baseball & physics: an intersection of passions
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Baseball & Physics: An Intersection of Passions. Alan M. Nathan Department of Physics University of Illinois [email protected]. A good book to read…. My friend and mentor, Prof. Bob Adair. - PowerPoint PPT PresentationTRANSCRIPT
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Baseball & Physics:An Intersection of Passions
Alan M. Nathan Department of Physics
University of [email protected]
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A good book to read….
“…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 physicist’s repertoire...”
“The physicist’s 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. It’s much harder”
My friend and mentor, Prof. Bob Adair
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And check out my web site…webusers.npl.uiuc.edu/~pob/a-nathan
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1927 Solvay Conference:
Greatest physics team ever assembled
The Baseball/Physics Connection
1927 Yankees:Greatest baseball team
ever assembled
MVP’s
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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”
UMass/Lowell
--Yogi Berra
Easton Sports
Daily Illini
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When ash meets cowhide….• forces large, time short
– >8000 lbs, <1 ms• ball compresses, stops, expands
– like a spring: KEPEKE– 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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• pitch speed• bat speed• “collision efficiency”: a property of the ball and bat
BBS = q vpitch + (1+q) vbat
• typical numbers: q = 0.2 1+q = 1.2example: 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
What Determines Batted Ball Speed?
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What does q depend on?
1. “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
BBS = q vpitch + (1+q) vbat
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The Ideal Bat Weight (or MOI)
Batters seem to prefer lower MOI bats, sacrificing power for “quickness”
BBS (mph)
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Is There an Advantage to “Corking” a Bat?
Based on best experimental data available:…for “harder” hit: no
…for frequency of good contact: probably
Sammy Sosa, June 2003
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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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What does q depend on?3. Impact location on bat
outside “sweet spot”
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Studying the Vibrations of a Baseball Batwww.kettering.edu/~drussell/bats.html
0
0.05
0.1
0.15
0 500 1000 1500 2000 2500
FFT(R)
frequency (Hz)
179
582
1181
1830
2400
frequency
-1.5
-1
-0.5
0
0.5
1
0 5 10 15 20
R
t (ms)
time
0 5 10 15 20 25 30 35
f1 = 179 Hz
f2 = 582 Hz
f3 = 1181 Hz
f4 = 1830 Hz
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Vibrations, COR, and the “Sweet Spot”
Evib
vf
e
+
0.1
0.2
0.2
0.3
0.3
0.4
0.4
0.5
0
20
40
60
80
100
120
0 5 10 15
e
vf (mph)
distance from tip (inches)
nodes4 3 2 1
Strike bat here
at ~ node 2vibrations minimizedCOR maximizedBBS maximizedbest “feel”
Note: COP is irrelevant to feel and performance
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• strike bat on barrel—look 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
-30.00
-20.00
-10.00
0.00
10.00
20.00
30.00
0 1 2 3 4 5
v (m/s)
t (ms)
Independence of End Conditions
Batter could drop bat just before contact and it would have no effect on ball!!!
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Aluminum has thin shell – Less mass in barrel—lower MOI
--higher bat speed and quickness --but smaller q --for many bats nearly cancels
» just like corked wood bat– “Hoop modes”
• trampoline effect • “ping”
Does Aluminum Outperform Wood?
YES!
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• 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 “bounce”—confirmed by experiment…and higher BBS
• Also seen in golf, tennis, …
The “Trampoline” Effect:A Simple Physical Picture
demo
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Flight of the Baseball• Gravity• Drag (“air resistance”)• Lift (or “Magnus”)
v
ω
mg
Fd
FM
Courtesy, Popular Mechanics
Fd=½ CDAv2
-v direction
FM = ½ CLAv2 CL = CMR/v
(ω v) direction direction leading edge is turning
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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
0
20
40
60
80
100
120
0 100 200 300 400 500 600 700distance (ft)
no drag or lift
drag, no lift
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Some Effects of Spin
0
20
40
60
80
100
120
0 100 200 300 400 500 600 700distance (ft)
no drag or lift
drag, no lift drag and lift
• 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.
v
ω
mg
Fdrag
FMagnus
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Oblique Collisions and Spin
Movie clip
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friction
normal forcev
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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
friction
velocity
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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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50
100
150
200
250
-100 0 100 200 300 400
1.5
0
0.25
0.5 0.75
1.02.0
0.75
Undercutting the ball backspin
Ball100 downward
Bat 100 upward
D = center-to-center offset
trajectories
“vertical sweet spot”
What’s this all about?
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Paradoxical Popups
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What are we learning from the PITCHf/x system?
A report from the summit
• 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.htmlsportvision.com/events/pfx.html
This section prepared with help from John Walsh, Mike Fast, Josh Kalk, Dan Brooks, and the good folks at Sportvison, mainly Marv White.
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PITCHf/x is a pitch-tracking system installed in every MLB venue—a joint venture of Sportvision & MLBAM
MLB Gameday
ESPN K-Zone
Fox Trak
MLB Gameday Screen
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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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65
70
75
80
85
90
70 75 80 85 90 95 100v
0 (mph)
y = m1 * M0ErrorValue
0.000868580.89296m1 NA56.865ChisqNA0.98879R
• Pitched ball loses about 10% of speed between pitcher and batter• Average speed <v> is ~95% of release speed
Example: Pitch Speed--PITCHf/x vs. the gun
PITCHf/x is almost surely more accurate than the gun
v0
vf
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Example: Pitching at High Altitude:Higher <v>, less movement in Denver vs. Toronto
10%
loss of velocity
total movement12”
7.5%
8”
PITCHf/x data contain a wealth of information about drag and lift!
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Example--20k pitches from Anaheim, 2007:Cd vs. v0 <Cd> vs. v0 in 2 mph bins
Drag Coefficient from Pitchf/x
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Drag Coefficient:no evidence for “drag crisis”
0.00
0.10
0.20
0.30
0.40
0.50
0.60
60 65 70 75 80 85 90 95 100
Cd
v (mph)
wind tunnel
Adair
older pitch tracking
Pitchf/x Anaheim 2007
Briggs
Good approximation: Cd = 0.35±0.05 in range 70-100 mph
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>90 mph
80-90 mph
<80 mph
4-seam fastball
2-seam fastball
cutter/slider
curveball
Pitch Classification: LHP Jon Lester, Aug. 3, 2007
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Josh Kalk, THT, 5/22/08
What makes an effective slider?—C. C. Sabathia
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”).
0
1
2
3
4
5
6
7
0 10 20 30 40 50
C. C. Sabathia: FB vs. Slider
Distance from home plate (ft)
95 mph fastball
82 mph slider
~4 inches
~12 inches
side view
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PITCHf/x tackles the knuckleball – John Walsh
• 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
• Example analysis: What happens when knuckleball does not “knuckle”?
• Split k-balls into 3 groups – small, medium, large break
fastball
curve
slider
change
knuckler
Amount of Break
Pitches put in play
OPS against
Small 47 .979Medium
71 .873
Large 79 .684
http://www.hardballtimes.com
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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 Analysis:Batting Average for Balls in Play
<-10 -5:0
5:10
15:2
0
25:3
0
35:4
0
>45
theta (deg)
BABIP0.800-1.0000.600-0.8000.400-0.6000.200-0.4000.000-0.200
w/o home runs home runs only
V0
V0
V0
<-10 -5:0
5:10
15:2
0
25:3
0
35:4
0
>45
theta (deg)
BABIP0.800-1.0000.600-0.8000.400-0.6000.200-0.4000.000-0.200
V0
<-10 -5:0
5:10
15:2
0
25:3
0
35:4
0
>45
theta (deg)
HR/balls in play
0.600-0.8000.400-0.6000.200-0.4000.000-0.200
V0
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Example of Hitf/x Analysis:Batting Average for Balls in Play
BABIP:V0>90 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
0
100
200
300
400
0 100 200 300 400Horizontal Distance (ft)
(379,20,5.2)
hitf/xhittracker
Full trajectory is constrained by • initial velocity vector• landing point• flight time
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Final example:The “carry” of a fly ball
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The “carry” of a fly ball
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Baseball Aerodynamics:Things I would like to know better
• Better data on drag– “drag crisis”?– spin-dependent drag?– drag for v>100 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– [email protected]
• I am living proof that knowing the physics doesn’t help you play the game better!
@ Red Sox Fantasy Camp, Feb. 1-7, 2009