THE DESIGN OF THE BOW

The invention of the bow and arrow probably ranks for social impact with the invention of the art of kindling a fire and the invention of the wheel. It must have been in prehistoric times that the first missile was launched with a bow, we do not know where and when. The event may well have occurred in different parts of the world at about the same time or at widely differing times. Numerous kinds of bows are known, they may have long limbs or short limbs, upper and lower limbs may be equal or unequal in length whilst cross-sections of the limbs may take various shapes. Wood or steel may be used, singly as in 'self' bows, or mixed when different layers are glued together. There are 'composite' bows with layers of several kinds of organic material, wood, sinew and horn, and, in modern forms, layers of wood and synthetic plastics reinforced with glassfibre or carbon. The shape of the bow when relaxed, may be straight or recurved, where the curvature of the parts of the limbs of the unstrung bow is opposite to the way they are flexed to fit the string. In previous papers we have dealt with the mechanics of the bow and arrow. The main subject of this paper is the design and construction of bows. Nondimensionalization of the problem leads to the introduction of the maximum elastic energy storage capacity per unit of mass as a material constant for strength. At the same time a coefficient is derived which measures the effectiveness of the form of the cross-section of a bending beam. The assumption that the limbs of a bow are fully loaded implies a relationship between a number of design parameters. It reduces the dimension of the design parameter space. When the strength of materials is taken into account constraints are imposed on a number of design parameters. This defines feasible regions. Sensitivity analysis gives the influence of a number of important parameters on quality coefficients, one of these is proportional to the amount of available energy and other are the efficiency and the velocity of the arrow at the onset of its flight. These quality coefficients measure the performance of a bow for specific purposes such as hunting, flight shooting and target shooting. We compare the performance of bows used in the past with that of modern competition bows. It appears that the superb features of man-made materials contribute most to the better performance of the modern bow and not its geometric shape.