Wind tunnel, CFD and free flight tests: how studies measure the air on an arrow

A force that is hard to pin down

The drag on an arrow is of the same order as its weight: for a compound arrow at 78.6 m/s an Australian measurement puts it at 0.94 times the weight. On so slender a body any support disturbs the very flow being measured, and studies have taken three routes: the wind tunnel, which holds the arrow still in a stream of air; free flight, which launches it and measures how it slows down; and computation (CFD, computational fluid dynamics).

Results come out as a drag coefficient, a dimensionless number, set against the Reynolds number, which combines speed, size and the viscosity of the air: taken on the shaft diameter it is about 20,000 for a recurve arrow at 57-58 m/s, while the crossbow bolt study takes it on the length and reaches millions.

The magnetic suspension tunnel

Almost everything goes through the 60 cm tunnel at JAXA, the Japanese space agency. Small neodymium magnets are slipped inside the shaft, ten coils hold the arrow in the chosen position and attitude, and drag, lift and pitching moment are worked out from the currents needed to keep it still (the 2012 journal paper describes the set-up).

This is where the doubling of drag caused by the vanes was measured, from about 0.75 to about 1.5, along with the threshold of roughly half a degree of tilt beyond which the layer of air along the shaft turns turbulent, and the slopes of lift and moment with which the vanes straighten the arrow. Three published entries rest on these measurements, all "reported": points and vanes change drag, an arrow at an angle suffers more drag and vane type changes how quickly the arrow settles. Together with free flight, the tunnel also measured the spin that grows with speed, and it is where the negligible damping was found by making the suspended arrow oscillate.

The tunnel tops out at 45 m/s, below the speed of a recurve arrow, and the arrow is held aligned or tilted on command, without the flexing that follows the release: aligned, it stayed laminar up to the highest speed, while tilted by 0.75 degrees its coefficient rose from about 1.6 to about 3.1. Nor will everything stay suspended. With Gas Pro vanes the arrow spun too fast for the control system and above a Reynolds number of 9,000 it would not hold its balance (2017 paper), and the enlarged X10 model spun far less than in flight.

Free flight and the compressed-air launcher

To reach competition speeds the group built a compressed-air launcher that goes up to 75 m/s. Two high-speed cameras, 13 metres from the launch point and 45 metres further on, film the arrow side-on, and the coefficient comes from the loss of speed. This is where the most quoted result comes from: between Reynolds numbers of 13,000 and 18,000 the same arrow gives two families of values, about 1.5-1.6 and about 2.6, the basis of the entry on the two drag regimes.

The launcher removes flexing on purpose, so the arrow flies as a rigid body, with no archer's paradox. That isolates the air, but once archers shot the picture changed. An experienced national-team archer, 36 arrows at 58 m/s, gave about 2.65, turbulent every time, and in a comparison of four launch methods the mean coefficient at a Reynolds number of around 20,000 lay between 2.51 and 2.77 in every condition, with the lowest standard deviation for the archers, 0.0727, and the highest for the launcher, 0.267. That is why the entry on flexing increasing drag is "contested".

In the air-launcher tests the angle of attack in flight, which the explanation of the two regimes rests on, is calculated from the tunnel coefficients and the launch conditions read off the footage (as the 2016 paper states). An inertial sensor inside the shaft saw the deceleration drop from 0.65 to about 0.30 G within one flight, but on a single launch shown; an automatic image analysis program reads speed and attitude to within 0.9% of the manual reading on the horizontal component, but it sees only the vertical plane and was validated on air-launched arrows.

Computation

The stability analysis of a shaft without vanes uses a criterion developed for flat plates, which the authors themselves say is not justified for a cylinder, and it is the only basis of the entry on the boundary layer along the shaft, which stays "transferred". The 2025 Chinese paper validated its turbulence model at 23 m/s, with a mean error of 6.44% on lift, and then used it at 57. The Turkish study of traditional arrows compares its simulation with no measurement.

Almost all from one group

Of the twenty studies on this page, thirteen list Takeshi Miyazaki among their authors and come from the same group in Tokyo, nearly always with the same tunnel, the same A/C/E shaft and the same launcher. Two of them publish the same test programme and count once; ten are conference papers, and several of them leave out the number of shots per condition. The group has also found its own contradictions: with Gas Pro vanes the layer of air stayed laminar up to a Reynolds number of 23,000 in 2013, whereas the tests repeated in 2015 gave the turbulent value every time.

Outside Tokyo the tests are few and use other methods. In an Australian water channel, with a shaft model scaled up 15.2 times, for an arrow at 85 m/s the layer would turn turbulent about 81 millimetres behind the ogive point and along the whole shaft with the short bulge point (2011 study). An arrow shot by a machine gave a coefficient of 1.94, the turbulent value. The open tunnel used to compare forty vanes ran at 20 m/s with a 100 mm piece of shaft (2019 study), and the Chinese water tunnel study appeared in a venue flagged as questionable.

From coefficient to target

The shift on the target caused by the drag of points, vanes or the state of the air is always calculated. The roughly 15 centimetres of height at 60 metres between the two regimes come from the ratio of drag to weight, which goes from about 0.50 to about 0.86, and the 5 millimetres out of 156 of drift at 70 metres between ogive and bulge points from a calculation that assumes the transition seen in water. Nobody has shot arrows with points or vanes of different drag and counted the impacts. The only group counted in these studies concerns spin: shot by a machine at 30 metres, arrows with vanes angled by about 0.25 degrees made a group less than half the size of the same arrows with straight vanes (Australian measurement from 2011). The entry on speed lost in flight is "corroborated" because there a slowing down is measured, with different instruments and in several laboratories.

What to check

• whether the arrow was held in a tunnel, fired by a machine or shot by an archer, and at what speed compared with the roughly 58 m/s of a recurve;
• what the Reynolds number is based on;
• whether the angle of attack in flight was measured or calculated;
• how many shots per condition, and whether the same test programme appears in more than one publication;
• for a calculation, which measurement it was validated against and at what speed.

How design and sample are weighed is explained in How we read a study; what the arrow does in the air, in the article on arrow flight, and the flexing of the first metres in the research line on the archer's paradox.

@misc{campagna2026_enresearchmethodswindtunnelcfd,
  author = {Campagna, Matteo},
  title = {Wind tunnel, CFD and free flight tests},
  year = {2026},
  howpublished = {Research, matteocampagna.com},
  url = {https://matteocampagna.com/en/research/methods/wind-tunnel-cfd},
  note = {accessed 2026-10-16}
}