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# 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).

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:

$P = \sqrt{\frac{T^3}{2 \rho A}}$

Where:

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