Introduction Spear thrower = atlatl = woomera = propulsore = propulseur Efficient propulsion of a lightweight projectile - PowerPoint PPT Presentation

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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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Late Magdalenian spear thrower, horse effigy carved in reindeer antler


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Magdelenian Spearthrower in shape of

An ibex kid, reindeer antler


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Another ibex kid spearthrower made from reindeer antler


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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


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Simple model of a spear thrower


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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


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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


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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)


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Spur and hand position versus time,

.005 second increments


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

Initial position on the left, final on the right.


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Force versus hand position


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Torque versus hand position


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The model used to predict velocity

(Note added spring)


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Velocity versus time, experimental and modeled


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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


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Velocity versus atlatl length and projectile mass


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Adding an atlatl weight


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Velocity versus atlatl stiffness


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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


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