Air flow around the arrow point: Park 2011 study

Using a 15.2 to 1 scale model in a water channel, the authors watched how the flow behaves over the point and the front of the shaft with two point shapes. With a bullet point, the same diameter as the shaft, the flow stayed laminar over the point and along the shaft and turned turbulent 1.0 metre along the model, at a Reynolds number of about 450,000; for a competition arrow at 85 m/s the authors estimate this at about 81 mm behind the tip. Tilting the model up to 3 degrees moved the transition about 0.1 metres forward on one side and back on the other, leaving the average unchanged. A circumferential groove 3.6 mm deep between point and shaft, like those used to identify point weights, made no difference.

With a short tungsten bulge point, which swells wider than the shaft, the flow broke away just behind the bulge, recirculated over the rear taper and was turbulent all along the shaft. The separation only disappeared when the water was slowed to 0.092 m/s, equivalent to an arrow at about 56 m/s; from 0.365 m/s upwards the flow was turbulent over the whole length tested. With the bulge point the model vibrated slightly, with the bullet point it did not. The authors calculate that, for a 25.03-gram arrow launched at 84.1 m/s in a 3 m/s crosswind, drift at 70 metres goes from 156 mm with the bullet point to 161 mm with the short bulge.

The shaft model was an aluminium tube 76 mm in diameter and 2 metres long, with aluminium points machined to the shape of real ones. The water ran at 0.456 m/s, chosen to give the same Reynolds number as an arrow in air. The real bulge point had a maximum diameter of 5.3 mm and came back to the shaft's 4.7 mm over 4.5 mm of length; a long stainless steel bulge point, shown for comparison, tapers over 19 mm.

The flow was made visible with a fluorescent dye mixed into honey and spread on the model, at angles from 0 to 3 degrees. For the bulge point the recirculation zone was also measured by particle image velocimetry: a laser sheet lit up hollow glass particles suspended in the water, and 1,000 image pairs taken at 1 Hz gave the velocity field behind the bulge, from 0 to 3 degrees. Wind drift was calculated with a method the first author had published earlier.

The water channel reproduces the Reynolds number but not the rest: the model is stationary, without the spin from the vanes or the flex and oscillation of an arrow in flight. Transition was judged by eye from the dye, and only two points were tested. The long stainless bulge point, with a taper about four times gentler, was not tested: that it has less drag is the authors' prediction. Neither drag nor drift was measured, and the 5 mm difference at 70 metres comes from a calculation that assumes the transition seen in water. The paper appeared online in 2011 but is printed in volume 227 of 2013, which is why other papers cite it under that year.

For outdoor archers the message is precise but small. A point with a short bulge and an abrupt rear taper, typical of tungsten points that are shorter for the same weight, makes the flow turbulent along the whole shaft and, according to the authors, adds drag. On the authors' calculation, at 70 metres in a 3 m/s crosswind the difference is about 5 mm, roughly one arrow diameter: measurable, but small beside the other sources of error on a windy day. Identification grooves on points make no difference.

The study does not say bulge points should be avoided. They serve a practical purpose, making arrows easier to pull and protecting the shaft in the boss, and the long bulge point, which was not tested, would not have the same problem according to the authors.