Measuring an arrow in flight: Jeong 2016 study

The study comes from a Korean university and an arrow maker, ShinKwang Leports of Busan, and proposes a way of measuring where an arrow passes without counting holes in target paper. A 65 by 65 centimetre steel frame, with two line lasers and 96 photodiodes per side, was placed one metre in front of the target: when the arrow passes through it casts a shadow on some photodiodes and the system calculates its position. Before correction the mean error on the test points was 2.288 millimetres according to the table (2.46 in the text); a neural network, the best of the four correction methods tried, brought it down to 0.452 millimetres.

The system was then used on 36 hunting arrows of three models, 12 per model, shot from a machine at about 40 metres. Each arrow was shot three times, with the nock turned 120 degrees between shots, and the index taken was the mean distance of the three impact points from their centre. The lightest model, the 150, had the lowest mean index, 6.85 mm, and the smallest variance (5.8); the 250 had 7.53 mm (16.13) and the heaviest, the 350, 8.76 mm (24.48). The lightest model also struck higher on the target and the heaviest lower.

The two lasers project a fan of red light at 60 degrees across the frame; the photodiodes on the opposite sides change voltage when the arrow blocks part of the light. A National Instruments CompactRIO system reads 24 channels at 20,000 samples per second each, finds the centre of the shadow on each side and works out the crossing point from where the two lines meet. For the correction the authors used an acrylic plate drilled every centimetre, inserting a metal rod into 361 holes: 181 points to train the correction methods and 180 to test them.

The arrows were three Maxima Blue Streak models (150, 250 and 350), 30 inches long, for a 51-pound bow mounted on a shooting machine in the company's test range. For each arrow the paper gives weight, diameter, straightness and spine, the last three normalised between 0 and 1; spine is the deflection of the shaft resting on two supports 28 inches apart with an 880 gram weight hung at the centre. Weights ranged from 15.49 to 15.60 grams for the 150, from 17.15 to 17.24 for the 250 and from 18.98 to 19.14 for the 350.

Three shots per arrow are few for measuring spread: with three points a single stray shot moves the index a lot, and within each model the index did range from 3.22 to 12.32 mm (150), from 1.81 to 17.04 (250) and from 2.27 to 20.07 (350). There is no statistical test between the models, so it is not known whether the mean differences of one or two millimetres rise above the noise. The index combines the spread of the arrow with that of the machine and the measuring system, which is not estimated separately, for instance with a reference arrow.

The paper does not link the weight, straightness or spine of individual arrows to the index, which would be the useful step for a manufacturer. The bow type on the machine is not given, and the arrow length is stated once as 30 inches and once as 31. The arrows are hunting arrows shot from a machine in a laboratory: no archers and no human release.

The principle is a check that some archers also run on their own arrows: shooting the same arrow with the nock turned and seeing whether the impact moves. Here it is done with a machine and a sensor frame, and it is of interest to anyone wanting to understand how a manufacturer can measure arrow consistency without counting holes in paper.

For archers the results say little: three models of hunting arrow, a single bow set-up and differences of a few millimetres at 40 metres, with no tests. Naming the 150 as the "optimal" model applies to that machine and that bow. The study says nothing about how spine or arrow weight affect an archer's group.