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Baseball & Physics:An Intersection of Passions

Alan M. Nathan Department of Physics

University of Illinoisa-nathan@uiuc.edu

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Is this heaven?

No, it’s ….

IowaDyersville, home of the Field of Dreams

In my younger days….

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2004 2007

But now I just watch and enjoy…

…and there’s been a lot to enjoy lately….

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A good 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.”

My 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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The Physics of Hitting a Home Run

• How does a baseball bat work?

• The flight of a baseball.

• Leaving the no-spin zone.

• Putting it all together.

• And what’s the deal with steroids?

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“Hitting is timing; pitching is

upsetting timing”

Hitting the Baseball:

the most difficult feat in sports

“Hitting is fifty percent above the shoulders”

1955 Topps cards from my personal collection

8Graphic courtesy of Bob Adair and NYT

Hitting and Pitching, Thinking and Guessing

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“You can observe a lot by watching”

Champaign News-Gazette

UMass/Lowell

--Yogi Berra

Easton Sports

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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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What Determines BBS?• pitch speed

• bat speed

• “collision efficiency”: a property of the ball and bat

• my only formula

BBS = q vpitch + (1+q) vbat

• typical numbers: q = 0.2 1+q = 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

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What does q depend on?

1. Weight of bat in the barrel

– Heavier bat more efficient

• larger q; less recoil to bat

– Heavier bat has smaller vbat (usually)

– What is ideal bat weight?

• effect of bat weight on q is easy

• effect of bat weight on vbat is harder

BBS = q vpitch + (1+q) vbat

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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

Sammy Sosa, June 2003

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What does q 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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What does q depend on?3. Impact location on bat

outside inside

sweet spot

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Vibrations and Broken Bats

movie

0.000 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

--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

YES!

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Additional Remarks on q

• 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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Aerodynamics of Baseball in Flight

• Gravity• Drag (“air resistance”)• “Magnus” force on

spinning baseball

v

ω

mg

Fdrag

FMagnus

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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-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

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Some Effects of Spin

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

Fdrag

FMagnus

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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?

For this to happen…• backspin must exceed 4000 rpm

>25 revolutions • not physically possible

v

ω

mg

Fdrag

FMagnus

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What’s the Deal with the Gyroball?

Courtesy, Ryutaro Himeno

Daisuke Matsuzaka:Does he or doesn’t he?

Definitely maybe!

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What’s the Deal with Denver?

• High altitude, reduced air density (80% of sea level)–Reduced drag: increases distance

–Reduced lift: decreases distance

• Net effect:–Fly balls travel ~5% farther

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Leaving the No-Spin Zone

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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

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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

280

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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• 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!

– But I wouldn’t bet the farm on it!

Can curveball be hit farther than fastball?

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• 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

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0

0.0025

0.005

0 100 200 300 400 500

Range (feet)

Pro

bab

ility

(p

er f

t)

Home Run Threshold

10%

To have 10% HR’s,there must be a lotof near-HR’s

Elite hitters:HR/BBIP = ~10%

Thanks to Roger Tobin

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0

0.0025

0.005

0 100 200 300 400 500

Range (feet)

Pro

bab

ility

(p

er f

t)

Home Run Threshold

10%

14.9%

Change in range distribution when batted ball speed increased by 3%:3% change in BBS gives 50% increase in HR rate!

Baseline

3% speedincrease

Thanks to Roger Tobin

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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!