Vertical flight of the helicopter rotor at speed V includes the operating states of hover (V = 0), climb (V > 0), and descent (V < 0) and the special case of vertical autorotation (power-off descent). Between the hover and autorotation states, the helicopter is descending at reduced power. Beyond autorotation, the rotor is producing power for the helicopter. The principal subject of this chapter is the induced power of the rotor in vertical flight, including descent. The key physics are associated with the flow states of the rotor in axial flight. Axial flight of a rotor also encompasses the propeller in cruise (V > 0) and static (V = 0) operation, and a horizontal axis wind turbine (V < 0).

Induced Power in Vertical Flight

In Chapter 3, momentum theory was used to estimate the rotor induced power Pi for hover and vertical climb. Momentum theory gives a good power estimate if an empirical factor is included to account for additional induced losses, particularly tip losses and losses due to nonuniform inflow. In the present chapter these results are extended to include vertical descent. Momentum theory is not applicable for a range of descent rates because the assumed wake model is not correct. Indeed, the rotor wake in that range is so complex that no simple model is adequate. In autorotation, the operating state for power-off descent, the rotor is producing thrust with no net power absorption. The energy to produce the thrust (the induced power Pi) and turn the rotor (the profile power Po) comes from the change in gravitational potential energy as the helicopter descends. The range of descent rates where momentum theory is not applicable includes autorotation.