The Physics of Baseball (or…Just How Did McGwire Hit 70?) Alan M. Nathan University of Illinois February 5, 1999

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The Physics of Baseball (orJust How Did
McGwire Hit 70?)Alan M. Nathan University of
IllinoisFebruary 5, 1999

• 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 Sporting Life, Davis and Stephens (Henry Holt
  and Company, New York, 1997), ISBN 0-8050-4540-6
• http//www.exploratorium.edu/sports
• ME!
• a-nathan_at_uiuc.edu
• www.npl.uiuc.edu/nathan

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Hitting the Baseball

• ...the most difficult thing to do in sports
• --Ted Williams,
• Professor Emeritus of
• Hitting

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Speed of Hit BallWhat does it depend on?

• Speed is important
• 105 mph gives 400 ft
• each mph is worth 5 ft
• The basic stuff (kinematics)
• speed of pitched ball
• speed of bat
• weight of bat
• The really interesting stuff (dynamics)
• bounciness of ball and bat
• weight distribution of bat
• vibrations of bat

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What Determines Batted Ball Speed?

• How does batted ball speed depend on ...
• pitched ball speed?
• bat speed?
• V 0.25 Vball 1.25 Vbat

Conclusion Bat Speed Matters More!
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What Determines Batted Ball Speed?

• Mass of bat
• Conclusion
• mass of bat matters
• ...but not a lot

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Dynamics of Ball-Bat Collision

• Ball compresses
• kinetic energy stored in spring
• Ball expands
• kinetic energy restored but...
• 70 of energy is lost!
• (heat, deformation,vibrations,...)
• Forces are large (gt5000 lbs!)
• Time is short (lt1/1000 sec!)
• The hands dont matter!

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Dynamics of Ball-Bat Collision

• Ball compresses
• kinetic energy stored in spring
• Ball expands
• kinetic energy restored but...
• 70 of energy is lost!
• (heat, deformation,vibrations,...)
• Forces are large (gt5000 lbs!)
• Time is short (lt1/1000 sec!)
• The hands dont matter!

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The Coefficient of Restitution

• COR measures bounciness of ball
• Final speed/Initial speed
• For baseball, COR.52-.58
• Changing COR by .05 changes V by 7 mph (35 ft!)
• How to measure?
• This is square of COR-------gt

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What About the Bat?(or, it takes two to tango!)

• Wood Bat
• Efficiently restores energy
• But only 2 energy stored
• Bat Performance Factor (BPF) 1 .02
• Aluminum Bat
• Stores 20 energy
• Efficiently restores energy
• Result trampoline effect
• BPF 1.2
• Ball flies off the bat!
• A more efficient bat and/or ball

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Properties of Bats

• length, diameter
• weight
• position of center of gravity
• where does it balance?
• distribution of weight
• moment of inertia
• center of percussion
• stiffness and elasticity
• vibrational nodes and frequencies

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Sweet Spot 1 Center of Percussion

• When ball strikes bat...
• Linear recoil
• conservation of momentum
• Rotation about center of mass
• conservation of angular momentum
• When CP hit
• The two motions cancel at handle
• No reaction force felt at handle

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Sweet Spot 2 Maximum Energy Transfer

• Barrel end of bat maximizes bat speed
• Center of Mass minimizes angular impulse
• MET must be in between
• Not on COP!
• Aluminum bat more effective
• for inside pitches

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Sweet Spot 3 Node of Vibration

• Collision excites bending vibrations in bat
• Ouch!!
• Energy lost gtlower COR
• Sometimes broken bat
• Reduced considerably if collision is a node of
  fundamental mode
• Fundamental node easy to find
• For an interesting discussion, see
• www.physics.usyd.edu.au/cross

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So you think bats cannot bend..
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So you think bats cannot bend..
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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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Advantages of Aluminum

• Length and weight decoupled
• Can adjust shell thickness
• More compressible gt springier
• Trampoline effect
• More of weight closer to hands
• Easier to swing
• Less rotational energy transferred to bat
• More forgiving on inside pitches
• Stiffer for bending
• Less energy lost due to vibrations

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Aerodynamics of a Baseball

• Forces on Moving Baseball
• No Spin
• Boundary layer separation
• DRAG!
• Grows with v2
• With Spin
• Ball deflects wake
• action/reactiongtMagnus force
• Force grows with rpm
• Force in direction front of ball is turning

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The Flight of the Balll

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

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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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The Role of Friction

• Friction induces spin for oblique collisions
• Spin gt 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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Pitching the Baseball

• Don Larsen, 1956 World Series
• Last pitch of perfect game

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

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Lets Get Quantitative!I. How Large are the
Forces?

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

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Lets Get Quantitative!II. How Much Does the
Ball Break?

• Depends on
• Magnitude and direction of force
• Time over which force acts
• 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 reduces fastball by about 8 mph
• Examples
• Hop of 90 mph fastball 4
• Break of 70 mph curveball 16
• slower
• force larger

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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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Examples of Trajectories
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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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Summary

• Much of baseball can be understood with
• basic principles of physics
• Conservation of momentum, angular momentum,
  energy
• Dynamics of collisions
• 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!