The Baseball-Bat Collision-III Lecture 9

1. 1 The Baseball-Bat Collision-IIILecture 9 Wood vs. aluminum The physics of the trampoline effect Regulating bat performance Glancing collisions and spin Derivation of q=(e-r)/(1+r) for point masses r for free bat—q vs.z Ideal bat weight, using bat mass Adair stuff—develop in spreadsheet using realistic M,MOI corked bats MOI swing speed studies steroids and bat speed bat vibrations q vs z and the sweet spot broken bats hands don’t matter ball-bat collision time and springs 6.aluminum bats and the trampoline effect 7. NCAA bat performance standards (BESR and MOI)Derivation of q=(e-r)/(1+r) for point masses r for free bat—q vs.z Ideal bat weight, using bat mass Adair stuff—develop in spreadsheet using realistic M,MOI corked bats MOI swing speed studies steroids and bat speed bat vibrations q vs z and the sweet spot broken bats hands don’t matter ball-bat collision time and springs 6.aluminum bats and the trampoline effect 7. NCAA bat performance standards (BESR and MOI)

2. 2 Hoop modes of plastic cupHoop modes of plastic cup

3. 3 The Trampoline Effect: A Closer Look “hoop” modes: cos(2?) Hoop mode largest in barrel, unlike bending modes The f-tau relationship is important…the reason why there is no trampoline effect from bending modes--see next slide Tricks: double wall bats; composite batsHoop mode largest in barrel, unlike bending modes The f-tau relationship is important…the reason why there is no trampoline effect from bending modes--see next slide Tricks: double wall bats; composite bats

4. 4 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 Relationship between eA and COR,r uses only conservation of momentum (for a free bat), conservation of angular momentum (for free or pivoted bat), and the definition of COR. For the experts, the definition is ratio of relative ball-bat speed after to before the collision, where only the rigid body motion of the bat is implied. There are no approximations in arriving at this expression. Given COR and inertial properties of bat, eA can be predicted. Conversely, given measurements of eA, one can get COR (and BPF). In fact, this is the basis of the Gilman proposal to measure the BPF. The same physics is contained in the Brandt technique, but the algebra is different because the recoil speed of the bat is measured rather than the post-impact speed of the ball. Keep in mind the following: angular momentum and/or momentum conservation implies that if the initial ball or bat speed is known, then a measurment of either the exit speed of the ball or the recoil speed of the bat uniquely determines the other. You do not need to measure both, unless you desire some redundancy. Lansmont has the ability to measure both.Relationship between eA and COR,r uses only conservation of momentum (for a free bat), conservation of angular momentum (for free or pivoted bat), and the definition of COR. For the experts, the definition is ratio of relative ball-bat speed after to before the collision, where only the rigid body motion of the bat is implied. There are no approximations in arriving at this expression. Given COR and inertial properties of bat, eA can be predicted. Conversely, given measurements of eA, one can get COR (and BPF). In fact, this is the basis of the Gilman proposal to measure the BPF. The same physics is contained in the Brandt technique, but the algebra is different because the recoil speed of the bat is measured rather than the post-impact speed of the ball. Keep in mind the following: angular momentum and/or momentum conservation implies that if the initial ball or bat speed is known, then a measurment of either the exit speed of the ball or the recoil speed of the bat uniquely determines the other. You do not need to measure both, unless you desire some redundancy. Lansmont has the ability to measure both.

5. 5 The Trampoline Effect:In 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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7. 7 The Trampoline Effect:

8. 8 The Trampoline Effect:

9. 9 The Trampoline Effect:

10. 10 The Trampoline Effect:

11. 11 The Trampoline Effect:

12. 12 Measuring Ball-Bat COR (e) Ball fired at stationary bat measure q=vf/vi q=(e-r)/(1+r) calculate r = mball/mbat,eff solve for e=q(1+r)+r

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14. 14 Single-Wall vs. Double-Wall The “Trampoline” Effect:A Closer Look Little effect of bending modes at sweet spot.Little effect of bending modes at sweet spot.

15. 15 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

16. 16 Why BPF? BPF ? BBCOR/COR (e/e0) Measure e0 by bouncing ball off wall Measure e by bouncing ball off bat eA = (e-r)/(1+r) 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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20. 20 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 directly—the ASA technique Regulating BBS indirectly—the NCAA technique Regulate BBS via BPF—the USSSA technique

21. 21 1. Regulating BBS directly Measure q in lab q = vf/vi Using prescription for vball and vbat, calculate BBS expected in field BBS = qvball + (1+q)vbat Reject bat if maximum BBS exceeded

22. 22 Regulating BBS directly: The ASA Implementation Measure q in lab at 110 mph (25+85) “typical” game conditions scan across barrel BBS = qvball + (1+q)vbat Vball= 25 mph (simple kinematics) Vbat = 85mph(9000/I)0.25(d+2.5)/30.5 d = distance from knob to impact in inches Assumes bat rotated about point 2.5” off knob I=MOI about point 6” from knob assumes 85 mph for 34” bat, 6” from tip Reject bat if maximum BBS exceeded Maximum BBS=97 mph for ASA

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25. 25 Include stuff here that I showed at the 2004 NCAA Rules Committee meetingInclude stuff here that I showed at the 2004 NCAA Rules Committee meeting

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27. 27 The NCAA certification protocol limits field performance of non-wood bats Under “standard” conditions--- Wood = 97 mph Non-wood < 102 mph Difference < 5 mph, or about 5%

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32. 32 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)

33. 33 Some Qualitative Effects Balls hit to left or right curve towards foul line Undercut balls have backspin Overcut balls have topspin

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35. 35 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