1. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 1 The Trampoline Effect: What is it all about? Alan M. Nathan Department of Physics University of Illinois at Urbana-Champaign a-nathan@uiuc.edu www.npl.uiuc.edu/~a-nathan/pob SGMA Meeting Dallas TX October, 2003

2. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 2 But first a digression... l 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 l With a year to think about it, here is an update

3. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 3 Take bat of given shell Adjust weights on ends to adjust MOI with weight=28 oz Do computer simulation to get BBCOR and BBS BBS calculated using ASA formula Computer simulation Conclusion: BBS a more robust metric than BPF

4. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 4 The Ball-Bat Collision l forces large (>8000 lbs!) l time is short (<1/1000 sec!) l ball compresses, stops, expands  bat compresses ball  ball bends/compresses bat l lots of energy dissipated  distortion of ball  vibrations in bat l ball-bat COR related to energy dissipation

5. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 5 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. high-speed video of collision

6. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 6 The “Trampoline” Effect: A Simple Physical Picture demo 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

7. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 7 “Trampoline” Effect tennis ball/racket strings Softball/bat

8. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 8 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)

9. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 9 The Trampoline Effect: In symbols k ball k bat k bat, k ball measures “stiffness” of bat, ball...sometimes called “compression” k bat /k ball (0 -  ) = (energy stored in ball)/(energy stored in bat) Assumes no energy loss in bat

10. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 10 The Trampoline Effect: k ball k bat This model is... very simple to understand captures most of essential physics qualitatively explains much of the data

11. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 11 The Trampoline Effect: k ball k bat Example 1: typical wood bat k bat /k ball >>1: little energy stored in bat  e  e ball

12. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 12 The Trampoline Effect: k ball k bat Example 2: the ideal situation (“happy/sad” ball on bongo paddle) k bat /k ball << 1: most of energy stored in bat  e  1, independent of e ball demo

13. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 13 The Trampoline Effect: k ball k bat Example 3: single-wall Aluminum bat k bat /k ball  7: 15% of energy stored in bat  e = 0.6, “BPF”  e/e ball = 1.20

14. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 14 The Trampoline Effect: k ball k bat Example 4: “high-performance” bat k bat /k ball  2: 33% of energy stored in bat  e = 0.75, “BPF”  e/e ball = 1.50

15. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 15 Note: The BPF is not a “ball-independent” quantity: It depends on the COR of the ball (e ball ) BPF decreases as e ball increases effect greater when k bat /k ball smaller (“high performance”)

16. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 16 More Realistic Calculation Energy left in hoop vibrations...e bat <1 More from Dan Russell later

17. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 17 Bending Modes vs. Hoop Modes k bat  R 4 : large in barrel  little energy stored f (170 Hz, etc) > 1/   stored energy  vibrations Net effect: e  e 0 on sweet spot e  e 0 off sweet spot k bat  (t/R) 3 : small in barrel  more energy stored f (1-2 kHz) < 1/   energy mostly restored Net Effect: e > e 0 “BPF”  e/e 0 = 1.20-1.35! The “Trampoline” Effect: A Closer Look

18. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 18 Single-Wall vs. Double-Wall The “Trampoline” Effect: A Closer Look k SW = at 3 k DW = a[(t/2) 3 +(t/2) 3 ] = at 3 /4 = k SW /4 ¼ the stiffness same strength

19. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 19 Ball-Bat COR l Depends on ball COR …which depends on v rel = v ball + v bat l Depends on “BPF” (BBCOR/ball COR) …which depends on  impact location  ball COR  which depends on v rel  more for high- than low-performance bats  ball compression (k ball )  which may depend on v rel  more for high- than low-performance bats

20. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 20 An Indirect Performance Metric Low-speed collision of hard steel ball with barrel of bat l As k bat gets smaller...  BBCOR gets larger  collision time gets longer l Basis for USGA “pendulum” test  see Dan Russell’s talk

21. SGMA Meeting Dallas, October 2, 2003 Go Red Sox! Page 21 Summary of Important Points l The essential physics behind the trampoline effect is understood l The bat is probably well understood l Equally important is the ball, which is less well understood  but we are making progress