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Physics of the Trampoline Effect baseball, golf, tennis, ...

Physics of the Trampoline Effect baseball, golf, tennis, . Alan M. Nathan a , Daniel Russell b , Lloyd Smith c a University of Illinois at Urbana-Champaign b Kettering University c Washington State University. The “Trampoline” Effect: A Simple Physical Picture.

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Physics of the Trampoline Effect baseball, golf, tennis, ...

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  1. Physics of the Trampoline Effectbaseball, golf, tennis, ... Alan M. Nathana, Daniel Russellb, Lloyd Smithc aUniversity of Illinois at Urbana-Champaign bKettering University cWashington State University

  2. The “Trampoline” Effect:A Simple Physical Picture • Two springs mutually compress each other • KE  PE  KE • PE shared between “ball spring” and “bat spring” • PE stored in ball mostly dissipated • PE stored in bat mostly restored • Net effect: less overall energy dissipated • e  e0: the trampoline effect • e0 COR for ball on rigid surface • 1-e02 = fraction of ball PE dissipated • e  COR for ball on flexible surface • 1-e2 = fraction of initial ball KE lost to ball

  3. kbat kball M m ball bat The Essential Physics: Toy Model • Cross (tennis, M=0) • Cochran (golf) • Naruo & Sato (baseball) • Numerically solve ODE to get e = vf/vi • Energy lost (e<1) due to... • Dissipation in ball • Vibrations in bat • Essentially a 3-parameter problem: • e0 • Controls dissipation of energy stored in ball • rk kbat/kball = PEball/PEbat • Controls energy fraction stored in bat • rm  m/M • f  (rk/rm) ( depends mainly on ball) • Controls energy transferred to bat (vibrations)

  4. Energy Flow wood-like: rk=75 (very stiff bat) aluminum-like: rk=10 (less stiff bat)

  5. kball kbat M m ball bat rm= m/M=0.25 • Strong coupling limit: • rk>>1, f>1 Ebat/Eball<<1 • e = e0 • 2. Weak coupling limit: • rk<<1, f<<1 • m on M • e=(e0-m/M)/(1+m/M) • Intermediate coupling • rk>1, f>1 • e > e0

  6. Dependence on rm = m/M f=1.1 • M  f max @ smaller rk • Conclude: e depends on bothrkand rM • Not unique function of f • Limiting case: rk<<1 and f>>1 (rm0) (thin flexible membrane) • e1, independent of e0

  7. Important Results(all confirmed experimentally) • Harder ball or softer bat decreases rk, increases e • Nonlinear baseball: kball increases with vi  e/e0 increases with vi • e/e0 (“BPF”) decreases as e0 increases • Collision time increases as rk decreases USGA pendulum test

  8. kbat (t/R)3: small in barrel •  more energy stored • f (1-2 kHz)  > 1 •  energy mostly restored • Net Effect: • e/e0 = 1.20-1.35 • trampoline effect • kbat R4: large in barrel •  little energy stored • f (170 Hz, etc)  < 1 •  stored energyvibrations • Net effect: • e  e0 on sweet spot • e<<e0 off sweet spot • no trampoline effect Realizing the Trampoline Effect in Baseball/Softball Bats Bending Modes vs. Hoop Modes

  9. bb< sb  curve “stretches” to higher f Trampoline Effect:Softball vs. Baseball • Net result: • ordering reversed • should be tested experimentally

  10. Summary • Simple physical model developed for trampoline effect • Model qualitatively accounts for observed phenomena with baseball/softball bats • Both rk and rM are important • e/e0 not a bat property independent of e0 • Relative performance of bats depends on the ball! • But this needs to be tested

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