Material testing: how shafts, limbs and woods are bent, vibrated and fatigued

Three questions for a test bench

Studies put three questions to the material of a piece of equipment. The first is how far it bends under a load: the piece rests on two supports and is loaded in the middle, which is three-point bending, and on arrows it gives the spine. The second is how it vibrates: it is set oscillating and the frequency is read, along with how quickly the oscillation dies away. The third is whether it changes with use, and a load is repeated for hundreds of thousands of cycles before the first two tests are run again. Alongside these come tension, which gives the elastic modulus, and compression, which shows when a shaft buckles.

Spine and three-point bending

The spine test hangs 880 grams from the middle of a shaft supported 711 mm apart and reads how far it bends: a ProTour 380 deflects 9.652 mm, or 380 thousandths of an inch. A physicist at Indiana University measured the same bending in his own way, with the shaft on two blades 0.550 m apart, weights hung from the middle and a dial gauge, and by converting the stiffness arrived at a spine of 492 against the 500 on the label.

The most elaborate bench belongs to Kuch and colleagues: one actuator loads the shaft in the middle, another rotates it, an optical sensor reads to two thousandths of a millimetre, and each shaft is bent 64 times over at least four turns. On 59 X10 shafts of spine 325, stiffness almost always follows a wave with two peaks and two troughs per turn, with an average amplitude of 0.014 mm on a deflection of 8.290 mm. This is the basis of the entry on spine that changes around the shaft, "reported". The bench reads a shaft at rest, though, as the authors point out: when shot, the arrow bends under the push of the string.

That is the limit of the spine test in general. To make their figures match on three competition shafts, Rieckmann and colleagues had to raise the stiffness at both ends of their model, where the nock pin and the point shank go in, while the static test reads a single deflection in the middle. So far only models say that static spine is not enough to predict how an arrow behaves when shot, and the entry on static and dynamic spine is "transferred".

Making the arrow vibrate

For vibration, what matters is how the shaft is held. In 2011 Park held it at a node and read the frequency with a stroboscope: 74, 77 and 80 hertz for three compound ProTour shafts, from the weakest to the stiffest. In 2012 Rieckmann's laser vibrometer, with the shaft free, found eight bending modes, the second at three times the first; three specimens of the same model agreed on the first mode with a standard deviation of 0.4 hertz, which rose to 12.5 and 16.5 at the eighth. The Indiana physicist excited the arrow with a coil: 84.8 hertz and a quality factor of 400, meaning about a second and a half for the oscillation to fall to just over a third of its starting amplitude. These measurements carry the entries on frequency rising with spine, on higher modes and on the arrow still vibrating at the target, all "reported".

The 2019 bench built by Fish and colleagues as a university course project clamps the shaft at both ends and shakes it in the middle. Frequencies drop to between 31.3 and 40.8 hertz, against 80-100 for a free shaft, so between laboratories it is the order that can be compared, not the value. The same bench cannot tell a carbon 500 from a 600, and within a single spine it gives stiffness values that vary by 14 to 22%. Damping comes out between 0.32 and 0.67, and at 0.32 the amplitude falls to 12% within a single cycle, whereas a free arrow keeps flexing for many cycles: the registry reads the figure as the damping of the clamps and the actuator more than of the shaft. That one bench is all that supports the entry stating that carbon damps less than aluminium and wood, "reported".

Limbs and risers

The Korean group led by Heo tested three carbon prepregs from three suppliers, with the same fibre and the same declared resin content, using the ASTM standards for tension, three-point bending and compression, five specimens per group: in tension they are alike, in bending and compression they are not. The values appear only in graphs, and the table and the caption assign the labels to two different companies. Then came an accelerometer on a 68.42 lb limb, four shots per condition and no standard deviation: with glass fibre in place of Bakelite, vertical vibration falls from 500 to 280 m/s². Both the entry on prepregs from different suppliers and the one on limb material are "reported".

The lightweight riser of Edelmann-Nusser and colleagues shows where testing ends and calculation begins. Bending tests, spectroscopy and microscopy were used to characterise the alloy of a Radian, the reference riser, to feed the model; the new riser, once built, was weighed, 871 grams against 1,114; its deflection, 1.94 against 1.85 mm, comes from the model. Nobody loaded the actual piece, and the entry on the lighter riser remains "transferred".

Woods and bamboo

On the Kyoto bow, Hamada tested the pieces a master bowyer had chosen for the two faces. Over a 400 mm span the inner bamboo was stiffer than the outer, with 18% hard fibre against 9, while over 80 mm the difference did not show: the span chosen decides what can be seen. The entries on the stiffer inner bamboo and on the core woods are "reported", resting on one bowyer's pieces, an undeclared number of specimens and values given only in graphs.

The largest sample is an analysis rather than a test: George gathered the modulus of rupture and elastic modulus of 431 samples from 326 species out of public databases. The modulus of rupture, however, comes from a single load to failure, not from the repeated bending a bow goes through with every shot, and within a species the properties vary by up to 30%. The entries on woods suited to bows and on Australian timbers are "reported".

Compression and fatigue

Suetsugu and colleagues compressed two models of duralumin kyudo shaft in a universal testing machine: they gave way at about 50 and 65 newtons, close to the 46.8 and 62.2 of the buckling formula, at a stress far below the yield point of the alloy, so the shaft breaks because it bends. The paper does not say how many shafts were tested, and the entry on the buckled shaft is "reported".

Fatigue is the rarest test, and the only one is again the 2019 bench: one arrow per material, about 600,000 cycles, one measurement afterwards. All of them come out stiffer, the carbon shaft from 486 to 737 newtons per metre, but its estimated mass drops from 10.3 to 9.0 grams, which an intact shaft does not do, and no control arrow was measured a second time. The entry on arrow fatigue is "contradicted", with little weight. The Korean study starts from the delamination of limbs but runs no cycles: no limb has been fatigue-tested.

What to check

• how the shaft is held, free, at a node or clamped: absolute values can only be compared under the same constraint;
• the span between the supports and the loading rate;
• how many pieces per condition, and whether a standard deviation is given;
• whether the figure was measured on the piece or calculated by a model, and whether the bench was calibrated;
• whether anyone then shot those pieces and recorded where they landed: only the study of the 59 X10 shafts did, with a machine at 70 m, and mean spine and wave amplitude explained 19% of the horizontal position.

How design and sample size are weighed is explained in How we read a study; what spine does when the arrow is shot, in the article on the archer's paradox and in the research line on arrow dynamics.

@misc{campagna2026_enresearchmethodsmaterialtestingbendingf,
  author = {Campagna, Matteo},
  title = {Material testing: bending, vibration, fatigue},
  year = {2026},
  howpublished = {Research, matteocampagna.com},
  url = {https://matteocampagna.com/en/research/methods/material-testing-bending-fatigue},
  note = {accessed 2026-10-16}
}