Blade-Element Theory

The momentum theory discussed here provides an estimate of induced power requirements for the rotor, but is not sufficient for designing the rotor blades. The origin of blade-element theory can be traced back to the work on marine propellers by Froude. Subsequently, Drzewiecki took up this study assuming the blade sections to act independently and considering two velocity components VR due to rotation and V due to the axial velocity of the rotor. His results indicated correct behavior but were quantitatively erroneous, which was primarily due to neglecting the induced velocity at the rotor disk [10].

Several attempts were made later on to account for the induced velocity from momentum theory into the blade-element theory. It was only after Prandtl developed the lifting line theory that the influence of the wake velocity at the rotor disk was incorporated. Thus, it was through the wake vortex theory rather than the momentum theory that the induced velocity at the blade section was finally incorporated into the blade-element theory. The blade sees the air coming to it due to rotor rotation, as well as due to downward-induced velocity. Today, the blade-element theory is the foundation for all analyses of helicopter dynamics and aerodynamics. Reference [8] describes in detail the blade-element theory for a rotor in vertical flight.