Movement coordination in recurve archers: Serrien 2018

Six recurve archers from a national team, five men and one woman aged between sixteen and forty-five, each shoot one hundred arrows at eighteen metres indoors with their own bow. The first ten serve to settle them into the room and the equipment, the other ninety enter the analysis. While they shoot, five cameras follow eight markers on the body, and from those movements the relative orientation of the two hands is reconstructed instant by instant through the aiming phase, and used as an approximation of the arrow's direction.

The question is not how much the body moves but how it moves. Ten elemental variables, the positions of the two acromia and three joint angles per arm, can combine in countless ways to give the same arrow direction: the system is redundant, because the quantity that counts has two degrees of freedom and the elements producing it have ten. The analysis therefore separates the variability that leaves the arrow's direction unchanged, because the segments compensate for one another, from the variability that changes it.

In arrows scoring nine and ten the first is significantly larger than the second across most of the aiming phase, in both planes, horizontal and vertical, and in the horizontal plane the organisation arrives earlier. In arrows scoring six, seven and eight the thresholds are largely not reached, and the difference between the two groups of arrows excludes zero across a wide part of the aiming phase. At the moment of release the index measuring this ratio sits between 0.4 and 0.6 in the good arrows and between 0.1 and 0.3 in the others, in both planes.

In every archer and in every condition the index starts out negative at the beginning of the aiming phase and turns positive as it proceeds: the organisation is not there at the instant full draw is reached, it is built during the aiming. The authors take from this that an elite archer does not need, and indeed cannot manage, to minimise the movement of every single segment; what happens is that the variability of the chain is exploited so the arrow's direction stays put.

The scores, as context: the mean per arrow runs from 8.22 to 8.94 over the ninety, the totals from 740 to 805, and the most accurate archer shot no sixes and no sevens.

The participants had been active for at least a year as elite archers in international competition, all right-handed on the draw. Approval from the ethics committee of the Brussels university hospital and written consent from everyone.

A forty centimetre face from the international federation, one hundred and thirty centimetres above the ground, at eighteen metres indoors. The instruction: hit the centre on every arrow. Scoring under the rules, from ten at the centre out to six on the outer ring, and zero for a miss. Ten ends of ten arrows with three minutes of rest between them, to keep fatigue out of the data.

Eight retroreflective markers of fourteen millimetres, paired left and right, on the acromion, the lateral epicondyle of the humerus, the styloid process of the radius and the head of the second metacarpal. Capture at fifty hertz with five cameras, traces filtered with a fourth-order zero-lag Butterworth low-pass at a six hertz cut-off. The reference frame has its origin on the shooting line, with the y-axis towards the target.

From there two geometric models are built, one in the horizontal plane and one in the vertical, expressing the position of each hand as a function of the acromion position and the three shoulder, elbow and wrist angles of that arm. The performance variable is the difference between the positions of the two hands, that is their relative orientation, taken as an approximation of the arrow's orientation. The elemental variables number ten per plane, the performance variable has two: hence the redundancy.

The arrow-to-arrow variability of the elemental variables is decomposed into two parts, relative to the space of configurations that leave the performance variable unchanged: the part lying within it, the compensations between segments, and the orthogonal part, which moves the arrow's direction. The ratio between the two, normalised for degrees of freedom, is the index of motor abundance. The calculation was done both linearising around time-dependent means and around time-independent ones, to test two different hypotheses about how the control is organised.

The tests were run across the whole time series of the aiming phase with statistical parametric mapping, which builds confidence bands point by point: first against the hypothesis that the index is zero, in both planes, under the two time hypotheses and in the two score classes; then on the paired difference between the accurate arrows and the rest. Nominal type one error at 5 per cent with Bonferroni correction within each of the two families of tests, that is thresholds of 0.00625 and 0.0125.

The arrows were grouped into two classes, nines and tens on one side, sixes, sevens and eights on the other, because the individual extreme scores were too few in nearly every archer. The motion capture was not synchronised with the clicker, so the instant of release was estimated from the kinematic traces. No external funding, no declared conflicts, and the model equations and Jacobian matrices are published in full in the article.

The limit that counts most is one of reporting. The time series of the index of motor abundance are shown, but the two variances it comes from, the one that leaves the arrow's direction unchanged and the one that moves it, are never shown separately. Without them one cannot tell whether the good arrows carry more compensation between segments or simply less disturbance, and the most interesting sentence in the study, that minimising every movement is not required, would need exactly that comparison: it would have to be shown that in the accurate arrows the total variability is no smaller, only differently organised. With the normalised index alone, a reader cannot check it.

The comparison between the two classes of arrows is also only nominally the same for everyone. Nines and tens sit on one side, sixes to eights on the other, but the composition changes from archer to archer, and the authors say so: the most accurate archer shot no sixes and no sevens, so his less accurate class consists of ten arrows worth eight, which for someone averaging 8.94 is very nearly a good arrow. In the least accurate archer the same class holds one six and fourteen sevens. The two categories mean different things for different people, and the result rests on that split.

There is a circularity to name precisely. Arrows landing close together have, by definition, more similar launch directions, hence less orthogonal variability: part of the result is another way of saying the group was tighter. What the work adds, and what is not a tautology, is the structure: the compensated variability comes out larger than the uncompensated kind, not merely small. But again, separating the two readings calls for the absolute variances.

The performance variable is an approximation, and the authors write as much: the arrow was not tracked, because the point could not be followed, so in its place stands the relative orientation of two markers on the backs of the hands. The arrow's direction depends on the nocking point and the rest, not on the back of the hand, and how far the substitute departs from the thing itself is not quantified.

The instant of release was derived from the kinematic traces, because the capture was not linked to the clicker, and the aiming phase was normalised in time. The durations of the aiming phase are not reported, nor whether they differed between the accurate arrows and the rest: if they did, the normalisation would be comparing different physical instants. The authors discuss the error on the release point and judge it harmless in a static task, but the question of durations is never taken up.

Six people, one woman, an age range from sixteen to forty-five and all right-handed on the draw. The authors extend nothing beyond this sample and point the way out: repeat across several days to gather enough arrows at each score, or take archers of differing levels and regress the score against the index, which was not possible here because the scores all sat within seven tenths of a point.

Finally there is the distance: eighteen metres on a forty centimetre face. The rings are wide, and the difference in arrow direction between a nine and an eight is a few thousandths of a radian. The result is interesting precisely for that reason, because the organisation of posture changes already at that scale, but it is fragile for the same reason, because the error of the substitute used as the performance variable is of the same order.

This study calls into question one of the most repeated ideas in clubhouses and manuals, the one holding that shooting well means standing still. In the six national team archers the difference between an arrow worth nine and an arrow worth eight lies not in the body moving less but in the movements compensating for one another: a shoulder giving a little and an elbow taking it back, with the result that the arrow's direction stays where it needs to be. In the poorer arrows that compensation is weaker.

The second point is perhaps more useful still, and it concerns timing. The organisation is not there at the instant full draw is reached: at the start of the aiming phase the index is negative in all six archers, and it turns positive as the aiming proceeds. The authors draw from this a hypothesis that will sound familiar to anyone who shoots, that the release comes when the system has found its stable configuration rather than after a fixed length of time. It is a hypothesis, not a measured result, because the durations of the aiming phase are not reported.

Where this card stops: no exercise follows from here. The authors float the idea of also training from unstable positions and varied configurations, to learn to compensate, and they are the first to say that in archery the idea has not yet been tested and should be evaluated before being handed to an elite archer. An archer taking from this study that stability no longer needs to be sought would have read something that is not written: the arrow's direction remains the quantity to be held still, and it is the way of holding it still that does not run through the immobility of every single segment.

The registry keeps this work as a cross-sectional comparison on six elite archers concerning the structure of variability rather than its quantity, and as the firmest argument available against the naive reading by which the less the body moves, the better one shoots.