Arrows with a stiffer spine vibrate at a higher natural frequency

The summary today

The measurements all point the same way, and mechanics says why: a stiffer shaft, at equal mass, vibrates faster. Three compound arrows from the same series, measured with the shaft free, vibrate at 74, 77 and 80 hertz from the weakest to the stiffest, and a second study with a laser vibrometer finds the same order, 78.3, 80.2 and 83.3 hertz. An independent group, with carbon, aluminium and cedar shafts, finds the stiffer spine higher in every material, with one pair where the difference lies within the uncertainty. The status stays reported for three reasons. The two most precise measurements come from the same group and the same arrow series, and the third study is a course project with an uncalibrated rig. In no test does spine change on its own: the stiffer shafts are also heavier, and the only comparison that varies stiffness alone, plus 20 per cent with the frequency going from 85.4 to 95 hertz, is calculated with a model. Finally, the step from one spine to the next is worth a few hertz, less than 3 per cent, and a more powerful bow lowers the arrow's frequency during launch: nobody has shown that measuring it helps in choosing the shaft.

Also phrased as: "arrow vibration frequency"; "spine and natural frequency"; "a stiff arrow vibrates faster"; "measuring dynamic spine"; "dynamic spine"

Evidence

• 2001
  For Model Published later

  In the model of the bow-arrow system the arrow's natural frequencies grow with the shaft's bending stiffness and fall with mass, in simulations with stiffnesses from 2.73 to 5.96 Nm². They also fall when the bow is more powerful, because the thrust compresses the shaft: the frequency during launch is not a property of the arrow alone.

  Lateral deflection of archery arrows · Zanevskyy

• 2011
  For Equipment tests Published later

  Three Easton ProTour compound arrows of 0.715 m with a 120 grain tungsten point, free bending frequency measured with a stroboscope holding the shaft at a node: 74 Hz for the 470, 77 for the 420, 80 for the 380, that is from the weakest to the stiffest, in agreement with the model's 75.2, 77.5 and 80.0 Hz. At 78.2 m/s the arrow completes a little under one bending cycle per metre travelled.

  The Behaviour of An Arrow Shot from a Compound Archery Bow · J L Park

• 2011
  Context Equipment tests Published later

  The stiffer shafts are also the heaviest: 23.0 g the 470, 23.7 the 420, 24.4 the 380, with about a third of the weight in the point. The extra mass pulls the frequency down, so spine is not isolated from mass, and the frequency still rises with stiffness.

  The Behaviour of An Arrow Shot from a Compound Archery Bow · J L Park

• 2012
  For Equipment tests Published later

  Three models of carbon-on-aluminium competition arrow, Easton ProTour 380, 420 and 470, 710 mm long, three specimens each, measured with a scanning laser vibrometer with the shaft free: first bending mode at 83.3, 80.2 and 78.3 Hz (± 0.4) from the stiffest to the weakest. The authors put the step from one model to the next at less than 3 per cent, and note that the shafts also differ in mass and geometry. The two numerical models predict the frequency within 2 per cent, the mode shape within 3 and the nodes within 5 mm.

  Modelling the three-dimensional vibration of composite archery arrows under free–free boundary conditions · Marianne Rieckmann, James L Park, John Codrington, Ben Cazzolato

• 2012
  Context Archers Published later

  In high-speed footage of 16 world-class recurve archers the first bending mode of the arrows in free flight lies between 80 and 105 Hz, with 13 arrows out of 16 between 80 and 87, nearly all Easton X10. It gives the real range of competition arrows, not a comparison between spines.

  High-speed video analysis of arrow behaviour during the power stroke of a recurve archery bow · James L Park, Oliver Logan

• 2015
  For Model Published later

  On a spine 500 carbon arrow the measured fundamental frequency is 84.8 ± 0.1 Hz, and a finite element model calibrated on that arrow reproduces it at 85.4. With the same model, stiffening the shaft by 20 per cent, like going from spine 500 to 400, takes the frequency to 95.0 Hz, 12 per cent more, and shortening it by 5 cm to 96.0 Hz, 13 per cent more. It is the only comparison that changes stiffness alone, but it is calculated, not measured.

  Applications of Physics to Archery · H. O. Meyer

• 2015
  Context Equipment tests Published later

  A shooting robot with a competition recurve: the way the fingers open at release does not change the arrow's bending frequency, between 83.68 and 88.47 Hz across the four release conditions, against 86.82 (SD 2.27) with a female archer. The frequency depends on arrow and bow, not on the release; it does not compare different spines.

  2A2-T08 Development of Archery Robot : Development of finger mechanism for controllable the bending vibration · Jun Wakatabe, Chisato Kanamori, Ryu Ando, Takeshi Miyazaki

• 2019
  For Equipment tests Published later

  Laboratory dynamic identification, with an actuator perturbing the shaft clamped at both ends, on carbon, aluminium and cedar shafts of different spines: carbon 300 at 40.3 ± 1.1 Hz against 34.5 ± 1.9 for the 500 and 35.3 ± 1.2 for the 600; aluminium 2219 at 40.8 ± 1.8 against 31.6 ± 1.5 for the 1916; cedar 405 around 37-38 against 31-32 for the 520. The stiffer spine vibrates higher in every material, the exception being carbon 500 and 600, which lie within the uncertainty. The authors warn that shafts of the same spine give widely different values and that the rig would need calibrating: it is a preprint that grew out of a course project.

  Dynamic Characterization of Arrows through Stochastic Perturbation · Ryan Fish, Youzhi Liang, Kyle Saleeby, Jonathan Spirnak, Mingxiu Sun, Xiang Zhang

• 2019
  Context Equipment tests Published later

  Clamped at both ends, the arrows vibrate between 31.3 and 40.8 Hz whatever the material, far below the 80-100 Hz measured with the shaft free: the clamping changes the absolute value, so figures from different laboratories cannot be compared with one another, only the order can.

  Dynamic Characterization of Arrows through Stochastic Perturbation · Ryan Fish, Youzhi Liang, Kyle Saleeby, Jonathan Spirnak, Mingxiu Sun, Xiang Zhang

Status history

1. 2001 Transferred The only indication is a calculation: in a model of the bow-arrow system the arrow's natural frequencies rise with the shaft's bending stiffness, fall with mass, and also fall when the bow is more powerful. No shaft has yet been set vibrating to check it, and with the model alone the claim is transferred.
2. 2011 Reported The first measurement arrives: three spines from the same series of compound arrows, measured with a stroboscope holding the shaft at a node, vibrate at 74, 77 and 80 hertz from the weakest to the stiffest, in agreement with the model. The same work notes that the stiffer shafts are also the heaviest, so spine is not isolated from mass. One direct test on equipment: reported.
3. 2012 Reported A second measurement, with a laser vibrometer and two numerical models, finds the same order on the same arrow series, 78.3, 80.2 and 83.3 hertz, and the model predicts the frequency within 2 per cent; the authors put the step from one spine to the next at less than 3 per cent. In the same year the arrows of sixteen world-class archers, measured in flight, lie between 80 and 105 hertz. There are two direct tests and they agree, but they come from the same group and the same arrow series, whose models also differ in mass: the status stays reported.
4. 2015 Reported On another arrow, in another laboratory, the measured frequency is 84.8 hertz, and a finite element model calibrated on that arrow calculates that stiffening it by 20 per cent, like going from spine 500 to 400, takes it to 95 hertz, and shortening it by 5 centimetres to 96: it is the only comparison that changes stiffness alone, but it is calculated. A shooting robot meanwhile shows that the way the fingers open does not change the arrow's frequency. No new measurement across spines: reported.
5. 2019 Reported The first comparison outside the group behind the earlier measurements, on carbon, aluminium and cedar shafts of different spines clamped at both ends: the stiffer spine vibrates higher in every material, the exception being carbon 500 and 600, which lie within the uncertainty, and the frequencies fall between 31 and 41 hertz because the clamping differs. It is a course project with an uncalibrated rig and shafts of the same spine that differ widely from one another: the direction is confirmed, the status stays reported.

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Research lines

• 29 studiesThe archer's paradox in research: from 1987 to today
• 12 studiesCompound mechanics: cams, limbs and symmetry

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

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