Hover is the operating state in which the lifting rotor has no velocity relative to the air, either vertical or horizontal. General vertical flight involves axial flow with respect to the rotor. Vertical flight implies axial symmetry of the rotor flow field, so the velocities and loads on the rotor blades are independent of the azimuth position. Axial symmetry greatly simplifies the dynamics and aerodynamics of the helicopter rotor, as is evident when forward flight is considered. The basic analyses of a rotor in axial flow originated in the 19th century with the design of marine propellers and were later applied to airplane propellers. The principal objectives of the analysis of the hovering rotor are to predict the forces generated and power required by the rotating blades and to design the most efficient rotor.
Momentum theory applies the basic conservation laws of fluid mechanics (conservation of mass, momentum, and energy) to the rotor and flow as a whole to estimate the rotor performance. The theory is a global analysis, relating the overall flow velocities to the total rotor thrust and power. Momentum theory was developed for marine propellers by W.J.M. Rankine in 1865 and R.E. Froude in 1885, and extended in 1920 by A. Betz to include the rotation of the slipstream; see Glauert (1935) for the history.