Dynamics of Spear Throwing presented to The American College of Sports Medicine by Richard Baugh, Ma

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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, Daves average speed gt 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