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 PhysicsKettering University

Flint, MI

drussell@kettering.edu

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

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

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

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

Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 6

Experimental Modal AnalysisFrequency Response Function (accel / force)

Impact at Barrel end Impact at Sweet Spot Impact at Handle

Accelerometer on barrel

Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 7

Experimental Modal AnalysisBending Modes

node node

node node node

Sweet Vibrations Zone (Cross, 1998)

Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 8

Hoop (cylinder) modesFirst hoop mode “ping” and “trampoline effect”

Higher order hoop modes

Modal Analysis Mode Shapes

Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 9

Modal Analysis Frequencies

Slowpitch Softball Bats

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 systeminitially 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 = v1out / v1in for a given bat stiffness s2

s2 / m2 = 2bat Hoop frequency of barrel

Simple Model Trampoline Effect

Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 11

Ball as a nonlinear spring

F = kxF = kxpLinear: force displacement

Nonlinear: force displacement

More ball compression = more energy lost

Compression & relaxation rates are different hysteresis

displacement

For

ce

Hysteresis model (Stulov, 1995)

time

forc

e

displacement

forc

e

time

dis

pla

cem

en

t

Area enclosed by hysteresis loop is energy lost during compression and relaxation of ball

p

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 Batbat 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

Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 13

0 0.0004 0.0008 0.0012 0.0016 0.0020

0.2

0.4

0.6

0.8

1

Simple Model Trampoline EffectRigid Bat fhoop= 5000 Hz “BPF”=1.02

2% energy stored in bat

En

erg

y F

rac t

ion

Time (s)

80% energy lost in ball

20% energy returned to ball

ball KEball PEbat KEbat PE

Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 14

0 0.0004 0.0008 0.0012 0.0016 0.0020

0.2

0.4

0.6

0.8

1

Simple Model Trampoline EffectElastic Bat fhoop= 1800 Hz “BPF”=1.19

18% energy stored in batE

ner

gy

Fra

c tio

n

Time (s)

71% energy lost in ball

27% energy returned to ball

ball KEball PEbat KEbat PE

Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 15

0 0.0004 0.0008 0.0012 0.0016 0.0020

0.2

0.4

0.6

0.8

1

Simple Model Trampoline Effect“Tuned” Bat fhoop= 900 Hz “BPF”=1.42

45% energy temporarily

stored in bat

En

erg

y F

rac t

ion

Time (s)

46% energy lost in ball

39% energy returned to ball

15% energy remains

in bat

ball compresses much less

ball KEball PEbat KEbat PE

Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 16

0 0.0004 0.0008 0.0012 0.0016 0.0020

0.2

0.4

0.6

0.8

1

Simple Model Trampoline EffectSoft Bat fhoop= 450 Hz “BPF”=1.23

58% energy temporarily

stored in bat

En

erg

y F

rac t

ion

Time (s)

38% energy lost in ball

30% energy returned to ball

ball KEball PEbat KEbat PE

Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 17

Simple Model Trampoline EffectModel Predictions for Softball Bats

Single Walled Aluminum

Graphite Bat

Double Walled Aluminum

Composite

Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 18

The Ball Trampoline EffectDo ball properties affect bat performance?

High performance bathigher COR ball

Lower performance bathigher compression ball

Dan Russell “Tuning a bat” SGMA Baseball & Softball Council Fall Meeting 2003 Page 19

1st bend 1st hoop “BPF”single wall #1 160 Hz 2056 Hz 1.11single wall #2 166 1841 1.15double wall #3 160 1461 1.23double wall #4 160 1273 1.26composite #5 158 1128 1.48composite #6 164 1096 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)

“BP

F”

Frequencies Performance

slowpitchsoftball bats(ERA study)

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 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

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 ballstiffness of bat

Hoop Freq t 2502 Hz 0.68ms1465 Hz 1.08ms1173 Hz 1.20ms

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

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 1.11single wall #2 1841 Hz 621 / 629 1.15double wall #3 1461 Hz 472 / 497 1.23double wall #4 1273 Hz 395 / 476 1.26composite #5 1128 Hz 278 / 259 1.48composite #6 1096 Hz 280 / 268 1.52

Bat Barrel Compression Test