Heavy-Lift Rotor in Hover

What is modelled

In hover the rotor thrust must equal the weight. Momentum theory ties thrust to how much air is accelerated downward, and blade element theory ties it to the lift of each blade section. Solving both together gives the inflow along the blade, the collective pitch, and the power: an induced part for lifting the air and a profile part for blade drag.

Equations

• Thrust coefficient CT = T / (ρ A (ΩR)²); ideal power P = T √(T / 2ρA).
• Local inflow from 8 F λ² / (σ a) + λ = θ x with Prandtl tip loss F; dCT = (σ a/2)(θ x² − λ x) dx.
• Power CP = ∫ λ dCT + σ Cd0 / 8; figure of merit FM = (CT3/2/√2) / CP.

Checks run in the page

• Blade-element thrust against the momentum-theory thrust over the blade stations.
• The collective found by bisection against the thrust target.
• The standard-atmosphere pressure by integrating the hydrostatic equation.
• The hyperbolic-twist limit, where the inflow becomes uniform.

Honest simplifications

Hover only, a single main rotor, constant chord, constant lift slope, no compressibility drag, no ground effect, no fuselage download, no tail rotor power and a simple altitude lapse for the engines. The default numbers are in the range of a very large helicopter but are not data for any particular type.

• Press High and hot (3000 m) to see the air thin out, the collective rise and the power margin shrink.
• Press Untwisted blades to see the figure of merit drop.
• Press Maximum take-off mass and compare the power needed with the engine power available.