fsu colloquium 9/1/05 1 thanks to j. j. crisco & r. m. greenwald medicine & science in...
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FSU Colloquium 9/1/05 2
1927
Solvay Conference:
Greatest physics team
ever assembled
Baseball and Physics
1927 Yankees:
Greatest baseball team
ever assembled
MVP’s
FSU Colloquium 9/1/05 4
Brief Description of Ball-Bat Collision• forces large, time short
– >8000 lbs, <1 ms
• ball compresses, stops, expands– KEPEKE
– bat bends & compresses
• lots of energy dissipated (“COR”)– distortion of ball
– vibrations in bat
• to hit home run….– large hit ball speed
– optimum take-off angle
– backspin
Courtesy of CE Composites
FSU Colloquium 9/1/05 5
Kinematics of Ball-Bat Collisionvball vbat
vff ball bat
e-r 1+ev = v v
1+r 1+r
r = mball /Mbat,eff : bat recoil factor = 0.25(momentum and angular momentum conservation)
e: “coefficient of restitution” 0.50 (energy dissipation)
typical numbers: vf = 0.2 vball + 1.2 vbat
vbat matters much more than vball
FSU Colloquium 9/1/05 6
Kinematics of Ball-Bat Collision
f ball bat
e-r 1+ev = v v
1+r 1+r
• r = mball /Mbat,eff: bat recoil factor = 0.25(momentum and angular momentum conservation)
• heavier bat better but…
FSU Colloquium 9/1/05 7
Crisco/Greenwald Batting Cage Study
40
42
44
46
48
50
1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9
Iknob
(104 oz-in2)
knob
(rad/s)
Crisco/Greenwald Batting Cage Study
vbat I-0.3
vbat I-0.5
60
70
80
90
100
110
120
20 30 40 50 60
n=0constant v
bat
n=0.5constant bat KE
vbat
= 65 mph x (32/Mbat
)n
Mbat
(oz)
vf (mph)
n=0.31 (expt)
FSU Colloquium 9/1/05 8
• Collision excites bending vibrations
in bat– Ouch!! Thud!! Sometimes broken bat
– Energy lost lower COR, vf
• Reduced if …
– Impact is at a node
– fn>1, where ~ 0.5-1.0 ms
• Calculate as non-uniform beam
Accounting for COR:
Dynamic Model for Ball-Bat CollisionAMN, Am. J. Phys, 68, 979 (2000)
FSU Colloquium 9/1/05 9
Modal Analysis of a Baseball Batwww.kettering.edu/~drussell/bats.html
0
0.05
0.1
0.15
0 500 1000 1500 2000 2500
FFT(R)
frequency (Hz)
179
582
1181
1830
2400
frequency
-1.5
-1
-0.5
0
0.5
1
0 5 10 15 20
R
t (ms)
time
0 5 10 15 20 25 30 35
f1 = 179 Hz
f2 = 582 Hz
f3 = 1181 Hz
f4 = 1830 Hz
FSU Colloquium 9/1/05 10
FSU Colloquium 9/1/05 11
-40.0
-20.0
0.0
20.0
40.0
0 2 4 6 8 10
v (m/s)
t (ms)
0.1
0.2
0.2
0.3
0.3
0.4
0.4
0.5
0
20
40
60
80
100
120
0 5 10 15
e
vf (mph)
distance from tip (inches)
nodes4 3 2 1
Evib
vf
e
Vibrations, COR, and Sweet Spot
• Center of percussion (~27”)• Node of fundamental (~27”)• Maximum e (~29”)
• Minimum Evib (~29”)
• Maximum vf (29”)
• Don’t feel a thing (?)
Node of 2nd mode
FSU Colloquium 9/1/05 12
Experimental Data
ball incident on bat at rest
Conclusion: essential physics understood
0.25
0.30
0.35
0.40
0.45
0.50
0.55
23 24 25 26 27 28 29 30 31
e
distance from knob (inches)
flexible bat
rigid bat
Louisville Slugger R161 Wood Batv
i=100 mph
FSU Colloquium 9/1/05 13
Boundary Conditions
• handle moves after ~0.6 ms
• ball leaves bat after ~0.6 ms
• ball doesn’t “know” about far end of bat
nothing on knob end matters:• size, shape• boundary conditions
• batter’s hands!
-40.0
-20.0
0.0
20.0
40.0
0 2 4 6 8 10
v (m/s)
t (ms)
FSU Colloquium 9/1/05 14
Aluminum has thin shell – Less mass in barrel
–easier to swing and control –but less effective at transferring energy
– Hoop modes –trampoline effect –larger COR
Why Does Aluminum Outperform Wood?
FSU Colloquium 9/1/05 15
•Two springs mutually compress each other KE PE KE
• PE shared between “ball spring” and “bat spring”
• PE in ball mostly dissipated (~80%!)
• PE in bat mostly restored
• Net effect: less overall energy dissipated...and therefore higher ball-bat COR
…more “bounce”
The “Trampoline” Effect:A Simple Physical Picture
FSU Colloquium 9/1/05 16
The Trampoline Effect: A Closer Look
“hoop” modes: cos(n)k (t/R)3: hoop mode largest in barrel
f2 (1-3 kHz) < 1/ energy mostly restored
(unlike bending modes)
“ping”
Thanks to Dan Russell
FSU Colloquium 9/1/05 17
Verification from Crisco/Greenwald Study
90
92
94
96
98
100
90 92 94 96 98 100 102
vf
' (mph)
vf (mph)
W
M2
M1
M4M5
M3
• Vf correlated with COR
• COR main factor for vf
–inertial factors “cancel out”
• COR correlated with fhoop
– fhoop main factor for vf
wood
FSU Colloquium 9/1/05 18
Effect of Spin on Baseball Trajectory
Drag: Fd = ½ CDAv2
-v direction
“Lift”: FL = CMARv(ω v) direction
v
ω
mg
Fd
FL (Magnus)
CD, CM ~ 0.2-0.5
(in direction leading edge is turning)
FSU Colloquium 9/1/05 19
0
20
40
60
80
100
0 100 200 300 400
y (ft)
x (ft)
Hubbard
100 mph, 2000 rpm backspin, 25o
Adair
444'367'
77'
Who is right?
Hubbard vs. Adair:
Large difference in FM at 100 mph
0
0.5
1
1.5
2
0 25 50 75 100 125 150Speed in mph
Drag/Weight
Lift/Weight@1800 rpm
solid: Hubbarddashed: Adair-3
1. Hubbard (AJP, 71, 1152, 2003)
2. Adair, The Physics of Baseball, 3rd Ed.
FSU Colloquium 9/1/05 20
New Experiment at Illinois
• Fire baseball horizontally from pitching
machine
• Use motion capture to track ball over ~5m
of flight and determine x0,y0,vx,vy,,ay
• Use ay to determine Magnus force as
function of v,
FSU Colloquium 9/1/05 21
Motion Capture ExperimentJoe Hopkins, Lance Chong, Hank Kaczmarski, AMN
Two-wheel pitching machine
Baseball with reflecting dot
Motion Capture System
FSU Colloquium 9/1/05 22
Experiment: Sample MoCap Datay
z
topspin ay > g
-3000
-2000
-1000
0
1000
2000
-20
0
20
40
60
80
100
120
140
0.00 0.02 0.04 0.06 0.08 0.10 0.12
z (mm)y (mm)
time (sec)
93.6 mph/3040 rpm/1.83g
Z
y
y = ½ ayt2
FSU Colloquium 9/1/05 23
0
0.1
0.2
0.3
0.4
0.5
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
CL
presentexperiment
Hubbardparametrization
(PRELIMINARY) Results
0
20
40
60
80
100
0 100 200 300 400
y (ft)
x (ft)
Hubbard
100 mph, 2000 rpm backspin, 25o
Adair
444'367'
77'
present
• Present data support Hubbard, not Adair--spin plays important role in flight of baseball
• More extensive experiment planned for early 2006
FSU Colloquium 9/1/05 25
Oblique Collisions:Leaving the No-Spin Zone
Friction … • sliding/rolling vs. gripping• transverse velocity reduced, spin increased
Familiar Results• Balls hit to left/right break toward foul line
• Topspin gives tricky bounces in infield
• Pop fouls behind the plate curve back toward field
• Backspin keeps fly ball in air longer
f
FSU Colloquium 9/1/05 26
0
50
100
150
200
250
-100 0 100 200 300 400
1.5
0
0.25
0.5 0.75
1.02.0
0.75
Undercutting the ball backspinBall100 downward
Bat 100 upward
D = center-to-center offset
trajectories
-5000
0
5000
10000
15000
-50
0
50
100
150
-0.5 0 0.5 1 1.5 2 2.5 3
vertical (rpm) (deg)
D (inches)D (inches)
FSU Colloquium 9/1/05 27
larger for curveball
-1000
0
1000
2000
3000
4000
5000
6000
0 0.2 0.4 0.6 0.8 1A
2000 rpm topspin
2000 rpm backspin
D (in)
(rpm)
Fastball: spin reverses
Curveball: spin doesn’t reverse
FSU Colloquium 9/1/05 28
In summary….Can a curveball be hit farther than a fastball?
• Higher pitch speed higher hit ball speed on fastball
• But…more backspin on curve ball
• Net result: curveball goes farther– by a little bit
• Mont Hubbard, AJP 71, 1152-1162 (2003) – See also February 2005 issue of AJP for a debate: Hubbard vs. Adair
FSU Colloquium 9/1/05 29
Work in Progress
• Collision experiments & calculations to elucidate trampoline effect
• New measurements of lift and drag
• Experiments on oblique collisions?– Rod Cross & AMN: rolling almost works at
low speed– AMN: studies in progress at high speed
FSU Colloquium 9/1/05 30
Final Summary
• Physics of baseball is a fun application of basic (and not-so-basic) physics
• Check out my web site if you want to know more– www.npl.uiuc.edu/~a-nathan/pob– [email protected]
• Go Red Sox!..and the Quantum Fielders too!