Introduction Spear thrower = atlatl = woomera = propulsore = propulseur Efficient propulsion of a lightweight projectile

1. Dynamics of Spear Throwingpresented to The American College of Sports Medicineby Richard Baugh, May 30, 2003, based on a paper published in the American Journal of Physics, 71, (4), April 2003. Pp 345 - 350

2. Introduction Spear thrower = atlatl = woomera = propulsore = propulseur Efficient propulsion of a lightweight projectile Dave Engvall threw 848 feet = 258.5 meters, Dave’s average speed > 165 feet/sec

3. A Magdelenian era Spearthrower carved from Reindeer antler

4. Late Magdalenian spear thrower, horse effigy carved in reindeer antler

5. Magdelenian Spearthrower in shape of An ibex kid, reindeer antler

6. Another ibex kid spearthrower made from reindeer antler

7. II. Objectives of the Modeling and Analysis: Projectile velocity depends on Dimensions, Weight distribution and Flexibility Human effort is inconsistent so… Mathematical modeling Simple enough to be tractable Detailed enough to give useful results

8. Simple model of a spear thrower

9. Assumptions and model Same moderate physical effort applied to all throws Forward force and wrist torque are functions only of horizontal hand position. Muscles contract with a force that is independent of contraction rate Consequently physical effort is independent of mass and dimensions of the projectile or spear thrower

10. The projectile center of gravity is far enough forward Vertical force can be absorbed into the applied torque Hand has measurable mass and radius of gyration. Logical progression: Heavy projectile: Throw from palm Baseball: Throw from finger tips Lighweight spear: Throw from the end of a stick Pretty simple

11. Determine applied force and torque dynamically: Measure position and angle versus time Numerically differentiate twice Do inverse dynamics using the known masses and moments of inertia Experimental data obtained at UC Davis (Mont Hubbard)

12. Spur and hand position versus time, .005 second increments

13. Atlatl position versus time. Time interval = .02 sec. Initial position on the left, final on the right.

14. Force versus hand position

15. Torque versus hand position

16. The model used to predict velocity (Note added spring)

17. Velocity versus time, experimental and modeled

18. Positive angular acceleration is due to wrist torque Negative angular acceleration is due to forward force The longer the lever arm, the more significant the negative angular acceleration becomes

19. Velocity versus atlatl length and projectile mass

20. Adding an atlatl weight

21. Velocity versus atlatl stiffness

22. Conclusions A simple computational model for the spear thrower Opportunities for improvement: More accurate model of muscle contraction force versus contraction rate Sensitivity study: How is accuracy is affected by atlatl and projectile dimensions and mass distribution? More experimental data