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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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A Brief Intoduction• My day job…

– experimental nuclear/particle physics– high-speed collisions between subatomic particles

• Nights and weekends...– physics of baseball– high-speed collision between baseball and bat

• Many similarities – And I get to watch/play baseball and call it work– A true intersection of passions

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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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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...”

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

“The physics of baseball is not rocket science. It’s much harder”

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

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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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 to study ballball trajectories– How far did that home run go?

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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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What Determines Batted Ball Speed?

• 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—Moment of Inertia (MOI) about

a point in the handle (“swing weight”)

– Heavier bat more efficient

• less recoil to bat larger q

– But….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 batting average: 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

– is the ball “juiced”

demo

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What does q depend on?

outside inside

sweet spot

3. Impact location on bat:

the “sweet spot”

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The 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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More on the trampoline effect…

• Trampoline effect increased by stiffer ball or more compliant bat

• Also see in tennis, golf, …

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Additional Remarks on q• Can be measured in the lab

– regulate non-wood bats (NCAA, ASA, …)

• Independent of “reference frame”• Independent of “end conditions”

– Not even the batter’s hands matter!

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• hit bat at barrel—measure movement at handle

• handle moves only after ~0.6 ms delay

• collision nearly over by then

• nothing on knob end matters• size, shape• boundary conditions• hands, grip• who is holding it

• Confirmed experimentally

Independence of End Conditions

Batter could drop bat just before contact and it would have no effect on ball!!!

-80

-40

0

40

80

0 2 4 6 8 10

y

t (ms)

impact @ 24.8"

26.8"

28.8"

displacement at handle

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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

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40

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80

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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

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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 can we learn from PITCHf/x?PITCHf/x is a pitch-tracking system installed in every MLB venue—a joint venture of Sportvision & MLBAM

MLB Gameday

ESPN K-Zone

Fox TrakMLB 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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>90 mph

80-90 mph

<80 mph

4-seam fastball

2-seam fastball

cutter/slider

curveball

The PITCHf/x pitch-tracking system:LHP Jon Lester, Aug. 3, 2007

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Jon Lester vs. sinkerball pitcher Brandon Webb

Jon Lester

Brandon Webb

Plots, courtesy of Dan Brooks

Comparing FB upward movement:• Lester ~ 11”• Webb ~ 3”

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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”).

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C. C. Sabathia: FB vs. Slider

Distance from home plate (ft)

95 mph fastball

82 mph slider

~4 inches

~12 inches

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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 .979

Medium

71 .873

Large 79 .684

http://www.hardballtimes.com

(small sample size, though)

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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—a pitcher’s nightmare!–Fly balls travel ~5% farther–Pitches don’t break as much

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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

330

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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The aerodynamics of batted balls:

How far did that home run travel?

• Ball leaves bat

• Ball hits horizontal distance D from home plate, H above ground

• How far would it have gone if no obstruction?

• There is no unique answer

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400 ft/30 ftRange=415-455Use time-of-flight to resolve

4 s

5 s7 s

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100

150

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0 100 200 300 400 500horizontal distance (ft)

0

5

10

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390 400 410 420 430 440 450 460horizontal distance (ft)

Calculations

Bob Brown, CWRUGreg Rybarczk, www.hittrackeronline.com

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The famous Mantle Home RunGriffith Stadium, April 17, 1953

Publicized as 565 ft

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How far did it really go?• Ball hit sign 460 ft (horizontal) and 60 ft (vertical)

from home plate• It was supposedly retrieved behind a house with

a 22-ft roof• Wind was blowing out at ~20 mph• Is there a plausible set of conditions consistent

with all these facts?

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0 50 100 150 200 250 300 350 400 450 500 550 600

sign

house

2000 rpm

4000 rpm

Range: 520-540 ft

Two Plausible Trajectories

Answer:Maybe!

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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, …

• Is the spin constant?

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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– a-nathan@illinois.edu

• I am living proof that knowing the physics doesn’t help you play the game better!

@ Red Sox Fantasy Camp, Feb. 1-7, 2009

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Example: Bond’s 756th home run

• tracking data from PITCHf/x video determines first 20 ft of trajectory• landing point and time of flight determined precisely from HD video• together, these are sufficient to determine the full trajectory, with very little uncertainty

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An example:Barry Bond’s 756th Home Run

Results:

• v0=112 mph

=270 up =160 to right of dead center =1186 rpm (backspin) and 189 rpm (sidespin, breaking to center)

• Total range: 442 ft