Title: Comparative Study of Wood and Aluminum Baseball Bats Seminar, UC/Davis, April 11, 2003 Alan M. Nathan University of Illinois at Urbana-Champaign a-nathan@uiuc.edu http://www.npl.uiuc.edu/~a-nathan/pob
1Comparative Study of Wood and Aluminum Baseball
BatsSeminar, UC/Davis, April 11, 2003Alan M.
Nathan University of Illinois at
Urbana-Champaigna-nathan_at_uiuc.eduhttp//www.npl.
uiuc.edu/a-nathan/pob
...the most difficult thing in sports --Ted
Williams 1918-2002
BA .344 SA .634 OBP .483 HR 521
2Description of Ball-Bat Collision
- forces large (gt8000 lbs!)
- time short (lt1/1000 sec!)
- ball compresses, stops, expands
- kinetic energy ? potential energy
- lots of energy dissipated
- bat is flexible
- bat bends, compresses
- the goal...
- large hit ball speed
3Kinematics of the Ball-Bat Collision
eA ? collision efficiency r ? bat recoil
factor mball/Mbat,effective e ? Coefficient of
Restitution (COR)
- superball on massive surface
- r 1 e 1 ? eA 1 and vf vball 2 vbat
- baseball on bat
- r ? 0.25 e ? 0.50 ? eA0.2 and vf 0.2 vball
1.2 vbat
4The Bat Recoil Factor r
Heavier bat is better but.
5Recent ASA Slow-Pitch Softball Field Tests(L. V.
Smith, J. Broker, AMN)
Conclusion bat speed more a function of mass
distribution than mass
6COR and Energy Dissipation(primary focus of this
talk)
- e ? COR ? vrel,after/vrel,before
- in CM frame (final KE/initial KE) e2
- e.g., drop ball on hard floor e2 hf/hi ?
0.25 - typically e ? 0.5
- 3/4 CM energy dissipated!
- depends on impact speed
- the bat matters too!
- vibrations ?
- trampoline effect ?
7Wood-Aluminum Differences
- Inertial differences
- CM closer to hands, further from barrel for
aluminum - ? Mbat,eff smaller ?
- larger recoil factor r, smaller eA
- effectively, less mass near impact location
- ? MOIknob smaller ? swing speed higher
- ? cancels ? for many bats
- Dynamic differences
- Ball-Bat COR significantly larger for aluminum
8Accounting for Energy Dissipation Dynamic Model
for Ball-Bat Colllision
- Collision excites bending vibrations
- Ouch!! Thud!! Sometimes broken bat
- Energy lost ? lower COR, vf
- Find lowest mode by tapping
- Reduced considerably if
- Impact is at a node
- Collision time (0.6 ms) gtgt Tvib
see AMN, Am. J. Phys, 68, 979
(2000)
9The Essential Physics A Toy Model
?? ?1 rigid limit ball sees MaMb (5 on 30)
?? ?1 flexible limit ball sees Ma (5 on 10)
10The Details A Dynamic Model
- Step 1 Solve eigenvalue problem for free
vibrations - Step 2 Nonlinear lossy spring for ball-bat
interaction - Step 3 Expand in normal modes and solve
11Normal Modes of the Bat Modal Analysis
frequencies and shapes
12Ball-Bat Force
- Details not important
- --as long as e(v), ?(v) about right
- Measureable with load cell
?
13Vibrations and the COR
the sweet spot
COR maximum near 2nd node
14Results Ball Exit Speed Louisville Slugger
R161 33-inch/31-oz. wood bat
only lowest mode excited
lowest 4 modes excited
Conclusion essential physics under control
15Some interesting insights
- Center of Percussion close to lowest node _at_ 27
- Coincides neither with max COR _at_ 29
- nor with max. vf
- Far end of bat doesnt matter
- mass, grip,
16Flexible Bat and the Trampoline Effect
Losses in ball anti-correlated with vibrations in
bat
17The Trampoline Effect A Closer Look
- Compressional energy shared between ball and bat
- PEbat/PEball kball/kbat (? s)
- PEball mostly dissipated (75)
- Ideal Situation like person on trampoline
- kball gtgtkbat most of energy stored in bat
- f? gtgt1 stored energy returned
- e2 ? (se02)/(s1)
- ? 1 for s gtgt1
- ? eo2 for s ltlt1
18Trampoline Effect toy model with dissipation
in ball
kbatgtgtkball
19The Trampoline EffectA Closer Look
- Bending Modes vs. Shell
Modes
k ? (t/R)3 small in barrel ? more energy
stored f (1-2 kHz) lt 1/ ? ? energy mostly
restored Net Effect e gt e0
k ? R4 large in barrel ? little energy
stored f (170 Hz, etc) gt 1/? ? energy lost to
vibrations Net effect e ? e0
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21Where Does the Energy Go?
22Some Interesting Consequences(work in progress)
- e/e0 increases with
- Ball stiffness
- Impact velocity
- Decreasing wall thickness
- Decreasing ball COR
- Note effects larger for high-s than for
low-s bats - Tuning a bat
- Tuning due to balance between storing energy (k
small) and returning it (f large) - Tuning not related to phase of vibration at time
of ball-bat separation
s ? kball/kbat e2 ? (se02 )/(s1) e ? 1 for s ? 1
23Some Interesting Consequences(work in progress)
- Simple measurements to predict BPF
- Measure static compression of bat
- Measure frequency of shell modes
- Measure collision time with massive steel ball
- mball gtgt mbat
- kball gtgt kbat
- Collision time ???(mball/kbat)
- Similar to USGA method for metal drivers
24Summary
- Dynamic model developed for ball-bat collision
- flexible nature of bat included
- simple model for ball-bat force
- Vibrations play major role in COR for collisions
off sweet spot - Far end of bat does not matter in collision
- Physics of trampoline effect mostly understood
and interesting consequences predicted - should be tested experimentally