Rotor Bending Moments in Plane of Flapping

Abstract

The present paper, a problem in autogiro rotor stress analysis, can be outlined as follows: 1. Calculation of the characteristics of a typical autogiro employed for illustrative purposes. 2. Derivation of formulas for bending moments in the plane of flapping taking into account the effects of the weight of the blade, centrifugal force, inertia forces in flapping and aerodynamic thrust. 3. Examination of the effect of the azimuth angle ^ on bending moments at a given point on the blade. 4. Effect of variations in /*, the tip speed ratio, on the bending moment a t a given point on the blade. 5. Examination of the effect of the ratio r/R on bending moments. 6. Formulas for the centrifugal relief of bending moments. 7. Comparison of bending moments obtained by the above methods with the bending moments obtained by the use of empirical formulas available hitherto. Certain simplifications have been employed. These are: (a) Only the first harmonic of the flapping motion is considered. (b) Terms of a higher order than A* are neglected. (c) The flow through the rotor disk is considered uniform. (d) Mass distribution along the span of the blade is uniform. (e) The product EI is uniform along the span of the blade. (f) Stalling effects that may occur at portions of the blade are neglected. (g) Periodic twisting of the blade is not taken into account. The underlying aerodynamic theory is well known to those interested in the autogiro and no presentation of such theory is made in the present paper.