Baseball

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Baseball PhysicsAn Intersection of Passions
Alan M. Nathan Department of Physics University
of Illinois a-nathan_at_illinois.edu
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A good book to read.
My friend and mentor, Prof. Bob Adair
the physics of baseball is not the clean,
well-defined physics of fundamental matters.
Hence conclusions must depend on approximations
and estimates. But estimates are part of the
physicists repertoire... The physicists
model of the game must fit the game. Our goal
is not to reform the game but to understand
it. The physics of baseball is not rocket
science. Its much harder
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And check out my web sitewebusers.npl.uiuc.edu/
pob/a-nathan
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The Baseball/Physics Connection
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Topics I Will Cover

• The ball-bat collision
• How a bat works
• Wood vs. aluminum
• Putting spin on the ball
• The flight of the baseball
• Drag, lift, and all that
• New tools
• How much does a ball carry?

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You can observe a lot by watching
Daily Illini
--Yogi Berra
Easton Sports
UMass/Lowell
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When ash meets cowhide.

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

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What Determines Batted Ball Speed?

• pitch speed
• bat speed
• collision efficiency a property of the ball
  and bat
• BBS q vpitch (1q) vbat
• typical numbers q 0.2 1q 1.2
• example 90 70 gives 102 mph (400)
• vbat matters much more than vpitch!
• Each mph of bat speed worth 6 ft
• Each mph of pitch speed worth 1 ft

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What does q depend on?
BBS q vpitch (1q) vbat

• Swing Weight MOI about the handle
• Larger MOI
• less recoil to bat ? larger q
• smaller swing speed (usually)
• What is ideal swing weight?
• effect of swing weight on q is easy
• effect of swing weight on vbat is harder

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The Ideal Bat Weight (or MOI)
BBS (mph)
Batters seem to prefer lower MOI bats,
sacrificing power for quickness
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Is There an Advantage to Corking a Bat?
Sammy Sosa, June 2003
Based on best experimental data available for
harder hit no for frequency of good contact
probably
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What does q depend on?

• 2. Bounciness of ball
• coefficient of restitution or COR
• COR vf/vi
• 0.5 for baseball
• 75 of energy dissipated

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Is the Baseball Juiced? Is COR larger than it
used to be?

• Measurements with high-speed cannon
• CORrebound speed/initial speed
• 1975 vs. 2004

• 1975 and 2004 equal to few
• No evidence for juiced ball

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What does q depend on?

• Impact location on bat

outside
sweet spot
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Studying the Vibrations of a Baseball
Bat www.kettering.edu/drussell/bats.html
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Vibrations, COR, and the Sweet Spot
at node 2 vibrations minimized COR
maximized BBS maximized best feel

e
vf
Evib
Note COP is irrelevant to feel and performance
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Independence of End Conditions

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

Batter could drop bat just before contact and it
would have no effect on ball!!!
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Does Aluminum Outperform Wood?
YES!

• Aluminum has thin shell
• Less mass in barrellower MOI
• --higher bat speed and quickness ?
• --but smaller q ?
• --for many bats ? nearly cancels ?
• just like corked wood bat
• Hoop modes
• trampoline effect ? ?
• ping

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The Trampoline Effect A Simple Physical
Picture

• Two springs mutually compress
• Energy shared between ball spring and bat
  spring
• Sharing depends on relative stiffnesses of
  springs
• Energy stored in ball mostly dissipated (80!)
• Energy stored 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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Flight of the Baseball

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

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Real vs. Physics 101 Trajectory Effect of Drag

• Reduced distance on fly ball
• Reduction of pitched ball speed by 8-10 mph
• Asymmetric trajectory
• Total Distance ? 1.7 x distance at apex
• Optimum home run angle 30o

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Some Effects of Spin

• 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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Oblique Collisions and Spin
Movie clip
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(No Transcript)
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Some Familiar Effects

• Balls hit to left/right break toward foul line
• Topspin makes line drives nose-dive
• Backspin keeps fly ball in air longer
• Tricky popups to infield

View from above
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Another familiar result
Balls hit to CF slice
Spin axis
From LHH, ball will curve toward LF
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Undercutting the ball ? backspin
trajectories
vertical sweet spot
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Paradoxical Popups
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What are we learning from the PITCHf/x system?A
report from the summit
This section prepared with help from John Walsh,
Mike Fast, Josh Kalk, Dan Brooks, and the good
folks at Sportvison, mainly Marv White.

• What is PITCHf/x and how does it work?
• What are we learning from it?
• Outlook for future

webusers.npl.uiuc.edu/a-nathan/pob/pitchtracker.h
tml sportvision.com/events/pfx.html
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PITCHf/x is a pitch-tracking system installed in
every MLB venuea joint venture of Sportvision
MLBAM
ESPN K-Zone
MLB Gameday
MLB Gameday Screen
Fox Trak
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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
• Software to identify and track pitch frame-by-
  frame in real time ? full trajectory

? lots of other stuff
Image, courtesy of Sportvision
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What kind of stuff can one learn?

• Pitch speed to 0.5 mph
• at release and at home plate (they are
  different!)
• Pitch location to 0.5 inches
• at release and at home plate
• movement to 2.0 inches
• both magnitude and direction
• Initial velocity direction
• Type of pitch
• more on this later
• And all these data are freely available online!

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Example Pitch Speed--PITCHf/x vs. the gun

• Pitched ball loses about 10 of speed between
  pitcher and batter
• Average speed ltvgt is 95 of release speed

vf
PITCHf/x is almost surely more accurate than the
gun
v0
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Example Pitching at High AltitudeHigher ltvgt,
less movement in Denver vs. Toronto
PITCHf/x data contain a wealth of information
about drag and lift!
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Drag Coefficient from Pitchf/x
Cd vs. v0
ltCdgt vs. v0 in 2 mph bins
Example--20k pitches from Anaheim, 2007
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Drag Coefficientno evidence for drag crisis
Good approximation Cd 0.350.05 in range
70-100 mph
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Pitch Classification LHP Jon Lester, Aug. 3,
2007
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What makes an effective slider?C. C. Sabathia
Josh Kalk, THT, 5/22/08
This slider is very effective since it looks like
a fastball for over half the trajectory, then
seems to drop at the last minute (late break).
side view
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PITCHf/x tackles the knuckleball John Walsh
http//www.hardballtimes.com
fastball

• Classify pitches using vertical and horizontal
  break plus speed
• Compare normal pitcher (C.C. Sabathia) with
  k-baller (Tim Wakefield)
• Randomness of k-ball break is evident in
  PITCHf/x data

knuckler
slider
change
curve

• Example analysis What happens when knuckleball
  does not knuckle?
• Split k-balls into 3 groups small, medium,
  large break

Amount of Break Pitches put in play OPS against
Small 47 .979
Medium 71 .873
Large 79 .684
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New Tools to Study Trajectories of Batted Balls

• Hitf/x
• Uses Pitchf/x cameras to track initial trajectory
• v0,?,?
• Hittracker (www.hittrackeronline.com)
• Measure landing point and flight time for home
  runs
• Trackman
• Phased array Doppler radar
• Measure full trajectory and spin

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Example of Hitf/x AnalysisBatting Average for
Balls in Play
w/o home runs
home runs only
? V0
? V0
? V0
? V0
V0
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Example of Hitf/x AnalysisBatting Average for
Balls in Play
BABIP V0gt90 mph
w/o home runs
home runs
Goal Establish outcome-independent hitting
metrics
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Tracking Everything
Movie clip
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Combining HITf/x with Hittracker

• Full trajectory is constrained by
• initial velocity vector
• landing point
• flight time

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Final exampleThe carry of a fly ball
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The carry of a fly ball
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Does the ball carry better in Yankee Stadium?
No evidence for better carry in YS in the present
data.
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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 Magnus on seam orientation,
  surface roughness,
• What is the time constant for spin decay?

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Work in Progress

• Collision experiments calculations to elucidate
  trampoline effect
• New studies of aerodynamics
• Experiments on high-speed oblique collisions
• To quantify spin on batted ball
• 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_illinois.edu
• I am living proof that knowing the physics
  doesnt help you play the game better!

_at_ Red Sox Fantasy Camp, Feb. 1-7, 2009