FM=(CT^(3/2))/(root(2*CQ))

In practice, the maximum is 0.75 to 0.80. [Source ~ RWP1 p.9]

Note that twin-rotor helicopters benefit from not having a tail rotor. The 1940 Flettner FL282 was 0.72 (out of ground effect). The value used in this site's database FORM: Momentum Method is set at 0.70 for single rotor helicopters and 0.75 for twin rotor helicopters.

"In a sense the ideal [induced] power is analogous to the induced drag of an airplane wing." [Source ~ RWP1 p 8]

"This form of the equation shows that the Figure of Merit is highest for high solidities...."." [Source ~ RWP1 p 26] To follow on from this statement see the PPRuNe posting between NL and self on the subject on web page DESIGN: UniCopter ~ Rotor - Disk - Large Chord & Low Tip Speed.

"The figure of merit can be misleading, since it is not directly concerned with the total hover power. By increasing the disk loading T/A the induced power is increased relative to the profile power, resulting in a higher power of merit. However, the total power required also increases, and this is unlikely to be considered as an improvement in the rotor efficiency. The use of the figure of merit for comparing rotor efficiencies should thus be restricted to constant disk loading only." [Source ~ HT p.35]

"Momentum Theory was quite extensively developed in the early part of the 20th century for airplane propellers, for which the actuator disk model is more reasonable because of the high axial speed." [Source ~ HT p.36]

The axial flow through the propeller allows for much greater blade twists than the helicopter can have. This make me think that the propeller probably has a more even induced velocity distribution across its actuator disk.

'Figure of Merit Definitions for Coaxial Rotors:'

• See 'A Survey of Theoretical and Experimental Coaxial Rotor Aerodynamic Research', page 2. I have hard copy.
• See paper by Leishman in 'Journal of the American Helicopter Society' - July 2008. This, or a very similar paper, is/was available on the Internet.

'Quiet Rotorcraft' ~ by Stepniewski touches on it lightly in respect to Intermeshing-ABC.

Last Revised: December 16, 2011