Measuring the archer's paradox: Kim 2014 study

The authors, Korean electronic engineers working with a sporting goods company (ShinKwang Leports), built a device to measure the archer's paradox without a high-speed camera: three frames of 65 by 65 cm, crossed by sheets of laser light, which record the arrow's position as it passes. From the position of the shaft in all three frames at the same instant they calculate how far the arrow is bent, as the distance of the middle point from the straight line joining the other two.

The experimental result is brief: four types of arrow, six shots each, with the first frame 80 cm from the bow, gave mean bends of 4.942, 5.527, 4.693 and 4.634 mm. Calibrating the device against a reference grid reduced the position error from about 3 mm to under 0.5 mm. According to the authors the device costs less than a high-speed camera, gives a number directly and sees the bend in any direction, not only in the plane a camera is pointed at.

Each frame has line lasers on one side and a row of photodiodes on the other: as the arrow passes it shades some of the sensors, and the centre of the shadow together with the laser position gives the shaft's location. The signals are read by National Instruments modules (NI 9205) at 20,000 samples per second per channel, with 24 channels per frame. The three frames stand in line in front of a bow held in a fixed mount, 20 cm apart, a spacing chosen so that the 75.4 cm arrow would be inside all three for at least three samples; in practice there are three or four. Distortion was corrected first with a grid machined at 1 cm intervals and then with a neural network trained on known positions.

The paper also explains how spine is measured (shaft on two supports 71.2 cm apart with an 880 g weight at the centre), but it does not give the spine, model or weight of the four arrows tested, the draw weight of the bow, or how the string was released. The text is in Korean, with the abstract and captions in English.

This is a methods paper: it describes the device and shows that it works, but it does not compare it with a high-speed camera or any other independent measurement, so it is not known how closely the number matches the shaft's actual bend. For each arrow the device sees only three or four instants, over a 40 cm stretch starting 80 cm in front of the bow, and the bend it records depends on where the arrow is in its oscillation at that moment: an arrow that flexes a lot can give a small value if it crosses the frames as it straightens. This is my own observation; the authors do not discuss it.

The spread across the six shots is not reported, and the four arrows are not described, so the differences between 4.6 and 5.5 mm cannot be tied to any of their properties. The idea, repeated in the introduction, that a higher spine number, meaning a more flexible shaft, goes with a larger paradox is taken as known, not measured here. The link between the size of the paradox and arrow accuracy is left to future work.

For an archer the study changes nothing in tuning: it does not say what size of paradox is preferable, or how it changes with spine, draw weight or release. It is of more interest to those who make or test arrows, because it shows a relatively cheap way of turning in-flight bending into a number that can be compared from one arrow to the next. The bends measured, around 5 mm about a metre from the bow, also give, with the caveats above, an order of magnitude to anyone watching slow-motion footage: just in front of the bow the arrow is still bent by a few millimetres.