String material changes the bow's vibration after release

The summary today

There is a single measurement, and it concerns the Japanese bow. Ten university kyudo archers shot with four strings, Kevlar, Technora, Vectran and hemp, fifty shots per string, with strain gauges on the bow near the grip. The material changes how quickly the vibrations die away, not the frequency at which the bow vibrates: the spectra are almost identical with every string, while the logarithmic decrement of bending runs from 0.61 with Kevlar to 0.70 with hemp and that of twisting from 0.32 with Technora to 0.51 with hemp, with almost every pair different from the others. The exceptions show that the difference is not always clear-cut, since Kevlar and Technora damp twisting in the same way and Technora and Vectran damp bending in the same way. The archers notice, but only just: in the free comments after each shot hemp collects more remarks on vibration and impact than would be expected, with a chi-square of 12.69 against a threshold of 12.59, and Kevlar is left out of that analysis because it was the usual string of eight archers out of ten. The models explain why the question makes sense but do not answer it: in 1981 a calculation with an elastic string leaves 22 per cent of the energy in the string and limbs after the arrow leaves and predicts two vibration frequencies instead of one, and in 2007 a model of the recurve estimates that the peak force in the string comes just after the arrow leaves, at about seven times the draw weight, without counting the damping that the kyudo study measures. On a modern recurve or compound, with stabilisers and dampers, there are no measurements.

Also phrased as: "bowstring material and vibration"; "string material"; "string damping"; "hemp bowstring"; "string feel at release"

Evidence

• 1981
  Context Model Published later

  A model of the bow with an elastic string, compared with the classic inextensible-string model: after the arrow leaves, 22 per cent of the energy stays in the string and limbs, against 9 in the inextensible model, and that energy sets them vibrating. With the inextensible string there is a single frequency, 82 hertz ignoring the non-linear terms and 65.5 including them; with the elastic string there are two, 55 and 87 hertz. The string's elasticity changes the vibrations in the calculation, but no real string is tested.

  Bow and arrow dynamics · W. C. Marlow

• 1991
  Context Model Published later

  A simulation of the modern recurve: after the arrow leaves, the string vibrates with a large amplitude, which according to the author calls for a high brace height. The result is graphical only, with no values, and the string material is not varied.

  On the mechanics of the modern working-recurve bow · B. W. Kooi

• 2001
  For Kyudo archers Published later

  Four strings on a fibreglass Japanese bow, fifty shots per string: the logarithmic decrement of bending is 0.61 ± 0.01 with Kevlar, 0.64 ± 0.13 with Technora, 0.65 ± 0.14 with Vectran and 0.70 ± 0.11 with hemp; that of twisting 0.32 ± 0.06 with Technora, 0.35 ± 0.08 with Kevlar, 0.42 ± 0.07 with Vectran and 0.51 ± 0.06 with hemp. Almost every pair differs on the t test; the exceptions are Kevlar and Technora in twisting and Technora and Vectran in bending, which damp in the same way.

  BOWSTRING EVALUATION BASED ON Kansei ENGINEERING TECHNOLOGY · Satoshi Hosoya, Takashi Kawamura, Yosuke Horiba

• 2001
  For Kyudo archers Published later

  In the free comments collected after each shot, with hemp the remarks on vibration and impact exceed what would be expected, while with Vectran those on sound fall short: a chi-square with 6 degrees of freedom of 12.69 against a threshold of 12.59 (p < 0.05), residuals beyond 1.96. Kevlar is left out of the analysis because it was the usual string of eight archers out of ten.

  BOWSTRING EVALUATION BASED ON Kansei ENGINEERING TECHNOLOGY · Satoshi Hosoya, Takashi Kawamura, Yosuke Horiba

• 2001
  Context Kyudo archers Published later

  The frequency spectra of bending and twisting, computed with the Fourier transform, are almost identical for every string, archer and trial: the material changes the damping, not the frequency at which the bow vibrates. With every string, moreover, twisting is damped much less than bending, with decrements between 0.32 and 0.51 against values between 0.61 and 0.70.

  BOWSTRING EVALUATION BASED ON Kansei ENGINEERING TECHNOLOGY · Satoshi Hosoya, Takashi Kawamura, Yosuke Horiba

• 2007
  Context Model Published later

  In the mathematical model of a recurve the peak force in the string comes after the arrow leaves and is higher than at full draw: a first estimate is about seven times the draw weight. The author calls it conservative, because the model includes neither internal and external damping nor hysteresis, which is exactly what brings bow and string back to rest.

  Design and materials in archery · B.W. Kooi

Status history

1. 1981 Not studied A model of the bow with an elastic string shows that after the arrow leaves 22 per cent of the energy stays in the string and limbs, against 9 in the inextensible-string model, and that there are two vibration frequencies, 55 and 87 hertz, instead of one. The string's elasticity changes the vibrations in the calculation, but no real string has been tested and the model says nothing about damping: not studied.
2. 1991 Not studied A simulation of the modern recurve shows that after the arrow leaves the string vibrates with a large amplitude, enough for the author to call for a high brace height. The string material is not varied and no vibration is measured: the question remains not studied.
3. 2001 Reported A repeated-measures experiment on four strings, fifty shots each, with ten university kyudo archers: hemp damps faster than the synthetic strings both bending, with a logarithmic decrement of 0.70 against values between 0.61 and 0.65, and twisting, 0.51 against values between 0.32 and 0.42, and almost every pair comes out different. The vibration frequency, on the other hand, does not change with the material: what changes is how quickly the vibration dies away. The archers recognise the difference when they shoot with hemp, with a chi-square just above the threshold. A single study, and kyudo only: reported.
4. 2007 Reported A model of the recurve estimates that the peak force in the string comes after the arrow leaves, at about seven times the draw weight, and the author warns that the estimate is conservative because the model ignores damping. Damping is precisely the quantity the kyudo study found to differ from one string to another. The model adds no measurements: the status stays reported.

Related

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Research lines

• 22 studiesHow much energy passes from bow to arrow: models and measurements since 1937
• 29 studiesThe archer's paradox in research: from 1987 to today

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