Measured in a wind tunnel, the aerodynamic damping of the arrow's oscillation is negligible

The summary today

The measurement comes from a single Japanese group, which set A/C/E arrows oscillating while suspended in a magnetic suspension wind tunnel, at 16 metres per second with an amplitude of half a degree and a frequency of 5 hertz. The damping coefficient comes out negative, so the air would tend to amplify the oscillation rather than kill it, but it is so small, a term of the order of one millionth, that the authors leave it out of their calculations. The result was published twice, in 2015 and 2016, with two types of vane, but these are the same tests and they count once. In the same work, though, the flight calculation made without that term shows the oscillation dying away anyway, almost entirely in the vertical plane, and in the model the only forces at work apart from weight are those of the air; a 2025 simulation links the fading to the moment that realigns the arrow with the flow and to the movement of the centre of pressure. An Australian model from 2011, checked against paper tests, had reached the same point from another direction: in flight the oscillation about the centre of mass dies away with a time constant of about 0.34 seconds, and what decides it is mainly the lift of the fletching. The reading is therefore a narrow one: what is negligible is the damping term measured in the tunnel, not the effect of the air on the oscillation in flight, which works another way. There is no independent measurement of the damping term in a tunnel.

Also phrased as: "aerodynamic damping of the arrow"; "the air straightens the arrow"; "arrow oscillation in flight"; "the arrow settles in flight"; "arrow pitching"

Evidence

• 2011
  Context Equipment tests Published later

  A flight model of an Easton Protour 470 shot from a compound, compared with paper tests carried out with a shooting machine: after leaving the bow the arrow oscillates about its centre of mass with a period of about 21.8 metres, or 0.28 seconds, and the oscillation dies away with a time constant of about 0.34 seconds, in which the arrow travels about 25.8 metres. What decides the period and the damping is mainly the lift of the fletching: with vanes 24 per cent larger the period shortens by 12 per cent and the damping grows, slightly more in the measurements than in the calculation. With fletching of normal size the oscillation stays underdamped.

  Arrow behaviour in free flight · J L Park

• 2015
  For Equipment tests Published later

  Dynamic stability tests in a magnetic suspension wind tunnel on Easton A/C/E arrows with Spin Wing and GAS Pro vanes, at 16 metres per second, with an amplitude of 0.5 degrees and a frequency of 5 hertz: the damping parameter comes out negative, and so amplifying, but with a term of the order of 10 to the minus 6, and it is left out of the calculations.

  The relation between the boundary layer transition and the attitude of archery arrow · T. Matsumoto, R. Ando, J. Ortiz, T. Miyazaki, S. Taguchi

• 2016
  For Equipment tests Published later

  The same measurement reported with two types of vane: the damping parameter is negative and negligible, of the order of 10 to the minus 6. These are the same tests as in the 2015 publication and they count once.

  The boundary layer transition and the attitude of archery allow · Takamasa Matsumoto, Ryu Ando, Takeshi Miyazaki, Satoshi Taguchi, Hiroki Sugiura

• 2016
  Context Equipment tests Published later

  In the flight calculation, with initial conditions measured by four cameras at 3,000 frames per second and the arrow launched at 60 metres per second, the oscillation of the angle of attack takes place almost entirely in the vertical plane and dies away; with ideal initial conditions the angle of attack stays close to zero and the boundary layer stays laminar. The calculation leaves out the damping term measured in the tunnel: the oscillation dies away in a model that contains only weight, lift, drag and the aerodynamic moment.

  The boundary layer transition and the attitude of archery allow · Takamasa Matsumoto, Ryu Ando, Takeshi Miyazaki, Satoshi Taguchi, Hiroki Sugiura

• 2025
  Context Model Published later

  Simulation of an Easton X10 shot at 57 metres per second over 70 metres: the oscillation of the angle of attack fades because the aerodynamic moment realigns the arrow with the flow; fixing the centre of pressure at 0.484 metres leaves a larger amplitude and increases the drift by 0.04 metres with a 3 metre-per-second crosswind, 0.02 with 2 and 0.008 with a headwind. It does not measure a damping coefficient.

  Influences of an Arrow’s Aerodynamic Pressure Center on Recurve Bow Shooting · Wenfeng Shen, Liang Hu, Jing Hu, Yiming Xu, Xixia Xu, Jieqing Zheng

Status history

1. 2011 Not studied Before any wind tunnel measurement, a flight model checked against paper tests shows that the arrow, once clear of the bow, oscillates about its centre of mass and that the oscillation dies away within a few tens of metres, with a time constant of about 0.34 seconds; what decides it is mainly the lift of the fletching. It says that in flight it is the air, through the fletching, that damps the oscillation, but nobody has yet measured the damping term with the arrow suspended in a tunnel, which is what the claim is about.
2. 2015 Reported The first measurement comes from dynamic stability tests in a magnetic suspension wind tunnel: with the arrow oscillating by half a degree at 5 hertz, the damping due to the air even comes out negative, meaning the air would tend to amplify the oscillation, but it is so small that the authors leave it out of their calculations. It is a direct test of the equipment, a single one and published in conference proceedings: reported.
3. 2016 Reported The same group republishes the measurement with two types of vane and finds the same order of magnitude. In the flight calculation, made without the damping term, the oscillation dies away anyway, almost entirely in the vertical plane: the model contains only weight and the forces of the air, so it is the air that settles it, by a route other than the damping measured in the tunnel. These are the same tests as in 2015 and they count once, so the status holds.
4. 2025 Reported A simulation of an X10 shot at 70 metres shows the oscillation of the angle of attack fading by itself and links the fading to the aerodynamic moment and the movement of the centre of pressure: when the centre is fixed, the amplitude stays larger and the drift in a crosswind grows by a few centimetres. It is a model with no measurements and it does not calculate a damping coefficient, but it confirms that in flight the air does settle the oscillation, by a route other than the one measured in the tunnel: the status holds, still resting on the single measurement.

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