The Design of the Bow 1

Theinventionofthebowandarrowprobablyranksforsocialimpactwiththeinvention of the art of kindling a flre and the invention of the wheel. It must have been in prehistoric times that the flrst missile was launched with a bow, we do not know where and when. The event may well have occurred in difierent parts of the world at aboutthe sametime orat widelydifiering times. Numerous kinds of bows are known, they may have long limbs or short limbs, upperandlowerlimbsmaybeequalorunequalinlengthwhilstcross-sectionsofthe limbs may take various shapes. Wood or steel may be used,singly as in ‘self’ bows, or mixed when difierent layers are glued together. There are ‘composite’ bows with layers of several kinds of organic material, wood, sinew and horn, and, in modern forms,layersofwoodandsyntheticplasticsreinforcedwithglassflbreorcarbon. The shapeofthebowwhenrelaxed,maybestraight orrecurved,wherethecurvatureof the partsof the limbsof the unstrungbowis opposite to the way they are ∞exedto fltthe string. Inpreviouspaperswehave dealt withthemechanics ofthebowandarrow. 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 timeacoe‐cientisderivedwhichmeasurestheefiectivenessoftheformofthecrosssection of a bendingbeam. 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 imposedona numberof designparameters. Thisdeflnesfeasible regions. Sensitivity analysis gives the in∞uence of a number of important parameters on