1 / 22

Introduction: Description of Ball-Bat Collision

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 dissipated bat is flexible bat bends, compresses the goal... large hit ball speed. v ball. v bat.

psyche
Télécharger la présentation

Introduction: Description of Ball-Bat Collision

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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 dissipated • bat is flexible • bat bends, compresses • the goal... • large hit ball speed

  2. vball vbat vf Kinematics of the Ball-Bat Collision r bat recoil factor = mball/Mbat,effective e Coefficient of Restitution (COR) typical numbers: r  0.25 e  0.50  vf = 0.2 vball + 1.2 vbat Note: this talk focuses entirely on COR

  3. COR and Energy Dissipation • e  COR  vrel,after/vrel,before • in CM frame: (final KE/initial KE) = e2 • e.g., drop ball on hard floor:COR2 = hf/hi 0.25 • typicallyCOR  0.5 • ~3/4 CM energy dissipated! • depends on impact speed • mostly a property of ball but… • the bat matters too! • vibrations  , “trampoline” effect 

  4. 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) >> Tvib see AMN, Am. J. Phys, 68, 979 (2000)

  5. bat ball Mass= 1 2  The Essential Physics: A Toy Model rigid limit   1 1 on  flexible limit  1 1 on 2

  6. y 20 y z 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

  7. f1 = 177 Hz f3 = 1179 Hz f2 = 583 Hz f4 = 1821 Hz Normal Modesof the Bat Louisville Slugger R161 (34”, 31 oz) Can easily be measured: Modal Analysis

  8. F vs. CM displacement F vs. time Ball-Bat Force • Details not important • --as long as e(v), (v) about right • Measureable with load cell 

  9. Vibrations and the COR the “sweet spot” COR maximum near 2nd node

  10. 24” 27” 30” Some interesting insights: • Center of Percussion close to lowest node @ 27” • Coincides neither with max COR @ 29” • …nor with max. vf • Far end of bat doesn’t matter • mass, grip, …

  11. T= 0-1 ms Ball leaves bat T= 1-10 ms Time evolution of the bat • Conclusions: • Knob end doesn’t matter • Batter’s grip doesn’t matter • vibrations and rigid motion • indistinguishable on • short time scale

  12. Bounce superballs from beam (Rod Cross) Conclusion: Nothing on far end of beam matters

  13. Flexible Bat and the “Trampoline Effect” Losses in ball anti-correlated with vibrations in bat

  14. The “Trampoline” Effect: A Closer Look • Compressional energy shared between ball and bat • PEbat/PEball = kball/kbat (= s) • PEball mostly dissipated (75%) • BPF = Bat Proficiency Factor  e/e0 • Ideal Situation: like person on trampoline • kball >>kbat: most of energy stored in bat • f >>1:stored energy returned • e2 (s+e02)/(s+1)  1 for s >>1  eo2 for s <<1

  15. Trampoline Effect: Toy Model, revisited Mass= 1 2  bat ball

  16. The “Trampoline” Effect:A Closer Look Bending Modes vs. Shell Modes • k  (t/R)3: small in barrel •  more energy stored • f (1-2 kHz) < 1/  •  energy mostly restored • Net Effect: BPF > 1 • k  R4: large in barrel •  little energy stored • f (170 Hz, etc) > 1/ •  energy lost to vibrations • Net effect: BPF  1

  17. Where Does the Energy Go?

  18. Some Interesting Consequences(work in progress) s  kball/kbat e2 (s+e02 )/(s+1) BPF = e/e0 • BPF 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

  19. 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

More Related