Extravagant claims have been made regarding the increased dart velocity achieved with a flexible atlatl. This report quantifies the increase in projectile velocity or kinetic energy caused by allowing the atlatl to flex. It is a summary of detailed mathematical analysis on flexing atlatls. The model for the human effort involved in throwing the dart with an atlatl was derived from experimental data cited in "Atlatl Dynamics" by Richard Baugh, published in Lithic Technology, Spring, 1998. The human effort (force and torque versus hand position) involved in throwing is assumed to be constant. It does not depend on the masses or dimensions of the atlatl and projectile. The model for the flexing atlatl, shown in Figure 1, consists of a rigid atlatl coupled to the dart via a lossless spring. The dart mass and atlatl length and mass are similar to those of BPS equipment. The dart velocity was computed for various values of spring stiffness. A perfectly rigid atlatl would be represented by very large spring stiffness. It is convenient to characterize the atlatl stiffness by the distance that the tip deflects during the act of throwing. Remember, the human effort remains the same so increased flexing is due to increased compliance (flexibility) in the atlatl. The results are summarized in Figures 2 and 3. These plots shows the kinetic energy and velocity of the projectile as function of the amount that the spur deflects. In order to achieve an 11 % increase in kinetic energy the tip of the atlatl would have to deflect approximately 0.1 meters. These results are for a specific thrower, atlatl and projectile. It is difficult to generalize the results however one can say that the increase in projectile kinetic energy can be no more than the potential energy stored in the flexing of the atlatl,
stored energy = (1/2)*applied torque*angular deflection of atlatl.
The deflection angle in radians = (distance the atlatl tip
deflects)/(atlatl length).
A copy of Atlatl Dynamics can be obtained from the author for
a $2.00 handling
fee.
Dick Baugh, (650) 493-5125
490 Gary Ct.
Palo Alto, CA 94306 dick_baugh@compuserve.com
E-mail your comments to "Richard A. Baugh" at richardbaugh@att.net
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