Momentum theory

The momentum theory or Disk actuator theory is a theory describing a mathematical model of an ideal propeller or helicopter rotor, by W.J.M. Rankine (1865), Alfred George Greenhill (1888) and R.E. Froude (1889).

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The rotor is modeled as an infinitely thin disc, inducing a constant velocity along the axis of rotation. The basic state of an helicopter is hovering. This disc creates a flow around the rotor. Under certain mathematical premises of the fluid, there can be extracted a mathematical connection between power, radius of the rotor, torque and induced velocity. Friction is not included.

The power required to produce a given thrust is:

Where:

• T is the thrust
• ρ is the density of air (or other medium)
• A is the area of the rotor disc

See also

• Blade element theory
• Circulation Theory
• Strip theory for fixed wing aerodynamics
• Conway non linear momentum theory
• Kutta-Joukowski Circulation