Within a certain speed band the arrow can fly in either of two regimes, and that shifts the point of impact in height

The summary today

That the same arrow, at the same speed, can fly with two very different drag levels has been measured several times, but always by the same research group in Tokyo and almost always with arrows fired by compressed air, which do not flex. Between Reynolds numbers of 1.3 and 1.8 times 10 to the fourth, the drag coefficient of an A/C/E arrow splits into two families, about 1.5 to 1.6 with a laminar air layer and about 2.6 with a turbulent one, and the two families stay apart even when the shots are raised to sixty. What decides it is the attitude: four to six tenths of a degree of incidence are enough to turn the flow turbulent, and within a single flight a sensor in the shaft sees the deceleration fall from 0.65 to 0.30 G as the oscillation dies away. That this shifts the point of impact in height is the authors' calculation: about 15 centimetres at 60 metres, worked out from the two drag levels at 60 metres per second. Two findings limit how much it matters to an archer. The arrow shot by an elite archer at 58 metres per second, already above the band at a Reynolds number of 2.0 times 10 to the fourth, gave the turbulent value, 2.65, and the same value, 2.68 and 2.63, turns up with two different vanes; and with a bow, the flexing of the shaft makes the flow turbulent across the whole band when a robot releases with mechanical fingers, while the two values return with a release aid, which barely flexes the shaft. Nobody has yet counted impacts at two heights.

Also phrased as: "laminar or turbulent arrow"; "arrow boundary layer transition"; "two identical arrows fly differently"; "two-valued arrow drag"; "the point changes the arrow's drag"

Evidence

• 2011
  Context Equipment tests Published later

  A crossbow bolt with three point shapes, fired by compressed air at 25 to 49 m/s and filmed by two high-speed cameras, plus tests in JAXA's magnetic suspension wind tunnel: over the tested range the air layer stays laminar with the streamlined point and turns turbulent with the bullet and bluff points. The transition falls at real flight speeds, but here it is the point that decides, not chance.

  Aerodynamic properties of an arrow: Influence of point shape on the boundary layer transition · Keita Mukaiyama, Kazuhiko Suzuki, Takeshi Miyazaki, Hideo Sawada

• 2012
  For Equipment tests Published later

  Easton A/C/E arrows in free flight fired by a compressed-air cannon, plus measurements in the magnetic suspension wind tunnel: with the streamlined point, between Reynolds numbers of about 1.3 and 1.8 times 10 to the fourth the drag coefficient values split in two, about 1.6 with a laminar layer and about 2.6 with a turbulent one, while at 1.0 times 10 to the fourth the value is laminar, about 1.5. The authors attribute the split to the angle of attack, which in free flight is never exactly zero. Proceedings of a national symposium.

  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/C/E arrows fired by compressed air over 60 m indoors and tested in the magnetic suspension wind tunnel. At a Reynolds number of 1.8 times 10 to the fourth the distribution of the drag coefficient has two peaks that stay apart even when the shots are raised to 60; with the streamlined point the two values, about 1.6 and about 2.6, appear between 1.3 and 2.4 times 10 to the fourth, and between 1.2 and 1.5 the laminar shot is about 1.7 and the turbulent one about 2.9 with both points. At 60 m/s a ratio the authors call "mass to drag", although it grows with drag, goes from about 0.50 to about 0.86, and the authors estimate about 15 cm of difference in height at 60 m. The 36 arrows shot by an expert national-team archer from her recurve at 58 m/s give 2.65. The shift in impact is calculated.

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

• 2013
  For Equipment tests Published later

  An Easton A/C/E competition arrow fired by compressed air at 28 to 73 m/s, with two points and two vanes: with a streamlined point and Spin Wings, in the intermediate band the drag coefficient takes two values, about 1.6 laminar and about 2.6 turbulent; with a bullet point and Spin Wings it turns turbulent above a certain speed; with Gas Pro vanes the layer stays laminar at every speed tested, whatever the point. An arrow shot by an elite recurve archer at 58 m/s gives 2.65, the turbulent value.

  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

  A/C/E arrows launched four ways: compressed air (no flexing), a recurve with a robot and mechanical fingers, a recurve with a robot and a release aid, and archers; flexing measured from above just after launch, around 86 Hz with every method. With compressed air the drag is laminar, about 1.5, at 1.0 to 1.1 times 10 to the fourth and two-valued between 1.3 and 1.8; with the mechanical fingers, which flex the shaft a lot, it is turbulent across the whole band; with the release aid, which flexes it little, the two values appear at 1.6. Above 1.9 times 10 to the fourth it is turbulent, about 2.5, with any launch, and the archers' arrows have the smallest spread in drag.

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

• 2015
  For Equipment tests Published later

  A/C/E arrows with Spin Wings in the magnetic suspension tunnel and in free flight with an air launcher, plus simulation: a laminar layer for Reynolds numbers below 1.3 times 10 to the fourth, turbulent above 1.8, and in the intermediate band two values of the drag coefficient, about 1.5 laminar and about 2.6 turbulent. The trajectory calculation ties the switch to the angle of attack during flight. Proceedings of a national congress.

  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 test programme as the 2015 work. With a launch that keeps the maximum angle of attack close to zero the drag coefficient stays laminar, about 1.5; with a deliberately non-ideal launch and Spin Wing vanes the values split between about 2.6 (turbulent) and about 1.8 (laminar and turbulent alternating during the flight); with Gas Pro vanes the value is always turbulent. At a Reynolds number of 1.75 times 10 to the fourth the layer stays laminar with a maximum angle below 0.4 degrees and turns turbulent above 0.6.

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

• 2017
  For Equipment tests Published later

  An A/C/E arrow fired by compressed air, and so without flexing, followed by five high-speed cameras, plus tests in the magnetic suspension wind tunnel. With Spin Wing vanes, at a Reynolds number of 1.3 times 10 to the fourth the 137 shots cluster around 1.4 and 3.1, and at 1.75 times 10 to the fourth the 155 shots, with four different nozzles, around 1.6 and 2.7; at 1.1 times 10 to the fourth the value is laminar, about 1.5, and at 1.9 turbulent, about 2.6. With Gas Pro vanes the distribution stays single. In the attitude calculation the switch to turbulent happens when the maximum angle of attack exceeds about 0.4 degrees, and with an ideal launch angular velocity the arrow could stay laminar. Part of the Spin Wing shots come from the same group's paper published in 2012.

  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

• 2017
  Context Equipment tests Published later

  In the same paper an expert woman archer shoots the arrow from her recurve at about 58 m/s, a Reynolds number of 2.0 times 10 to the fourth, that is above the band: the coefficient is 2.68 with Spin Wing vanes and 2.63 with Gas Pro, 36 shots each, with a spread of about 3%. The authors put the turbulent flow down to the flexing of the shaft, 6.9 mm at the point at 87 Hz, and conclude that a suitable amount of flex makes expert archers' shots more consistent.

  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

• 2018
  Context Model Published later

  Simulation of an A/C/E arrow's flight over 70 m with the measured drag coefficients, 1.50 laminar and 2.69 turbulent: at 57 m/s the ratio of drag to weight is 0.45 in the first case and 0.80 in the second, and in the same wind the deviation is larger when the layer is turbulent. With a 3 m/s crosswind the impact moves 0.36 m from the centre. It is a model, not a measurement of the effect on the target.

  Trajectory and attitude of an archery arrow in free flight:: estimation of the influence of the background wind. · Julio Ortiz, Masato Ando, Takeshi Miyazaki

• 2020
  For Equipment tests Published later

  A/C/E 1206 arrows with straight vanes, fired by compressed air over 55 m indoors with an inertial sensor inside the shaft: a drag coefficient of about 1.35 for Reynolds numbers below 1.8 times 10 to the fourth and about 2.45 above 1.85, with both values present between 1.55 and 1.95. In the same shot at 56.4 m/s the average deceleration falls from 0.65 G over the first 0.40 s to about 0.30 G after 0.45 s, once the calculated angle of attack drops below 0.3 degrees: the regime changes within a single flight.

  Experimental and Computational Study of Archery Arrows Fletched with Straight Vanes · Julio Ortiz, Atsushi Serino, Toshinari Hasegawa, Takahito Onoguchi, Hiroki Maemukai, Takeshi Miyazaki, Hiroki Sugiura

• 2025
  Context Model Published later

  A model of recurve shooting with an Easton X10 arrow at 57 m/s, built on the Tokyo group's wind tunnel data: at the switch from a laminar to a turbulent layer the drag coefficient goes from 1.63 to 3.23; in a headwind the angle of attack stays at 0.49 degrees at most, the transition does not happen and the drift is much smaller. A calculation, not a measurement.

  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 It becomes clear that the air layer around the shaft can be laminar or turbulent right at real flight speeds, but it is the point that decides: on a bolt fired by compressed air at 25 to 49 metres per second the flow stays laminar with the streamlined point and turns turbulent with the other two. That the same arrow at the same speed can fly either way has not yet been seen.
2. 2012 Reported Free-flight tests see it. On A/C/E arrows fired by compressed air, between Reynolds numbers of 1.3 and 1.8 times 10 to the fourth the drag coefficient splits into two values, about 1.6 with a laminar layer and about 2.6 with a turbulent one, and the two groups stay apart even when the shots are raised to sixty: it is not an effect of the number of trials. The authors put it down to attitude, since in the wind tunnel a tiny angle of attack is enough to turn the flow turbulent, and they calculate that at 60 metres per second the switch from one regime to the other gives about 15 centimetres of difference in height at 60 metres. In the same work an expert national-team archer shoots the same arrow from her recurve at 58 metres per second, already above the band, and gets the turbulent value, about 2.65: it is the first limit for an archer. The phenomenon is measured on the equipment, the shift in impact is a calculation, and there is one group: reported.
3. 2013 Reported The two-valued band turns up again with Spin Wing vanes and a streamlined point, between 28 and 73 metres per second, with the same 1.6 and 2.6; with Gas Pro vanes, by contrast, the layer stays laminar at every speed tested. The same work reports the arrow shot by the elite archer at 58 metres per second once more, with the turbulent value, 2.65, and the authors infer that the oscillation of an arrow shot from a bow turns the flow turbulent. A confirmation from the same group: the status does not change.
4. 2014 Reported Four launch methods separate out the role of flexing. With compressed air, which does not flex the shaft, the drag is laminar, about 1.5, below 1.1 times 10 to the fourth and two-valued between 1.3 and 1.8; with a bow and a robot releasing with mechanical fingers, which flex the shaft a lot, it is turbulent across the whole band; with a bow and a release aid, which barely flex it, the two values return at 1.6 times 10 to the fourth. Above 1.9 times 10 to the fourth it is turbulent with any launch, and arrows shot by archers have the steadiest drag. It is the first time the phenomenon appears with an arrow shot from a bow, but it depends on flexing: the status stays.
5. 2015 Reported The band is drawn more precisely: a laminar layer below 1.3 times 10 to the fourth, turbulent above 1.8, two values in between, about 1.5 and about 2.6, and a trajectory calculation that ties the switch to the angle of attack during flight. Same group and no measurement on the target: the status does not rise.
6. 2016 Reported With a launch arranged to keep the angle of attack close to zero, the drag stays laminar, about 1.5; with a deliberately imperfect launch and Spin Wing vanes the values split between about 2.6 and about 1.8, a mixed regime in which the flow changes during the flight, while with Gas Pro vanes it is always turbulent. The switch happens when the maximum angle exceeds four to six tenths of a degree. These are the same data as the previous year's work, read more closely, and on the Gas Pro vanes they point the opposite way to the 2013 test: the status holds.
7. 2017 Reported The same group brings its compressed-air shots together in a single paper, some already published in 2012, and the two-valued band shows clearly: with Spin Wing vanes, at a Reynolds number of 1.3 times 10 to the fourth 137 shots split around 1.4 and 3.1, and at 1.75 times 10 to the fourth 155 shots around 1.6 and 2.7, while with Gas Pro vanes the distribution stays single. The attitude calculation puts the threshold at about four tenths of a degree of incidence. The same arrow shot by an archer from her recurve, above the band, stays turbulent with both vanes, 2.68 and 2.63. Confirmation from the same line of work, and impact at two heights is still a calculation: reported.
8. 2018 Reported A simulation over 70 metres uses the two values, 1.50 laminar and 2.69 turbulent, and finds that at 57 metres per second the ratio of drag to weight is 0.45 in the first case and 0.80 in the second, and that in the same wind the turbulent arrow drifts further. It puts figures on the consequences inside the model without adding measurements: the status stays.
9. 2020 Reported An inertial sensor inside the shaft sees the two regimes in real flight, and even within the same flight: a drag coefficient of about 1.35 below 1.8 times 10 to the fourth and about 2.45 above 1.85, with both values present between 1.55 and 1.95; in a shot at 56.4 metres per second the deceleration goes from 0.65 to 0.30 G once the angle of attack drops below three tenths of a degree. Tests consistent with those already on record, but from the same line of work, and the jump in height at the target is still a calculation: reported.
10. 2025 Reported A recurve model built on the Tokyo group's wind tunnel data, with an X10 arrow at 57 metres per second, has the drag doubling at the switch from laminar to turbulent, from 1.63 to 3.23, and finds that in a headwind the angle of attack stays under half a degree, the transition does not happen and the drift stays much smaller. It is a calculated confirmation, not a new measurement: the status does not move.

Related

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Research lines

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

Other claims in this domain

• CorroboratedAlong its flight the arrow loses an appreciable part of its launch speed12 studiesStatus since 2011
• CorroboratedAs it leaves the bow, the arrow flexes and snakes around the riser instead of leaving straight19 studies · 47 archers measuredStatus since 2012
• ReportedA camera-based scoring system misreads some arrows: the ones barely sticking out and the ones that shift the target face7 studies · 2 archers measuredStatus since 2017
• ReportedA chest band with fibre optic sensors measures breathing and mean heart rate with small errors, and an archer can wear it while shooting2 studiesStatus since 2019
• ReportedA compound bow stores between 70 and 100 joules and sheds about two thirds of the force at full draw4 studiesStatus since 2015

See all claims on equipment and tuning