Bow and arrow dynamics
1981; American Institute of Physics; Volume: 49; Issue: 4 Linguagem: Inglês
10.1119/1.12505
ISSN1943-2909
Autores Tópico(s)Sports Dynamics and Biomechanics
ResumoPast analyses of bow and arrow dynamics have assumed the string to be inextensible. This results in predictions of efficiencies that are significantly higher than measured values (efficiencies over 90% are predicted versus 70% to 85% for measurements, circa 1960). The present analysis allows for an elastic string. It is found that arrow exit then takes place when the string and bow limbs still have substantial kinetic energy, and therefore this energy is unavailable for kinetic energy of the arrow. Moreover, the potential energy remaining in the string and bow limb system can also reduce the amount of energy available for the arrow. For the Hickman model of a long bow used in this study, the elastic string prediction of efficiency is 78%, whereas the inelastic prediction is 92%. The analysis utilizes a Lagrangian distributed mass formulation to develop the governing equations of motion and to generate an equivalent point mass model. The equations of motion were numerically integrated to obtain efficiency, arrow velocity, virtual masses, string tension, string extension, arrow exit time, string and limb potential energies, system momentum, and the dynamic force required to hold the bow handle stationary. Estimates of the effect of air resistance were made and found to be less than 2% of the total system energy. The vibratory dynamics of the string and bow limbs subsequent to arrow exit was analyzed. The results of the elastic string considerations are in reasonable agreement with experimental data and negate the usual explanation for the long-standing discrepancy between theory and experiment as due to air resistance and hysteresis losses in the string and bow limbs.
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