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 Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 1

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

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

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 1 st bending frequency results in higher COR Lower 1 st 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

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

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

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

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

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

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 = v 1 out / v 1 in for a given bat stiffness s 2 / m 2 = w 2 bat Hoop frequency of barrel Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 10

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

Simple Model Trampoline Effect Optimal Bat hoop frequency tuned for maximum trampoline effect ball parameters softball 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 Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 12

Simple Model Trampoline Effect Rigid Bat fhoop= 5000 Hz “BPF”=1. 02 Energy Fraction 80% energy lost in ball 20% energy returned to ball 2% energy stored in bat Dan Russell ball KE ball PE bat KE bat PE “Tuning a bat” Time (s) SGMA Baseball & Softball Council Fall Meeting 2003 Page 13

Simple Model Trampoline Effect Elastic Bat fhoop= 1800 Hz “BPF”=1. 19 Energy Fraction 71% energy lost in ball 18% energy stored in bat ball KE ball PE bat KE bat PE 27% energy returned to ball Time (s) Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 14

Simple Model Trampoline Effect Energy Fraction “Tuned” Bat fhoop= 900 Hz “BPF”=1. 42 ball KE ball PE bat KE bat PE ball compresses much less 46% energy lost in ball 45% energy temporarily stored in bat 39% energy returned to ball 15% energy remains in bat Time (s) Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 15

Simple Model Trampoline Effect Energy Fraction Soft Bat fhoop= 450 Hz “BPF”=1. 23 ball KE ball PE bat KE bat PE 58% energy temporarily stored in bat 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

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

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

Frequencies Performance Compare frequencies with BBCOR from impact tests slowpitch softball bats (ERA study) 1 st bend single wall #1 160 Hz single wall #2 166 double wall #3 160 double wall #4 160 composite #5 158 composite #6 164 1 st hoop 2056 Hz 1841 1461 1273 1128 1096 “BPF” 1. 11 1. 15 1. 23 1. 26 1. 48 1. 52 Compare data to simple model “BPF” Model looks promising, but ball parameters to obtain this “fit” are probably not realistic Frequency of lowest hoop mode (Hz) Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 19

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

Pendulum Test (preliminary results) Concept: Use a very heavy, very stiff ball to impact 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. 68 ms 1465 Hz 1. 08 ms 1173 Hz 1. 20 ms Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 21

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

Bat Barrel Compression Test Bat single wall #1 single wall #2 double wall #3 double wall #4 composite #5 composite #6 Dan Russell “Tuning a bat” hoop 2056 Hz 1841 Hz 1461 Hz 1273 Hz 1128 Hz 1096 Hz Force (lb) 789 / 769 621 / 629 472 / 497 395 / 476 278 / 259 280 / 268 “BPF” 1. 11 1. 15 1. 23 1. 26 1. 48 1. 52 SGMA Baseball & Softball Council Fall Meeting 2003 Page 23