Vane shape and arrow spin: Hirano 2019 study

In a wind tunnel, on an arrow model free to spin and to oscillate, forty vanes were compared on two things: how many turns per second they make the shaft perform, and how long it takes for the oscillation to die away. The two qualities do not go together. Vanes that produced more spin tended to damp the oscillation more slowly, and the clearest example is the comparison between two commercial products: XS vanes reached 42.74 turns per second while the model was still oscillating and 34.97 once it had settled, a difference of 18.18% between the two conditions, and settled in 1.283 seconds; Spin Wings spun less, 37.31 turns per second while oscillating and 24.75 once settled, a difference of 33.67%, but settled in 0.934 seconds.

From that percentage difference the author draws a distinction between two families of rotating vanes. Those that spin from the curl of the surface alone lose turns once the angle of attack returns to zero, that is once the oscillation has died away, which is the case of the Spin Wing; those that also have a pitch angle at the tip keep some angle of attack afterwards and lose few turns, as the XS does. The author notes that the vanes most used around the world belong to the first family, the one without tip pitch, and concludes that the quality that matters is not spin but how quickly the oscillation settles. Of the thirty-two prototypes with a worked surface, twenty-five both spun and settled, some did neither, and the differences between surface textures did not come out clearly; the prototypes with more area settled faster than the commercial products, which the author attributes to greater damping and which is presumably paid for in speed.

The wind tunnel is driven by a 75 kW direct current motor and allows speeds from 0 to 90 metres per second; its outlet is rectangular, 1200 millimetres wide by 200 high, with a 500 millimetre parallel section upstream, and the speed was set with a hot-wire anemometer. All the tests were run at 20 metres per second, that is a third of the speed of a shot arrow.

The model is not a whole arrow. It is a piece of 5 millimetre shaft, 100 millimetres long, with the first 10 millimetres machined down to 1 millimetre and a 25 millimetre point fitted at the front. The model is supported at its centre of gravity by a bearing on top of a 3 millimetre vertical spindle, so that it can turn about its own axis and oscillate in the horizontal plane about the support point, and it sits roughly in the centre of the outlet section. Turns per second are read from a Keyence LR-W500 optical sensor aimed at a white strip stuck on the black shaft; the oscillation is read from the output voltage of a Midori QP-2HC potentiometer coupled to the support spindle. The data pass from a digital oscilloscope to a computer.

Forty vanes were tested: eight commercial products and thirty-two prototypes, made by laser-cutting two outlines, one round and one square, with sixteen combinations of surface texture (lattice, honeycomb, wave, horizontal slits, vertical slits, dots and a plain surface, each at two or three scales). Spin is measured in two conditions, during the oscillation and once it has died away; settling is measured by releasing the model at a 45 degree angle of attack and timing how long it takes for the angle to come back inside zero plus or minus 5%. For the non-rotating vanes only the settling time was measured.

No arrow is shot, and the model is a long way from an arrow. The speed is a third of the real one, the shaft is 100 millimetres long instead of seventy centimetres, it is pivoted at its centre of gravity on a bearing and can oscillate only in the horizontal plane: three simplifications that leave out the flexing of the shaft, the spine, the mass and inertia of a real arrow, the wake behind the bow and everything that happens in the first few metres after release. The settling time measured here is the return to attitude of a rigid body in a uniform flow, not the behaviour of an arrow in flight.

The number of runs is not stated: the paper reports single values, a peak instantaneous spin rate and a time, with no repetitions, means or spread, and no statistical test. The section on the prototypes stops halfway because of a manufacturing problem, since laser cutting concentrated heat and raised bumps on the back of the vane as well, and the author himself writes that the effect of the texture cannot be clearly distinguished and that the curl, which is what makes the commercial vanes spin, was not added to the prototypes. The statement that the vanes most used around the world have no tip pitch is an observation about which products sell, not a measurement. No data concern score, group size on the target or arrow speed, and the loss of speed attributed to the larger area is an inference rather than a reading. The paper is a three-page contribution to an engineering symposium, in Japanese, without peer review.

For anyone choosing vanes the contribution is a well-posed question rather than an answer. The common idea is that a vane which makes the arrow spin more will stabilise it better; here, under laboratory conditions, the two move in opposite directions, because the drag that produces the spin is the same drag one would rather not pay, and the vanes that spun most settled more slowly. That the Spin Wing, among the commercial products measured, sits in the lower range for spin and the best for settling time is an interesting observation alongside how widely it is used, but it comes from a model in a wind tunnel and not from arrows shot at a target.

What stays useful is the technical distinction between a vane that spins from its curl alone and one that also has a pitch angle at the tip: in the first the spin falls off once the arrow has aligned with the flow, in the second it holds. It is the kind of difference that cannot be seen by looking at the vane and that no archer can confidently read off the target, because in the spread of a group the shot itself weighs far more than the choice of vane, as the author notes about amateur archers. The study does not allow anyone to say which vane scores better, and it measures no effect on arrow speed.