Vibration in bow limbs: Heo 2023 study

A materials science study from Pusan National University, prompted by a workshop problem: competition limbs delaminate, and the Bakelite part that joins them to the handle loses durability over time. The vocabulary needs care, because the paper calls that part the "stabilizer", meaning the flat section at the base of the limb that attaches to the riser, not the rods in front of the bow.

The first part compares three carbon prepregs from three Korean suppliers for the body of the limb, measuring tensile, flexural and compressive properties to ASTM standards. The sample named as best, with the highest fibre volume fraction and the lowest resin content, comes out ahead in every test except tensile strength.

The second part replaces the Bakelite with a glass fibre laminate co-cured in an autoclave together with the carbon, and measures the vibration of a 68.42 pound limb during shooting, on three axes, with four repetitions. With Bakelite the mean acceleration is 500, 2000 and 1200 metres per second squared on the X, Y and Z axes. With the 1.5 millimetre glass laminate it falls to 280, 1500 and 800; with the lighter 1 millimetre version it rises slightly to 290, 1600 and 950, a reduction of 42% on the X axis, 20% on Y and 21% on Z compared with Bakelite. Averaged over both thicknesses the authors state reductions of 45, 25 and 33%.

The modal simulation in Catia gives, for the first three modes, 38.437, 126.87 and 156.82 hertz with Bakelite and 39.378, 135.53 and 162.71 with glass fibre. The glass laminate has a larger amplitude of its own on the first mode, but the damping curve is smoother, with less marked peaks and troughs.

The unidirectional carbon prepregs come from three Korean suppliers, with a resin content of 38%, while the outer skin of the limb uses a 3k plain weave fabric with 42% resin. The glass laminate is a 7628 fabric in two thicknesses, 1.0 and 1.5 millimetres.

The lay-up puts two unidirectional sheets at 45 degrees on the outside and, between them, the supplier's unidirectional prepreg at 90 degrees, twelve sheets in all; two maple veneers also go into the stack, bonded with epoxy. Everything goes into a vacuum bag in an autoclave for 120 minutes at about 8 kilograms per square centimetre of pneumatic pressure, after which the temperature comes down to about 30 degrees over 40 minutes using chilled water. The glass laminate and the carbon are cured in the same cycle, which is the technical point of the work.

The mechanical tests use an Instron 5882 universal testing machine: ASTM D638 for tension at 5 millimetres per minute on dog-bone specimens, ASTM D790 for three-point flexure at 2 millimetres per minute, ASTM D695 for compression at 1.3 millimetres per minute, with five specimens per group. Prepreg cross-sections were examined under an electron microscope.

The shape of the limb comes from a three-dimensional scan of a Win&Win limb, from which the moulds were designed in CAD. The structural simulation, run in Catia, applies a force at the curved tip and pulls it 50 to 100 millimetres, with the carbon properties stated as a Young's modulus of 1.35 by 10 to the eleventh newtons per square metre, a Poisson's ratio of 0.46, a density of 1600 kilograms per cubic metre and a yield strength of 1.3 by 10 to the ninth.

The vibration was recorded at 25 degrees with a TSVA-PRO receiver, Easton arrows and a Win&Win riser, measuring on three axes the vibration produced by shooting an arrow, with four repetitions per configuration. The paper does not say who or what drew and released the bow.

There is no archer in the results, no score, no group on the target, and the paper does not state who was shooting or whether a person or a machine was shooting at all. There are four repetitions per configuration, on a single limb, with no standard deviations and no statistical test: the reductions of 42, 20 and 21% are differences between means of four measurements.

Many numbers stay inside the figures. The tensile, flexural and compressive values for the three prepregs can only be read off the charts, so this record does not quote them. Worse, the supplier labels are inconsistent, because the materials table and the figure caption assign the codes to two different companies, which makes it impossible to say whose prepreg performed best.

Some figures cannot be read as printed. The autoclave pressure is given as "950 MPa" of vacuum, which is not a possible value. In the text on the simulation the amplitude percentages do not match the tables: one passage gives 28.36 and 24.26%, the next paragraph 6.58 and 73.57% for the same direction. The definition of the axes also shifts, with the X direction described as vertical in one place and as up and down in another. The accelerations of 2000 metres per second squared are reported without saying how the signal was filtered or integrated.

Finally the stated motivation, durability and delamination over time, is never tested: there are no fatigue cycles and no ageing, only static tests on specimens and four shots per configuration. The authors close by acknowledging that the quality of a product cannot be judged from the material alone.

First a point of vocabulary, because it alone keeps this study from being read as something it is not. The "stabilizer" the paper discusses is not the long rod in front of the bow: it is the section at the base of the limb that fits into the riser. The study says nothing about rods, weights or their effect on aiming.

What it does say is that changing the material of that section, from Bakelite to a glass laminate co-cured with the carbon, lowers the accelerations measured on the bow during the shot on all three axes, most on the one the authors call X. The thinner 1 millimetre version vibrates slightly more than the 1.5 millimetre one but makes the limb lighter, and it stays well below Bakelite.

Nothing follows from this about scoring. Nobody shot for points, nobody measured a group, and the question whether a bow that vibrates less shoots better is as open in this work as in the rest of the equipment literature. Nothing follows about the feel in the hand either: "vibration" here is an acceleration read by a sensor on the bow, not an archer's judgement.

For anyone buying limbs the useful information concerns the process rather than performance: the carbon of the body and the glass of the base can be cured in a single autoclave cycle, and the resulting part damped better than the Bakelite reference in the authors' tests. That is a workshop finding, with four measurements behind it.