The single flapping rotor: detailed physical explanations

Abstract

A motor-driven helicopter rotor generates a reaction torque. This torque would accelerate the airframe of the helicopter about the yaw axis opposite to the rotor rotation if no measures are taken to compensate it. In the early days of helicopter development, a diversity of measures was considered: Henrich Focke has discussed these different measures. Not well known is a torque compensation measure which is restricted to only one main rotor, thus skipping the tail rotor or any additional rotor as well. This principle is worth looking into the details of the physical mechanism involved. The German scientist Prof. Hans-Georg Küssner of the AVA-Göttingen, Germany (Aerodynamic Research Institute with heads at this time: L. Prandtl and A. Betz) was the first to study the method successfully. He constructed a wind tunnel model and showed that the reaction torque could indeed be completely compensated. The present author has reviewed Küssner’s experimental data and could show that numerical calculations are in good correspondence with the measured results. In the present paper, the details of the method to compensate the reaction torque will be discussed. Corresponding numerical data will be presented taking into account Navier–Stokes calculations on rotor blade sections. Blade element theory will then be applied and combined with the Navier–Stokes data. Calculated forces and moments of a complete four-bladed helicopter rotor will be presented.