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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

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Corked Bats and Rising Fastballs: Using Physics to Debunk Some

Myths of Baseball

October 27, 2004:the day the curse was

broken

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References

“Our goal is not to reform the game but to understand it.

“The physicist’s model of the game must fit the game.”

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References

“The book is written for the inquiring layperson…”

“…many controversial claims about the game are addressed and…resolved by this book.”

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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.

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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?

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“You can observe a lot by watching”

Champaign News-Gazette

CE Composites

--Yogi Berra

Easton Sports

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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– a-nathan@uiuc.edu

• Thanks for your attention and go Red Sox!