The Trampoline Effect: What is it all about?

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The Trampoline EffectWhat is it all about?
Alan M. Nathan Department of Physics University
of Illinois at Urbana-Champaign a-nathan_at_uiuc.edu
www.npl.uiuc.edu/a-nathan/pob
SGMA Meeting Dallas TX October, 2003
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But first a digression...

• Last year at SGMA meeting, I gave a talk
  advocating use of batted ball speed (BBS) rather
  than bat-ball COR (or BPF) as a performance
  metric
• With a year to think about it, here is an update

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• Take bat of given shell
• Adjust weights on ends to adjust MOI with
  weight28 oz
• Do computer simulation to get BBCOR and BBS
• BBS calculated using ASA formula

Conclusion BBS a more robust metric than BPF
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The Ball-Bat Collision

• forces large (gt8000 lbs!)
• time is short (lt1/1000 sec!)
• ball compresses, stops, expands
• bat compresses ball
• ball bends/compresses bat
• lots of energy dissipated
• distortion of ball
• vibrations in bat
• ball-bat COR related to energy dissipation

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high-speed video of collision
These movies are owned by CE Composites Baseball
(combatbaseball.com), designers and manufacturers
of composite baseball bats, Ottawa, Ontario,
Canada, and are shown here with their permission.
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The Trampoline Effect A Simple Physical
Picture

• Two springs mutually compress each other
• Energy of motion ? Compressional energy
• Energy shared between ball spring and
• bat spring
• Energy stored in ball mostly dissipated (80!)
• Energy stored in bat mostly restored
• Net effect less overall energy dissipated
• ...and therefore higher ball-bat COR

demo
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Trampoline Effect
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The Trampoline EffectIn Words

• Fraction of energy restored
• (Fraction of initial energy stored in ball)
• x (Fraction of stored energy returned)
• (Fraction of initial energy stored in bat)
• x (Fraction of stored energy returned)

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The Trampoline EffectIn symbols

• kbat, kball measures stiffness of bat, ball
• ...sometimes called compression
• kbat/kball (0 - ?)
• (energy stored in ball)/(energy stored in bat)

Assumes no energy loss in bat
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The Trampoline Effect

• This model is ...
• very simple to understand
• captures most of essential physics
• qualitatively explains much of the data

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The Trampoline Effect
Example 1 typical wood bat kbat/kballgtgt1
little energy stored in bat ? e ? eball
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The Trampoline Effect
demo
Example 2 the ideal situation (happy/sad ball
on bongo paddle) kbat/kball ltlt 1 most of energy
stored in bat ? e ? 1, independent of eball
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The Trampoline Effect
Example 3 single-wall Aluminum bat kbat/kball ?
7 15 of energy stored in bat ? e 0.6,
BPF ? e/eball 1.20
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The Trampoline Effect
Example 4 high-performance bat kbat/kball ?
2 33 of energy stored in bat ? e 0.75,
BPF ? e/eball 1.50
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Note The BPF is not a ball-independent
quantity It depends on the COR of the ball
(eball)

• BPF decreases as eball increases
• effect greater when kbat/kball smaller (high
  performance)

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More Realistic Calculation
More from Dan Russell later
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The Trampoline EffectA Closer Look

• Bending Modes vs. Hoop Modes

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The Trampoline EffectA Closer Look

• Single-Wall vs. Double-Wall

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Ball-Bat COR

• Depends on ball COR
• which depends on vrel vball vbat
• Depends on BPF (BBCOR/ball COR)
• which depends on
• impact location
• ball COR
• which depends on vrel
• more for high- than low-performance bats
• ball compression (kball)
• which may depend on vrel
• more for high- than low-performance bats

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An Indirect Performance Metric

• Low-speed collision of hard steel ball with
  barrel of bat
• As kbat gets smaller...
• BBCOR gets larger
• collision time gets longer
• Basis for USGA pendulum test
• see Dan Russells talk

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Summary of Important Points

• The essential physics behind the trampoline
  effect is understood
• The bat is probably well understood
• Equally important is the ball, which is less well
  understood
• but we are making progress