Archery shooting machine: Lin 2009 study

Four Taiwanese engineers built a shooting machine in order to take the archer out of the picture and compare pieces of equipment against one another. With that machine they measured the speed of 29 inch Easton A/C/E 470 arrows shot at 44.8 pounds, varying three things: the type of vane, where it is glued, and the number of strands in the string.

With a 20 strand string the fastest arrow is the bare shaft, at 215.65 ± 0.1968 feet per second. The 1-3/4 inch Spin Wings follow closely at 215.1 ± 0.202, the 2-13/16 inch ones drop to 214.4 ± 0.2951, and the larger Tite Flights lose more: 212.5 ± 0.327 for the P175 and 212.4 ± 0.241 for the P200. Between the bare shaft and the slowest Tite Flight there are about 3.2 feet per second, which is 1.5%.

With a 12 strand string instead of 20 the order stays the same and every speed rises a little: 215.93 ± 0.1155 bare, 215.6 ± 0.221 for the small Spin Wing, 215.2 ± 0.283 for the large one, 213.6 ± 0.233 for the P175, 213 ± 0.228 for the P200. The gain runs from two to six tenths of a foot per second depending on the vane, and the spread narrows for every vane except the small Spin Wing.

The position of the vane relative to the nock, tested at 0, 3, 6 and 9 centimetres with 1-3/4 inch Spin Wings and the 20 strand string, does not appreciably change the mean speed: 215.18, 215, 215 and 215.4 feet per second. The standard deviation does rise a little, from 0.2307 to 0.275, and the authors read that trend as confirming the habit archers have of gluing vanes close to the nock.

The machine is built around a single-axis robot with a 600 millimetre stroke, a ball screw of 5 millimetre pitch and a rail guide with a stated repeatability of one hundredth of a millimetre; the motor has an encoder of 4000 counts per revolution, which is 1.25 micrometres per count. The release is not a finger but a mechanical Stinger aid, a trigger release for compound with Teflon-coated jaws, chosen because it opens without torque and its sensitivity can be adjusted. The release was built into one body with a HANDY HF series digital force gauge, which measures draw force directly and stores up to 256 readings, with a resolution of one hundredth of a newton on a 100 newton scale.

Speed is read by an arrow chronograph with an infrared illuminator, which makes indoor measurement possible, placed one metre from the rest. For tuning the bow the authors use Easton's bow force mapping system.

The arrows are Easton A/C/E 470, that is with a deflection of 0.470 inches on a 28 inch span: that is how the spine of those shafts is declared. They were selected for practically equal weight and screened by a preliminary 18 metre shooting test, to ensure uniform behaviour. Four vanes were compared: Tite Flight P175 (1.75 inches long, 0.375 high) and P200 (2.00 and 0.330), plus Spin Wings of 1-3/4 and 2-13/16 inches.

The paper does not say how many shots were fired in each condition, and reports no statistical test: the tables contain only a mean and a standard deviation. The bow itself is not described either, and only its draw force is known.

The number of shots is missing. Without knowing how many arrows the means and standard deviations rest on, none of these differences can be judged, and the paper contains no statistical test. The differences at stake are tiny: 3.2 feet per second out of 215 between the first and last vane, and less than half a foot per second between the two strings.

On the glueing position the conclusion goes beyond the data. The four means lie within four tenths of a foot per second and the highest is the one at 9 centimetres from the nock, not the one at 0; the only quantity that rises with distance is the standard deviation, from 0.2307 to 0.275, four hundredths. Calling that a confirmation of what archers already do is a generous reading.

The chronograph sits one metre from the rest, and the authors say so: at that distance neither drag along the trajectory nor the effect of a crosswind can be seen. Many of the paper's sentences about Spin Wings, reduced drift and forgiveness of poor releases do not come from the measurements: they are properties attributed to the design of the vane, in language close to that of a catalogue. The tests were indoors, so none of those claims was put to the test here.

Two details are worth checking if the paper is cited. The stated heights of the Tite Flights are 0.375 inches for the P175 and 0.330 for the P200, which would make the shorter vane the taller one; and the bow is not described, so the 44.8 pound draw force remains the only piece of equipment data. Nothing in this study concerns accuracy: there are no measured groups and no scores, and the photographs of arrows driven into one another are there to show the machine's repeatability, not the merit of a vane.

The figure to remember is the order of magnitude of the aerodynamic cost of vanes just outside the bow: about 1.5% of initial speed between a bare shaft and a generously sized plastic vane, and less than half a percentage point between a bare shaft and a small Spin Wing. One metre from the bow, then, vanes take almost nothing; what happens over the seventy metres that follow is not measured here.

The second point is that moving the vanes along the shaft, between 0 and 9 centimetres from the nock, did not change the speed. A minimal tendency for variability to grow with distance remains, four hundredths of a foot per second, which on its own supports no guidance on fletching.

The third concerns strands. Going from 20 strands to 12, the arrows left slightly faster, by at most half a foot per second, and generally with less spread. The difference is of the order of tenths of a percentage point, and the study measured neither string life, nor stretch, nor feel at release, which are the reasons a strand count is usually chosen in the first place.

The most solid contribution is not a result but a tool: a machine that draws with a ball screw and releases with a mechanical aid, with draw force read by a built-in gauge, compares two pieces of equipment with the variability of the release taken out. This study shows that it can be done, and at the same time how little can be read into a speed difference measured one metre from the bow.