An arrow's flexing in flight increases its drag

The summary today

All the evidence comes from a single Japanese laboratory, which between 2011 and 2017 measured arrow drag in a magnetic suspension wind tunnel and in free flight filmed at high speed. Read together, the studies say that flexing matters because it can decide the regime of the layer of air round the shaft: when it makes that layer turbulent, the drag coefficient rises from about 1.5, the laminar value, to about 2.6, and arrows shot by an expert archer at 57 to 58 metres per second always sit there, between 2.6 and 2.7. At recurve arrow speeds, though, the layer turns turbulent even without flexing: above a Reynolds number of 19,000 the coefficient is around 2.5 with every launch method, compressed air included, and in the only experiment that measures flexing and drag together the flexing amplitude bears no relation to mean drag. At lower speeds flexing is not the only route either, because an arrow that does not flex needs a tilt of just over half a degree. Flexing raises drag where the layer could stay laminar; at competition speeds the regime may already be decided, and on that point the studies disagree.

Also phrased as: "arrow flex and drag"; "arrow oscillating in flight"; "aerodynamic drag of an arrow"; "turbulent boundary layer on an arrow"; "arrow drag coefficient"

Evidence

• 2011
  For Equipment tests Published later

  JAXA's 60 centimetre magnetic suspension wind tunnel and free-flight launches filmed at high speed, with X10 arrows: arrows shot by an archer have a drag coefficient about 0.5 higher than the tunnel value, and the authors put it down to flexing in flight.

  A10 Aerodynamic Properties of an Archery Arrow : JAXA's 60cm MSBS Experiments · Yuta Komori, Keita Mukaiyama, Takeshi Miyazaki, Hiroki Sugiura

• 2011
  Against Equipment tests Published later

  In the same work, arrows launched by compressed air, which get no flexing from a bow, also have a coefficient about 20 per cent higher than in the tunnel at Reynolds numbers between 12,000 and 13,000, and the authors attribute it to poorly controlled attitude at launch. The extra drag of free flight appears without flexing too, so this result runs against the idea that flexing is what raises it.

  A10 Aerodynamic Properties of an Archery Arrow : JAXA's 60cm MSBS Experiments · Yuta Komori, Keita Mukaiyama, Takeshi Miyazaki, Hiroki Sugiura

• 2012
  For Equipment tests Published later

  Wind tunnel and free flight with an air launcher, a robot and an archer: the A/C/E arrow shot by an archer at 57 metres per second, Reynolds number 20,000, has a drag coefficient of about 2.6 with a relative error of 2.9 per cent, the turbulent value, and the robot that flexes the arrow gives the same value.

  117 Aerodynamic Properties of an Archery Arrow : Free Flight Experiments and JAXA's 60cm MSBS Experiments · Kyohei Okawa, Yuta Komori, Takeshi Miyazaki, Hiroki Sugiura

• 2012
  For Equipment tests Published later

  A journal article by the group, published online in 2012: 36 shots by an expert recurve archer with the A/C/E arrow at 58 metres per second give a coefficient of about 2.65 at a Reynolds number of 20,000, against about 1.5 in the tunnel, and the authors attribute the turbulence to the oscillation of the arrow after it leaves the bow. Launched by compressed air, without flexing, the same arrow with a bullet point turns turbulent above 13,000, at about 2.6, while with a streamlined point it gives two values, about 1.6 and about 2.6.

  Aerodynamic properties of an archery arrow · Takeshi Miyazaki, Keita Mukaiyama, Yuta Komori, Kyouhei Okawa, Satoshi Taguchi, Hiroki Sugiura

• 2013
  Context Equipment tests Published later

  A 2013 conference paper that takes up the 36 shots by the archer at 58 metres per second already published in 2012 (coefficient about 2.65, relative error under 3 per cent) and sets them beside a comparison of vanes: launched by a machine, the arrow with Spin Wing vanes turns turbulent, at about 2.6, above a certain speed, while with GAS PRO vanes the layer stays laminar at every speed tested. The authors conclude that the oscillation of an arrow shot from a bow always makes the layer turbulent. These are the same shots, which is why this line is context.

  Free Flight and Wind Tunnel Measurements of the Drag Exerted on an Archery Arrow · K. Okawa, Y. Komori, T. Miyazaki, S. Taguchi, H. Sugiura

• 2014
  For Equipment tests Published later

  Below competition speeds flexing decides the regime: without flexing, with compressed air, the coefficient is about 1.5, the laminar value, at Reynolds numbers between 10,000 and 11,000, and between 13,000 and 18,000 it jumps between two values depending on the angle of attack; with large flexing the layer is always turbulent. With the mechanical release the jump between the two values appears at 16,000.

  J0520102 Aerodynamic properties of an archery arrow : Influence of flexural oscillation · Ryu Ando, Kyouhei Okawa, Takeshi Miyazaki, Hiroki Sugiura

• 2014
  Against Equipment tests Published later

  At competition speeds flexing does not change mean drag: at a Reynolds number around 20,000 the flexing amplitude has no significant correlation with the mean coefficient, and above 19,000 the coefficient is about 2.5 with all four launch methods, compressed air included. Mean coefficients at that speed: 2.69 with the archers, 2.67 with the mechanical fingers, 2.77 with the release, 2.51 with compressed air; the arrow that does not flex stays slightly lower, but with no link to how much the others flex.

  J0520102 Aerodynamic properties of an archery arrow : Influence of flexural oscillation · Ryu Ando, Kyouhei Okawa, Takeshi Miyazaki, Hiroki Sugiura

• 2017
  Context Equipment tests Published later

  A journal article by the same group. An expert archer shoots the A/C/E arrow from her recurve, 36 arrows with Spin Wing vanes and 36 with Gas Pro vanes, at 58 metres per second, as in the 2012 protocol: the arrow flexes with an amplitude of 6.9 millimetres at the point and a frequency of 87 hertz, which according to the authors gives the point an oscillating angle of attack of about 3.7 degrees, and the boundary layer is turbulent every time, with a coefficient of 2.68 with Spin Wings and 2.63 with Gas Pros and a spread of about 3 per cent. The authors make flexing the cause of the turbulence. In compressed-air launches, without flexing, they show however that the arrow's tilt is enough on its own: at a Reynolds number of 17,500 the coefficient stays around 1.5 only if the largest angle, worked out by simulation, is below 0.4 degrees, and rises to about 2.7 above 0.6. Launched by compressed air at a Reynolds number of 19,000 to 20,000, the rigid arrow already gives 2.6 with Spin Wings and 2.7 with Gas Pros, close to the archer's values; the authors do not set the two series side by side, and the line stays context.

  Indeterminacy of drag exerted on an arrow in free flight: arrow attitude and laminar-turbulent transition · T Miyazaki, T Matsumoto, R Ando, J Ortiz, H Sugiura

Status history

1. 2011 Contested The first comparison between wind tunnel and free flight: X10 arrows shot by an archer have a drag coefficient about 0.5 higher than the one measured in the tunnel, and the authors put it down to flexing. The same work, though, finds about 20 per cent more in compressed-air launches too, where the arrow does not flex, and explains it by an imperfect attitude at launch. The study therefore points two ways: the extra drag of free flight is there with flexing and without it, so flexing does not emerge as its cause: contested.
2. 2012 Contested The same group measures the arrow shot from a bow: at 57 metres per second the coefficient is around 2.6, the turbulent value, and a robot that makes the arrow flex reproduces it; over 36 shots by an expert archer at 58 metres per second it is 2.65. The authors put the turbulence down to flexing. In the same article, though, the arrow launched by compressed air, which does not flex, turns turbulent on its own with a bullet point above a Reynolds number of 13,000, at about 2.6: flexing matters where the layer could stay laminar. The arguments for flexing as the cause grow, but they come from the same laboratory and the extra drag without flexing found in 2011 still stands: contested.
3. 2014 Contested The only experiment that measures flexing and drag together, across four launch methods, splits the answer in two. Below competition speeds flexing decides: without it the layer stays laminar at about 1.5; with large flexing it is always turbulent. At recurve speeds, above a Reynolds number of 19,000, the layer is turbulent with every launch method, compressed air included, and the flexing amplitude bears no relation to mean drag. In the very range that matters to the archer the studies point in opposite directions: contested.
4. 2017 Contested A journal article from the same laboratory measures the arrow shot by the expert archer again, 36 shots per vane type at 58 metres per second: it flexes by 6.9 millimetres at the point at 87 hertz, the boundary layer is turbulent every time and the coefficient sits between 2.63 and 2.68, and the authors make flexing the cause of the turbulence. The same data, however, show that an arrow that does not flex gets there on its own: launched by compressed air at a Reynolds number of 17,500, it stays around 1.5 only if the largest angle is below 0.4 degrees and rises to about 2.7 above 0.6, and at a Reynolds number of 19,000 to 20,000, that of the archer's shots, it already gives 2.6 to 2.7. Flexing remains one possible cause, not the only one, and at competition speeds the conflict of 2014 is not resolved: contested.

Related

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Research lines

• 32 studiesArrow aerodynamics: drag, boundary layer, vanes
• 29 studiesThe archer's paradox in research: from 1987 to today

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