Bow accelerometer and shooting: Ogasawara 2021

An acceleration sensor the size of a matchbox, 70 by 36.7 by 9.5 millimetres and 25 grams, mounted on the bow and linked by radio to a tablet, is enough to estimate how still an archer holds the bow while aiming and, from that, what score they will shoot. The authors recorded eleven male students of the Waseda University archery club, all right-handed and with at least three years of practice, over 36 arrows at 30 metres and 36 at 50 metres with recurve bows.

Tremor was measured as the standard deviation of the magnitude of acceleration during the second before the release, from 1.2 to 0.2 seconds beforehand, and for each archer the lowest value among the 36 arrows at 50 metres was taken. The more the bow trembled, the lower the total score: the correlation is strong and negative (R = -0.79, p < 0.01), and the line linking the two measures gives a theoretical ceiling of 331 points out of the 360 available. The system recognises a shot on its own, with a precision of 0.72 and a recall of 0.80 with no outside information about the moment of release, and 0.97 and 0.94 if it is given that information. Putting automatic detection and estimation together, and testing each archer with a model trained on the other ten, the correlation with the score stays at 0.74. On a single arrow, by contrast, no significant correlation appears.

The sensor measures accelerations up to four g and samples 25 times a second, transmitting live to a tablet over Bluetooth; a video camera filmed the sessions so that the exact moments of aiming, release and follow through could be marked by hand from the footage, giving the reference against which automatic detection is judged. The 36 arrows per distance are those set by the Japanese university rules.

Three quantities are derived from the acceleration: the change in magnitude from one sample to the next, which marks the release, and the roll and pitch angles of the bow, which mark the follow through, when the bow rotates forwards. A decision tree was trained on these three, chosen because its rules can be read: recognising a shot requires the bow to be still while aiming, the acceleration to change sharply at the release and the bow to rotate immediately afterwards. As negative examples the authors used, besides randomly chosen moments, the two actions that most resemble a shot, namely letting down without releasing and resting the bow on the foot between arrows. Tremor was computed over a one second window, twenty-five samples, because the shortest aiming period observed was 1.8 seconds. The system was tested by leaving one archer at a time out of the training set.

The authors devote a section to the limits of their sample: eleven university students from the same club, all of one sex, all right-handed and all of intermediate level, neither beginners nor top athletes. It is not known whether the line linking tremor and score holds above or below the range of scores observed, and shot detection might work less well with a beginner, whose movement is less steady.

The correlation concerns the sum of 36 arrows: on a single arrow it disappears, because one arrow depends on too many other things, from wind to the straightness of the shaft to the control of the hand at release, and these cancel out only over a total. Tremor, in short, explains part of the score and not all of it, and the authors say so. The index used is the lowest value among the 36 arrows, that is the best-held arrow rather than the average, a choice made because it stands up better to detection errors. The sampling rate is low, 25 hertz, and the system has to be calibrated by hand by holding the bow upright before starting. Finally the study offers no way of reducing tremor: it measures, and that is all. Scores were collected at 50 metres only.

This work puts a figure on a common impression: among archers of the same club and the same experience, those who hold the bow steadier in the last second before the release score higher, and the difference can be read from the acceleration of the bow with no cameras involved. The link is strong over a total of 36 arrows and absent on a single arrow, which is an elegant way of saying that tremor counts as a tendency and not as an explanation of the nine at three o'clock that has just happened.

The second contribution is practical in the narrow sense: a 25 gram accelerometer on the bow can count shots and isolate their aiming phase on its own, telling them apart even from a let-down, which is the hardest action to distinguish. Anyone using bow or string sensors and an app today is using the same idea. It is worth remembering that the figures come from eleven Japanese club archers at a single distance, and that the study says nothing about how that tremor might be reduced.