Transcript Tuning a bat to optimize the trampoline effect

Tuning a bat to optimize
the trampoline effect
Dan Russell
Applied Physics
Kettering University
Flint, MI
[email protected]
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 1st bending 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
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
node
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 = 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
Linear: force  displacement
p
Nonlinear: force  displacement
Force
Ball as a nonlinear spring
F = kxp
F = kx
Compression & relaxation rates
are different  hysteresis
displacement
Hysteresis model (Stulov, 1995)
force
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
1
80% energy lost in ball
0.8
ball KE
ball PE
bat KE
bat PE
0.6
0.4
20% energy returned to ball
0.2
0
0
0.0004
0.0008
2% energy stored in bat
Dan Russell
“Tuning a bat”
0.0012
0.0016
0.002
Time (s)
SGMA Baseball & Softball Council Fall Meeting 2003
Page 13
Simple Model  Trampoline Effect
fhoop= 1800 Hz
Elastic Bat
“BPF”=1.19
1
0.8
71% energy lost in ball
ball KE
ball PE
bat KE
bat PE
0.6
0.4
27% energy returned to ball
18% energy
stored in bat
0.2
0
0
0.0004
0.0008
0.0012
0.0016
0.002
Time (s)
Dan Russell
“Tuning a bat”
SGMA Baseball & Softball Council Fall Meeting 2003
Page 14
Simple Model  Trampoline Effect
“Tuned” Bat
fhoop= 900 Hz
“BPF”=1.42
1
ball KE
ball PE
bat KE
bat PE
0.8
ball compresses
much less
0.6
46% energy lost in ball
0.4
39% energy returned to ball
45% energy
temporarily
stored in bat
0.2
15% energy
remains
in bat
0
0
0.0004
0.0008
0.0012
0.0016
0.002
Time (s)
Dan Russell
“Tuning a bat”
SGMA Baseball & Softball Council Fall Meeting 2003
Page 15
Simple Model  Trampoline Effect
Soft Bat
fhoop= 450 Hz
“BPF”=1.23
1
0.8
ball KE
ball PE
bat KE
bat PE
58% energy
temporarily
stored in bat
0.6
38% energy lost in ball
0.4
30% energy
returned to ball
0.2
0
0
0.0004
0.0008
0.0012
0.0016
0.002
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)
1st bend
single wall #1
160 Hz
single wall #2
166
double wall #3 160
double wall #4 160
composite #5
158
composite #6
164
1st 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 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
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