Is There
Advantage
Bat?
...or
is thean
cork
better lefttoin“Corking”
the wine abottle?
Page 2
Does Corking the Bat Give an
Advantage?
A Physicist’s Approach
www.npl.uiuc.edu/~a-nathan/pob
 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 3
Baseball and Physics
1927 Yankees:
Greatest baseball team
ever assembled
1927
Solvay Conference:
Greatest physics team
ever assembled
MVP’s
Page 4
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 5
Kinematics of Ball-Bat Collision
 e-r 
1+e 
vf = 
v ball  
v bat


1+r 
 1+r 
eff
vball vbat
vf
1+ eff
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
Page 6
Kinematics of Ball-Bat Collision
 e-r 
1+e 
vf = 
v ball  
v bat


1+r 
 1+r 
vball vbat
vf
Z
For maximum vf:
• r = mball/Mbat,eff small  Mbat,eff large
Mbat,eff  Ih/z2
• vbat large
a tradeoff
vbat ~ (Ih)-n
• e large
Page 7
The vbat-Mbat tradeoff: General Considerations
v (mph)
f
120
110
n=0.5
constant bat KE
100
90
80
70
60
n=0
constant v
bat
vbat = 65 mph x (32/Mbat)n
20
30
M
bat
40
(oz)
50
60
0  n  0.5 are physically sensible bounds
Page 8
Swinging the Bat
Page 9
Experimental Swing Speed Studies
Thanks to J. J. Crisco & R. Greenwald
Medicine & Science in Sports & Exercise 34(10): 16751684; Oct 2002
Page 10
X
3”
Z
0.8”
70 mph
@ 28”

45 rad/s
z
x
vbat vs. z
Crisco/Greenwald Batting Cage Study: College Baseball
Page 11
bat speed versus MOI
Crisco/Greenwald Batting Cage Study
50
48

knob
46
(rad/s)
vbat  I-0.3
44
42
vbat  I-0.5
40
1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9
•
I-n
knob
I
knob
4
2
(10 oz-in )
• n = 0.31  0.04
• 13% reduction in I gives ~4% increase in bat speed
Page 12
Recent ASA Slow-Pitch Softball Field Tests
(L. V. Smith, J. Broker, AMN)
Bat Speed at 6" Point vs. W
Bat Speed at 6" Point vs. MOI
1.06
fixed M
1.04
1.02
1.02
1
1
0.98
dashed: n=0.25
solid: n=0.23
fixed MOIknob
1.04
~(1/M)
0.25
0.98
0.96
0.96
0.94
6000
7000
8000
9000
2
MOI (oz-in )
10000
11000
24
25
26
27
28
29
30
31
32
W (oz)
Conclusions:
• bat speed more a function of mass distribution than mass
• n~ 0.25
Page 13
The vbat-Mbat tradeoff revisited
v (mph)
f
120
110
n=0.5
constant bat KE
n=0.31 (expt)
100
90
80
70
60
n=0
constant v
bat
vbat = 65 mph x (32/Mbat)n
20
30
M
bat
40
(oz)
50
60
Looks like corking reduces vf! More later...
Page 14
Kinematics of Ball-Bat Collision
 e-r 
1+e 
vf = 
v ball  
v bat


1+r 
 1+r 
vball vbat
vf
Z
For maximum vf:
• r = mball/Mbat,eff small  Mbat,eff large
Mbat,eff  Ih/z2
• vbat large
a wash—at best
vbat ~ (Ih)-n
• e large  does corking bat increase COR?
Page 15
Accounting for Energy Dissipation:
Dynamics of Ball-Bat Colllision

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
Page 16
02
A Dynamic Model of the Bat-Ball Collision
51
y
20
01
Euler-Bernoulli Beam Theory‡
5
2  2y 
2y
 EI 2   A 2  F(z, t)
2 
z  z 
t
0
5-
y
-10
z
• Solve eigenvalue problem for free oscillations (F=0)
-15
-20
0
 normal modes (yn, n)
5
01
51
02
52
03
53
• 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
Page 17
Modal Analysis of a Baseball Bat
www.kettering.edu/~drussell/bats.html
f1 = 179 Hz
f3 = 1181 Hz
f2 = 582 Hz
f4 = 1830 Hz
FFT(R)
1
0.15
582
0.5
0
R
5
10
15
20
25
30
1181
0.1
0
-0.5
-1
1830
179
0.05
-1.5
35
frequency
time
0
5
10
t (ms)
15
2400
20
0
0
500
1000
1500
frequency (Hz)
2000
2500
Effect of Bat Vibrations on COR
nodes
4 3 2
0.5
0.4
e
v (mph)
f
1
120
COR
f1 = 179 Hz
100
0.4
vf
0.3
80
60
0.3
Evib
0.2
0.2
0.1
0
5
10
distance from tip (inches)
40
20
f2 = 582 Hz
0
15
0
5
10
15
20
25
30
35
COR depends strongly on impact location
Page 19
Relation to Reality: Experimental Data
Ball incident on bat at rest
v
final
/v
CM
initial
v
node
final
/v
initial
nodes
0.35
0.4 rigid bat
0.3
rigid bat
0.25
0.3
0.2
flexible bat
0.2
flexible bat
0.15
data from Rod Cross
freely suspended bat
v = 2.2 mph
0.1
0.1
0.05
i
0
16
20
24
28
distance from knob (inches)
only lowest mode excited
32
0
23
data from Lansmont BBVC
bat pivoted about 5-3/4"
v
=100 mph
initial
24
25 26 27 28 29 30
distance from knob (inches)
31
lowest 4 modes excited
Conclusion: essential physics understood
Page 20
time evolution of bat
displacement (mm)
10
0 - 1 ms
0.1 ms intervals
8
6
• rigid-body motion develops only4
after few ms
2
0
• far end of bat has no effect on
-2
ball
-4
 knob moves after >0.6 ms
 collision over after 0.6 ms
impact point
200
150
1-10 ms
1 ms intervals
100
 nothing on knob end matters
50
• size, shape
• boundary conditions
0
• hands
-50
impact point
0
5
10 15 20 25 30
distance from knob (inches)
Page 21
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 22
Aluminum Bats: The “Trampoline” Effect:

Ball and bat mutually compress each other
 Compressional energy shared
 Essential parameter: kbat/kball
Demo
• 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!
Page 23
Measuring the Ball-Bat COR
MOVIE
Sports Science Laboratory
Washington State University
Lloyd Smith, Dan Russell, AMN
ball-bat COR
July 2003
0.495
0.490
0.485
original
corked
2%
0.480
drilled
0.475
Conclusion:
no trampoline effect!
Page 24
Putting it All Together
Vbat dependence on I:
Conclusions:
-n : purely
most swing
speed scenarios, increased swing
~• Iunder
phenomenological
speed
does not compensate for reduced eff
-1/2
~ (I+I
)
: fixed energy shared between
0
• “anti-corking” is probably better
bat (I) and batter (I0)
v (mph)
v
100
0.5
unmodified
0.4
95
Nomar
0.3
n=0.50
90
n
85
0.2
Sosa
0.1
0
drilled
80
75
0
2
4
6
I /<I>
8
n=0
10
3
4
5
6
7
distance from tip (inches)
8
0
Page 25
Subtle Effects where Corking May Help
Bat Control
Hitting and Pitching, Thinking and Guessing
“Hitting is fifty percent
above the shoulders”
“Hitting is timing; pitching is
upsetting timing”
1955 Topps cards from my personal collection
Page 26
Example
Ball100 downward
D = center-to-center offset
Bat 100 upward
pitcher
batter
250
7
200
1.5
6
2000 rpm
y (f)
5
4
1500 rpm
20
30
x( f)
0.75
100
40
0.5
50
90 mph fastball with backspin
10
1.0
150
3" (!)
30
fastball
50
60
0
0.25
0
0
50
100 150 200 250 300 350 400
Page 32
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!
Page 33