Vanes and drag on an archery arrow: Okawa 2013

This paper takes up the apparatus of the same group's two earlier studies and adds a variable the others had not tested: the type of vane. The same A/C/E arrow was measured in the magnetic-suspension wind tunnel and in free flight, with two point shapes, bullet and streamlined, and two of the most widely used competition vanes, Spin Wings and Gas Pros.

In the tunnel the bare shaft, with the point but without vanes, keeps its boundary layer laminar up to a Reynolds number of 1.35 times ten to the fourth. With Spin Wings the change to turbulent happens around 1.0 times ten to the fourth, and the drag coefficient jumps abruptly from 1.6 to 3.1. With Gas Pros the arrow did not rotate in the tunnel and the boundary layer stayed laminar up to 1.15 times ten to the fourth, the highest value reached in that condition.

Varying the angle of attack at 1.0 times ten to the fourth, the two points behave the same way: with Spin Wings the change to turbulent happens once the angle exceeds about 0.6 degrees, with Gas Pros at a slightly larger angle.

In free flight, over the range from 0.90 to 2.4 times ten to the fourth, that is, from 28 to 73 metres per second, the boundary layer is laminar with both vanes below 1.0 times ten to the fourth. With Spin Wings it becomes turbulent above 1.9 times ten to the fourth and the coefficient rises to about 2.6; between 1.0 and 1.9 times ten to the fourth two distinct values are found, about 1.6 and about 2.6. With Gas Pros the boundary layer stays laminar at every speed tested, up to 2.3 times ten to the fourth. With the streamlined point the picture is the same: two possible regimes with Spin Wings, laminar only with Gas Pros.

The authors conclude that Gas Pros stabilise the arrow's attitude more than Spin Wings do, and that it is the vanes, more than the point, that decide when the flow along the shaft changes its nature.

Finally the same arrow, with bullet point and Spin Wings, was shot by an elite recurve archer at 58 metres per second: the drag coefficient came out at about 2.65, the turbulent value, with a relative error under 3 per cent.

The arrow is an Easton A/C/E, a barrel-shaped shaft whose middle is slightly thicker than its ends: length 0.626 metres, mean diameter 0.00524 metres, weight 0.0094 kilograms without the point. The bullet point is a commercial ACE Screw Point, the streamlined one purpose-built. The vanes compared are Spin Wings and Gas Pros.

In the tunnel the arrow is suspended by JAXA's 60 cm magnetic system: cylindrical permanent magnets inside the shaft, coils around the test section, and currents adjusted so that the arrow stays still against gravity and against the aerodynamic forces. The forces are derived from the currents. The tunnel's maximum speed is 45 metres per second.

For free flight the compressed-air launcher developed in the earlier work was used, reaching 75 metres per second at a pressure of 7 megapascals, with an accuracy comparable to that of an elite archer. An expert archer was added to this, shooting 36 arrows with Spin Wings precisely in order to isolate the effect of the shaft's oscillation. The filming was done by two Phantom V310 cameras at 2,000 frames per second, one 13 metres from the launcher and the other 45 metres further on, both to the side; the images give the horizontal and vertical components of the velocity at the two points, and from these the drag coefficient, on the assumption that no lift is acting. The tests took place in the indoor range of the Japan Institute of Sports Sciences.

These are six pages of conference proceedings, and much of what would be needed to judge the numbers is absent: how many shots per condition, what error bars, how the values were distributed in the zone where two of them appear. The paper refers readers to the same group's journal article, published shortly before, for the details, but that article did not include Gas Pros.

The comparison between the two vanes is not like for like. With Gas Pros the arrow did not rotate in the tunnel, and rotation is one of the conditions that move the transition point: if the two vanes produce different rotation rates, the comparison mixes the shape of the vane with the spin it induces. In the tunnel, moreover, the Gas Pros were taken only up to 1.15 times ten to the fourth, well below the value reached by the bare shaft, so saying they stay laminar in that test means they did not change regime over the stretch measured.

Some numbers do not agree within the paper itself: the abstract says the boundary layer becomes turbulent above 1.0 times ten to the fourth, while the text reports 1.0 for the tunnel and 1.9 for free flight. The camera frame rate also differs from the one declared in the reference article, 2,000 frames per second instead of 2,800.

There is one archer, with one combination of point and vane: there is no comparison at all between Spin Wings and Gas Pros shot from a bow, which is the test that would settle the question for anyone choosing. The conclusion that Gas Pros stabilise the attitude better is an inference from the boundary layer's behaviour, not a measurement of the attitude.

No scores, no groups, no target: the study measures the drag on an arrow and stops there.

This is the only one of the group's three papers that compares two competition vanes, and the finding is that they do not behave the same way in the air. With Spin Wings the flow along the shaft changed its nature at competition speeds and the drag coefficient jumped from about 1.6 to about 2.6; with Gas Pros it stayed laminar across the whole range tested, up to 2.3 times ten to the fourth. Put that way it would sound like an advantage for the Gas Pros, but the numbers are worth reading in full: the laminar value is the lower of the two, so a laminar arrow loses less speed, while an arrow that switches between regimes from shot to shot is the one that changes behaviour without warning.

And here comes the figure that cuts the comparison down to size. In the archer's thirty-six shots, with Spin Wings, the regime was turbulent on every single shot: the oscillation of an arrow leaving a bow settles the question before the vanes do. The study had nobody shoot Gas Pros from a bow, so whether the shaft stays laminar behind a bow with those, or turns turbulent too, is unknown.

For anyone choosing vanes, the honest conclusion is that this study does not choose. It says that the two shapes produce different aerodynamic conditions when the arrow flies straight, and that the bow, by making the arrow flex, changes the terms. Scores, groups and drift in wind were not measured.