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1
Physics and Baseball:Having Your Cake and Eating it Too
Alan M. [email protected]
webusers.npl.uiuc.edu/~a-nathan/pobDepartment of Physics
University of Illinois
2
1927
Solvay Conference:
Greatest physics team
ever assembled
Baseball and Physics
1927 Yankees:
Greatest baseball team
ever assembled
MVP’s
3
A great book to read….
“Our goal is not to reform the game but to understand it.
“The physicist’s model of the game must fit the game.”
4
A Physicist’s Approach to Current Issues in Baseball
• Should aluminum bats be banned?
• Corked bats and juiced balls—do they matter?
• What the deal with the gyroball?
• Can steroid use increase home run production?
• Is the game different in Denver?
– and what about that humidor?
5
Some Experimental Tools
• Bat testing facility
• High-speed video or motion analysis“You can observe a lot by watching” ---Yogi– swinging the bat – ball-bat collision 1– ball-bat collision 2
• PITCHf/x tracking system
• Trackman radarmore on these later
See http://webusers.npl.uiuc.edu/~a-nathan/pob/video.html for some nifty videos.
6
Some Physics Background
• Physics of ball-bat collision
• Aerodynamics of a baseball
• Oblique collisions and spin
7
Description of Ball-Bat Collision• forces large, time short
– >8000 lbs, <1 ms
• ball compresses, stops, expands– KEPEKE– 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
8
Kinematics of Ball-Bat Collision
ball bat
e-rq =
1+re-r 1+e
BBS = v v1+r 1+r
e: “coefficient of restitution” 0.50 (energy dissipation—mainly in ball, some in bat)
r mballz2/I6 : bat recoil factor = 0.25(momentum and angular momentum conservation)
---heavier is better but…
q=0.20
BBS = q vball + (1+q) vbatvball vbat
BBS
z
9
40
42
44
46
48
50
8.5 9 9.5 10 10.5 11 11.5
I6"
(103 oz-in2)
knob
(rad/s)
y = m1*(9/m0)^m2
ErrorValue
0.392146.218m1
0.0574220.28747m2
NA3.8574Chisq
NA0.93138R
Crisco/Greenwald Batting Cage Study
woodaluminum
Batting cage study show how bat speed depends on I for college baseball players
~ [1/I6]n
0<n<0.5n 0.3
10
Accounting for COR:
Dynamic Model for Ball-Bat CollisionAMN, 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
11
Modal Analysis 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
12
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
best performance & feel
@ ~ node 2
13
• strike bat in barrel—look 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
-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
14
Aluminum has thin shell – Less mass in barrel
--lower MOI, higher bat speed, easier to control --but lower collision efficiency --partially canceling effects
– “Hoop modes” • trampoline effect • “ping” (~2000 Hz)
Why Is Aluminum Better Than Wood?
demo
15
•Two springs mutually compress each other KE PE KE
• PE shared between “ball spring” and “bat spring”
…sharing depends on “kball/kbat”
• PE in ball mostly dissipated (~80%!)
• PE 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
16
Regulating Performance of Non-Wood Bats:A Science-Based Approach Used by NCAA
• Specify maximum q – approx. same as for wood bats of similar wt.– 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%– does that mean aluminum should be banned?
• an issue many are struggling with
BBS = q vball + (1+q) vbat
17
What About Corked Bats?or..What was Sammy thinking?
Conclusion:• No increase in BBS
increase in swing speed decrease in collision efficiency
~ [1/I6]n
0<n<0.5
no trampoline effect!
Wood Bat RW01
unmodified
drilled
corked
0.475
0.480
0.485
0.490
0.495
ball-bat COR
18
What About Juiced Baseballs?
Conclusion:No evidence for juiced ball
19
Aerodynamics of a Baseball• Gravity• Drag (“air resistance”)• Lift (or “Magnus”)
v
ω
mg
Fd
FM
Courtesy, Popular Mechanics
Fd=½ CDAv2
-v direction
(ω v) direction FM = ½ CMARv
direction leading edge is turning
20
Typical values of drag and lift
0
0.5
1
1.5
2
0 25 50 75 100 125 150Speed in mph
Drag/Weight
Lift/Weight@1800 rpm
“Drag crisis?”
21
Effect of Drag and Lift on Trajectories
• drag effect is huge
• lift effect is smaller but significant
0
20
40
60
80
100
120
0 100 200 300 400 500 600 700
distance (ft)
no drag or lift
drag, no lift drag and lift
v
ω
mg
Fd
FM
220
50
100
150
200
250
300
350
400
10 20 30 40 50 60 70 80 90
Range (ft)
(deg)
Range vs.
2000 rpm
0 rpm
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
0
20
40
60
80
100
120
0 100 200 300 400 500 600 700
distance (ft)
no drag or lift
drag, no lift
23
Some Effects of Magnus
0
20
40
60
80
100
120
0 100 200 300 400 500 600 700
distance (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
Fd
FM
24
The PITCHf/x Tracking SystemA Quantitative Tool to Study Pitched Baseball Trajectories
25
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 establishes ht. of strike zone
• 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
26
Example: Drag and Drag Coefficients
20k pitches from Anaheim, 2007
27
Using PITCHf/x to Classify PitchesJon Lester, Aug 3, 2007 @ Seattle
I: Nearly overhand fastballII: Slider or cut fastballIII: ¾ FastballIV: Curveball
LHPCatcher’s View
spin axis
break direction = -90o
28
What’s the Deal with the Gyroball?
Courtesy, Ryutaro Himeno
Daisuke Matsuzaka:Does he or doesn’t he?
29
From PITCHf/x to HITf/xBarry Bond’s 756th Home Run
• PITCHf/x data tracked hit ball over first 20 ft• Precision measurement of endpoint and time-of-flight
• Inferred: v0=112 mph; =27o up; =16o to right of dead center; =1186 rpm (backspin) and 189 rpm (sidespin, breaking to center)
30
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, …
• Is the spin constant?
31
Trackman: The Wave of the Futuresee www.trackmangolf.com
• 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
– already in use for golf, currently being adapted for baseball
32thanks to Fredrik Tuxen, CTO of Trackman
33
Oblique Collisions:Leaving the No-Spin Zone
Oblique friction spin• still need a good collision model• my model: slide, then roll
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
340
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 going on here??
35
Another familiar result:
Catcher’s View
bat hits under ball:popup to opposite field
bat hits over ball:grounder to pull field
bat tilted downward
36
• Steroids increases muscle mass
• Increased muscle mass increases swing speed
• Increased swing speed increase BBS
• Increased BBS means longer fly balls
• Longer fly balls means more home runs
Steroids and Home Run Productonsee Roger Tobin, AJP, Jan. 2008
Home Run Distances, 2007www.hittrackeronline.com
Delta = distance beyond fence (ft)
~4% per foot
Tobin’s Conclusion: increase of BBS by few mph can increase HR rate by 30-50%!
38
Steroids and Bat Speed
• Batter supplies energy proportional to M• Energy shared between bat and some fraction
2 of M• Roughly: 2 ~ 0.01 • So roughly, 10% increase in M gives
– ~2.5% increase in vbat
– ~2 mph increase in BBS– ~12 additional ft. on long fly ball– ~20% (Adair) -50% (Tobin) more home runs!
39
Work in Progress
• Collision experiments & calculations to elucidate trampoline effect
• New studies of aerodynamics using Trackman and PITCHf/x
• Experiments on high-speed oblique collisions—does slide-then-roll model work?
• A book, with Aussi Rod Cross
40
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]
• Thanks for your attention and go Red Sox!
2004 2007