Point shape and arrow drag: Mukaiyama 2011 study

The study measures how much the shape of the point changes air resistance on an arrow, but the arrow is a crossbow bolt (Horton Steelforce), 0.502 m long, shorter and stiffer than an archery arrow. Three points were tried: a bullet point, a blunt one and a streamlined one made by the authors by filing down the blunt point, giving the bolt a final weight of 27.5, 28.3 and 27.6 grams. Flight tests and wind tunnel tests give a consistent picture: with the streamlined point the drag coefficient is clearly lower, a sign that the boundary layer along the shaft stays laminar, while with the other two it is turbulent across the whole range tested in flight (Reynolds numbers from 0.78 to 1.65 million, speeds from 25 to 49 m/s).

The wind tunnel also showed that with the bullet point, close to the transition threshold, a small angle of attack is enough to make drag jump: a slightly crooked flight can tip the boundary layer from laminar to turbulent. Lift and pitching moment change linearly with the angle and depend little on the point, because they act mainly on the vanes; the sign of the moment shows that the vanes bring the bolt back into line. The coefficient values appear only in the graphs, not in the text.

There are two sets of tests. In flight, a compressed-air launcher built by the authors fired the bolt at an adjustable speed of up to 60 m/s, with pressures up to 4.4 MPa, on the archery range of the University of Electro-Communications in Tokyo. Two Phantom cameras at 2,000 frames per second, the first 5 metres from the launcher and the second 30 metres further on, filmed the bolt from the side; the drag coefficient comes from the loss of speed between the two points, assuming that the bolt flies perfectly in line, with no lift.

In the wind tunnel the authors used JAXA's 60 cm magnetic suspension system: the bolt, with magnets inside the shaft, is held in place without any mechanical support disturbing the flow, and the forces are worked out from the current needed to keep it still. Because the tunnel tops out at 45 m/s, a model 2.05 times larger was tested alongside the real bolt, to cover Reynolds numbers from 0.29 to 2.92 million. The Reynolds number is based on the length of the bolt.

The main limitation is the object itself: a short, stiff crossbow bolt, which spins about its axis around 4 times a second against roughly 60 for an archery arrow, and which does not flex the way an arrow pushed by the string does. The authors chose it deliberately as a first step and name the A/C/E and X10 arrows as the subject of later work. The launcher also removes the archer's paradox and the oscillations at launch, so the flight measured is cleaner than any shot from a bow.

The streamlined point is a one-off made by the authors, not a commercial product, and the differences between the real bolt and the model (transition at different Reynolds numbers with the bullet point, drag about 10% higher on the model with the blunt point) are put down to small differences in shape, which shows how much the result depends on detail. The text does not say how many launches were made and gives no numerical values, and because the Reynolds number is based on length it cannot be compared directly with studies that base it on the shaft diameter.

For archers this work makes a point of principle: the shape of the point can decide whether air flows smoothly along the shaft or turns turbulent, and that changes drag far more than such a small detail might suggest. It also shows that the state of the boundary layer is delicate, and that near the threshold a slightly crooked flight is enough to raise drag.

It does not say which point to fit to an archery arrow, nor how much the drop at 70 metres or the score would change: the measurements are on a crossbow bolt, at speeds and Reynolds numbers unlike those of a recurve arrow, and the best-performing point was custom-made. In the registry it counts as one of the first in a series of papers from the same Japanese group, which later repeated similar measurements on archery arrows.