Computation of the trajectory and attitude of arrows subject to background wind

Abstract

In this work are performed numerical computations of the trajectory and attitude of archery arrows under the influence of background wind. The aerodynamic response of two commercial arrows with different mass is investigated. The maximum angle of attack increases to $$3.0^{\circ }$$ under a uniform side-wind of $$3\,\hbox {ms}^{-1}$$ , if the arrow was shot with zero angle of attack and zero angular velocity. The maximum angle of attack can be reduced by two orders of magnitude by keeping the boundary layer laminar throughout the arrow’s flight if ideal initial conditions are achieved. The ratio of the drag force to the gravitational force plays a key role in determining the deviation in the trajectory. The radial deviation from the centre of the target for a uniform side-wind of $$3\,\hbox {ms}^{-1}$$ was 0.34 m for the lighter arrow and 0.26 m for the heavier arrow at a distance of 70 m. The deviations decrease to 0.18 m and 0.12 m, for the lighter and the heavier arrow, respectively, if the boundary layers remain laminar. The heavier arrow shows a smaller deviation compared with the lighter arrow under identical background wind conditions. Keeping the arrow’s boundary layer laminar may reduce the wind drift significantly, regardless of the mass.