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Tuning a bat to optimize the trampoline effect

Tuning a bat to optimize the trampoline effect. Dan Russell. Applied Physics Kettering University Flint, MI. drussell@kettering.edu. The Quest for the “perfect” bat. Moment of Inertia  swing speed. Trampoline Effect  BBCOR. What is the Trampoline Effect?. Ball impacting solid bat.

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Tuning a bat to optimize the trampoline effect

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

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

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

  4. Experimental Evidence Hoop frequency  performance predictor? Naruo & Sato (1997): 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. Higher 1st bending frequency results in higher COR Lower 1st hoop frequency results in higher COR Lower 1st hoop frequency results in higher COR Highest COR for high bending mode and low hoop mode Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 4

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

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

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

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

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

  10. Simple Model  Trampoline Effect (Cochran,1998,2002) mass-spring model of golf ball/club Ball modeled as a non-linear, damped mass-spring system with initial velocity Bat modeled as a linear, damped mass-spring system initially at rest and fixed to rigid foundation Coupled equations of motion solved numerically Determine COR = v1out / v1in for a given bat stiffness s2 s2 / m2 = w2bat  Hoop frequency of barrel Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 10

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

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

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

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

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

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

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

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

  19. Frequencies  Performance “BPF” Frequency of lowest hoop mode (Hz) Compare frequencies with BBCOR from impact tests 1st bend 1st hoop “BPF” single wall #1 160 Hz 2056 Hz 1.11 single wall #2 166 1841 1.15 double wall #3 160 1461 1.23 double wall #4 160 1273 1.26 composite #5 158 1128 1.48 composite #6 164 1096 1.52 “BPF” 1.11 1.15 1.23 1.26 1.48 1.52 slowpitch softball bats (ERA study) Compare data to simple model Model looks promising, but ball parameters to obtain this “fit” are probably not realistic Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 19

  20. “Tuning” theTrampoline 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 Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 20

  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 Dt 2502 Hz 0.68ms 1465 Hz 1.08ms 1173 Hz 1.20ms Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 21

  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 Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 22

  23. Bat Barrel Compression Test 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 Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 23

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