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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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Presentation Transcript
slide1

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

slide2

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

slide3

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

slide4

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

slide5

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

slide6

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

slide7

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

slide8

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

slide9

Modal Analysis  Frequencies

Slowpitch Softball Bats

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

slide10

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

slide11

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

slide12

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

slide13

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

slide14

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

slide15

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

slide16

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

slide17

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

slide18

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

slide19

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

slide20

“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

slide21

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

slide22

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

slide23

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