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.

Minimising the impact of arrow mass and stiffness variations on an archer’s score

“…The path of the arrow’s centre of mass as it left the bow also changed by −0.03°. Using the models in Park, 11,12 this led to a lateral displacement of approximately 16 mm at a target distance of 70 m for a typical recurve bow, with the displacement varying linearly with target distance. Assuming a linear distribution of arrow spine over a range of ±1% for a world-class archer using a recurve bow, that variation could lead to lowering scores (using Table 2) approximately equivalent to an arrow mass variation of ±0.5 grains.…”

“…The trajectory of arrows and the required launch angles for a given target distance were calculated iteratively for the nominal arrow mass using the method used by Park. 11 The arrow mass was then changed, and the same launch angle and new arrow speed were used to calculate the trajectory, giving the height difference at the target distance. The Monte Carlo model was then used to calculate the expected score loss for a given ASL as the mass was varied according to the expected distribution.…”

“…The model of dynamic arrow behaviour used in Park, 12 together with the arrow’s behaviour down-range as modelled in Park, 11 was used to analyse an X10 size 600 arrow shaft with 120 grain point in the lateral plane, shot from the author’s recurve bow. It was assumed that the equipment was adjusted such that the nominal angular rotation of the arrow as it left the bow was close to zero (that is, that the bow was ‘well-tuned’).…”

The impact of lateral bow angle variation on an archer’s score

“…where r i is the radius of the ring plus the arrow shaft radius, Q(r) is the cumulative probability for that radius, assuming a normal distribution with m = 0 and that s is as calculated from the bow cant standard deviation and equation (1). Target rings are numbered from 1 for the innermost, with P 0 = 0…”

“…The launch angle of elevation can be calculated by modelling the arrow’s trajectory for a given initial velocity using the method proposed by Park. 1 The launch angle of elevation was calculated for the author’s recurve bow (Hoyt Formula X with Velos limbs, draw force set to 164.5 N, draw length of 700 mm, shooting an Easton Technical Products X10 arrow size 600 with mass of 22.4 g and an arrow speed of 58.2 m/s). Figure 1 shows the tangent of the launch angle, together with a linear line of best fit (using a least squares method).…”