Recurve riser flex under load: Fauzi 2016 study

The study calculates how much a recurve riser flexes at full draw, taking the body measurements of Malaysian teenagers aged 13 to 17 as its reference. No archer was measured: the riser is a 25-inch Hoyt Matrix, rebuilt on the computer from a 3D scan, and the loads are those that, by the authors' calculations, reach the limb pockets with a draw weight of 200 newtons.

The starting point is arm span: 175.05 cm for boys and 163.46 cm for girls in the anthropometric database used. Divided by 2.5, this gives a draw length between 654 and 702 mm. The calculations, however, were run on three longer draw lengths, 710, 760 and 810 mm, with a 68-inch bow. The forces on the limb pocket fall as draw length rises: the largest of the three goes from 1,725 newtons at 710 mm to 1,642 and 1,600, the smallest from 217 to 190 and 170. Under these loads the finite element analysis gives a maximum riser displacement of 1.85 mm. The authors consider this in agreement with an earlier study of a competition riser, and conclude that young Malaysian archers can use that riser with a 710 mm draw length and a 68-inch bow.

The work has three steps. The first takes arm span from an anthropometric database of Malaysian secondary school students aged 13 to 17 and turns it into draw length by dividing by 2.5: this is a rule from equipment guides, which the authors prefer to measuring at full draw because it depends less on posture and anchor. The second writes out the static equilibrium of the bow at full draw and, with equations from an earlier paper by Edelmann-Nusser, derives the forces on the limb pocket. The draw weight read from a force-draw curve is 169 N (38 lb) and 178 N (40 lb); to leave a safety margin the calculations use 200 N.

The third step is the structural analysis. The riser, scanned with a FARO arm and modelled in SolidWorks, was loaded with those forces in finite element software (Autodesk Simulation Mechanical 2015), with 36,500 elements and the properties of a generic aluminium alloy: a Young's modulus of 7.1 × 10¹⁰ Pa and a density of 2,770 kg/m³. The output is a single number, the maximum displacement.

The title refers to under-15 and under-17 archers, but no archer was measured or shot: the body measurements come from a general database of students and draw length is estimated with a formula. The numbers do not fully hang together either. The draw length derived from arm span runs from 654 to 702 mm, yet the simulations use 710, 760 and 810 mm, adult draw lengths, and the draw weight is fixed at 200 N for all three, whereas on a real bow it would change with draw length. The explanation offered for the higher forces at the short draw length (a shorter bow would transfer more energy) does not hold, because the bow length in the calculations is always the same.

The analysis is static only, on a generic material, with no vibration after the release and no fatigue, and the comparison with the reference study is made in words, without the figure against which 1.85 mm should be set. Two of the results figures carry the same caption, "force-draw curve", which describes neither of them. The conclusion about a riser suited to young Malaysian archers does not come from any comparison with other risers or other measurements: it says only that this riser withstands the load.

For anyone who shoots, the study changes little. It says that a 25-inch aluminium riser under a static load of 200 newtons (about 45 lb, more than the 38 to 40 lb read from the force-draw curve) flexes by 1.85 mm at most according to the model: loaded statically, that riser deforms very little. It does not say how the riser behaves at the release, which bow length or draw weight suits a young archer, or how the riser's dimensions affect accuracy.

The starting idea, choosing equipment from the archer's body measurements, is reasonable, but here it remains an intention. For a coach choosing a bow for a youngster, the only practical element is the rule of arm span divided by 2.5, and that is a rule from equipment guides cited by the authors, not a finding of the study.