Bow and Arrow Efficiency

by Dick Baugh (2/16/11)


People have been shooting bows and arrows at animals, targets and each other for over 5,000 years. Even the earliest bows were marvels of design efficiency, taking advantage of the unique structural properties of wood. What better way was there of utilizing wood, a material that can only be compressed or stretched a mere 1 %, for propelling a projectile at over 49 meters/second (160 ft/sec)? An interesting and underestimated feature is that a bow transfers, with over 60 % efficiency, human effort to potential energy in the bow limbs weighing on the order of .36 kilograms (0.8 pounds) to kinetic energy of an arrow weighing .0226 kilogram (350 grains ), a mass ratio of 16 to 1. This remarkable efficiency is due to efficient leverage. Just before the arrow separates from the bowstring a very small movement of the bow limbs causes a large movement of the arrow.

The objectives of this paper are:
1. To present an accurate but tractable physical model for the performance of a straight-limbed wooden bow. Contemporary archers have available bows with exotic designs made from space-age materials but there has always been a desire to gain a deeper understanding of how our early ancestors did things.
2. To compare the results of detailed computer simulation with the simpler model presented here. Other investigators have applied very sophisticated computer analytical tools to the analysis of bow and arrow dynamics. This simpler model presented here is worthwhile only if it gives similar accurate results.
3. To compare modeling results with experimental performance of straight-limbed wood bows. The immediate conclusion drawn from a comparison between actual performance and the computer modeling based solely on the elastic modulus and density of the bow limb material is that internal friction (hysteresis) in the bow limbs in a major contributor to inefficiency in a wooden bow. Internal friction is also very difficult to characterize.

To read the complete article, acceess the link to the PDF file entitled "Bow and Arrow Efficiency".



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