The dynamic behaviour of an arrow in wind

Abstract

Target archery competitions are conducted outdoors, exposed to the prevailing weather conditions. Competition takes place over long target distances and wind drift of the arrows is a significant cause of score loss. In this article, the dynamic behaviour of an arrow in free flight and wind drift are modelled, allowing for both the arrow initially aligning itself with the resultant airflow and the arrow flexing. The arrow has been modelled as an inextensible flexible beam, and the resulting partial differential equations solved using a finite difference method. Lift and drag for the various arrow components have been calculated using the local angle of attack for those components. It is shown that archers should use small diameter arrow shafts with a high density in order to minimise wind drift. Even for the best arrows, the drift for a 3-m/s side wind is greater than four score rings for a recurve bow at a target distance of 70 m with a 1220-mm diameter target face and nearly two score rings for a compound bow at a target distance of 50 m with an 800-mm diameter target face.