How a Physicist Analyzes the Game of Baseball

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How a Physicist Analyzes the Game of Baseball
Alan M. Nathan a-nathan_at_uiuc.edu webusers.npl.uiuc
.edu/a-nathan/pob Department of
Physics University of Illinois
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Baseball and Physics
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A great book to read.
Our goal is not to reform the game but to
understand it. The physicists model of the
game must fit the game.
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Some Topics I Will Cover

• How does a baseball bat work?
• The flight of a baseball
• Leaving the no-spin zone
• Putting it all together

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You can observe a lot by watching
--Yogi Berra
Easton Sports
CE Composites
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Description of Ball-Bat Collision

• forces large, time short
• gt8000 lbs, lt1 ms
• ball compresses, stops, expands
• KE?PE?KE
• bat recoils
• lots of energy dissipated (COR)
• distortion of ball
• vibrations in bat
• to hit home run.
• large batted ball speed
• 100 mph?400 ft, each additional mph 5-6
• optimum take-off angle (300-350)
• lots of backspin

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Kinematics of Ball-Bat Collision
BBS q vball (1q) vbat

• q ? Collision Efficiency
• Joint property of ball bat
• independent of reference frame
• independent of end conditionsmore later
• weakly dependent on vrel
• Superball-wall q ? 1
• Ball-Bat near sweet spot q ? 0.2
• ? BBS ? 0.2 vball 1.2 vbat

Conclusion vbat matters much more than vball
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Kinematics of Ball-Bat Collision
BBS q vball (1q) vbat
e coefficient of restitution ? 0.50
(energy dissipationmainly in
ball, some in bat) r mball /Mbat,eff bat
recoil factor ? 0.25 (momentum and angular
momentum conservation) ---heavier is better but
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Batting cage study show how bat speed depends on
MOI for college/semipro baseball players
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Collision Efficiency q Can Be Measured

• Air cannon fires ball onto stationary bat
• q vout/vin
• Used by NCAA, ASA, to regulate/limit
  performance of bats

Sports Sciences Lab _at_ WSU
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Regulating Performance of Non-Wood Bats (NCAA)
BBS q vball (1q) vbat

• Specify maximum q (BESRq1/2)
• relative to wood
• implies bats swung alike will perform alike
• Specify minimum MOI to limit bat speed
• smaller than wood
• Together, these determine a maximum BBS
• gap between wood and aluminum ? 5

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BESR
MOI
aluminum
-5 rule
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Accounting for COR Dynamic Model for Ball-Bat
Collision AMN, Am. J. Phys, 68, 979 (2000)

• Collision excites bending vibrations in bat
• hurts! breaks bats
• dissipates energy
• lower COR, BBS
• Dynamic model of collision
• Treat bat as nonuniform beam
• Treat ball as damped spring

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Modal Analysis of a Baseball Bat www.kettering.edu
/drussell/bats.html
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Vibrations, COR, and the Sweet Spot
Strike bat here

best performance feel _at_ node 2
e
vf
Evib
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Independence of End Conditions

• strike bat in barrellook at response in handle
• handle moves only after 0.6 ms delay
• collision nearly over by then
• nothing on knob end matters
• size, shape
• boundary conditions
• hands!
• confirmed experimentally

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q independent of end conditions experimental
proof
Conclusion mass added in knob has no effect on
collision efficiency (q)
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Vibrations and Broken Bats
movie
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Why Is Aluminum Better Than Wood?

• Aluminum has thin shell
• Less mass in barrel
• --lower MOI, higher bat speed, easier to control
  ?
• --but less effective at transferring energy ?
• --for many bats ? cancels ?
• just like corked wood bat
• Hoop modes
• trampoline effect ? ?
• ping

demo
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The Trampoline Effect A Simple Physical
Picture

• Two springs mutually compress each other
• KE ? PE ? KE
• PE shared between ball spring and bat spring
• PE in ball mostly dissipated (80!)
• PE in bat mostly restored
• Net effect less overall energy dissipated
• ...and therefore higher ball-bat COR
• more bounceconfirmed by experiment
• and higher BBS
• Also seen in golf, tennis,

demo
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Aerodynamics of a Baseball

• Gravity
• Drag (air resistance)
• Lift (or Magnus)

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Measuring drag and Magnus forces by high-speed
tracking
Magnus force is much easier to measure than drag
force
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Typical values of drag and lift
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Effect of Drag and Lift on Trajectories

• drag effect is huge
• lift effect is smaller but significant

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Some Effects of Drag

• Reduced distance on fly ball
• Reduction of pitched ball speed by 10
• Asymmetric trajectory
• Total Distance ? 1.7 x distance at apex
• Optimum home run angle 30o-35o

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Some Effects of Magnus

• Backspin makes ball rise
• hop of fastball
• undercut balls increased distance, reduced
  optimum angle of home run
• Topspin makes ball drop
• 12-6 curveball
• topped balls nose-dive
• Breaking pitches due to spin
• Cutters, sliders, etc.

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The PITCHf/x Tracking SystemA New Tool to Study
Baseball Flight
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How Does PITCHf/x Work?

• Two video cameras track baseball in 1/60-sec
  intervals
• usually high home and high first
• third CF camera used establises ht. of strike
  zone for each batter
• Pattern-recognition software to identify blobs
• Camera calibration to convert pixels to (x,y,z)
  9-parameter fit to trajectory
• constant acceleration for x(t),y(t),z(t)
• Use fit to calculate lots of stuff
• The full trajectory
• The break
• Drag and Magnus forces

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Pitch ClassificationJon Lester, Aug 3, 2007 _at_
Seattle
LHP Catchers View
I Nearly overhand fastball II Cut
Fastball III ¾ Fastball IV Curveball
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Whats the Deal with the Gyroball?
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Barry Bonds 756th Home Run

• PITCHf/x data tracked hit ball over first 20 ft
• Precision measurement of endpoint and time
• Inferred v0112 mph ?27o up ?16o to right
  of dead center ?1186 rpm (backspin) and 189 rpm
  (sidespin, breaking to center)

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Baseball AerodynamicsThings I would like to
know better

• Better data on drag
• drag crisis?
• Spin-dependent drag?
• Drag for vgt100 mph
• Dependence of drag/lift on seam orientation
• Is the spin constant?

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Oblique CollisionsLeaving the No-Spin Zone

• Oblique ? friction ? spin
• Familiar Results
• Balls hit to left/right break toward foul line
• Topspin gives tricky bounces in infield
• Backspin keeps fly ball in air longer
• Tricky popups to infield

demo
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Undercutting the ball ? backspin
trajectories
vertical sweet spot
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Another familiar result
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Putting it all TogetherCan curveball be hit
farther than fastball?

• Bat-Ball Collision Dynamics
• A fastball will be hit faster
• A curveball will be hit with more backspin

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curveball can be hit with more backspin WHY?
Fastball spin must reverse
Net effect backspin larger for curveball
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Can Curveball Travel Farther than Fastball?

• Bat-Ball Collision Dynamics
• A fastball will be hit faster
• A curveball will be hit with more backspin
• Aerodynamics
• A ball hit faster will travel farther
• Backspin increases distance
• Which effect wins?
• Curveball, by a hair!

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Work in Progress

• Collision experiments calculations to elucidate
  trampoline effect
• New studies of aerodynamics using Doppler radar
• Experiments on high-speed oblique collisions
• A book, with Aussi Rod Cross

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Final Summary

• Physics of baseball is a fun application of basic
  (and not-so-basic) physics
• Check out my web site if you want to know more
• webusers.npl.uiuc.edu/a-nathan/pob
• a-nathan_at_uiuc.edu
• Thanks for your attention and go Red Sox!