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 - PowerPoint PPT Presentation

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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

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Title: When Ash/Metal Meets Cowhide: The Physics of the Ball-Bat Collision Seminar, UMass/Lowell March 12, 2003 Alan M. Nathan University of Illinois at Urbana ... – PowerPoint PPT presentation

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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


1
Comparative 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
2
Description 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

3
Kinematics 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

4
The Bat Recoil Factor r
Heavier bat is better but.
5
Recent ASA Slow-Pitch Softball Field Tests(L. V.
Smith, J. Broker, AMN)
Conclusion bat speed more a function of mass
distribution than mass
6
COR 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 ?

7
Wood-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

8
Accounting 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)
9
The Essential Physics A Toy Model
?? ?1 rigid limit ball sees MaMb (5 on 30)
?? ?1 flexible limit ball sees Ma (5 on 10)

10
The 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

11
Normal Modes of the Bat Modal Analysis
frequencies and shapes
12
Ball-Bat Force
  • Details not important
  • --as long as e(v), ?(v) about right
  • Measureable with load cell

?
13
Vibrations and the COR
the sweet spot
COR maximum near 2nd node
14
Results 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
15
Some 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,

16
Flexible Bat and the Trampoline Effect
Losses in ball anti-correlated with vibrations in
bat
17
The 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

18
Trampoline Effect toy model with dissipation
in ball
kbatgtgtkball
19
The 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
20
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21
Where Does the Energy Go?
22
Some 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
23
Some 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

24
Summary
  • 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
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