The lift generated by a translating wing of known translational speed, lift coefficient and area is calculated by a simple equation. A propeller or rotor generating thrust share the same aerodynamic principles but their different kinematics cause the calculation of their thrust to be laborious. This paper derives a thrust equation from an algebraic expansion of the Prandtl’s dynamic pressure term qby adding the rotational kinetic energy of a propeller or rotor to the existing translational kinetic energy term. This thrust equation can be applied directly to propellers and rotors and assumes these to operate as cycles with their available kinetic energy as input and work as output. The thrust equation is a function of the normalized thrust ηT, a nondimensional figure of merit that quantifies the ability to generate thrust and allows for a meaningful comparison with other aerodynamic systems, regardless of their kinematics.




The author is grateful to Daniel Uhlig for propeller data from UIUC wind tunnel tests that made Section 7 possible, and Christy Anderson for discussions.