Bow micro-movement measured by sensor: Sien Phang 2024

A group of engineers fitted an inertial sensor to the bow of sixteen archers aged between ten and twenty and used the Fourier transform on the acceleration recorded during aiming, to find out at which frequencies the bow oscillates and to try to derive a stability score from them.

The distribution of frequencies averaged over the sixteen archers follows a bell curve, and the authors estimate a standard deviation of 26 hertz, which they use as the boundary beyond which the signal counts as noise. Within that boundary they counted, among the ten highest of one hundred and twenty-five peaks, which frequencies recur in everyone: 1, 3, 6 and 10 hertz. Above 20 hertz the occurrences fall off sharply, and this becomes the second boundary.

From there the authors derive two bands and read them in two different ways: from 1 to 10 hertz the micro-movement of the bow arm, from 10 to 20 hertz tremor. For each band they compute a score that rises as the amplitude of the signal in that band falls, and report it for all sixteen archers: in the low band the values run from 43.01 to 89.97, in the high band from 69.45 to 93.19. Six archers used a compound bow at fifty metres, ten a recurve at thirty.

The work stops there. It is openly a proposal for a method: the authors show that the profile separates the archers from one another, and write that the next step, relating that score to arrow scores, remains to be done, along with analysing the gyroscope data and recruiting more archers.

The sensor is a commercial inertial unit fixed to the bow, connected over bluetooth to a computer, sampling 250 times a second, the maximum the device is rated for. The axes are oriented with x towards the target, y upwards and z towards the observer. Of the sixteen archers, those with compound bows shot at fifty metres, those with recurves at thirty.

The analysis is a discrete Fourier transform applied to the accelerometer data during the aiming phase. The reference profile comes from stacking the frequencies of the sixteen archers: on that histogram the authors apply the rule of the normal distribution, reading as the standard deviation the point within which 34.1 per cent of the amplitudes fall, and obtain 26 hertz. Beyond that threshold the frequencies are discarded. They then count, for each archer, the ten highest peaks out of one hundred and twenty-five, and gather them into a histogram of occurrences to see which frequencies recur most often.

The stability score is the ratio between a threshold and the sum of transform amplitudes in the band concerned, normalised and expressed as a percentage: the threshold used in the examples is 0.5, which the text describes as more than twice the maximum value of the overall amplitude. The two bands are 1 to 10 hertz and 10 to 20 hertz, chosen for symmetry once the upper limit had been set at 20 hertz.

The paper does not report how many arrows each archer shot, how the aiming phase was identified within the signal, how long the analysed window lasts, whether the data are filtered, or how the acceleration due to gravity is handled.

This is a five-page conference paper, and should be read as what it says it is: the proposal of an index, not evidence that the index works. There is no shooting score, no target and no group size, and the authors write that relating the profile to arrow scores is the next piece of work. The reading of the two bands, bow arm micro-movement in the first and tremor in the second, has therefore not been tested against anything: it is an interpretation of the frequencies.

The method has steps that are stated but not justified. The standard deviation of 26 hertz is read off a stacked histogram by applying the 34.1 per cent rule, that is by assuming normality rather than checking it. The score threshold of 0.5 is described in a sentence that does not allow its derivation to be reconstructed. The transform equation is written with a definition of the symbols that does not match the computation, and the two band limits overlap at 10 hertz without the text saying which side that value falls on.

The commentary on the results does not match the table. The text names archer number four as the steadiest on both band scores, whereas in the table the highest values belong to archer number three; and it describes archer number ten as the one with a low score in the low band, when the lowest value in the table belongs to archer number nine. These are printing inconsistencies, but they fall on the two people held up as examples.

Finally the sample. Sixteen archers between ten and twenty, called elite in the abstract without the level being described in the methods, with two bow types and two distances folded into the same average profile: the frequencies of a compound bow at fifty metres and a recurve at thirty were averaged together, and a compound bow at full draw behaves differently. The venue is conference proceedings and the peer review status is not known.

For someone who shoots, the reusable finding is the timescale. The bow at full draw does not stand still, and its movement concentrates on a few recurring frequencies, around 1, 3, 6 and 10 hertz, while above 20 hertz there is next to nothing. That means the oscillations of the bow during aiming are slow, on the order of a few tenths of a second per cycle: slow enough to be seen through the sight, not slow enough to be corrected one by one.

The study does not say that an archer with higher scores in the two bands shoots better, because no scores were collected. Nor does it say that tremor sits in the 10 to 20 hertz band and arm movement below 10: that split is the authors' reading, leaning on the fact that physiological hand tremor usually falls around 8 to 12 hertz.

What can be taken from it is that an inexpensive sensor fitted to the bow records a signal that separates one archer from another, and that the useful content of that signal lies in a narrow band. That is the technical premise of any instrument of this kind, including the use of inertial data in preparation work: useful as a starting point, not yet as a criterion for judging anyone.