Shaft material and arrow choice: Park 2013 study

Park works out how the shaft material limits the relationship between diameter and mass of an arrow of a given spine, and from that which shafts suit target, field and indoor archery. For a 400-spine arrow in unidirectional carbon fibre, the outside diameter cannot go below 5.05 mm, at which point the shaft would be a solid rod; in practice the limit is slightly higher, because the point's shank has to fit inside (the calculation assumes a bore of at least 3.0 mm). At the other end, beyond about 6 mm the wall becomes too thin to resist crushing, and in any case World Archery rules cap the diameter at 9.3 mm.

If a minimum wall of 0.45 mm is kept by adding circumferential fibres, the arrow's mass first falls to a shallow minimum and then rises as the diameter increases. Easton catalogue arrows of similar spine sit close to the calculated curve. Overlaying contours of equal wind drift at 70 metres and equal down-range velocity at 50 metres, calculated for a Hoyt Maxxis 35 at 87.3 m/s, the author concludes that target archery favours the thinnest available shaft (among Easton arrows, the Protour or X10), field archery the lowest mass per metre (the ACE or LightSpeed, or the ACE on a windy course) and indoor archery the largest permitted diameter. A stiffer carbon would move the limit towards smaller diameters but also lighten the shaft, so wind drift would change little.

It is a desk analysis, with no shooting. The author starts from the spine test: the shaft rests on two supports 711 mm (28 inches) apart with 880 grams hung at the centre, and the deflection in thousandths of an inch is the spine, so 400 means 10.16 mm. Using the beam-bending formula, he derives for each bore the outside diameter that gives that deflection, the wall thickness and the shaft mass. For the material he assumes a density of 1.59 g/cm³ and a Young's modulus of 200 GPa; he adds 9.27 grams for point, nock and fletching and uses a 711 mm shaft.

The model ignores any inner aluminium tube and the taper of some shafts, which the author treats as minor because the centre section dominates stiffness. As a check, he compares the curve with the mean diameters and masses of several Easton arrows of similar spine (Protour, X10, ACE, LightSpeed, FatBoy). The drift and velocity contours come from his own previously published models.

There are no new measurements: the comparison with Easton arrows is made by eye on a chart, and the author calls it satisfactory without giving any numerical gaps. The model holds for a shaft of one material and constant diameter, whereas some premium competition shafts, such as the Protour and X10, are tapered and have an aluminium core (the author considers the effect small). The drift and velocity contours are calculated for a single compound bow; for a bow of different energy the author says they shift, not that they stay the same, and the recurve is not calculated.

The selection rules assume that every shaft groups equally well without wind, and they leave out straightness and tolerances on mass and spine, which the author mentions only as secondary criteria. The indoor advantage of fat arrows, which comes from touching the line, is not quantified either.

The useful idea for anyone choosing arrows is that, for a given spine and material, diameter and mass are not chosen separately: below a certain diameter, a thinner shaft must have a thicker wall and is therefore heavier, and that combination is exactly what makes it less sensitive to wind. That is why, outdoors at known distances, the calculation favours the thinnest shafts; in field archery, where estimated distances and slopes weigh more, a light, fast arrow reduces sight-setting errors; indoors, with no wind, all that matters is the chance of touching the line.

The author adds that arrows from different makers using the same material, spine and diameter will have similar mass and behaviour, so the choice between them can rest on other things: straightness, tolerances, the fit between point and shaft. The reasoning is built on compound bows and on arrows from 2011, not a ranking of today's models.