Title: The Physics of Baseball (or…Just How Did McGwire Hit 70?) Alan M. Nathan University of Illinois February 5, 1999
1The 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
2REFERENCES
- 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
3Hitting the Baseball
- ...the most difficult thing to do in sports
- --Ted Williams,
- Professor Emeritus of
- Hitting
4Speed 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
5What 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!
6What Determines Batted Ball Speed?
- Mass of bat
- Conclusion
- mass of bat matters
- ...but not a lot
7Dynamics 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!
8Dynamics 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!
9The 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
10What 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
11Properties 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
12Sweet 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
13Sweet 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
14Sweet 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
15So you think bats cannot bend..
16So you think bats cannot bend..
17How 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
18Advantages 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
19Aerodynamics 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
20The Flight of the Balll
- Role of Drag
- Role of Spin
- Atmospheric conditions
- Temperature
- Humidity
- Altitude
- Air pressure
- Wind
21The 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!
22(No Transcript)
23The 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
24Pitching 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
25Lets Get Quantitative!I. How Large are the
Forces?
- Drag is comparable to weight
- Magnus force lt 1/4 weight)
26Lets 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
27Example 1 Fastball
85-95 mph 1600 rpm (back) 12 revolutions 0.46
sec M/W0.1
28Example 2 Split-Finger Fastball
85-90 mph 1300 rpm (top) 12 revolutions 0.46
sec M/W0.1
29Example 3 Curveball
70-80 mph 1900 rpm (top and side) 17
revolutions 0.55 sec M/W0.25
30Example 4 Slider
75-85 mph 1700 rpm (side) 14 revolutions 0.51
sec M/W0.15
31Examples of Trajectories
32Effect 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
33Summary
- 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!