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Baseball

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Title: Baseball


1
Baseball PhysicsAn Intersection of Passions
Alan M. Nathan Department of Physics University
of Illinois a-nathan_at_illinois.edu
2
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... Our goal is not to
reform the game but to understand it. The
physics of baseball is not rocket science. Its
much harder The physicists model of the game
must fit the game.
3
And check out my web sitewebusers.npl.uiuc.edu/
pob/a-nathan
4
The Baseball/Physics Connection
5
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 far did that home run go?

6
You can observe a lot by watching
Daily Illini
--Yogi Berra
Easton Sports
UMass/Lowell
7
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

8
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

9
What does q depend on?
BBS q vpitch (1q) vbat
  • Weight of bat near the impact region (MOI about
    the handle)
  • Heavier bat more efficient
  • less recoil to bat ? larger q
  • Heavier bat has smaller vbat (usually)
  • What is ideal bat weight (or MOI) ?
  • effect of bat weight on q is easy
  • effect of bat weight on vbat is harder

10
The Ideal Bat Weight (or MOI)
Batters seem to prefer lower MOI bats,
sacrificing control for power
corked bats?
11
Is There an Advantage to Corking a Bat?
Sammy Sosa, June 2003
Based on best experimental data available for
home run distance no for home run frequency
maybe
12
What does q depend on?
  • 2. Bounciness of ball
  • coefficient of restitution or COR
  • COR2 rebound ht/initial ht
  • 0.5 for baseball

13
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

14
What does q depend on?
  • Impact location on bat

sweet spot
inside
outside
15
Studying the Vibrations of a Baseball
Bat www.kettering.edu/drussell/bats.html
16
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
17
Independence of End Conditions
  • handle moves only after 0.6 ms delay
  • collision nearly over by then
  • nothing on knob end matters
  • size, shape
  • boundary conditions
  • hands, grip
  • who is holding it
  • Confirmed experimentally

Batter could drop bat just before contact and it
would have no effect on ball!!!
18
  • Measuring collision efficiency
  • Sport Sciences Lab _at_ Washington State
  • Baseball Research Center _at_ UMass/Lowell
  • Regulating bat performance
  • Independence of end conditions and ref. frame
    crucial


19
Does Aluminum Outperform Wood?
YES!
  • Aluminum has thin shell
  • Less mass in barrellower MOI
  • --higher bat speed, easier to control ?
  • --but smaller q ?
  • --for many bats ? nearly cancels ?
  • just like corked wood bat
  • Hoop modes
  • trampoline effect ? ?
  • ping

20
Hoop Modes and the ping
Hoop (cylinder) modes
First hoop mode ? ping and trampoline effect
Thanks to Dan Russell for this slide
21
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
22
Softball Data and Model
Russell, Smith, AMN
alum
wood
Wood
change kbat
change kball
  • Conclusions
  • COR of Al bat can be significantly higher
  • essential physics is understood

23
Trivia Timeout
Why is this famous? Last pitch, perfect game in
WS Year? 1956 Pitcher? Don Larsen 2B? Billy
Martin Batter? Dale Mitchell Hitting for Sal
Maglie
Bonus deep trivia Who was the home plate umpire?
Babe Pinelli, in his last game
24
Flight of the Baseball
  • Gravity
  • Drag (air resistance)
  • Lift (or Magnus)

25
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-35o

26
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.

27
Oblique Collisions and Spin
friction
28
(No Transcript)
29
Some Familiar Effects
  • 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

30
Another familiar result
31
Undercutting the ball ? backspin
trajectories
vertical sweet spot
32
Paradoxical Popups
33
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
34
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
35
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
36
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 of this can be correlated with what the
    batter does!
  • a complete digital record exists!

37
And the good news is.
  • all these data are freely available online! For
    info on how to download, establish data base,
    etc., see
  • mvn.com/mlb-stats/2008/01/14/a-pitchfx-primer/
  • Mike Fast
  • http//brooksbaseball.net/pfx/
  • Dan Brooks
  • http//blog.stealingfirst.com/2008/03/07/how-to-li
    nk-pitchfx-to-retrosheet/
  • Dan Turkenkopf

38
What can we potentially learn from these data?
  • Things of interest to physicists
  • Effect of air drag and spin
  • How much does a ball break?
  • Is there late break?
  • Can the effects of drag be quantified?
  • How does drag depend on atmospheric conditions?
  • Does drag depend on spin?
  • Is there a drag crisis?
  • The mysteries of the knuckleball

39
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

PITCHf/x is almost surely more accurate than the
gun
40
Example Pitching at High AltitudeHigher ltvgt,
less movement in Denver vs. Toronto
PITCHf/x data contain a wealth of information
about drag and lift!
41
Compare to sinkerball pitcher Brandon Webb
Brandon Webb
  • Comparing FB upward movement
  • Lester 11
  • Webb 3

Jon Lester
Plots, courtesy of Dan Brooks
42
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).
43
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
http//www.hardballtimes.com/main/article/butterfl
ies-are-not-bullets/
  • Example analysis What happens when knuckleball
    does not knuckle?
  • Split k-balls into 3 groups small, medium,
    large break

(small sample size, though)
44
The aerodynamics of batted ballsHow far did
that home run travel?
  • Ball leaves bat
  • Ball hits horizontal distance D from home plate,
    H above ground
  • How far would it have gone if no obstruction?

45
Calculations
400 ft/30 ft Range415-455 Use time-of-flight to
resolve
Bob Brown, CWRU Greg Rybarczk, www.hittrackeronlin
e.com
4 s
5 s
7 s
46
Example Bonds 756th home run
  • tracking data from PITCHf/x video determines
    first 20 ft of trajectory
  • landing point and time of flight determined
    precisely from HD video
  • together, these are sufficient to determine the
    full trajectory, with very little uncertainty

47
An exampleBarry Bonds 756th Home Run
  • Results
  • v0112 mph
  • ?270 up
  • ?160 to right of dead center
  • ?1186 rpm (backspin) and 189 rpm (sidespin,
    breaking to center)
  • Total range 442 ft

48
The famous Mantle Home RunGriffith Stadium,
April 17, 1953Publicized as 565 ft
49
How far did it really go?
  • Ball hit sign 460 ft (horizontal) and 60 ft
    (vertical) from home plate
  • It was supposedly retrieved behind a house with a
    22-ft roof
  • Wind was blowing out at 20 mph
  • Is there a plausible set of conditions consistent
    with all these facts?

Answer Maybe!
50
Sci-Fly The Wave of the Futureanother toy for
me to play with!
  • Doppler radar to measure radial velocity
  • 3-detector array to measure phase
  • two angles
  • Sidebands gives spin magnitude
  • Result
  • in principle, full trajectory can be
    reconstructed, including spin and spin axis
  • originally developed for golf (Trackman)
  • now adapted for baseball

51
Safeco Field Experiment , October 2008The goal
study fly ball trajectories and check the
validity of SciFly
  • Project fly balls with pitching machine
  • Track with Sci-Fly and measure spin
  • Measure initial velocity spin with high-speed
    video
  • Measure time of flight with camcorder
  • Measure total distance with tape measure

Many thanks to the Ms management and to Rawlings
for making this happen
52
Typical Sci-Fly Trajectory
initial parameters 81.7 mph, 30.80, 2004 rpm
backspin TOF4.62 sec D317 ft.
Data still being analyzed
53
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,
  • Is the spin constant?

54
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

55
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
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