The BaseballBat CollisionIII Lecture 9

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The Baseball-Bat Collision-IIILecture 9

• Wood vs. aluminum
• The physics of the trampoline effect
• Regulating bat performance
• Glancing collisions and spin

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Wood vs. Aluminum

• Aluminum has thin shell
• Less mass in barrel
• --lower MOI, higher bat speed, easier to control
  ?
• --but less effective at transferring energy ?
• --for many bats ? cancels ?
• just like corked wood bat
• Hoop modes
• trampoline effect ? ?
• ping

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The Trampoline Effect A Closer Look

• hoop modes cos(2?)

Thanks to Dan Russell
ping
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What do we know about the Trampoline Effect?

• Ball and bat mutually compress each other
• Just like springs
• Ball very inefficient at returning compressional
  energy to kinetic energy
• Bat can be very efficient
• Net results less energy loss, higher COR
• Question tighter/looser strings on tennis
  racket for greater power?
• Demo with happy and sad balls

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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
• Force kcompression
• larger k means larger force required to compress
• smaller k means smaller force required to
  compress
• kbat/kball (0 - ?)
• (energy stored in ball)/(energy stored in bat)

fraction stored in bat kball/(kballkbat) retur
ned e2bat fraction stored in ball
kbat/(kballkbat) returned e2ball
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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
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!)
demo
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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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Measuring Ball-Bat COR (e)

• Ball fired at stationary bat
• measure qvf/vi
• q(e-r)/(1r)
• calculate r mball/mbat,eff
• solve for eq(1r)r

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Data vs. theory
Note hoop frequency fhoop sqrt(kbat/mass) sma
ller fhoop means smaller kbat
to learn more, see http//www.kettering.edu/druss
ell/bats.html
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The Trampoline EffectA Closer Look

• Single-Wall vs. Double-Wall

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Important Results(all confirmed experimentally)

• Harder ball or softer bat increases e
• Nonlinear baseball kball increases with vi
• e/e0 increases with vi
• Collision time increases as kbat decreases (USGA)
• e/e0 (BPF) decreases as e0 increases

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Why BPF?

• BPF ? BBCOR/COR (e/e0)
• Measure e0 by bouncing ball off wall
• Measure e by bouncing ball off bat
• eA (e-r)/(1r)
• Measure eA, calculate r to determine e
• Some organizations use BPF as a measure of bat
  performance
• Rationale a property of the bat alone, since
  effect of ball has been divided out
• Validity assumes BPF is independent of e0
• Reasonably valid for wood bats
• Not valid for trampoline effect
• Verified by models
• Demo with happy/sad balls on Bongo paddle
• Verified by impact data

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Note The BPF is not a ball-independent
quantity It depends on the COR of the ball
(eball)
In simple model, e?1 as kbat/kball?0, independent
of eball. Therefore, BPF?1/eball

• BPF decreases as eball increases
• effect greater when kbat/kball smaller (high
  performance)
• For happy ball, BPF1 for sad ball, BPF ? ?

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Verification from Impact Data
0.417
0.462
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• Conclusions
• BPF is not independent of ball COR
• BPF decreases as ball COR increases
• Variation is more for high- than
  low-performance bats
• The physics is
• well understood
• verified by experiment
• Implications
• BPF less useful as performance metric

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Regulating Bat Performance

• The ultimate performance metric
• BBS in field
• The challenge
• Develop lab tests that will predict BBS in field
• Three different techniques
• Regulating BBS directlythe ASA technique
• Regulating BBS indirectlythe NCAA technique
• Regulate BBS via BPFthe USSSA technique

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1. Regulating BBS directly

• Measure q in lab
• q vf/vi
• Using prescription for vball and vbat, calculate
  BBS expected in field
• BBS qvball (1q)vbat
• Reject bat if maximum BBS exceeded

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Regulating BBS directly The ASA Implementation

• Measure q in lab at 110 mph (2585)
• typical game conditions
• scan across barrel
• BBS qvball (1q)vbat
• Vball 25 mph (simple kinematics)
• Vbat 85mph(9000/I)0.25(d2.5)/30.5
• d distance from knob to impact in inches
• Assumes bat rotated about point 2.5 off knob
• IMOI about point 6 from knob
• assumes 85 mph for 34 bat, 6 from tip
• Reject bat if maximum BBS exceeded
• Maximum BBS97 mph for ASA

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2. Indirect The NCAA Bat Certification Process

• Each bat is characterized by two regulated
  numbers
• BESRq1/2 performance metric for fixed bat
  speed
• MOI metric related to field bat speed
• Together, these determine BBS

Higher BESR, higher MOI ? same BBS
Same BESR, lower MOI ? Higher BBS
Same MOI, lower BESR ? Lower BBS
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Example 34 Bats
All bats below horizontal line and to right of
vertical line are allowed
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NCAA Sliding BESR and MOI scale
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• MOI limits on non-wood bats

Limits, 2001
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The NCAA certification protocol limits field
performance of non-wood bats

• Under standard conditions---
• Wood 97 mph
• Non-wood lt 102 mph
• Difference lt 5 mph, or about 5

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NCAA Regulations How well do they work?
BESR
MOI
aluminum
-5 rule
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Options for Making Bats more wood-like
101.6
97
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3. Indirect Regulating BBCOR or BPF
(slow-pitch softball USSSA)

• Why does this approximately work?
• BBS vbat(1e)/(1r) small part from vball
• vbat decreases as MOI increases (BBS ?)
• 1/(1r) increases as MOI increases (BBS ?)
• If two effects cancel, then BBS depends on (1e),
  independent of MOI
• prescribing maximum e is nearly equivalent to
  prescribing maximum BBS
• ...leading some to propose using a BBCOR or BPF
  standard
• Why is this not a good idea?

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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

Computer simulation

• For MOIgt7500...
• BBCOR constant
• BBS keeps increasing
• ...sweet spot closer to tip
• ...where bat speed higher

Conclusion BBS a more robust metric than BPF
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Glancing Collisions and Spin

• thus far we only considered head-on collisions
• If not head-on, then a component of initial ball
  velocity is tangent to bat surface
• friction slows tangential velocity
• torque due to friction rotates ball (spin)

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Some Qualitative Effects

• Balls hit to left or right curve towards foul
  line
• Undercut balls have backspin
• Overcut balls have topspin

friction
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Example Balls hit to left or right
foul
fair
fair
foul
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Papers and Presentations

• Papers
• Due Monday, December 3
• at least 4 pages, double spaced, 12-pt font
• figures and references are extra
• Presentations
• Presented Monday, December 3
• 12 minutes 3 for questions
• Powerpoint