Direct Propeller Forces in Yaw (or at Angle of Attack)

In contrast to the somewhat unsatisfactory state of the theory for propeller slip­stream effects, the theories for direct propeller forces in yaw are well established, and those theories were around as early as needed. According to Dr. Herbert S. Ribner:

It was realized as early as 1909 that a propeller in yaw develops a side force like that of a fin. In 1917, R. G. Harris expressed this force in terms of the torque coefficient for the unyawed propeller.

A1914 British R & Mby Relf, Bramwell, Fage, and Bryant presented experimental results onpropeller side forces. Two 1945 NACA reports by Ribner are usually taken as the definitive modern work on the subject. These reports provide a blade-element analysis applicable to any single – or dual-rotation system, sample calculations for two representative propellers with an interpolation scheme for other propellers, experimental verification of the blade – element method, and, finally, a remarkably simple rule-of-thumb side force estimate for preliminary design. This is to take the yawed propeller as a fin of area equal to the projected side area of the propeller. This fin’s effective aspect ratio is taken as 8, and the effective dynamic pressure at the fin is that for the propeller disk augmented by inflow. The side force for a propeller in yaw or sideslip is clearly the same as the propeller normal force at angle of attack.

For tractor airplanes, direct propeller forces in yaw act as a fin ahead of the airplane’s center of gravity. This is a major destabilizing contribution to static directional stability, especially at large propeller blade angles. The destabilizing effect depends on the propeller plane distance to the center of gravity, which is relatively greater for single-engine airplanes than for multiengine airplanes with wing-mounted engines. The same can be said for the effects of propeller normal force at angle of attack, in relation to static longitudinal stability. The classical NACA design method for satisfactory longitudinal stability (Gilruth, 1941) accounts for idling power effects using a propeller normal force calculation.