1. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 1 Tuning a bat to optimize the trampoline effect Dan Russell Applied Physics Kettering University Flint, MI drussell@kettering.edu

2. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 2 The Quest for the perfect bat Moment of Inertia swing speed Trampoline Effect BBCOR

3. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 3 What is the Trampoline Effect? Ball impacting solid bat Ball impacting hollow bat

4. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 4 Hoop frequency performance predictor? Naruo & Sato (1997): Experimental Evidence Higher 1st bending frequency results in higher COR Measured bat-ball COR for composite pipes with varying radial and bending stiffness. Also used modal analysis to find frequencies for bending and hoop modes. Lower 1st hoop frequency results in higher COR Highest COR for high bending mode and low hoop mode Lower 1st hoop frequency results in higher COR

5. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 5 Experimental Modal Analysis Impact hammer (force transducer) 35 points along length FFT Analyzer Frequency Response Function ( accel / force) Accelerometer fixed location on barrel

6. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 6 Experimental Modal Analysis Frequency Response Function (accel / force) Impact at Barrel endImpact at Sweet SpotImpact at Handle Accelerometer on barrel

7. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 7 Experimental Modal Analysis Bending Modes node Sweet Vibrations Zone (Cross, 1998)

8. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 8 Hoop (cylinder) modes First hoop mode ping and trampoline effect Higher order hoop modes Modal Analysis Mode Shapes

9. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 9 Modal Analysis Frequencies Slowpitch Softball Bats

10. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 10 (Cochran,1998,2002) mass-spring model of golf ball/club Bat modeled as a linear, damped mass-spring system initially at rest and fixed to rigid foundation Ball modeled as a non-linear, damped mass-spring system with initial velocity Coupled equations of motion solved numerically Determine COR = v 1out / v 1in for a given bat stiffness s 2 s 2 / m 2 = 2 bat Hoop frequency of barrel Simple Model Trampoline Effect

11. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 11 Ball as a nonlinear spring F = kx F = kx p Linear: force displacement Nonlinear: force displacement More ball compression = more energy lost Compression & relaxation rates are different hysteresis displacement Force Hysteresis model (Stulov, 1995) time force displacement force time displacement Area enclosed by hysteresis loop is energy lost during compression and relaxation of ball p

12. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 12 Simple Model Trampoline Effect Very Stiff Bat ball deforms more, energy lost Elastic Bat bat deforms, ball deforms less (energy lost) bat < (energy lost) ball Optimal Bat hoop frequency tuned for maximum trampoline effect Soft Bat bat dents or cracks ball parameters softball

13. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 13 Simple Model Trampoline Effect Rigid Bat f hoop = 5000 Hz BPF=1.02 2% energy stored in bat Energy Fraction Time (s) 80% energy lost in ball 20% energy returned to ball ball KE ball PE bat KE bat PE

14. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 14 Simple Model Trampoline Effect Elastic Bat f hoop = 1800 Hz BPF=1.19 18% energy stored in bat Energy Fraction Time (s) 71% energy lost in ball 27% energy returned to ball ball KE ball PE bat KE bat PE

15. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 15 Simple Model Trampoline Effect Tuned Bat f hoop = 900 Hz BPF=1.42 45% energy temporarily stored in bat Energy Fraction Time (s) 46% energy lost in ball 39% energy returned to ball 15% energy remains in bat ball compresses much less ball KE ball PE bat KE bat PE

16. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 16 Simple Model Trampoline Effect Soft Bat f hoop = 450 Hz BPF=1.23 58% energy temporarily stored in bat Energy Fraction Time (s) 38% energy lost in ball 30% energy returned to ball ball KE ball PE bat KE bat PE

17. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 17 Simple Model Trampoline Effect Model Predictions for Softball Bats Single Walled Aluminum Graphite Bat Double Walled Aluminum Composite

18. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 18 The Ball Trampoline Effect Do ball properties affect bat performance? High performance bat higher COR ball Lower performance bat higher compression ball

19. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 19 1st bend 1st hoop BPF single wall #1160 Hz2056 Hz 1.11 single wall #21661841 1.15 double wall #31601461 1.23 double wall #41601273 1.26 composite #51581128 1.48 composite #61641096 1.52 Compare frequencies with BBCOR from impact tests Compare data to simple model BPF 1.11 1.15 1.23 1.26 1.48 1.52 Frequency of lowest hoop mode (Hz) BPF Frequencies Performance slowpitch softball bats (ERA study) Model looks promising, but ball parameters to obtain this fit are probably not realistic

20. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 20 Tuning the Trampoline Effect Higher performance bats lower hoop mode frequencies Simple model correctly…... separates high and low performance bats responds to changes in ball parameters Improvements needed: experimental (dynamic) ball parameters is the bat linear or nonlinear? (double walled) does MOI matter? Working model could be used….. to aid design of bats w.r.t. performance standards develop simple, portable tools for field testing bats

21. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 21 Pendulum Test (preliminary results) Concept: Use a very heavy, very stiff ball to impact bat barrel. Measure contact time between ball and bat. Expect that contact time determined by mass of ball stiffness of bat Hoop Freq t 2502 Hz 0.68ms 1465 Hz 1.08ms 1173 Hz 1.20ms

22. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 22 USGA Pendulum Test Acceleration integrated to obtain velocity change during impact Measure characteristic time Repeat 9 times for three velocities Extrapolate to find effective CT for higher impact velocities

23. Dan Russell Tuning a bat SGMA Baseball & Softball Council Fall Meeting 2003 Page 23 Bat hoop Force (lb) BPF single wall #1 2056 Hz 789 / 769 1.11 single wall #2 1841 Hz 621 / 629 1.15 double wall #3 1461 Hz 472 / 497 1.23 double wall #4 1273 Hz 395 / 476 1.26 composite #5 1128 Hz 278 / 259 1.48 composite #6 1096 Hz 280 / 268 1.52 Bat Barrel Compression Test