Lightweight Olympic bow riser: Edelmann-Nusser 2004

A group at the University of Magdeburg asked whether the lightweight risers on the market are in fact light, and tried to beat one with an optimisation algorithm. The benchmark was the 25 inch Hoyt Radian, the lightest riser in use on the German recurve team at 1114 grams, against 1154 for the Avalon, 1245 for the Matrix, 1302 for the Aerotech and 1374 for the Axis.

Starting from the loads computed on a drawn bow, the authors built a CAD model with 24 free parameters and let it evolve, generating 1650 risers and evaluating each for mass, maximum displacement and spread of stresses. The riser they selected and then manufactured weighs 871 grams including the threaded inserts for the stabilisers, which is 243 grams and 22% less than the Radian, with a maximum displacement of 1.94 millimetres against the Radian's 1.85 and a peak stress of 160 newtons per square millimetre against a yield point of 403.

The scatter plot of all the generated solutions says more than the riser that was built: the algorithm found risers with both lower mass and lower displacement than the Radian, and the lightest of all weighed 779 grams with 3.53 millimetres of displacement. The Radian, the authors write, is optimised neither for mass nor for stiffness.

Three archers of the German national team tried the riser at the Olympic training centre in Berlin, two shooting nine arrows each and one three hundred. They reported it stiff, light and good at damping vibration after the shot; the one who shot three hundred said the bow groups well and asked to use it the following season. Nobody measured a score.

The work has four parts: computing the loads on a drawn riser, a structural analysis of the Radian under those loads, a parametric CAD model, and optimisation of its parameters.

The loads come from a static equilibrium of the bow at aim, with the string forces on the limbs and the reaction of the bow hand. Geometry was measured on a bow with a 25 inch riser and long limbs at three draw lengths: 710, 760 and 810 millimetres. The draw weight used for the calculation is 200 newtons, higher than the German team's own and higher than the 152 newtons the Hoyt manual gives for that combination, chosen to leave a safety margin; the 710 millimetre draw length was kept for the same reason, since it produces the largest forces. At that draw length the computed forces on the limb bearings are 1583 and 1729 newtons, plus 216 newtons across.

The Radian was scanned in three dimensions and rebuilt in Pro/ENGINEER. Bending tests, atomic emission spectroscopy and electron microscopy identified the alloy, an AlMg1SiCu, with a density of 2.77 grams per cubic centimetre, a yield point below 400 newtons per square millimetre and a Young's modulus between 69 and 75 gigapascals, of which the median value of 72 was used. The structural analysis is static, run in Pro/MECHANICA: no dynamic analysis, because earlier work shows that release adds about 5% of stress for less than 10 milliseconds. The model of the Radian gives a peak stress of 135 newtons per square millimetre, a maximum displacement of 1.85 millimetres and a mass of 1048 grams, less than the actual 1114 because it leaves out the three steel bushings for the stabilisers.

The optimisation works on 24 parameters treated as a chromosome. It starts from 31 random individuals, pairs fifteen couples by selection proportional to fitness, recombines with a probability of 80%, gives each child a 5% chance of mutating one parameter and 0.8% of being reinitialised entirely; the best of each generation passes to the next. Two runs, of 20 and 35 generations, with different weightings between mass, displacement and spread of stresses. From the best ten, candidates were picked by hand for displacement below 2 millimetres, symmetrical displacement between the two limb pockets and minimal torsion in the upper one. The part was CNC-milled from an aircraft aluminium alloy, AS 28, with a density of 2.71 and a yield point of 403 newtons per square millimetre.

Nobody shot for a score. The riser was assessed in two ways: by structural computation and by the impressions of three athletes, two of whom shot nine arrows. There are no measured groups, no points, nobody was unaware of which bow they were holding, and no comparison riser was used in the same session. "Groups well" is one archer's judgement, reported as such.

The analysis is static and covers a single load case, justified by a finding from a 1990s paper on the extra stress at release. The search space is constrained: the 24 parameters were chosen for plausibility and inspired by the shape of the Radian, and the authors are the first to write that a different set of parameters, a different shape or a different fitness function would give different results. Only one family of materials was tried, aluminium alloys.

The most interesting limitation is the one they state themselves. Riser stiffness is treated as a virtue by the literature, by coaches and by archers, yet no empirical study shows it, and when the limbs move 700, 800 or 900 millimetres during the draw it is implausible that one or two millimetres of riser displacement change the shot. The authors suggest torsion of the upper limb pocket as a more plausible criterion, and they offer it as a hypothesis. Their own constraint of staying below 2 millimetres is therefore a cautious choice dictated by the habits of the sport, not a measured threshold.

The premise about weight is also left open: the idea that a lighter bow scores better rests on an earlier paper by the same first author, where adding 200 grams to the bow widened the sway during aiming, and where that sway was associated with poorer scores. That is an indirect step, not a measurement made here.

What an archer can take away is that a fifth of the mass can be taken off a competition riser without losing stiffness, and that the German team's benchmark riser was nowhere near the limit of what can be done: 871 grams against 1114, with the same displacement under load to within a tenth of a millimetre.

The second point is less comfortable. The criterion archers use when they choose a stiff riser has no measurement of shooting behind it. The authors say so explicitly: no empirical study shows that riser stiffness affects the result, and their own suggestion is that what matters is torsion of the upper limb pocket, because marked torsion accelerates the arrow across its own axis as well as along it. That stays a hypothesis, not a finding of this work.

On bow weight the record authorises no conclusions. The idea that a lighter riser is less tiring over a day of more than two hundred arrows is reasonable and is stated in the introduction, but nobody here measured fatigue, sway at aim or score. What was observed is three athletes who tried the bow and found it good, one of them over three hundred arrows.

Anyone tuning a recurve will find no usable figure in these pages. Anyone looking at the market will find something more useful: among the five Hoyt risers listed in 2004 the difference in mass reached 260 grams, and the link between mass and stiffness across production models was far weaker than price and advertising suggested.