Transcript Document 7816217

Elastic and Rigid Body Properties of
Bats
by
Larry Noble, Professor
Department of Kinesiology
Kansas State University
Manhattan, KS
Kansas State University
Biomechanics Lab
Acknowledgements
• Collaborators –
– David Dzewaltowski, Professor and Head, Department
of Kinesiology, Kansas State University
– John Eck, Professor of Physics and Dean, College of
Natural Sciences and Mathematics, Indiana University
of Pennsylvania
– Hugh Walker, Professor Emeritus, Department of
Mechanical Engineering, Kansas State University
• Sponsors
– Easton Aluminum, Inc.
– Kansas State University Research Foundation
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Acknowledgements
• Graduate Research Assistants
– Deanna Deppen, Rob Dorgan, Geoffrey Ringer,
Marty Ponte, Christy Allen, Denise Harper,
Chris Dudley, Panteleimon Ekkekakis, Kostas
Pothakos, Tim Benson, Dana Davidson, Joyce
McConnell, Kasee Hildenbrand
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Outline
• Brief history of bat development
• Rules on baseball and softball bats
• Rigid body properties
– Mass
– Moment of inertia
– Center of percussion
• Elastic properties
– Longitudinal vibrational nodes and modes
• During impact
• During the swing
– Coefficient of restitution
• Is a very rigid bat or a very flexible bat more effective?
• What and where is the “sweet spot”
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Brief History of Bat Development:
In the Beginning
• Began with basically a
stick around 1830
• In 1850’s, handle and
barrel were emerging
• Around 1900,
modern-day
shape had
evolved
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History of Bat Dev: Late Wood Era
• From the early 1900’s until ~1970, the wood bat
was used exclusively with minor design changes
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History of Bat Dev: Aluminum Era
• Aluminum bats first appeared
around 1970
• Since 1980 materials with
higher strength/mass ratios
have emerged
• The plethora of recent
innovations are causing concern
by softball & baseball governing
bodies
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Recent Softball and Baseball Bat
Rule Changes
• Softball
– Upper limit on “liveness”, or
Coefficient of Restitution (COR) –
Max Bat Performance Factor = 1.20
• Baseball
– Max barrel diameter 2.625 in
(.067 m)
– Length-weight diff(< 3 units diff.)
– Max Ball Exit Speed Ratio (BESR) – 94 MPH (Amateur only)
– Rules committee is considering a MOI rule
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Center of Percussion (COP)
• The COP is the point where an impact does not cause a
reaction impulse at the axis, causing the axis to tend to
translate
• Distance from axis to
center of percussion (q):
q = T2g/4B2
= .248387T2
Where T = period of
oscillation
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Center of Percussion
• Impacts on COP do not cause an impact reaction
impulse at the axis (Noble & Eck, MSSE 1986)
• COP has a conjugate point on the handle. Each
point on the handle is associated with a different
COP on barrel. (Cross, Am J Phys 1998)
• If the conjugate point of the COP should be near
the center of the hand-bat interface (approx 6
inches from knob end), then impact reaction
forces will be minimized.
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Center of Percussion
• In most 34-in bats, COP is
approx 6 in (15 cm) from barrel
end if hitter grips bat on knob
end
• COP can be displaced predictably
by changing the weight
distribution of the bat (Noble &
Eck, Proc ISBS 1986)
• The best site for COP
displacement is in the knob end
• COP displacement can cause
some vibration-related problems
because of the node-COP
difference discussed later
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Center of Percussion & the sweet spot
• Earlier studies indicated that the COP is the sweet spot, the
best place to hit the ball (Bryant, RQES 1977; Noble, ISB
Proc 1983)
• The sweet spot has since been defined in terms of two
criteria:
– The most comfortable location
• The COP has a direct effect on pain/annoyance at impact (Noble, JAB 1994;
Noble)
• Fundamental vibrational node location also has a profound effect on impact
pain/annoyance (Noble, JAB 1994)
– The location for maximum post-impact ball velocity
• Determined by characteristics other than COP (Brody, Am J Phys 1986)
– e.g., bat/ball mass and bat vel/ball vel ratios
• Vibrational node locations
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Longitudinal vibrational modes of bat:
clamped boundary condition
• Normal modes of oscillation for
a clamped bat showing diving
board mode and 1st & 2nd
harmonics
(Noble & Walker, JAB 1994;
Proc ISBS 1994)
• Diving board mode & 1st
harmonic are ~ 13 Hz & 150 HZ,
respectively, for an aluminum
bat
(Noble, Proc ISBS 1999)
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Longitudinal vibrational modes of
bat: free-free boundary condition
• Diving board mode is missing from
hand-held bat (Brody, Am J Phys
1990)
• Bat behaves as a free-free body
during impact
• Fundamental frequency involves
most of the displacement and ranges
from 150 to 300 Hz in most
aluminum bats
• First harmonic ranges from 500 to
1000 Hz
• Impact time ~1.5 ms for
baseball and ~3.5 ms for
softball
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Longitudinal vibrational modes of bat:
•Antinode of all modes is at barrel end
•Frequency can be changed substantially by changing
stiffness/mass ratio (Noble & Walker, Proc ISBS 1994)
•Higher freq vibrations are dampened quicker with a tight grip
•Time for waves to travel up and down the bat is >2 ms, longer
than impact time (Cross, Proc ISBS 1999)
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Impact vibrations and annoyance
• Node of fund mode approx 17 cm (6.7 in)
from each end and 170 Hz (Cross, Am J Phys
1998)
• First harmonic is approx 530 Hz with nodes
at approx 13 cm from BE, 5 cm from COM
toward hands, and 7 cm from KE.
• Impacts on the node will not excite that
mode.
• Mode excitation increases linearly with
impact-node distance
• Thus we have a “sweet vibrations” zone
approx 13-17 cm (5-6.7 in) from BE.
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Vibrations, COP & Impact Annoyance
• Node-COP distance is determinant of bat
preference (Noble & Dzewaltowski, Tech
Report to Easton Aluminum1994)
• Impact annoyance is least at a point between
node of fundamental & COP (Noble &
Walker Proc ISBS, 1994)
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Vibrations and Post-impact Ball Velocity
• Theoretical model included
lowest 20 vibrational modes of
a standard wood bat was
developed to estimate ratio of
exit to initial speed of a
baseball in a 1 m/s impact on
standard wood bat which is
initially stationary.
• Red curve is calculated result
for a flexible bat, blue curve is
estimate for a rigid bat. Points
with error bars are empirical
measurements. (Nathan, Am J
Phys 2000.
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Vibrations and Post-impact Ball Velocity
• Estimates of post-impact ball
velocity of wood and aluminum
bat
• Aluminum bats are better
because
– COR is higher
– Length and weight are
independent
– Aluminum bats have lower
Moment of inertia
– Stiffness can be a design feature
– Node-COP location can be a
design feature
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Vibrations and Post-impact Ball Velocity
• Estimates of exit speed
with 90 mph ball colliding
with wood bat with COM
speed of 54 mph and
rotational speed about
COM of 51 sec-1. Red
curve is for rigid bat, blue
curve is for flexible bat.
• More recently, empirical
data supports these
estimates
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Bat Vibrations During Swing
• Manufacturer’s are
claiming “diving board
effect”
• This implies that bat bends
back during the swing and
“releases the stored elastic
energy at impact, as
depicted here
• Is this implication valid?
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Bat Flexibility Field Test
• First, a controlled blind field test involving 6 different bat
flexibilities with 32 elite softball players was funded by a bat
manufacturer
• Results indicated that these hyper-flexible bats resulted in greater
post-impact velocity and were
preferred by elite slow-pitch
hitters over stiffer bats (Noble,
Tech Rep to Easton Aluminum
1994)
• An examination of bat bending
characteristics during the swing
followed this study (Noble,
Proc ISBS 2001)
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Bat bending during swing and impact
Bat Vibrations During Swing & Impact
4
Peak 41 ms PC
Begin Swing
233ms PC
3
Horiz Pk 38 ms PC
Strain (v)
2
1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
-1
-2
-3
-4
Time (s)
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Horiz Dir
Vert Dir
Magnitude
Horiz Dir
Vert Dir
Magnitude
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0.7
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Begin swing 183 ms PC
Peak bending and peak
torque ~ 50 ms PC
Impact – bat still bent
back approx 20% of max
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Bat Vibrations During Swing and
Impact: Conclusions
• During the swing, the bat bends back and stores elastic
energy that is released during impact
• Thus, a more flexible bat would appear to be more effective
if the ball impacts at the sweet spot
• During impact, the bat behaves as a free-free body
• A stiffer bat would appear to be more effective if the ball
does not impact at the sweet spot.
• Perhaps a stiff bat is better for baseball and fast-pitch
softball and a flexible bat is better for slow-pitch softball
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So, Where and What is Sweet Spot?
• It is the best place on the bat to hit the ball,
considering
– Annoyance/comfort
– Post-impact ball velocity
• This location is:
– Location of minimal vibrations (approx 6.5 in from
barrel end)
– Location of COP with axis approx 6 in from knob end
(approx 6 in from barrel end)
– Preferably these two areas are close together
References for this presentation are on this course
website in word format under filename
“acsmpresbiblio.rtf “
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References for this presentation can be found on this
website: http://www:ksu-personal.edu/~lnoble
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