Wind drift of a compound arrow: Park 2011 study

Park calculates how far a crosswind pushes a compound arrow sideways and checks the calculation against two tests. The drift has two parts: the arrow lines itself up with the sum of its own velocity and the wind's, and the air drag, acting along that direction, has a sideways component. For an Easton Protour 470 shot from an AR34 compound bow, at 70 metres the first part accounts for 16% of the total drift and the second for 84%. Drift grows roughly with the square of the distance and in proportion to wind speed: at 90 metres it is 62% larger than at 70 in the same wind. A 3 m/s head or tail wind, by contrast, moves the impact height at 70 metres by about 24 mm either way, far less than the same wind moves the arrow sideways.

In a wind tunnel, over 10.3 metres, five Easton arrows drifted in the order the calculation predicted, from the Protour 470 (9 mm measured against 11 calculated at 4.41 m/s) to the X7 2512 (18 against 19); at 8.49 m/s the gaps between calculation and measurement stayed within the estimated error. Outdoors at 70 metres, with gusts above 10 m/s, 36 Protour and 36 LightSpeed arrows shot from a machine gave a lateral spread (standard deviation) of 44.6 and 58.6 mm: the ratio, 1.41, is close to the predicted 1.45.

With a 3 m/s crosswind at 70 metres, the calculation gives 151 mm of drift for an X10 and 154 mm for a Protour shot from a Hoyt Maxxis 35. According to figures the author takes from an earlier paper of his, the fletching accounts for about 13% of the arrow's drag and the nock for about 11%, rising to 16% with large over-nocks; flow separation behind the point adds about 5%, and 50 mm of extra shaft on a 700 mm arrow increases drift by about 7%.

The calculation uses the models of free flight, aerodynamic drag and compound shooting that Park had published in earlier papers, applied step by step along the trajectory in both the horizontal and the vertical plane. The reference arrow is a Protour 470 with three X vanes, a G pin nock and a full-mass stainless steel point: 0.715 m long, 23.4 grams, 79.2 m/s at launch.

The tunnel test was run in the large wind tunnel at Monash University: the shooting machine stood outside, and the arrow crossed the airflow over 10.3 metres at a height of 1 metre, with the wind at 4.41 and 8.49 m/s. The bow, again the AR34, was set to its lowest draw weight so that the arrows were slow and the drift larger. Before the tests, 12 arrows shot in a row at 12 metres had all gone into the same hole, with a maximum error of 1 mm. The arrows were five Easton models with mean diameters from 5.04 to 9.92 mm and masses from 20.97 to 29.35 grams; drift was read from the hole in the target, to about 1 mm in the lighter wind and about 3 mm in the stronger one, where the holes became oval.

Outdoors, a machine with a Hoyt Maxxis 35 shot Protour and LightSpeed arrows alternately at 70 metres, 36 of each, with the same sight setting and aiming point, while the wind came on average from 135 degrees (0 being a headwind). Since outdoors there is no way to know where the arrow would land without wind, Park uses the lateral spread of the two groups as a relative measure. Without wind, at 35 metres, both arrows grouped with a standard deviation under 10 mm. For the final charts the arrows chosen were those closest to a spine of 400 in the Easton charts, all 0.715 m long, with the heaviest recommended point and the same fletching.

The tunnel test covers only 10.3 metres, where drifts are a few millimetres; the author himself points out that both drift and error grow with the square of the distance, so a good match at that range does not guarantee the figures at 70 or 90 metres. Outdoors there is a single session, with two arrow types and a wind that was not measured shot by shot: the comparison rests on the ratio between two spreads, not on the drift itself. The 3 m/s threshold above which scores drop comes from average wind speeds recorded at some events, comments from the author and other top archers, and the scores they shot: the author himself presents it as a subjective check, not a systematic test.

Everything is calculated and tested with compound bows; for the recurve the author expects larger drift, because the arrow carries less energy, but he does not calculate it. The charts with contours of equal drift treat shafts as cylinders of constant diameter, while the Protour and X10 are tapered, and they assume that every arrow groups equally well without wind. One figure also does not add up: the outdoor spreads are converted into scores of 697 and 672 "for 36 shots", values that are only possible over 72 arrows.

For anyone shooting outdoors the study gives a useful order of magnitude: in a 3 m/s crosswind, a little over 10 km/h, a typical competition compound arrow drifts about 15 centimetres at 70 metres, more than the width of two scoring rings on a 122 cm face. In the same wind, drift at 90 metres is more than half as large again, and a crosswind matters far more than a head or tail wind. Below 1 m/s, according to the author, it can largely be set aside except at the longest distances.

Arrow choice matters as much as reading the wind: for the same spine, a thin, heavy shaft drifts less than a fat or light one, and in the outdoor test the difference in spread between the Protour and the LightSpeed was clear. Small details carry a measurable weight too: a shaft longer than it needs to be, a large over-nock, thick or high vanes and a point with an abrupt step onto the shaft all add drag and so add drift. These figures come from compound bows; for the recurve, which launches the arrow more slowly, the direction should be the same and the drift larger, but the study does not measure it.