Air flow around the point of an arrow

Abstract

The aerodynamic drag of an arrow is of importance in relation to the arrow’s drift in wind and to its down-range velocity. A significant contributor to that drag is the viscous drag from the arrow shaft, and consequently the nature of air flow over the arrow point and the location of the transition from laminar to turbulent flow are of interest. In this paper the flow was investigated using a scale model in a water channel for two arrow point profiles and for circumferential gaps at the rear of the arrow point. The normal ‘bullet point’ was found to have laminar flow along the front of the shaft and transition at a Reynolds number of approximately 450,000, and that circumferential gaps did not affect the flow. The frequently used ‘short bulge point’ was found to have flow separation at the rear taper of the point and turbulent flow for the full length of the shaft, which would be expected to result in greater drag than for the bullet point or for a bulge point with less aggressive rear taper.

The impact of material selection on arrow design and optimal selection for competition

“…Since it is highly undesirable to have the arrow shaft external diameter greater than that of the arrow point (as that would lead to carbon fibre splinters when the arrow entered the target), diameter mismatches can be expected to be a sharp reduction in diameter from the arrow point to the arrow shaft. The diameter mismatch is then likely to result in increased aerodynamic drag as shown by Park et al 3 and hence to increased wind drift as shown by Park. 2…”

“…Park et al 3 considered the airflow over the arrow’s point. It was shown that for some arrow points, the flow remained laminar for the first portion of the arrow shaft, while for others, it immediately transitioned to turbulent and thus had increased aerodynamic drag.…”

The dynamic behaviour of an arrow in wind

“…As noted above, Park et al 12 found that with an appropriate point profile, laminar flow could be sustained up to at least an angle of attack of 3°. In each case, arrow shafts were modelled to have the same spine, maximum diameter and mass per unit length as shown for that arrow shaft in Easton Technical Products, 18 with minor modifications made to ensure consistent values for Young's Modulus and density for the carbon fibre composite material for the given arrow shaft type.…”

“…Careful design of the point profile can result in laminar flow along the first portion of the arrow shaft until a Reynolds number of approximately 450,000 is reached (where the characteristic length is the distance along the arrow shaft from the front of the arrow), after which the flow will be turbulent. Park et al showed that the laminar flow could be obtained up to an angle of attack of at least 3°.Figures 4-7in Park et al12 show the turbulent flow obtained with a normal point and flow transition further along the arrow shaft when an appropriately modified point profile is used. For the recurve bow and arrow noted above, transition could be expected approximately 120 mm behind the point if the modified point profile is used.…”

“…The measured speed for an Easton Technical Products X10 Protour arrow, size 380, with a shaft length of 710 mm, with Easton G pin nock, 115 grain point and three 45-mm Easton Tite Flight fletches and a mass of 24.86 g, was 78.9 m/s. The calculated stored energy was 92.8 J, and the virtual mass was 5.05 g.Air flow over the arrowPark et al12 showed that for the arrow point shapes used almost exclusively by archers, the air flow can be expected to be turbulent for the full length of the arrow for normal arrow speeds. This is primarily due to the decreasing diameter of the arrow point to where the point joins the arrow shaft.…”