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Thanks to J. J. Crisco & R. M. Greenwald Medicine & Science in Sports & Exercise 34(10): 1675-1684; Oct 2002. Corked Bats and Rising Fastballs: . Alan M. Nathan Department of Physics University of Illinois. Using Physics to Debunk Some Myths of Baseball September 23, 2006. - PowerPoint PPT Presentation
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Corked Bats and Rising Fastballs: Using Physics to Debunk Some
Myths of BaseballSeptember 23, 2006
Thanks to J. J. Crisco & R. M. GreenwaldMedicine & Science in Sports & Exercise
34(10): 1675-1684; Oct 2002
Alan M. NathanDepartment of Physics
University of Illinois
2
Corked Bats and Rising Fastballs: Using Physics to Debunk Some
Myths of Baseball
October 27, 2004:the day the curse was
broken
3
References
“Our goal is not to reform the game but to understand it.
“The physicist’s model of the game must fit the game.”
4
References
“The book is written for the inquiring layperson…”
“…many controversial claims about the game are addressed and…resolved by this book.”
5
References
http://www.npl.uiuc.edu/~a-nathan/pob
Is this heaven?
No, it’s ….Iowa
Dyersville, home of the Field of Dreams
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Outline
• How does a baseball bat work?
• The flight of a baseball.
• Leaving the no-spin zone.
• Putting it all together.
7
Issues I Will Address• What matters more: pitch speed or bat speed?• Is the ball “juiced”?• What/where is the “sweet spot”?• Is corking the bat effective?• Does aluminum outperform wood?• Does a fastball rise?• What’s the deal with Denver?• Can a curveball be hit farther than a fastball?
8
“You can observe a lot by watching”
Champaign News-Gazette
CE Composites
--Yogi Berra
Easton Sports
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10
When Ash Meets Cowhide• A violent collision!
– forces large (>8000 lbs!); time short (<1/1000 sec!)– ball compresses, stops, expands
• like a spring: kinetic energy potential energy• inefficient: lots of energy dissipated bat recoils, vibrates
– bat recoils, vibrates
• GOAL: maximize batted ball speed (BBS) – BBS 105 mph, 30o d 400 ft – each additional mph ~5 ft
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What Determines BBS?• pitch speed, bat speed, “collision efficiency”• my only formula
BBS = e vpitch + (1+e) vbat
• typical numbers: e = 0.2 1+e = 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
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What does e depend on?
1. Weight and weight distribution of bat
– Heavier bat more efficient
• larger e; less recoil to bat
– Heavier bat has smaller vbat (usually)
– What is ideal bat weight?
• effect of bat weight on e is easy
• effect of bat weight on vbat harder
BBS = e vpitch + (1+e) vbat
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Experiments to Determine vbatUse high-speed videoMeasure dependence of vbat on …
--bat weight W--“swing weight” or MOI
Conclusion: MOI matters more than WObservation: Batters prefer lighter bats—31-34 oz
--control vs. power
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Is There an Advantage to “Corking” a Bat?
Based on best experimental data available:…for home run distance: no
…for home run frequency: maybe
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What does e depend on?
2. Bounciness of ball– “coefficient of restitution” or COR
– COR2 = rebound ht/initial ht
– ~0.5 for baseball
demo
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Is the Baseball “Juiced”?Is COR larger than it used
to be?
• MLB rules allow ~ 10% range of COR 35 ft• 1975 and 2004 equal to few %• No evidence for juiced ball
Measurements with high-speed cannon• COR=rebound speed/initial speed• 1975 vs. 2004
COR vs. velocity
0.4400
0.4600
0.4800
0.5000
0.5200
0.5400
0.5600
0.5800
50 60 70 80 90 100 110 120 130
velocity (mph)
CO
R
old 2new 13new 12old 1new 11old 3old/new
MLB specs
17demos
What does e depend on?3. Impact location on bat: the “sweet spot”
• Minimize recoil to bat—at Center of Gravity
• Maximize bat speed—at tip
• Minimize vibrations which…• sting!
• sometimes break the bat
• reduce COR lower BBS
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The “Sweet Spot Zone”
computer simulation…which agrees with experiments
nodes CG
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Vibrations and Broken Bats
movie0.000 5.000 10.000 15.000 20.000 25.000 30.000 35.000
pitcher
catcher
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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”
Does Aluminum Outperform Wood?
demo
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•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 “bounce”—confirmed by experiment…and higher BBS
• Also seen in golf, tennis, …
The “Trampoline” Effect:A Simple Physical Picture
demo
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Does Aluminum Outperform Wood?
YES!
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Additional Remarks on e
• can be measured in the lab– regulate non-wood bats (NCAA, ASA, …)
• “end conditions” don’t matter– Not even the batter’s hands!
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Forces on a Baseball in Flight
• Gravity• Drag (“air resistance”)• Lift (or “Magnus”)
v
ω
mg
Fdrag
FLift
demo
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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 700distance (ft)
no drag or lift
drag, no lift drag and lift
v
ω
mg
Fd
FL (Magnus)
260
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 700distance (ft)
no drag or lift
drag, no lift
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Some Effects of Lift
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
v
ω
mg
Fd
FL (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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Does a Fastball Rise?
• Can a ball thrown horizontally rise?• Is there a net upward acceleration?• Can Magnus force exceed gravity?
v
ω
mg
Fd
FL (Magnus)
For this to happen…• backspin must exceed 4000 rpm
>25 revolutions • not physically possible
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What’s the Deal with Denver?• High altitude, reduced air pressure
–80% of sea level–Reduced drag–Reduced lift
• Net effect:–Fly balls travel ~5% farther
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Oblique Collisions:Leaving 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
350
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”
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• Bat-Ball Collision Dynamics– A fastball will be hit faster– A curveball will be hit with more backspin
Putting it all Together:Can curveball be hit farther
than fastball?
37Net effect: backspin larger for curveball
Fastball: spin must reverse
curveball can be hit with more backspin: WHY?
Fastball with backspin
Curveball: spin doesn’t reverse
Curveball with topspin
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• 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!
Can Curveball Travel Farther than Fastball?
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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– www.npl.uiuc.edu/~a-nathan/pob– [email protected]
• Thanks for your attention and go Red Sox!