Page 2

Is There an Advantage to “Corking” a Bat?...or is the cork better left in the wine bottle?

Page 3

Does Corking the Bat Give an Advantage?

A Physicist’s Approach

Introduction: The Ball-Bat Collision

Kinematics

Dynamics: a long (but interesting) detour

Kinematics revisited

Hitting the Ball Squarely...or not

Pitching and Hitting, Thinking and Guessing

Summary/Conclusions

Page 4

1927

Solvay Conference:

Greatest physics team

ever assembled

Baseball and Physics

1927 Yankees:

Greatest baseball team

ever assembled

MVP’s

Page 5

Introduction: Description of Ball-Bat Collision

forces large (>8000 lbs!) time short (<1/1000 sec!) ball compresses, stops, expands

kinetic energy potential energy

lots of energy lost

bat is flexible it compresses too

to hit a home run... large hit ball speed

optimum take-off angle

backspin

Courtesy of CE Composites

Page 6

Kinematics of Ball-Bat Collision

vball vbat

vff ball bat

e-r 1+ev = v v

1+r 1+r

r: bat recoil factor = mball/Mbat,eff 0.25(momentum and angular momentum conservation)

e: coefficient of restitution 0.50 (energy dissipation)

typical numbers: vf = 0.2 vball + 1.2 vbat

eA 1+ eA

Page 7

Kinematics of Ball-Bat Collision

f ball bat

e-r 1+ev = v v

1+r 1+r

For maximum vf:

• r = mball/Mbat,eff small Mbat,eff large

Mbat,eff Ih/z2

• vbat large

vbat ~ (Ih)-x

• e large

vball vbat

vf

Z

a tradeoff

Page 8

The vbat-Mbat tradeoff: General Considerations

60

70

80

90

100

110

120

20 30 40 50 60

n=0constant v

bat

n=0.5constant bat KE

vbat

= 65 mph x (32/Mbat

)n

Mbat

(oz)

vf (mph)

0 n 0.5 are physically sensible bounds

Page 9

Swinging the Bat

Page 10

Thanks to J. J. Crisco & R. GreenwaldMedicine & Science in Sports & Exercise

34(10): 1675-1684; Oct 2002

Experimental Swing Speed Studies

Page 11

z

x

Crisco/Greenwald Batting Cage Study: College Baseball

Z

0.8”

X3”

45 rad/s

vbat vs. z

70 mph@ 28”

Page 12

• I-n knob

• n = 0.31 0.04• 13% reduction in I gives ~4% increase in bat speed

bat speed versus MOI

40

42

44

46

48

50

1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9

Iknob

(104 oz-in2)

knob

(rad/s)

Crisco/Greenwald Batting Cage Study

vbat I-0.3

vbat I-0.5

Page 13

Recent ASA Slow-Pitch Softball Field Tests(L. V. Smith, J. Broker, AMN)

Conclusions:

• bat speed more a function of mass distribution than mass

• n~ 0.25

0.94

0.96

0.98

1

1.02

1.04

1.06

6000 7000 8000 9000 10000 11000

Bat Speed at 6" Point vs. MOI

MOI (oz-in2)

dashed: n=0.25solid: n=0.23

0.96

0.98

1

1.02

1.04

24 25 26 27 28 29 30 31 32

W (oz)

Bat Speed at 6" Point vs. W

~(1/M)0.25

fixed M fixed MOIknob

Page 14

The vbat-Mbat tradeoff revisited

Looks like corking reduces vf! More later...

60

70

80

90

100

110

120

20 30 40 50 60

n=0constant v

bat

n=0.5constant bat KE

vbat

= 65 mph x (32/Mbat

)n

Mbat

(oz)

vf (mph)

n=0.31 (expt)

Page 15

Kinematics of Ball-Bat Collision

f ball bat

e-r 1+ev = v v

1+r 1+r

For maximum vf:

• r = mball/Mbat,eff small Mbat,eff large

Mbat,eff Ih/z2

• vbat large

vbat ~ (Ih)-x

vball vbat

vf

Z

a wash—at best

• e large what about this?

Page 16

Collision excites bending vibrations in

bat

Ouch!! Thud!! Sometimes broken bat

Energy lost lower e, vf

Find lowest mode by tapping

Reduced considerably if

Impact is at a node

Collision time (~0.6 ms) > TN

Accounting for Energy Dissipation:

Dynamics of Ball-Bat Colllision

Page 17

20

-2 0

-1 5

-1 0

-5

0

5

10

15

20

0 5 10 15 20 25 30 35

y

z

y

A Dynamic Model of the Bat-Ball Collision

• Solve eigenvalue problem for free oscillations (F=0)

normal modes (yn, n)

• Model ball-bat force F

• Expand y in normal modes

• Solve coupled equations of motion for ball, bat‡ Note for experts: full Timoshenko (nonuniform) beam theory used

Euler-Bernoulli Beam Theory‡

t)F(z, t

yA

z

yEI

z 2

2

2

2

2

2

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

Page 19

0 5 10 15 20 25 30 35

f1 = 179 Hz

f2 = 582 Hz

Effect of Bat Vibrations on COR

COR depends strongly on impact location

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

Evib

vf

COR

Page 20

Relation to Reality: Experimental Data

Ball incident on bat at rest

Conclusion: essential physics understood

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

23 24 25 26 27 28 29 30 31

vfinal

/vinitial

distance from knob (inches)

data from Lansmont BBVCbat pivoted about 5-3/4"

vinitial

=100 mph

rigid bat

flexible bat

nodes

only lowest mode excited lowest 4 modes excited

0

0.1

0.2

0.3

0.4

16 20 24 28 32

vfinal

/vinitial

distance from knob (inches)

rigid bat

flexible bat

CM node

data from Rod Crossfreely suspended bat

vi = 2.2 mph

Page 21

time evolution of bat

• rigid-body motion develops only after few ms

• far end of bat has no effect on ball

knob moves after >0.6 ms

collision over after 0.6 ms

nothing on knob end matters• size, shape• boundary conditions• hands

-4

-2

0

2

4

6

8

10

displacement (mm)

0 - 1 ms0.1 ms intervals

impact point

-50

0

50

100

150

200

0 5 10 15 20 25 30

1-10 ms1 ms intervals

impact point

distance from knob (inches)

Page 22

Why is Aluminum Different (Better)?• Inertial differences

Hollow shell more uniform mass distribution

effectively, less mass near impact location swing speed higher ~cancels for many bats definite advantage for “contact” hitter

• Dynamic differences

Ball-Bat COR significantly larger for aluminum (“trampoline effect”)

Page 23

Aluminum Bats: The “Trampoline” Effect:

Ball and bat mutually compress each other

Compressional energy shared

Essential parameter: kbat/kball

• large for wood; smaller for Al Ball inefficient, bat efficient at returning energy Net effect: less overall energy dissipation Effect occurs in tennis, golf, aluminum bats, ...

>20% increase in COR!

Demo

Page 24

“Corking” a Wood Bat (illegal!)

• ~1” hole, 10” deep + filler

• Is there a trampoline effect?

MOVIE

Page 25

Conclusion:no trampoline effect!

drilled

original corked

0.475

0.480

0.485

0.490

0.495

ball-bat COR

COR Measurements

Lloyd Smith,Dan Russell,

AMN, July 2003

2%

Page 26

Kinematics and Swing Speed, Revisted

Vbat dependence on I:

~ I-n : purely phenomenological

~ (I+I0)-1/2 : fixed energy shared between

bat (I) and batter (I0)

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10

n

I0/<I>

75

80

85

90

95

100

3 4 5 6 7 8

vv (mph)

unmodified

drilled n=0

distance from tip (inches)

n=0.50

Sosa

Nomar

Conclusions:• under most swing speed scenarios, increased swing

speed does not compensate for reduced eA

• “anti-corking” is probably better

Page 27

“Hitting is timing; pitching is

upsetting timing”

Subtle Effects where Corking May HelpBat Control

Hitting and Pitching, Thinking and Guessing

“Hitting is fifty percent above the shoulders”

1955 Topps cards from my personal collection

Page 28

Graphic courtesy of Bob Adair and NYT

Hitting, Pitching, and Thinking

Page 29

Quick Guide to Aerodynamics:Effect of Spin on Trajectory

V??????????????

dragF??????????????

MagnusF

•Drag Force opposite to velocity vector

•Magnus Force in direction the leading edge is turning

--curve balls break

--backspin keeps fly ball in air longer

Magnus F ~ x v

Page 30

Oblique Collisions:Leaving the No-Spin Zone

--Oblique collisions and friction cause hit ball to spin

--Early or later: sidespin--Undercut: backspin--Overcut: topspin

f

Page 31

Application: Swinging Early or Late

0

20

40

60

80

0 2 4 6 8 10 12 14

f (deg)

t (ms)

foul

fair

~11 inches

Initial takeoff angledown the line

0

20

40

60

80

100

120

0 100 200 300 400

height vs. distance

angle vs. distanze

• Balls hit to left or right curve towards foul line

• 90 mph pitch misjudged by 3 mph (!) over last 30’

--swing is early or late by ~7 ms

--ball goes down the line and curves foul

Page 32

Application: Hitting Strategies and Undercutting the Ball

Ball100 downward

Bat 100 upward

D = center-to-center offset

-2000

-1000

0

1000

2000

3000

4000

0.0 0.2 0.4 0.6 0.8 1.0

(rpm)

D (inches)

curveball, -2000 rpm

fastball, +2000 rpm

0

50

100

150

200

250

0 50 100 150 200 250 300 350 400

1.5

0

0.25

0.50.75

1.0

fastball

Can a curveball be hit farther than a fastball?

Page 33

And Finally....

0

50

100

150

200

250

0 50 100 150 200 250 300 350 400

1.5

0

0.25

0.50.75

1.0

fastball

3

4

5

6

7

0 10 20 30 40 50 60

y (f)

x( f)

2000 rpm

1500 rpm

3" (!)

90 mph fastball with backspin

pitcher batter

Ball100 downward

Bat 100 upward

D = center-to-center offset

Page 34

Summary Kinematic factors do not favor corked bat

Higher swing speed does not compensate reduced collision efficiency

No evidence for trampoline effect in corked bat

Corked bat can help in subtle ways bat control bat acceleration

Sammy probably didn’t take Physics 101!

...but he may have taken Biology 101!