Short or long straight vanes on arrows: Ortiz 2020

The study compares two arrows that are identical apart from the fletching: three straight plastic Easton Diamond vanes in size 175 (short) or 280 (large). In the wind tunnel, at a Reynolds number of 12,000, the drag coefficient was 1.56 with the short vanes and 2.05 with the large ones. In flight, an accelerometer inside the shaft recorded the deceleration: on a launch at 56.4 m/s lasting 1.04 seconds, the arrow lost about 8% of its speed. Deceleration averaged 0.65 g over the first 0.40 seconds and about 0.30 g after 0.45 seconds, a drop the authors read as the boundary layer switching from turbulent to laminar flow, which happened once the calculated angle of attack had fallen below 0.3 degrees.

In the flight measurements the drag coefficient was around 1.35 at Reynolds numbers below 18,000 and around 2.45 above 18,500. The large vanes give more lift and a stronger stabilising moment: in the simulations the maximum angle of attack was 0.36 degrees with the short vanes and 0.27 with the large ones, and the arrow oscillated about its path at 4 Hz against 5.3 Hz. The authors conclude that the large vanes give a more stable flight.

The arrows used an Easton A/C/E 1206 shaft from the H/1000 series (carbon wrapped around an aluminium tube), a bulge point, a length of 0.638 m and a mass of 14.2 grams with the short vanes and 15.3 with the large ones. The sensor (Logical Product LP-UUEC002, 1.37 grams with holders and battery) sat in the front part of the shaft and logged accelerations and angular velocities at 200 Hz.

The launches took place on a 55-metre indoor range using a compressed-air launcher, at pressures of 4.5 to 7 MPa and launch speeds of 48 to 57 m/s, with the ventilation switched off; a high-speed camera 1 metre from the launcher measured the initial speed and angle. Static forces were measured in JAXA's magnetic suspension wind tunnel (60 by 60 cm), which holds the arrow in place without supports. Finally, using the measured lift and moment, the authors simulated the flight treating the arrow as a rigid body, with no flex and no wind.

The arrow is fired by compressed air, slid onto the launcher's nozzle, and the authors themselves note that this removes the flex that a recurve bow would produce. So the archer's paradox, the release and the oscillations of the early flight are all missing, and with a bow these affect the very angle of attack on which drag depends. The vanes are straight, whereas many archers fit them with some offset or helical, and the comparison with an elite archer's shot (a coefficient of 2.69 with curved vanes) comes from another paper.

The transition in flight is shown for a single launch, the total number of launches is not given, and the angle of attack that is meant to explain it is calculated by the model rather than measured. The wind tunnel values reported are at Reynolds numbers of 10,000 and 12,000, about half the typical value for a recurve arrow, which the authors put at 20,000 and above. It is a six-page conference paper, with the data summarised in graphs.

For anyone who builds arrows, the most concrete finding is the trade-off between drag and stability: larger vanes slow the arrow more (a coefficient of 2.05 against 1.56 in the wind tunnel) but bring it back into line more firmly and keep its oscillations smaller. The study adds that drag is not constant along the flight: it depends on how well the arrow is lined up with its own path, and an arrow that settles well can switch to a lower-drag regime during the flight.

It does not say which vane to choose, nor how much the drop or the score would change at a competition distance: the tests had no bow and no archer, the speeds were a little lower than an elite recurve's, and the simulations treat the arrow as rigid. What can be taken from it is qualitative. It fits the idea that an arrow leaving the bow with less oscillation meets less drag, but how much this matters for an arrow shot from a bow is not something the study measures.