A thinner shaft meets less air resistance

The summary today

Nobody has measured the force with which the air slows shafts of different diameter: there is only an inference from another figure. In a magnetic suspension wind tunnel, where the arrow is held in the air with no supports to disturb the flow, two competition shafts of different slenderness were compared without vanes: the barrelled A/C/E and the thinner, more elongated X10, tested on a cylindrical model one and a half times life size. At the same Reynolds number the drag coefficient, that is the force referred to the shaft's cross-section, came out the same for both, even though cylinder theory predicted a higher one for the X10. If the coefficient does not change, the force slowing the shaft grows with cross-section, so the thinner one should receive less. The force itself is not reported, though, the comparison holds for shafts without vanes and at lower Reynolds numbers than in a competition shot, and the authors themselves put the matching coefficients down partly to the way they calculated the mean cross-section of the barrelled shaft. A calculation on crosswind starts from the same idea, a push proportional to the exposed surface, and finds that a 5.24-millimetre competition arrow receives about two thirds of the push on a 7.5-millimetre training arrow. How far the arrow drifts, however, also depends on mass and flight time, which do not come into this.

Also phrased as: "shaft diameter and drag"; "thin shafts cut through the air"; "thinner shaft is faster"; "arrow cross-section and air resistance"; "thin arrows outdoors"

Evidence

• 2011
  Context Equipment tests Published later

  JAXA's magnetic suspension wind tunnel, shafts without vanes: between Reynolds numbers of 1.1 and 1.3 times 10⁴ the drag coefficient of the X10, thinner and more elongated, and of the barrelled A/C/E coincide, whereas laminar cylinder theory gave a higher value for the X10. Drag is referred to each shaft's mean cross-section, so at an equal coefficient the force is smaller for the thinner shaft. The force is not reported, the X10 is tested on a cylindrical model scaled up one and a half times, and the authors put the matching coefficients down partly to the use of the mean cross-section for the barrelled shaft. That the force is smaller is an inference from the coefficient, not a measurement: for this reason it stays as context.

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

• 2011
  Context Equipment tests Published later

  With the shaft inclined between minus 3.5 and 3 degrees, at similar Reynolds numbers, the different slenderness of the two shafts changes drag and pitching moment but not lift, which according to the authors depends mainly on the vanes. The A/C/E, less elongated, has the stronger restoring moment, that is a more stable attitude.

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

• 2019
  Context Model Published later

  A calculation of crosswind push with a force proportional to the exposed surface, length times diameter, and a coefficient of 1.2: the competition arrow (5.24 mm by 774.7 mm) receives about 0.67 times the push on the training arrow (7.5 mm by 809 mm). It is a calculation that assumes the proportionality, not a measurement; the drift compared in the same work puts together arrows shot at 18 and at 70 m, so it does not isolate diameter.

  Statics Investigation about Archery Robot in Drawing a Bow · Takuto Nakamura, Yogo Takada, Hitoshi Watanabe

Status history

1. 2011 Not studied The first wind tunnel test arrives, but it does not measure what the claim asks. In JAXA's magnetic suspension tunnel, with arrows without vanes between Reynolds numbers of 1.1 and 1.3 times 10 to the fourth, the drag coefficient of the X10, thinner and more elongated and tested on a model scaled up one and a half times, matches that of the A/C/E, whereas laminar cylinder theory gave a higher one for the X10. A smaller force on the thinner shaft would follow, but the force is not reported, and the authors put the matching coefficients down partly to the way the mean cross-section of the barrelled A/C/E was calculated. On an inference like this the question remains unstudied.

Related

Related articles

• How much the air slows an arrow down, and what really changes the dragHow much speed an arrow loses in flight, how much the shaft, vanes and point add to air drag, and how much of it actually reaches the target.
• Which arrow drifts least in the windA thinner shaft or a heavier arrow for windy competitions? What the models say about diameter, mass, speed and a clean exit, and what is still unmeasured.

Research lines

• 32 studiesArrow aerodynamics: drag, boundary layer, vanes
• 12 studiesWind and heat in archery: research since 2011

Other claims in this domain

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See all claims on equipment and tuning