Helicopter blade droop as an application of simple beam theory

Abstract

It is a commonly observed fact that the blades of a helicopter droop under their own weight when the aircraft is static but become almost straight when they start spinning. This phenomenon is commonly attributed to ‘rotational stiffness’. In this short article we present a simple calculation for the shape of the blades of a helicopter in static and rotating condition. We show that the deflection or droop of the tip of the blade reduces by a factor of about 30 when it changes from static to full-speed rotation. This calculation is at the undergraduate level and can complement a course in differential equations, elementary statics or elasticity theory.