At release the string tension rises well above the draw weight

The summary today

Three models of the bow say so, and nobody has measured it: in 1981 the author of the second wrote that no experimental data existed on string tension when the arrow leaves. The 1937 calculation for a yew bow finds that at the loose the tension dips slightly and then rises, the more so the heavier the limb tips, to the point that a fully inextensible string would break. The 1981 model, which lets the string stretch, gives the most useful figure: when the arrow leaves, 369 newtons on a bow that weighs 175 newtons at full draw, that is 2.1 times the draw weight, against 3.7 times in the model with a rigid string. With the rule of thumb that a string should hold four times the draw weight, the safety margin is 1.9 in the first case and 1.1 in the second. The 2009 compound model finds string and cable tensions that rise at the end of the power stroke to many times the peak draw weight, and grow as the arrow gets lighter. All three point the same way; how far the tension rises depends on how much the string stretches, which is exactly the part nobody has measured.

Also phrased as: "peak string tension"; "dynamic string tension"; "string load at release"; "dry fire and string"; "string safety factor"

Evidence

• 1937
  For Model Published later

  Dynamic model of a yew bow with an inextensible string: at the loose the dynamic string tension dips slightly and then begins to rise, and heavier limb tips make it rise further. The author writes that if the string could not stretch a little, that tension would break it. Curves only, no values.

  The Dynamics of A Bow and Arrow · C. N. Hickman

• 1981
  For Model Published later

  Analytical model of a longbow of 175.2 N (39 pounds) at full draw with an elastic string: string tension when the arrow leaves is 369 N, 2.1 times the draw weight, against 653 N and 3.7 times with an inextensible string; static tension is 260 N at brace and 205 N at full draw. With the rule that a string should hold four times the draw weight, the safety margin is 1.9 with the elastic string and 1.1 with the rigid one. The author writes that no measurements of string tension at arrow exit exist; the ratio of about two reported by another source does not say how it was obtained.

  Bow and arrow dynamics · W. C. Marlow

• 2009
  For Model Published later

  Dynamic model of a single-cam AR34 compound: in the last part of the power stroke string and cable tensions rise sharply, to many times the peak static draw weight. The author adds that the real elasticity of the string would lower those peaks, which nevertheless remain substantial and grow as the arrow gets lighter. Graph only, no values.

  A compound archery bow dynamic model, suggesting modifications to improve accuracy · J L Park

Status history

1. 1937 Transferred The first dynamic model of the bow, for a yew bow with the string treated as inextensible, finds that at the loose the string tension dips slightly and then begins to rise, the more so the heavier the limb tips. The author adds that if the string could not stretch a little, that tension would break it. It is a calculation with qualitative curves and no values: transferred.
2. 1981 Transferred A model that allows for the elasticity of the string gives the first figure: when the arrow leaves, the tension is 369 newtons on a bow of 175 newtons, 39 pounds, at full draw, that is 2.1 times the draw weight, a little over half the 653 newtons predicted with a rigid string. The value agrees with the only indication cited, a ratio of about two reported without saying how it was obtained, and the author writes that no actual measurements exist. With the rule that a string should hold four times the draw weight, the safety margin is 1.9. It is still a calculation: transferred.
3. 2009 Transferred A dynamic model of the compound finds that in the last part of the power stroke string and cable tensions rise to many times the peak draw weight, and that the peaks grow as the arrow gets lighter; the author adds that the real elasticity of the string would lower them while leaving them substantial. Three models in agreement, two on the same yew longbow and one on the compound, and no direct measurement: transferred.

Related

Research lines

• 22 studiesHow much energy passes from bow to arrow: models and measurements since 1937
• 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

See all claims on equipment and tuning