In the Japanese bow draw force does not rise steadily through the draw

The summary today

That the yumi's force-draw curve is not a straight line is stated by two models from the same authors, and by no measurement of the curve on a real bow. The first, in 2017, treats the bow as a flexible beam under large deflection and checks it on a strip of PVC: at first the deflection rises quickly, then it almost stops even as the force goes up. The second, in 2019, splits a commercial 4.2 kg shihan-yumi into nine sections, each with its own curvature and stiffness, and finds a three-stage curve: force rises quickly at first, slows in the middle and climbs again towards the end, and the pattern becomes more marked the more the central sections curve outwards. On that bow the model reproduces the measured shape well, but the force curve is calculated, not measured. On the other side there is no contrary measurement: a 2001 experiment on bowstrings treats a glass-fibre kyudo bow as a linear spring between zero and 80 centimetres, but that is the assumption behind its energy calculation, not a curve it shows. Three replicas of Western traditional bows, measured on a dynamometer in 2018 up to 50 centimetres, give nearly straight curves instead: the yumi, if the models are right, behaves differently.

Also phrased as: "yumi force-draw curve"; "the yumi stiff at the start and the end"; "draw weight of the Japanese bow through the draw"; "kyudo bow and draw curve"; "stacking in the Japanese bow"

Evidence

• 2001
  Context Equipment tests Published later

  In an experiment on bowstrings with 10 university kyudo archers, the glass-fibre test bow is treated as a linear spring between 0 and 0.8 metres of draw, with a spring constant of 198.6 newtons per metre. The authors use it to calculate stored energy: it is a working assumption, and the curve is not shown.

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

• 2013
  Context Equipment tests Published later

  Bench test on a carbon-fibre yumi: at 700 millimetres of draw from the string's resting position, that is 850 from the grip, the measured horizontal force is 300 newtons, about 31 kg. It is a single point, not a curve.

  Motion Analysis of the Japanese Bow for Archery · Hajime Shoji, Shinya Hashimoto, Toshiaki Sakurai, Ikuo Hibino

• 2017
  For Model Published later

  Model of the Japanese bow as a flexible beam under large deflection (elastica theory), checked on a 300 millimetre PVC strip, elastic modulus 3.40 gigapascals, with strings from 210 to 450 millimetres: good agreement between theory and experiment, and a deflection at the nocking point that rises quickly at first and then almost stops even as the force increases.

  Analysis of Nonlinear Deformations in Japanese Bows (Application of Elastica Theory) · Atsumi Ohtsuki, Shigemichi Ohshima

• 2018
  Context Equipment tests Published later

  Three replicas of Western traditional bows (recurve horse bow, flatbow, English longbow) measured on a dynamometer up to 50 centimetres: nearly linear force-draw curves, with coefficients from 0.2498 to 0.3001. The yumi does not appear in the study: it serves only as a point of comparison.

  An Interactive Haptic System for Experiencing Traditional Archery · Silviu Butnariu, Mihai Duguleană, Raffaello Brondi, Florin Gîrbacia, Cristian Postelnicu, Marcello Carrozzino

• 2019
  For Model Published later

  Nine-section large-deflection model built on a 4.2 kg shihan-yumi, 164 centimetres, 157 centimetre string: force rises quickly at first, slows in the middle and climbs again towards the end, and the three-stage pattern becomes more marked the further the central sections curve outwards. The force curve is calculated, not measured.

  Nonlinear Dynamic Analysis of a Japanese bow (Nonlinear Spring Characteristics and Dynamic Behavior) · Atsumi Ohtsuki, Shigemichi Ohshima

• 2019
  Context Equipment tests Published later

  On the real bow, loaded with weights through a pulley, tip displacements and angles read off a millimetre grid and a protractor agree well with the calculated ones: the check covers the bow's shape under load, not the force curve.

  Nonlinear Dynamic Analysis of a Japanese bow (Nonlinear Spring Characteristics and Dynamic Behavior) · Atsumi Ohtsuki, Shigemichi Ohshima

Status history

1. 2001 Not studied The first study in the bibliography to touch on yumi draw force is an experiment on bowstrings with ten university kyudo archers, and it treats the glass-fibre test bow as a linear spring between zero and 80 centimetres of draw, with a spring constant of 198.6 newtons per metre. That is the assumption the authors use to calculate stored energy, not a curve they measured and show, so it says nothing about the shape of the curve: the question has not yet been studied.
2. 2017 Transferred A model of the Japanese bow as a flexible beam under large deflection, solved with elastica theory and checked on a 300 millimetre PVC strip with strings from 210 to 450, finds a strongly non-linear relationship between load and deflection: deflection rises quickly at first and then almost stops even as the force increases. Theory and experiment agree well, but the model is a symmetric beam and the test is on plastic, not a bow: transferred.
3. 2018 Transferred A point of comparison arrives, not a measurement on the yumi: three replicas of Western traditional bows, a recurve horse bow, a flatbow and an English longbow, taken on a dynamometer up to 50 centimetres of draw, give nearly straight force-draw curves. It shows that what the models find for the Japanese bow is not something all traditional bows share, but it adds nothing on the yumi itself: the status holds.
4. 2019 Transferred The same authors take the model to a real bow: a commercial 4.2 kg shihan-yumi, 164 centimetres long with a 157 centimetre string, split into nine sections with measured curvatures and stiffness. The calculated shape under load matches the measured one well, and the force curve comes out in three stages: it rises quickly at first, slows in the middle and climbs again towards the end, all the more so the further the central sections curve outwards. The experimental check, though, covers the shape, while the force curve remains calculated: it is still a model, and the status does not change.

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