Bow design and materials: Kooi 2007

This is a book chapter in which Kooi summarises more than twenty years of work on the mechanics of the bow and uses it to explain the role of materials in modern recurves. It mixes three things: predictions from his model, laboratory measurements published in 1992 by Tuijn and Kooi on a 68-inch, 30-pound Greenhorn Comet TD 350 recurve, and practical points taken from a guide for archers.

For the Greenhorn, with a 0.597 m draw and an actual draw weight of 123.6 N, the model gives 32.9 joules of stored energy driving an 18.3-gram Easton 1616X75 arrow at 51.39 m/s, an efficiency of 72.9%. The laboratory tests, with the bow mounted in a rack and a mechanical release, compare four strings of almost the same weight: with an 18.1-gram arrow Dacron gives 49.73 m/s and an efficiency of 0.70, Kevlar 51.25, Twaron 51.68 and Fast Flight 52.09 m/s, with an efficiency of 0.762. Removing 2, 4 and 6 strands from a 16-strand Fast Flight string brings its mass down from 6.45 to 4.64 grams, but the speed stays between 51.43 and 51.88 m/s: a lighter string and a stretchier one cancel each other out. The measurements also give the limbs' virtual mass, 4.6 grams each.

The conclusion matches the earlier papers: the mechanical performance of modern recurves is only slightly better than that of historical bows, and the gain comes from materials, which store more energy per unit of mass and are much less affected by heat and humidity.

The chapter does not present a new study with its own method. The theory repeats the model from the earlier papers: limbs as elastic beams with varying stiffness and mass, an elastic string with a third of its mass added to the arrow, the arrow as a point mass, the bow held still, and three dimensionless coefficients (stored energy, efficiency, speed) for comparing bows at equal draw length, draw weight and limb mass. To these it adds the energy a material can store per unit of mass and a shape factor for the limb cross-section, which measures how well the material is used in bending: it is 0.333 for a rectangular section.

The measurements come from a 1992 paper, with the bow in a fixed rack and a mechanical release; the chapter reports mean values for each type of string without saying how many shots were taken or how much they varied. The arrow shapes in flight are those from the 1997 paper on the archer's paradox, compared with Pękalski's high-speed film. The sections on the materials of limbs, arrows, strings and risers largely report data and opinions from a guide for recurve archers and from manufacturers' websites.

As a review chapter it should be read knowing that it nearly always points elsewhere: the evidence for most of what it says lies in those other papers. The measurements are on a single bow, fixed in a rack and shot with a mechanical release, so without the variability of fingers, and the differences between strings (at most 2.36 m/s between Dacron and Fast Flight) come with no estimate of error. The calculation of peak string force, about seven times the draw weight after the arrow has left, ignores damping, and the author himself regards it as conservative.

Several practical claims come from non-scientific sources and the chapter does not test them: that carbon and foam limbs are the most consistent, that aluminium-carbon arrows are the favourite outdoors, that a light arrow is more affected by wind, that stabilisers compensate for faults in the bow hand. The conclusion that better materials will bring faster, and therefore more accurate, arrows at long distances is also the author's forecast.

For anyone who shoots, the chapter has three concrete points. The first concerns strings: in these tests Dacron sent the arrow off more slowly, 1.5 to 2.4 m/s below the modern fibres, while removing strands from a modern string made no appreciable difference to speed; the author advises keeping to the number of strands the manufacturer recommends, for safety. The second concerns the arrow: acceleration at the release is enormous (about 12,500 m/s², 1,250 times gravity, for a 50-pound bow and a 20-gram arrow) and the arrow always flexes; spine is what lets the tail pass around the button without touching it, and the chapter describes how it is measured (a 1.94-pound weight at the centre of the shaft, with supports 28 inches apart for a 29-inch arrow).

The third is a correction of expectations: the mechanical performance of a modern recurve is not very different from that of a good historical bow, and what makes the difference, according to the author, is lighter, stronger materials that are more stable in changing weather. None of these points says anything about an archer's measured accuracy.