Tiltrotor Conversion

What is modelled

In steady level flight the weight is carried by the wing lift plus the vertical part of the rotor thrust, and the drag is balanced by the forward part of the rotor thrust. For each speed and wing lift coefficient these two balances fix both the thrust and the angle to which the nacelles must tilt. The rotors are then treated as two actuator discs with the induced velocity of Glauert's momentum theory.

Equations

• Lift L = ½ ρ V2 S CL, drag D = ½ ρ V2 S (CD0 + CL2/(π e AR)).
• Thrust T = √(D2 + (W − L)2), tilt i = atan2(W − L, D).
• Induced velocity T = 2 ρ A vi √((V cos i + vi)2 + (V sin i)2), hover vh = √(T / (2 ρ A)).
• Power P = T (V cos i + vi); best glide V = √(2W/ρS) (k/CD0)1/4.

Checks run in the page

• Both force balances to rounding error.
• The Glauert equation residual, the hover power law and the high-speed limit of the induced velocity.
• The minimum-drag speed and drag from a scan against the closed forms.
• The stall speed at which the wing alone carries the weight.

Honest simplifications

The two rotors share one induced velocity, the profile power of the blades, the rotor download on the wing, the pitch and the flap angles are left out and the drag is one lump. Real tiltrotors fly a speed corridor that these numbers only sketch.

• Press Hover, then raise the speed in steps and watch the nacelles tilt forward as the wing lift share grows.
• Press Small rotors: the induced power in hover rises sharply with disc loading.
• Raise the wing lift coefficient at a fixed speed and see the nacelle tilt go back toward hover.