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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

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

the trampoline effect a simple physical picture
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
the essential physics toy model

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)
slide4

Energy Flow

wood-like: rk=75

(very stiff bat)

aluminum-like: rk=10

(less stiff bat)

slide5

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
slide6

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
important results all confirmed experimentally
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

realizing the trampoline effect in baseball softball bats

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

trampoline effect softball vs baseball

bb< sb  curve “stretches” to higher f

Trampoline Effect:Softball vs. Baseball
  • Net result:
  • ordering reversed
  • should be tested experimentally
summary
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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