In flight the arrow oscillates in pitch, one cycle every fourteen to twenty-two metres, and the waviness shows mostly over the first stretch

The summary today

The calculations show that the arrow oscillates about its centre of mass after leaving the bow, and since 2011 a measurement has shown it too. The mechanism is always the same: the centre of pressure sits at the back, towards the vanes, the centre of mass sits in front, and as soon as the shaft is tilted against the airflow a moment appears that brings it back into line and makes it swing. Paper tests at several distances on arrows shot from a compound, in 2011 by a shooting machine, find one cycle every nineteen to twenty-two metres and an oscillation that dies away over some twenty-six metres, in line with the same author's model; in simulations of recurve arrows at 57 to 60 metres per second the cycle is fourteen to eighteen metres, and the waviness of the trajectory shows over the first twenty of the seventy metres. The amplitudes are small: in still air the maximum angle stays between a quarter and half a degree, and in the calculation with a three metre per second crosswind it reaches three degrees. The measurements have two limits, though: they come from a single researcher and from a compound, and they look at the oscillation in the horizontal plane rather than in pitch, so for the recurve and in the vertical plane the figures are still model figures.

Also phrased as: "the arrow settles after the first few metres"; "the arrow wobbles in flight"; "arrow porpoising"; "arrow oscillation in flight"; "the arrow groups better far than near"

Evidence

• 2011
  For Equipment tests Published later

  A model of the arrow as a flexible beam in the horizontal plane, checked against paper tests at several distances on Protour 470 arrows shot from a compound by a shooting machine at 78.9 m/s; the bow was deliberately tuned to exaggerate the lateral oscillation. The arrow oscillates about its centre of mass with a period of about 21.8 m (0.28 s) and a damping time constant of 0.34 s, about 25.8 m of flight; with Titeflight vanes 24% larger the period falls to 19.4 m and the damping increases. The tears measured in the paper match the calculated ones satisfactorily. Paper tests by several compound archers of the Australian national team also agree with the model in both planes, although the author cannot rule out that they were twisting the bow. The oscillation measured with the machine is in yaw rather than pitch, but the mechanism is the same.

  Arrow behaviour in free flight · J L Park

• 2014
  Context Equipment tests Published later

  In a wind tunnel, on a 2:1 scale model arrow at 30 m/s, the pitching moment stays negative from 0 to 16 degrees of incidence while the lift rises: the arrow tends to realign itself with the airflow, which is the condition for it to oscillate. It measures static stability, not oscillation in flight, and the venue is flagged as questionable.

  Experimental Hydro- and Aerodynamics Research on Arrow Questionable venue · Xiao An Long

• 2016
  For Model Published later

  An A/C/E arrow with a bullet point and Spin Wing or Gas Pro vanes, fired by compressed air at 60 m/s; the initial attitude comes from four cameras at 3,000 frames per second and the coefficients from a magnetic suspension wind tunnel. In the calculation the angle of attack oscillates and dies away almost entirely in the vertical plane; with ideal launch conditions it stays close to 0 degrees and the air layer stays laminar. In the same work the dynamic test in the tunnel finds the damping term small enough to be neglected. The oscillation is calculated, not measured in flight.

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

• 2017
  For Model Published later

  Simulation of the flight of an A/C/E arrow launched at 60 m/s, with lift and moment coefficients measured in a magnetic suspension wind tunnel and turbulent drag: the angle of attack oscillates in the vertical plane at 3.95 Hz with Spin Wing vanes and 3.28 Hz with Gas Pro vanes, roughly one cycle every 15 to 18 m, and the amplitude falls by 0.92 and 0.68 per second. The authors note that the frequencies are close to those of the 2011 study and the damping slower, perhaps because the model does not let the shaft flex. The oscillation is calculated.

  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
  For Model Published later

  Simulation of the flight of a 14 g A/C/E arrow over 70 m, launched at 57.3 m/s, with coefficients measured in the wind tunnel and in free flight. The angle of attack oscillates at 3.59 Hz with a 3 m/s crosswind, 4.09 Hz with a headwind and 3.50 Hz with a tailwind, and the amplitude falls by 0.87 per second through the effect of the vanes. The waviness of the trajectory is evident over the first 20 m, the first 0.40 s of a flight lasting under 1.3 s, and then fades. With a 3 m/s crosswind the maximum angle reaches 3.0 degrees. The arrow is treated as a rigid body, with no flexing.

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

• 2019
  For Review Published later

  A narrative review of outdoor target archery. Summarising the author's own free-flight model, it reports that fletched arrows oscillate in pitch or yaw about their centre of mass with a period corresponding to about 20 m travelled, that the calculated period matched the measured one, and that the moment comes mainly from the lift of the vanes, which act on a far longer lever arm than the drag does. It does not report the measurement data.

  The impact of the atmosphere on target archery · James L Park

• 2020
  Context Equipment tests Published later

  A/C/E 1206 arrows with straight vanes, fired by compressed air over 55 m indoors with a 200 Hz inertial sensor inside the shaft. In a shot at 56.4 m/s, with 1.04 s of flight, the average deceleration is 0.65 G up to 0.40 s and about 0.30 G after 0.45 s, which the authors read as the return to laminar flow once the calculated angle of attack drops below 0.3 degrees, from a maximum of about 0.36. In the calculation the angle oscillates at 4 Hz with the small vanes and 5.3 Hz with the large ones. What is measured is drag, not the oscillation.

  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

• 2020
  For Equipment tests Published later

  In the paper on wind drift the author reports a paper test at several distances with a Protour 380 shot from his compound, which launches that arrow at 78.9 m/s: the measured oscillation has a frequency of about 3.7 Hz, the same as the model, which gives it a damping time of 0.49 s. At that speed this is about 21 m per cycle. The author warns that the flexing of the shaft makes the measurement approximate.

  The dynamic behaviour of an arrow in wind · James L Park

• 2022
  Context Equipment tests Published later

  Automatic analysis of footage at 3,000 frames per second on A/C/E arrows fired by compressed air at 40 to 60 m/s in a 55 m hall: measured angles of attack under 1 degree and angular velocities under 0.5 rad/s over the filmed stretch. Using those data as a starting point, the calculation gives a maximum angle of attack of 0.46 or 0.51 degrees with a streamlined point and 0.44 with a bullet point. It measures the attitude near the launch, not the oscillation along the flight.

  Automatic image analysis of an archery arrow in free flight using high-speed video cameras · Riku Murakami, Hiroya Mamori, Takeshi Miyazaki, Naoya Takahashi

Status history

1. 2011 Reported The first data already include a measurement. A model treating the arrow as a flexible beam is checked against paper tests at several distances on Protour 470 arrows shot from a compound by a shooting machine at 78.9 metres per second: the arrow oscillates about its centre of mass with a period of about 21.8 metres, and the oscillation dies away over about 25.8 metres of flight; with vanes 24 per cent larger the period drops to 19.4 metres. The tears in the paper match the calculation. It is a single study, on a compound, and the oscillation measured is the one in the horizontal plane, which follows the same mechanism as pitching: reported.
2. 2014 Reported A wind tunnel test on a 2:1 scale model arrow finds the pitching moment negative throughout from 0 to 16 degrees of incidence: the arrow tends to realign itself with the airflow, which is the condition for it to oscillate. This is static stability, not oscillation in flight, and the journal is flagged as a questionable venue: the status does not change.
3. 2016 Reported The first calculation in the vertical plane arrives. Starting from the launch attitude measured with four cameras at 3,000 frames per second, on an A/C/E arrow fired by compressed air at 60 metres per second, the simulation shows an angle of attack that oscillates and dies away, almost entirely in the vertical plane; with a perfect launch the angle stays close to zero. It is the pitching the claim describes, but calculated and without a period: the status stays reported on the strength of the 2011 measurement.
4. 2017 Reported The same Japanese group puts a figure on the pitching of a recurve arrow. In the simulation at 60 metres per second, with coefficients measured in the wind tunnel, the angle of attack oscillates at 3.95 hertz with Spin Wing vanes and 3.28 with Gas Pro, roughly one cycle every fifteen to eighteen metres, and with the larger vanes it dies away sooner. The authors note that the frequencies are close to those of the 2011 study, while the damping is slower. It is a model, so the status does not change.
5. 2018 Reported More figures, again from a simulation with parameters taken from the wind tunnel and from free flight. At 57 metres per second the angle of attack oscillates 3.59 times per second in a crosswind, 4.09 in a headwind and 3.50 in a tailwind, roughly one cycle every fourteen to sixteen metres, and the amplitude falls by 0.87 per second thanks to the vanes. The waviness of the trajectory shows mostly over the first twenty of the seventy metres, the first four tenths of a second of a flight lasting under 1.3. It is the picture the claim describes, but calculated: the status does not change.
6. 2019 Reported A review gives the round figure: fletched arrows oscillate in pitch and yaw about their centre of mass with a period corresponding to about twenty metres travelled, and the calculated period matched the measured one. It is the author of the 2011 measurement summarising his own work, and a review does not decide the status: reported.
7. 2020 Reported Two papers in the same year. An inertial sensor inside the shaft, on arrows fired by compressed air at 56.4 metres per second over 55 metres indoors, records an average deceleration of 0.65 G over the first four tenths of a second and of about 0.30 G after forty-five hundredths, which the authors read as the airflow turning laminar again once the calculated angle of attack drops below three tenths of a degree: it is consistent with an oscillation dying away over the first stretch, but what it measures is drag. The same year the author of the 2011 tests repeats the paper test at several distances with a Protour 380 from his compound and finds about 3.7 hertz, the frequency of his model, roughly one cycle every twenty-one metres. The direct studies become two, but they come from the same researcher, with the same instrument, on a compound and in the horizontal plane, and the author himself warns that the flexing of the shaft makes the test approximate: that is not enough for corroborated, and the status stays reported.
8. 2022 Reported Automatic analysis of high-speed footage measures the arrow's attitude over the stretch covered by the cameras: angles of attack under one degree and angular velocities under half a radian per second, and in the calculation built on them a maximum angle of 0.44 to 0.51 degrees. It confirms that the oscillation is small, but measures neither its period nor its damping along the flight: the status stays reported.

Related

Related articles

• Fishtailing and porpoising: what arrow flight saysDoes your arrow wag sideways or wave up and down? What causes fishtailing and porpoising, which to fix first, and how to confirm it with a bare shaft test.
• The archer's paradox: the physics of the flexing arrowAt full draw the arrow points to one side and still reaches the centre: how it flexes and clears the riser in the first twenty milliseconds, and how spine matches it to the bow.
• Vanes, feathers or Spin Wings: what actually changesLarge or small vanes, feathers or plastic, vane angle and orientation on the shaft: what the studies measure, and where research has not yet reached the target.

Research lines

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

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