Rotor Figure of Merit

The figure of merit is ideal hover power divided by the power the rotor actually takes: $FM = P_{ideal}/P_{actual}$. It is a number between zero and one, good modern rotors reach 0.70 to 0.80, a poor or heavily compromised one sits near 0.6, and 1.0 is physically unreachable.

Let us be plain about what it is. The figure of merit is a fudge factor with a respectable name. Momentum theory refused to model the rotor — no blades, no chord, no twist, no aerofoil, no profile drag, no tip loss, no swirl — and every one of those omissions has to be paid for somewhere. The figure of merit is where. It is a single measured ratio into which the entire difference between an ideal disc and a real machine has been swept, and it cannot be derived from anything on this site. It is measured, on a whirl stand or in a careful hover trial, and it is an INPUT everywhere it appears. This page will never tabulate one for you, because a tabulated figure of merit without the rotor and the thrust it was measured at is not information.

That said, the shortfall is not mysterious, and it is worth knowing roughly where it goes. About two thirds of it is blade profile drag: the blades are aerofoils being dragged edgewise through the air at 200 metres per second, and they charge for it continuously, lifting or not. Most of the remainder is non-uniform inflow — real induced power exceeds the ideal uniform value by ten to fifteen percent — plus tip loss and wake swirl. Since profile power depends on blade area and induced power does not, adding solidity lowers the figure of merit in hover while buying thrust margin in forward flight, which is one of the sharper trades in rotor design.

It is not a constant for a given rotor. Figure of merit varies with how hard the blades are working, rising as blade loading rises, peaking somewhere near the design point, and falling away as sections approach stall. That is because induced power grows as $T^{3/2}$ while profile power stays roughly flat, so at very light loading the fixed profile cost dominates the small induced one and the ratio is poor. Quoting a figure of merit without the thrust coefficient it was measured at is close to meaningless, and comparing two rotors at different loadings is worse than useless.

Two things it is not. It is not the aircraft's efficiency: tail rotor power, transmission loss and accessory drives all sit outside it, and together they take another ten to fifteen percent before the engine is asked for anything. And it is not a forward-flight measure at all — it is defined in hover and nowhere else. Cruise efficiency is a different accounting, in which induced power has mostly gone away and parasite drag has arrived.

If a calculation ever hands you a figure of merit above 1, it is not a discovery. Three things usually cause it. The disc area used is too small, which inflates the ideal power. The measured power is the main rotor's share while the ideal figure was computed from the whole aircraft weight. Or the aircraft was not in free air: within about one rotor diameter of the surface, in ground effect, a rotor genuinely does need less power than the free-air floor, because the ground interferes with the wake contraction the theory assumes. That last one is real physics, not an error, and it is worth several percent of gross weight to a working helicopter.

The wind-energy reader will recognise the shape of all this. $C_p$ is read against Betz's 16/27 exactly as $FM$ is read against 1, and for the same reason: both denominators come from the same Rankine–Froude control volume with no losses in it.