Dynamics of Spear Throwing
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Dynamics of Spear Throwing presented to The American College of Sports Medicine by Richard Baugh, May 30, 2003, based on a paper published in the American Journal of Physics, 71, (4), April 2003. Pp 345 - 350. Introduction Spear thrower = atlatl = woomera = propulsore = propulseur

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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


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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


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A Magdelenian era

Spearthrower carved from

Reindeer antler



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Magdelenian Spearthrower in shape of reindeer antler

An ibex kid, reindeer antler



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II. Objectives of the Modeling and Analysis: reindeer antler

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



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Assumptions and model reindeer antler

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


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The projectile center of gravity is far enough forward reindeer antler

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


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Determine applied force and torque dynamically: reindeer antler

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)


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Spur and hand position versus time, reindeer antler

.005 second increments


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Atlatl position versus time. Time interval = .02 sec. reindeer antler

Initial position on the left, final on the right.




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The model used to predict velocity reindeer antler

(Note added spring)



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Positive angular acceleration is due to wrist torque reindeer antler

Negative angular acceleration is due to forward force

The longer the lever arm, the more significant the negative angular acceleration becomes



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Adding an atlatl weight reindeer antler



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Conclusions reindeer antler

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


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