Baseball: Its Not Nuclear Physics or is it Alan M' Nathan University of Illinois FNAL Colloquium, Ju

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Baseball Its Not Nuclear Physics(or is it?!)
Alan M. Nathan University of IllinoisFNAL
Colloquium, July 12, 2000

• Introduction
• Hitting the Baseball
• The Flight of the Baseball
• Pitching the Baseball
• Summary

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REFERENCES

• The Physics of Baseball, Robert K. Adair (Harper
  Collins, New York, 1990), ISBN 0-06-096461-8
• The Physics of Sports, Angelo Armenti (American
  Institute of Physics, New York, 1992), ISBN
  0-88318-946-1
• H. Brody, AJP 54, 640 (1986) AJP 58, 756 (1990)
• P. Kirkpatrick, AJP 31, 606 (1963)
• L. Van Zandt, AJP 60, 172 (1992)
• R. Cross, AJP 66, 772 (1998) AJP 67, 692 (1999)
• AMN, AJP 68, to appear in Sept. 2000
• L. Briggs, AJP 27, 589 (1959)
• R. Mehta, Ann. Ref. Fluid Mech. 17, 151 (1985)
• www.npl.uiuc.edu/a-nathan/pob

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A Philosophical Note
the physics of baseball is not the clean,
well-defined physics of fundamental matters but
the ill-defined physics of the complex world in
which we live, where elements are not ideally
simple and the physicist must make best judgments
on matters that are not simply calculableHence
conclusions about the physics of baseball must
depend on approximations and estimates.But
estimates are part of the physicists
repertoirea competent physicist should be able
to estimate anything ... The physicists model
of the game must fit the game. Our aim is not
to reform baseball but to understand
it. ---Bob Adair in The Physics of
Baseball, May, 1995 issue of Physics Today
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Hitting the Baseball

• ...the most difficult thing to do in sports
• --Ted Williams

BA .344 SA .634 OBP .483 HR 521
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Heres Why..
(Courtesy of Robert K. Adair)
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Description of Ball-Bat Collision

• forces large (gt8000 lbs!)
• time is short (lt1/1000 sec!)
• ball compresses, stops, expands
• kinetic energy ? potential energy
• bat affects ball.ball affects bat
• hands dont matter!
• GOAL maximize ball exit speed vf
• vf ? 105 mph ? x ? 400 ft ?x/?vf 4-5 ft/mph
  ? more later

What aspects of collision lead to large vf?
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How to maximize vf?

• What happens when ball and bat collide?
• The simple stuff kinematics
• conservation of momentum
• conservation of angular momentum
• The really interesting stuff energy dissipation
• compression/expansion of ball
• vibrations of the bat

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• The Simple Stuff Kinematics

r ? recoil factor ? 0.25
e ? Coefficient of Restitution ? 0.5

vball,f 0.2 vball,i 1.2 vbat,i
Conclusion vbat much more important than
vball Question what bat/ball properties make
vball,f large?
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Sosas 500 Blast(s) in Home Run Derby A
Numerical Analysis

• D 500?
• ? vf ? 127 mph
• vball,i? 60 mph
• ? vbat,i ? 96 mph!
• if vball,i were 90 mph
• D 530?

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Energy in Bat Recoil

• Important Bat Parameters
• mbat, xCM, ICM
• wood vs. aluminum

Want r small to mimimize recoil energy
0.17 0.07 0.24
Conclusion All things being equal, want
mbat, Ibat large
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• But
• All things are not equal
• Mass Mass Distribution affect bat speed

Conclusion mass of bat matters.but probably not
a lot see Watts Bahill, Keep Your Eye on the
Ball, 2nd edition, ISBN 0-7167-3717-5
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Energy Dissipated Coefficient of Restitution
(e)

• in CM frame Ef/Ei e2
• massive rigid surface e2 hf/hi
• typically e ? 0.5
• 3/4 CM energy dissipated!
• depends on ball, surface, speed,...
• is the ball juiced?

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COR and the Juiced Ball Issue

• MLB e 0.546 ? 0.032 _at_ 58 mph on massive rigid
  surface

Conclusion more systematic studies needed
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Effect of Bat on COR Local Compression

• CM energy shared between ball and bat
• Ball is inefficient ? 75 dissipated
• Wood Bat
• kball/kbat 0.02
• ?80 restored
• eeff 0.50-0.51
• Aluminum Bat
• kball/kbat 0.10
• ?80 restored
• eeff 0.55-0.58
• trampoline effect
• Bat Proficiency Factor ? eeff/e

Recent BPF data (Lansmont BBVC/Trey Crisco) ?
0.99 wood ? 1.12 aluminum
More later on wood vs. aluminum
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Beyond the Rigid Approximation A Dynamic Model
for the Bat-Ball collision

• Collision excites bending vibrations in bat
• Ouch!! Thud!!
• Sometimes broken bat
• Energy lost ? lower vf
• Lowest modes easy to find by tapping
• Location of nodes important

see AMN, Am. J. Phys, 68, in press (2000)
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A Dynamic Model of the Bat-Ball Collision
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Euler-Bernoulli Beam Theory

• Solve eigenvalue problem for normal modes (yn,
  ?n)
• Model ball-bat force F
• Expand y in normal modes
• Solve coupled equations of motion for ball, bat

Note for experts full Timoshenko (nonuniform)
beam theory used
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Normal Modes of the Bat Louisville Slugger R161
(33, 31 oz)
Can easily be measured (modal analysis)
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Measurements via Modal Analysis Louisville
Slugger R161 (33, 31 oz)
frequency barrel node Expt Calc Expt
Calc 179 177 26.5 26.6 582
583 27.8 28.2 1181 1179 29.0 29.2 1830 1821 30.0 2
9.9
Conclusion free vibrations of bat can be well
characterized
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Model for the Ball
3-parameter problem k ? ? n ? v-dependence of
? m ? COR
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Putting it all together.
Expectation only modes with fn ? lt 1 strongly
excited
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Results Ball Exit Speed Louisville Slugger
R161 33-inch/31-oz. wood bat
only lowest mode excited
lowest 4 modes excited
Conclusion essential physics under control
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• Under realistic conditions
• 90 mph, 70 mph at 28

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Results The sweet spot
Possible sweet spots 1. Maximum of vf
(28) 2. Node of fundamental (27) 3. Center
of Percussion (27)
Hands dont matter!
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Wood versus Aluminum

• Length and weight decoupled
• Can adjust shell thickness
• Fatter barrel, thinner handle
• More compressible
• COR larger
• Weight distribution more uniform
• Easier to swing
• Less rotational recoil
• More forgiving on inside pitches
• Less mass concentrated at impact point
• Stiffer for bending
• Less energy lost due to vibrations

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How Would a Physicist Design a Bat?

• Wood Bat
• already optimally designed
• highly constrained by rules!
• a marvel of evolution!
• Aluminum Bat
• lots of possibilities exist
• but not much scientific research
• a great opportunity for ...
• fame
• fortune

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Things I would like to understand better

• Relationship between bat speed and bat weight and
  weight distribution
• Effect of corking the bat
• Location of physiological sweet spot
• Better model for the ball
• FEA analysis of aluminum bat
• Why is softball bat different from baseball bat?

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Conclusions

• The essential physics of ball-bat collision
  understood
• bat can be well characterized
• ball is less well understood
• the hands dont matter approximation is good
• Vibrations play important role
• Size, shape of bat far from impact point does not
  matter
• Sweet spot has many definitions

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Aerodynamics of a Baseball

• Forces on Moving Baseball
• No Spin
• Boundary layer separation
• DRAG!
• FD½CD?Av2
• With Spin
• Ball deflects wake gtMagnus force
• FM??RdFD/dv
• Force in direction front of ball is turning

Drawing courtesty of Peter Brancazio
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How Large are the Forces?

?1800 RPM

• Drag is comparable to weight
• Magnus force lt 1/4 weight)

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The Flight of the BallReal Baseball vs. Physics
101 Baseball

• Role of Drag
• Role of Spin
• Atmospheric conditions
• Temperature
• Humidity
• Altitude
• Air pressure
• Wind

Max _at_ 350
approx linear
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The Role of Friction

• Friction induces spin for oblique collisions
• Spin ? Magnus force
• Results
• Balls hit to left/right break toward foul line
• Backspin keeps fly ball in air longer
• Topspin gives tricky bounces in infield
• Pop fouls behind the plate curve back toward field

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The Home Run Swing

• Ball arrives on 100 downward trajectory
• Big Mac swings up at 250
• Ball takes off at 350
• The optimum home run angle!

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Pitching the Baseball

• Hitting is timing. Pitching is
• upsetting timing
• ---Warren Spahn
• vary speeds
• manipulate air flow
• orient stitches

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Lets Get Quantitative!How Much Does the Ball
Break?

• Kinematics
• zvT
• x½(F/M)T2
• Calibration
• 90 mph fastball drops 3.5 due to gravity alone
• Ball reaches home plate in 0.45 seconds
• Half of deflection occurs in last 15
• Drag ?v ? -8 mph
• Examples
• Hop of 90 mph fastball 4
• Break of 75 mph curveball 14
• slower
• more rpm
• force larger

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Examples of Pitches

• Pitch V(MPH) ? (RPM) T M/W
• fastball 85-95 1600 0.46 0.10
• slider 75-85 1700 0.51 0.15
• curveball 70-80 1900 0.55 0.25

What about split finger fastball?
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Effect of the Stitches

• Obstructions cause turbulance
• Turbulance reduces drag
• Dimples on golf ball
• Stitches on baseball
• Asymmetric obstructions
• Knuckleball
• Two-seam vs. four-seam delivery
• Scuffball and juiced ball

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Example 1 Fastball
85-95 mph 1600 rpm (back) 12 revolutions 0.46
sec M/W0.1
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Example 2 Split-Finger Fastball
85-90 mph 1300 rpm (top) 12 revolutions 0.46
sec M/W0.1
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Example 3 Curveball
70-80 mph 1900 rpm (top and side) 17
revolutions 0.55 sec M/W0.25
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Example 4 Slider
75-85 mph 1700 rpm (side) 14 revolutions 0.51
sec M/W0.15
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Summary

• Much of baseball can be understood with
• basic principles of physics
• Conservation of momentum, angular momentum,
  energy
• Dynamics of collisions
• Excitation of normal modes
• Trajectories under influence of forces
• gravity, drag, Magnus,.
• There is probably much more that we dont
  understand
• Dont let either of these interfere with your
• enjoyment of the game!