Helicopter Rotor Controls

What is modelled

A 3.63 m radius rotor is treated as an actuator disc. Collective pitch changes the thrust coefficient, cyclic tilts the disc so part of the thrust pushes sideways, and the helicopter then moves as a point mass under thrust, weight and drag.

Equations

• Thrust T = ρ A (Ω R)2 CT, C_T = 0.0007 × collective.
• Induced velocity vi = √(T / 2ρA).
• Shaft power P = T vi / FM, figure of merit 0.66; torque Q = P/Ω; tail-rotor thrust Q / 4 m.
• Blade-element thrust dT = 4π ρ CT Ω2 r3 dr.
• Motion m az = T cosθ - m g - drag, m ax = T sinθ - drag.

Checks run in the page

• The 160-annulus blade-element sum equals the disc formula.
• Momentum-theory power relation.
• Hover trim holds altitude for 10 s.
• Thrust scales with density and with the square of rotor speed.

Honest simplifications

No blade flapping dynamics, ground effect, translational lift or rotor wake skew; thrust follows its demand through a 0.4 s lag. Weight and drag areas are illustrative additions to the 3D page's rotor numbers.

• Raise the collective until thrust passes the weight and the helicopter lifts off.
• Tilt the cyclic forward in flight: the vertical thrust falls and the helicopter loses height unless you add collective.
• Choose Hot and high: thin air cuts thrust and power needs.