My Favorite Experiment Series PART 5: THE MECHANICS OF SIMPLE BOWS by R.M. French and T. Kirk A s engineers and archers, we have often thought about the physical underpinnings of the sport. Experienced archers must intuitively understand energy and structural dynamics concepts including structural nonlinearities. 1 There is even a specialized collo- quial vocabulary to describe the effects of phenomena engi- neers and physicists would find familiar. This paper is the first of a series of three that describe experiments designed to explore basic mechanical principles and experimental methods using the simple bow as the subject. A simple bow is just a carefully shaped spring, which stores energy from the archer’s body as strain energy in the limbs. When the string is released, the strain energy in the limbs is converted to kinetic energy in the arrow, string, and the limbs. The force–deflection curve shown in Fig. 1 is intuitively familiar to any archer and similar curves appear in many archery magazines. It shows the force required to draw the bow versus the length to which it is drawn. Neglecting losses, the strain energy stored in the bow is equal to the area under the force–displacement curve. Ideally, the bow should convert all the strain energy stored in the limbs into kinetic energy in the arrow. However, this is impossible because the limbs and string also accelerated for- ward. The percentage of stored energy transferred to the arrow is the mechanical efficiency of the bow. Careful shaping of the limbs can reduce the energy lost in accelerating the limbs and, so, increase the efficiency. 2 This is one reason the traditional Welsh longbow is seldom used now. The recurved limbs now prevalent in simple bows generally dissipate less energy than the straight limbs of the longbow 3 and store more energy for a given draw weight. Figure 2 is an illustration from a medieval manuscript showing English Archers using longbows against French crossbowmen at the Battle of Cre´cy in 1346. Figure 3 shows one of us (M.F.) shooting a large recurve bow at an archery tournament. MEASURING DRAW FORCE CURVE The first simple experimental investigation is to measure the draw force curve. The obvious method is to fix the bow in a support and draw the string using a load cell or spring scale. Figure 4 shows the draw force curve measured using a spring scale and the bow in Fig. 3. Integrating the cubic polynomial approximation gives the stored strain energy. The string’s rest position is 9.5 inches from the arrow rest and the string is 30 inches from the rest at full draw (right before the arrow Fig. 1: Draw force curve for a simple bow Fig. 2: The Battle of Cre´cy showing the English using longbows (from 15th-century illuminated manuscript, Jean Froissart’s Chronicles, Wikipedia Commons) R.M. French (SEM member) and T. Kirk are assistant professors affiliated with the Department of Mechanical Engineering Technology, Purdue University, West Lafayette, IN. FEATURE 66 EXPERIMENTAL TECHNIQUES November/December 2006 doi: 10.1111/j.1747-1567.2006.00110.x Ó 2006, Society for Experimental Mechanics