Arrow aerodynamics: Komori 2011 study

In a JAXA wind tunnel the arrow is held still in the air by magnetic fields from ten coils, with no mechanical support disturbing the flow: the aerodynamic forces are worked out from the currents needed to keep it in place. The maximum wind speed is 45 metres per second and the flow fluctuation at 30 metres per second is 0.06 per cent. Two shafts were tested, a model of the X10 enlarged 1.5 times and a real A/C/E, with two point shapes, bullet and streamlined, and Spin Wing vanes.

The arrow's rotation rises in proportion to speed and does not depend on the point shape. With the A/C/E the rotation measured in the tunnel matches that in free flight, so the tunnel reproduces the flight; with the X10 model the rotation in the tunnel was much lower, which the authors put down to the magnets inside the shaft being poorly symmetric and braking the rotation, or to the model's vanes not reproducing the curl of the real Spin Wings.

Varying the angle of attack between -3 and +3 degrees, the drag coefficient behaves much the same for the two shafts, and around half a degree a tendency appears for the boundary layer to go from laminar to turbulent. Lift is proportional to the angle and is not affected by the shaft's length-to-diameter ratio, so it comes mainly from the vanes. The pitching moment is also proportional to the angle, and acts in the direction that brings the arrow back parallel to the flow; its slope is smaller for the X10, so the A/C/E, with the lower length-to-diameter ratio, is the more stable in attitude.

On the X10 model's drag coefficient as a function of Reynolds number: with no vanes the two points give almost the same values, falling with speed and agreeing with the theoretical laminar value for a cylinder, up to about 1.8 times ten to the fourth; with the streamlined point a jump appears around 2.0 times ten to the fourth, earlier than with the bullet point, which the authors attribute to the roughness of the point's surface. With vanes the coefficient rises by about 0.5 and the change to turbulent happens whatever the point: with the arrow spinning, at a Reynolds number about 25 per cent lower than without vanes, and with the arrow not spinning, about 10 per cent lower. Rotation therefore moves the place where the boundary layer changes its nature.

Comparing with free flight at Reynolds numbers between 1.2 and 1.3 times ten to the fourth, the compressed-air launcher gives a drag coefficient about 2.0 higher than the tunnel, which the authors explain by insufficient control of the arrow's attitude. And an arrow shot by an archer, which flexes as it goes, gives a coefficient about 0.5 higher than the tunnel value, attributed to exactly that flexing.

This is a four-page communication presented at the Japan Society of Mechanical Engineers symposium on sports and human dynamics, held in Kyoto between 31 October and 2 November 2011. The text is in Japanese with an English abstract, and it has not been through peer review.

The wind tunnel is JAXA's 60 cm closed-circuit low-speed tunnel, with ten coils arranged around the test section. The currents in the coils are adjusted so the arrow stays still in the chosen position and attitude, first against gravity alone and then against gravity and the aerodynamic forces together; the difference between the currents gives the drag, the lift and the pitching moment.

The X10 model, enlarged one and a half times, has a constant section and does not reproduce the barrel shape of the real shaft, which is thicker towards the middle; neodymium magnets were placed inside the shaft for the magnetic suspension. The A/C/E, by contrast, is the real shaft. The two points tested are bullet and streamlined, and the vanes are Range-O-Matic Spin Wings, three per arrow.

The free flight tests were run at the indoor facility of the Japan Institute of Sports Sciences, with a compressed-air launching device and two high-speed cameras; the drag coefficient is derived from the rate at which the velocity decays.

It is a four-page communication, and almost everything needed to judge it is missing: how many runs per condition, what the uncertainties were, how the flight data were processed. There is no peer review.

The X10 tested is a model enlarged one and a half times, with a constant-section shaft rather than a barrelled one, and its rotation in the tunnel did not match the rotation in flight; the authors themselves write that reproducing the real flight of the X10 still needs work. The X10 results therefore describe a model, not an X10 in flight.

The English abstract says the boundary layer stays laminar across the whole measured range, from 0.3 to 2.5 times ten to the fourth, while the body of the paper and the conclusions report transitions to turbulent around 1.5 and 2.0 times ten to the fourth. The two statements do not agree, and this record follows the body and the conclusions.

The available copy is an optically recognised scan of a Japanese typescript: several tables are illegible, which is why this record quotes none of the dimensions of shafts, points or vanes. The comparison with free flight, which would give a gap of about 2.0 on the coefficient, is reported in a single line with no legible figure; the same authors' later journal paper finds instead that tunnel and flight agree below 1.2 times ten to the fourth, which is worth keeping in mind.

Finally, no score is measured here. The study measures forces on an arrow and says nothing about where the arrow lands.

For an archer, the useful part is the order of magnitude of things. The vanes add drag, about 0.5 on the coefficient, and bring with them both the lift and the moment that straightens the arrow in flight: without them the arrow is both slipperier and less stable. The shape of the point decides when the flow along the shaft changes its nature, and in these tests the streamlined point did it earlier than the bullet point. The arrow's spin moves that moment earlier still, by about a quarter in terms of Reynolds number.

Then there is a number that bears directly on the archer: the same arrow, shot from a bow and so flexing as it leaves, showed a drag coefficient about 0.5 higher than the same arrow held still and straight in the tunnel. An arrow's drag measured in a laboratory is therefore not the drag of that same arrow as it leaves a bow.

What the study does not give is a basis for choosing between components. The two points differ in when the change happens, not in which flies better, and none of these numbers is translated into arrow drop, drift in wind or group size. It remains a baseline measurement, to be read alongside the same authors' later work, which took the same apparatus further with more data.