Arrow behaviour in free flight

Abstract

As an arrow exits a bow, it may have a non-zero angle of attack in both the vertical and the horizontal planes. It might also have a non-zero angular rotation about its centre of mass and will probably be flexing longitudinally. In this paper, the arrow behaviour in free flight in the horizontal plane and without wind has been analysed. A finite difference method was used to solve the equations of motion. This was compared with the measured behaviour for arrows shot from a compound archery bow (although the results are also applicable for recurve bows). Given typical initial conditions, the arrow oscillates longitudinally about its centre of mass, with the period and damping largely determined by the fletch area, and gains a lateral velocity component and lateral displacement. For normal fletch sizes the oscillation will be under-damped. In the absence of archer technique error, the longitudinal oscillation was found to have minimal effect on the accuracy.