Wind and air in target archery: Park 2019 review

A survey of the research on how air and wind act on the arrow and on the archer, written by an engineer affiliated to Archery Australia who is himself one of the main contributors to that research.

The figures that set the scale. A recurve man needs around 665 points out of 720 over the 72 arrows of the qualification round, an average of about 9.2 per arrow, to be around the top sixteen and have a reasonable chance of a medal; a compound man needs around 700 points, which is about 9.7 per arrow, to be around the top twenty. Against that precision, a recurve arrow can drift three or four rings at 70 metres in a moderate wind, and a compound arrow one or two at 50 metres.

During the power stroke the arrow takes a peak acceleration of about a thousand times gravity. In free flight a fletched arrow oscillates in pitch and yaw about its own centre of gravity with a period corresponding to roughly twenty metres travelled, and flexes sideways at 80 to 90 hertz, keeping a reduced but still significant amplitude all the way to the target.

On the air around the point the finding is specific: observing large-diameter shafts in a water channel, points wider than the shaft made the flow turbulent immediately behind the step in every case, while points blending smoothly into the shaft left it laminar and let it turn turbulent further along the shaft, at a Reynolds number of about 450,000, for angles of attack up to two degrees.

On drift, the wind tunnel tests and the long-distance ones agree: all else being equal, the smaller-diameter shaft drifted less. And in shooting machine tests, straighter arrows grouped better, while making the arrow spin about its own axis reduced the group size markedly.

The gaps the author declares are just as informative: there is nothing published on how humidity, temperature and rain act on arrow flight, nothing on the surface condition of points and shafts, nothing on the archer's own equipment and clothing in wind, and nothing on the widespread practice of adding mass to the bow against gusts, which the author notes is demanding to hold and may carry a risk of injury.

There is no protocol to describe: this is a narrative survey, with no search strategy, inclusion criteria or quality appraisal, and the article presents itself as what it is, an overview with pointers to the directions worth exploring. The text was received on 14 March 2018 and accepted on 17 December of the same year.

What the survey retraces is a chain of work going back to 1930, and in doing so it says what each link rested on. English, in 1930, derived equations for range, trajectory, time of flight, maximum height and angle of fall, but assumed drag proportional to velocity rather than to its square, which is the law that holds at very low speeds. Higgins, in 1933, assumed a drag coefficient of 0.005 without saying where it came from. Liston, in 1988, divided the arrow into four parts and used for the shaft an equation which its own source declares applicable below a Reynolds number of a million, whereas an arrow's is a good deal higher. The 2011 work by the survey's own author lets the flow type and the coefficients vary along the shaft and obtains the drag by integration.

Direct measurement is the weak link in the chain, because supporting an arrow in a wind tunnel without disturbing the flow is hard. The solution cited as the most promising is the magnetic suspension used by Miyazaki and colleagues, which holds the arrow clear of any supports and allows the angle of attack to be chosen: they measured the drag of the whole arrow up to 45 metres per second, below the 55 to 65 of a recurve and the 75 to 90 of a compound. The arrow tested was an Easton ACE with Spin Wing vanes and no nock, since the compressed-air launcher needed the rear end free.

The models of the power stroke run from Klopsteg and Pekalski to Kooi and Sparenberg's finite-difference solution, which treats the arrow as an inextensible Euler-Bernoulli beam. They were compared with flash photography and with the high-speed video of sixteen archers filmed at the test event for the London Games, which has a record of its own in this registry.

This is one author's survey of a field in which he is one of the main contributors: nine of the twenty-eight references are his own. There is no declared method of selection, so what goes in and what stays out is a judgement, and even the areas marked as unstudied are marked according to one person's knowledge of the literature.

Some statements have no published source behind them. The passage about arrows that leave the bow already spinning about their own axis, even without fletching, rests on work described as not yet published, and the author writes that he has seen no satisfactory explanation of why it happens.

The figures on drift, three or four rings at 70 metres and one or two at 50, are given as what is not unusual to see rather than as a measurement with a wind speed attached, and a moderate wind is nowhere defined. The score thresholds, 665 and 700, are approximations for the men's field at the time of writing, and they move with the level of the competition.

The limitations of the underlying work are stated clearly, and they are substantial. The drag of a whole arrow has still not been measured directly at competition speeds. The wind tunnel drift test was compromised by the fact that at high wind speeds the arrows arrived at the target at an angle, leaving elongated holes that made the displacement hard to read accurately. And every free-flight model assumes still air or air moving at a uniform velocity, which is exactly the condition an outdoor competition does not offer: wind on a field comes in gusts and changes from one point of the distance to another.

The practical content lies in the ordering of causes. Among the things an archer can change about an arrow for the wind, the one with evidence behind it is the diameter of the shaft: in these measurements the thinner shaft, all else being equal, drifted less. The second is the shape of the point, where the finding is specific: a point that stands out beyond the shaft makes the air turbulent from that step onwards, while a blended point leaves the flow laminar for part of the length. Then straightness and spin, both of which tightened the group in shooting machine tests.

What the survey does not support is the rest of what gets said about weather. On humidity, temperature and rain the author's position is that nothing has been published, and that is a gap, not a result in either direction. The same holds for clothing, for the stabiliser's behaviour in a crosswind and for the habit of adding mass to the bow against gusts: it is practice without published measurement, and the author adds that the extra mass is tiring to hold and may carry a cost of its own.

The last point concerns the archer rather than the arrow, and it is the one the survey presses hardest. A gust does not act on the flight alone: it moves the body and the bow, it takes the sight off the point of aim, and it makes the release harder to run cleanly, whether through a clicker or with a mechanical release aid. Neither of those has ever been measured, and the author names it as the area where most could be gained. In this registry the paper serves as the framing of a line of work rather than as evidence on a claim: the measurements are in the studies it cites.