1. ...or is the cork better left in the wine bottle?
Outline:
Talk about events of June Describe corking bat.
Pose the question: Does a corked bat give a hitter an advantage?
Refine the question:
Imprecise: Does corked bat give more “power”?
Better: Does a corked bat give greater distance on fly ball?
What determines distance on fly ball?
initial speed of ball
takeoff angle
backspin on ball
Initially...address only initial speed.
Give the quick answer
higher bat speed (+)
reduced collision efficiency (-)
any other effects?
What determines speed of ball coming off the bat?
Speed of pitched ball
Speed of bat
Collision efficiency
Formula and digression.
Effective mass
COR
Swing speed study
Show optimum weight of bat for n=0,.25,..50
Digress on BBCOR
Vibrations, sweet spot
Trampoline effect
Corking and trampoline effect
Hitting the ball squarely....
Is There an Advantage to “Corking” a Bat?

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 1

3. Greatest baseball team
Baseball and Physics
1927 Yankees:
Greatest baseball team
ever assembled
MVP’s
1927
Solvay Conference:
Greatest physics team
ever assembled

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

5. Kinematics of Ball-Bat Collision
vball
vbat vf
eff
1+ eff
r: bat recoil factor = mball/Mbat,eff  0.25
(momentum and angular momentum conservation)
e: coefficient of restitution  0.50
(energy dissipation)
Primary dependence of vf on ball, bat speeds is in the relationship…weaker dependence through e,
Mass is effective mass due to extended nature of bat.
Inefficient collision (1 for superball on rigid wall)
Bat speed matters much more than ball speed
typical numbers: vf = 0.2 vball vbat

6. Kinematics of Ball-Bat Collision
vball
vbat vf Z
For maximum vf:
r = mball/Mbat,eff small  Mbat,eff large
Mbat,eff  Ih/z2
vbat large
vbat ~ (Ih)-n
e large
a tradeoff
Note that it is primarily the mass in the barrel that matters (Ip)
Typical numbers for 32 oz bat:
Ih = 19,000 oz-in2
Z=28”
Meff=24 oz
Removing 3 oz at ave distance of 5” from tip changes Ih by 2500, or 13%

7. The vbat-Mbat tradeoff: General Considerations
-assume fixed shape and scaling of density to change mass (and therefore Ih)...only for ease of presentation.
-asymptotic nature for n=0
13% is 4 oz for 32 oz bat
0  n  0.5 are physically sensible bounds

8. Swinging the Bat
The usual words about complex action, energy transfer, timing, etc. Our focus is very narrow, and certainly not the only focus—namely, getting the highest bat speed.

9. Experimental Swing Speed Studies
Thanks to J. J. Crisco & R. Greenwald
Medicine & Science in Sports & Exercise 34(10): ; Oct 2002
Computer rendition of the swinging bat, the incoming and outgoing ball, and the collision between them, from a study in which high-speed video was used to track the location of the ball and several points on the bat as the batter swung at a ball delivered by a pitching machine. The separation between adjacent frames is 4 ms. Data from images such as these can be used to determine the relationship between the outgoing speed, incoming speed, and bat speed, as a function of impact location along the bat. For example, the above image clearly shows that the outgoing ball, shown as the upper set of images, has a higher speed than the incoming ball, shown as the lower set of images. The purple dot shows the evolution of the instantaneous rotation axis of the bat. Interestingly, just prior to the collision, the rotation axis approximately coincides with the wrist of the lower hand.

10. Z
0.8” X 3” 
45 rad/s
vbat vs. z z x
70 mph
@ 28”
Crisco/Greenwald Batting Cage Study: College Baseball

11.   I-n knob vbat  I-0.3 vbat  I-0.5 bat speed versus MOI
Caveat...batting machine set to be ~65 mph, which is slow. This may therefore result in overestimate of n, since batter can “load up.”
  I-n knob
n = 0.31  0.04
13% reduction in I gives ~4% increase in bat speed

12. Recent ASA Slow-Pitch Softball Field Tests (L. V. Smith, J
Recent ASA Slow-Pitch Softball Field Tests (L. V. Smith, J. Broker, AMN)
fixed M
fixed MOIknob
NB: MOI wrt 6” point, not knob.
Conclusions:
bat speed more a function of mass distribution than mass
n~ 0.25

13. The vbat-Mbat tradeoff revisited
-assume fixed shape and scaling of density to change mass (and therefore Ih)...only for ease of presentation.
-asymptotic nature for n=0
13% is 4 oz for 32 oz bat
Looks like corking reduces vf! More later...

14. Kinematics of Ball-Bat Collision
vball
vbat vf Z
For maximum vf:
r = mball/Mbat,eff small  Mbat,eff large
Mbat,eff  Ih/z2
vbat large
vbat ~ (Ih)-n
Note that it is primarily the mass in the barrel that matters (Ip)
Typical numbers for 32 oz bat:
Ih = 19,000 oz-in2
Z=28”
Meff=24 oz
Removing 3 oz at ave distance of 5” from tip changes Ih by 2500, or 13%
a wash—at best
e large  does corking bat increase COR?

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
So far, just kinematic, plus a phenomonlogoical treatment of energy losses via COR. Now we want to dissect th ecollision process, time slice by time slice, to see what is really going on during the time the ball and bat are in contact. In doing so, we want to try to do a strict accounting for where the energy goes in the collision. So, we want to go beyond kinematics and talk about dynamics. We know that a purely rigid body treatment cannot be right…for example, we know that the collision can excite vibrations in the bat.

16. A Dynamic Model of the Bat-Ball Collision20
Euler-Bernoulli Beam Theory‡ y z
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
Two “free” parameters…Young’s and shear modulus
‡ Note for experts: full Timoshenko (nonuniform) beam theory used

17. Modal Analysis of a Baseball Bat
f1 = 179 Hz
f2 = 582 Hz
f3 = 1181 Hz
f4 = 1830 Hz
time
frequency
Note: nodes stack up at barrel end-->”sweet spot zone”

18. COR depends strongly on impact location
Effect of Bat Vibrations on COR
Evib vf
COR
f1 = 179 Hz
f2 = 582 Hz
So, what role does the bat play in the COR of the ball-bat collision?
The collision can excite bending vibrations in the bat. These vibrations can be felt…it is the sting that is felt for off-sweet-spot hits. Sometimes the vibrational amplitude is so large that the bat even breaks. There are characteristic vibrational modes (frequencies and shapes), much like a guitar string. Lowest mode (shown here) is about Hz with a node about 6-7” from barrel end. Next higher mode is about 580 Hz, with a node a little further out. The possibility of exciting vibrations in the bat means that the ball-bat COR is not uniform across the length of the bat but looks something like this, peaked 4-7” from the end, where the nodes of the lowest few modes of vibration are clustered together (so that very little energy goes into vibrations), and dropping fairly rapidly on either side as the vibrations take more and more energy from the ball.
COR depends strongly on impact location

19. Relation to Reality: Experimental Data Ball incident on bat at rest
For rigid, peak is at CM
For full calculation, peak determined by interplay between rotational recoil and vibrational nodes.
At lowest node, rigid-full
only lowest mode excited
lowest 4 modes excited
Conclusion: essential physics understood

20. 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

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”)

22. 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
Ask question:
Which give more “power”: tighter strings or looser strings on tennis racket?
Then ask (if they get it wrong): can a person bounce higher from a hardwood floor or from a trampoline?

23. MOVIE
Measuring the Ball-Bat COR Sports Science Laboratory Washington State University Lloyd Smith, Dan Russell, AMN July 2003 2%
Conclusion:
no trampoline effect!

24. Putting it All Together
Vbat dependence on I:
~ I-n : purely phenomenological
~ (I+I0)-1/2 : fixed energy shared between
bat (I) and batter (I0)
Conclusions:
under most swing speed scenarios, increased swing speed does not compensate for reduced eff
“anti-corking” is probably better
Sosa
Nomar

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

26. D = center-to-center offset
Example
Ball100 downward
Bat 100 upward
D = center-to-center offset
fastball

27. 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!