During the release the arrow buckles under the load on its point

The summary today

The models have agreed since 1997 that the string's thrust compresses the arrow and makes it flex more; none of the available calculations has it pushing the arrow past the instability threshold. The model that put figures on the phenomenon places the loss of stability at a dimensionless force of 14.79 and the peak thrust of an average target bow and arrow at 12.3: above the threshold of the static column test, 9.87, but below the one that applies in the shot. The only estimate on real equipment, a compound with a spine 500 arrow, gives a peak axial load of about 60 newtons against a critical load of about 100, a little over half the threshold. A second model by the same author writes in its conclusions that the launch is characterised by instability, but the arrow it uses for verification sits at 5.28, well short of the threshold of 15. The aluminium kyudo shafts tested on the bench give way at 50 and 65 newtons, far below the force of their bows, through instability rather than because the material is overloaded, but in the case where the point slips behind the bow and the arrow is trapped, not in a normal launch. The evidence therefore goes against the claim, but it is scant and indirect: an estimate on a single bow, with the models pointing the same way without measuring anything. The margin shrinks with more draw weight, more point weight, and longer or weaker shafts, and nobody has instrumented an arrow during a shot close to the limit.

Also phrased as: "the arrow bends under the string's thrust"; "axial load on the arrow"; "the arrow flexes like a column"; "an arrow too weak goes unstable on release"; "arrow buckling at release"

Evidence

• 1997
  Context Model Published later

  A model of the archer's paradox on a 30 lb recurve, compared with high-speed footage: the large longitudinal force the string exerts on the nock has a buckling effect and increases the arrow's bending, and the axial force in the shaft slows the frequency of its oscillation. According to the authors, though, the oscillation starts from the displacement forced on the nock during release, and what matters is the transverse forces, the lateral flexibility of the bow and the push of the pressure button. It does not calculate instability thresholds.

  On the mechanics of the arrow: Archer's Paradox · B.W. Kooi, J.A. Sparenberg

• 1998
  Context Model Published later

  A model of a competition recurve with an Easton X7 1714 arrow, compared with footage of a single shot: taking into account the longitudinal compression due to acceleration, the arrow flexes more than in the earlier model that left it out, because of the rather large initial normal force tied to the thrust. It does not calculate instability thresholds.

  Bow-arrow interaction in archery · B. W. Kooi

• 2001
  Context Model Published later

  A mathematical model of the archer-bow-arrow system: the arrow loses stability, with its oscillations turning into a bend that grows in one direction, when the dimensionless compressive force reaches 14-15 (14.79 in the exact solution), whereas in the static column test the first threshold is 9.87, a third lower. With the average values of target bows, 180 N of draw weight, a 700 mm arrow of 20 g, stiffness 4 Nm², the peak thrust is 12.3: above the static test threshold, below the bow-arrow system's. The model contains no new measurements.

  Lateral deflection of archery arrows · Zanevskyy

• 2009
  Context Model Published later

  A model of an average-sized Olympic bow and an aluminium arrow: instability appears at a dimensionless acceleration of 14.79 with the one-node shape and 56.47 with the two-node one (exact solution; about 15 and 65 in the simulations), and the shaft's frequencies fall as acceleration rises. The experimental check uses a 712 mm arrow filmed at high speed, for which the dimensionless acceleration is 5.28, well below the first threshold, even though the conclusions speak of instability as a defining feature of the launch.

  Modeling of the Archery Bow and Arrow Vibrations · I. Zaniewski

• 2015
  Against Equipment tests Published later

  A compound and a spine 500 carbon arrow 0.696 m long, with a measured stiffness equivalent to spine 492: of the force accelerating the arrow, the share needed to push the point, which therefore compresses the shaft, is estimated at about 30 per cent, a peak axial load of about 60 newtons. The Euler critical load calculated from the measured stiffness is about 100 newtons, so the arrow works at a little over half the threshold, a margin the author judges acceptable. More draw weight, more point weight, a longer or weaker shaft bring the threshold closer, and with spine above 800 failure is expected. It is an estimate derived from the measured force, not a measurement of the load on the shaft, in a preprint without peer review.

  Applications of Physics to Archery · H. O. Meyer

• 2019
  Context Equipment tests Published later

  A review of the atmosphere's effect in target archery: during the bow's power stroke the arrow undergoes a peak acceleration of around a thousand g. It gives a measure of how violent the thrust is, and says nothing on whether the arrow exceeds the instability threshold.

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

• 2024
  Context Equipment tests Published later

  Static and dynamic compression tests on two aluminium kyudo shafts cut to 850 mm: they give way end-on at about 50 newtons (shaft A, for bows from 98 newtons up) and 65 newtons (shaft B, from 147 up), against 46.8 and 62.2 newtons from the Euler formula and 46.7 and 62.0 from finite elements. A real shaft's critical load therefore sits far below the bow's force, but the study concerns the case where the point slips behind the bow and the arrow is trapped between string and bow: it does not measure the load during a regular launch. In the dynamic test the initial compressive peak gives a stress of about 30 megapascals, against the roughly 500 of the proof stress of 7000 series aluminium alloys: the shaft does not give way because the material is overloaded but through instability, and it snaps in two at the middle as in the static test.

  Buckling Fracture Behavior of Duralumin Arrows used for Japanese Archery · Masahiro Suetsugu, Kaori Shirakihara, Minoru Tamiaki

Status history

1. 1997 Not studied The first model to mention the end load treats it as an amplifier: the string's force on the nock increases the arrow's bending and slows the shaft's oscillation, but the oscillation starts from the nock's displacement at release and from the transverse forces. Whether the arrow crosses an instability threshold is not asked: there is still no evidence for the claim.
2. 1998 Not studied A model of the interaction between bow and arrow, by the same author, shows that the compression along the shaft, caused by the string's thrust, makes the arrow flex more than the models that left it out predicted. It says the end load matters, not whether it drives the arrow into instability: the question, in these terms, has not yet been asked.
3. 2001 Not studied A model of the bow-arrow system calculates the threshold: the arrow loses stability when the dimensionless force reaches 14 or 15, 14.79 in the exact solution, a third higher than the threshold of the classic column test on an isolated shaft, 9.87. For the average target bow and arrow the peak thrust is 12.3, above the static test threshold but below the one that applies in the shot. In the calculation the arrow gets close to instability without entering it, but it is a model with no new measurements, and on a real arrow the question has not yet been measured.
4. 2009 Not studied A second model by the same author finds two thresholds again, around 15 for the one-node bending shape and between 56 and 65 for the two-node one, and shows the shaft's frequencies falling as the arrow accelerates. In its conclusions it writes that the joint motion of bow and arrow is characterised by instability, but the filmed arrow used to verify the model sits at a dimensionless acceleration of 5.28, far from the first threshold. There are still two models by the same author, and a measurement on real equipment is still missing.
5. 2015 Contradicted The first estimate on real equipment arrives, a compound with a spine 500 arrow: from the force measured during the thrust the peak axial load is about 60 newtons, against a Euler critical load of about 100 calculated from the shaft's measured stiffness. The arrow stays below the threshold, with a margin the author judges acceptable, and the threshold would come closer with more draw weight, more point weight, and longer or weaker shafts: beyond spine 800 failure is expected. It is the first evidence on equipment, an estimate on a single bow that points the same way as the models: contradicted.
6. 2024 Contradicted A bench test on two aluminium kyudo shafts measures the end load at which they give way, about 50 and 65 newtons, far less than the force of the bows they are meant for, 98 and 147 newtons, and the Euler formula reproduces them within a few percentage points. The case studied, though, is the one where the point slips behind the bow and the arrow is trapped between string and bow, not the normal launch. The threshold of real shafts is now measured, but nothing shows an arrow exceeding it in a regular shot: contradicted.

Related

Related articles

• 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.
• When to retire an arrow, and why a shaft snaps on releaseWhich knocks damage an arrow, why a shaft snaps on release, and what the tests say about straightness, wear and defective arrows.

Research lines

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

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