Bow movement at the release: Huang 2009 study

A single archer, described as good and technically stable, shot 36 arrows at 30 metres with a laser pointer fixed to the bow's grip, filmed by a camera at 1,200 frames per second. For each shot the authors analysed the last second and a half before the arrow left, 1,800 frames: they used the first 1,740 to build a mathematical model of the aiming path, then used it to predict the last 60 frames, a twentieth of a second, as if there had been no release. In their view, the gap between predicted and actual paths measures the effect of the release on the bow.

They then looked for correlations between a range of parameters drawn from these paths and where the arrows landed. All of those reported concern the vertical direction. The slope of the predicted path over the final frames always pointed upwards, and the steeper it was the further the arrow landed from the centre: a correlation of −0.5164 with distance from the centre and −0.6575 with vertical error. The predicted vertical shift from before to after the release correlated 0.4453 with distance from the centre and 0.6814 with vertical error; the other correlations reported range from 0.4971 to 0.6611. Overall, correlations with vertical error were higher than those with distance from the centre: for this archer the error was mostly in elevation.

The laser mounted on the bow traces the horizontal and vertical movement of the aim, and the camera records it; the data were processed in Matlab. The arrows had been selected in a preliminary test at 18 metres, keeping those of nearly equal weight. The test followed competition procedure: three arrows to adjust the sight, then 12 ends of 3 arrows. The text mentions a clicker and a pressure button, so this is a recurve bow; draw weight and arrows are not described.

The model is a third-order autoregressive model with a constant term (ARX), estimated separately for each direction. From inspecting the recordings, the authors take the last 20 frames to be, on average, after the arrow has left the bow, which they check roughly from an arrow of about 2.5 feet and a launch speed of about 200 feet per second, and the 40 before them to cover the string leaving the fingers. Over these intervals they define slopes, offsets and mean shifts, actual and predicted, and correlate them with the arrows' distance from the centre of the target, their distance from the group centre, and horizontal and vertical error.

One archer and 32 analysed arrows (the text says 36 were shot and then refers to 32 shots for the correlations, without explaining the difference) do not allow any generalisation, and the authors themselves present the results as that archer's style. Correlations are reported without p values and without saying how many were calculated in total: only those described as significant are listed, so some may be chance findings.

There is also a problem of interpretation. The parameters with the strongest correlations come from the predicted path, that is, from the model built on the aim before the release: they therefore describe how the aim was moving in the final moments rather than the effect of the release. The laser measures bow movement, not the string or the fingers, and the split into 40 frames of release and 20 of arrow flight is an average, checked only with a rough calculation, not identified shot by shot. The units of the path measurements are not given.

For archers the clearest result concerns the aim just before the shot: in this archer the aiming path predicted by the model tended to rise in the final moments, and the more it rose the further the arrow landed from the centre, mostly in elevation. It is an observation about one person, consistent with the experience of many archers who link vertical errors to what happens between the end of aiming and the release.

Above all the study shows a method: a laser on the bow and a fast camera make it possible to follow the aim right up to the release, and a model of the aim, as the authors see it, allows the intended movement to be separated from what comes with the release. For archers who film themselves it is an idea rather than a finding: the trace of the aim over the last few tenths of a second may say something about vertical error, but how much, and whether it applies to other archers, this paper does not establish.