ubc colloquium 10/5/06 1 thanks to j. j. crisco & r. m. greenwald medicine & science in...
DESCRIPTION
UBC Colloquium 10/5/06 3 Adair’s Book: An Excellent Reference “Our goal is not to reform the game but to understand it. “The physicist’s model of the game must fit the game.”TRANSCRIPT
UBC Colloquium 10/5/06 1
Thanks to J. J. Crisco & R. M. GreenwaldMedicine & Science in Sports & Exercise
34(10): 1675-1684; Oct 2002
Alan M. Nathan,University of Illinoiswww.npl.uiuc.edu/~a-nathan/pob
a-nathan @uiuc.edu
The Physics of Hitting a Home Run
UBC Colloquium 10/5/06 2
1927 Solvay Conference:
Greatest physics team ever assembled
Baseball and Physics
1927 Yankees:Greatest baseball team
ever assembled
MVP’s
UBC Colloquium 10/5/06 3
Adair’s Book: An Excellent Reference
“Our goal is not to reform the game but to understand it.
“The physicist’s model of the game must fit the game.”
UBC Colloquium 10/5/06 4
1. How does a baseball bat work?
2. Aerodynamics: flight of a baseball
3. Leaving the no-spin zone
4. Putting it all together
The Physics of Hitting a Home Run
UBC Colloquium 10/5/06 5
“You can observe a lot by watching”
Champaign News-Gazette
CE Composites
--Yogi Berra
Easton Sports
UBC Colloquium 10/5/06 6
Brief Description of Ball-Bat Collision• forces large, time short
– >8000 lbs, <1 ms• ball compresses, stops, expands
– KEPEKE– bat recoils
• lots of energy dissipated (“COR”)– distortion of ball – vibrations in bat
• to hit home run….– large hit ball speed (100 mph~400 ft)– optimum take-off angle (300-350)– lots of backspin
UBC Colloquium 10/5/06 7
vf = q vball + (1+q) vbat
Conclusion:
vbat matters much more than vball
• q “Collision Efficiency” • Joint property of ball & bat
independent of reference frame ~independent of “end conditions”—more later weakly dependent on vrel
• Superball-wall: q 1• Ball-Bat near “sweet spot”: q 0.2
vf 0.2 vball + 1.2 vbat
vball vbat
vf
Kinematics of Ball-Bat Collision
UBC Colloquium 10/5/06 8
Kinematics of Ball-Bat Collision
f ball bat
e-rq = 1+r
e-r 1+ev = v v1+r 1+r
r = mball /Mbat,eff : bat recoil factor = 0.25(momentum and angular momentum conservation)
---heavier is better but…
e: “coefficient of restitution” 0.50 (energy dissipation—mainly in ball, some in bat)
vball vbat
vf
q=0.20
UBC Colloquium 10/5/06 9
Collision Efficiency q Can Be Measured• Air cannon to fire ball onto stationary bat• q = vout/vin
• Used by NCAA, ASA, … to regulate/limit performance of bats
Sports Sciences Lab @ WSU
UBC Colloquium 10/5/06 10
Accounting for COR:Dynamic Model for Ball-Bat Collision
AMN, Am. J. Phys, 68, 979 (2000)
• Collision excites bending vibrations in bat– hurts! breaks bats– dissipates energy
• lower COR, vf
• Dynamic model of collision– Treat bat as nonuniform beam– Treat ball as damped spring
UBC Colloquium 10/5/06 11
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
UBC Colloquium 10/5/06 12
Vibrations, COR, and the “Sweet Spot”
Evib
vf
e
Node of 1nd mode
+
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
-30.00
-20.00
-10.00
0.00
10.00
20.00
30.00
0 1 2 3 4 5
v (m/s)
t (ms)
Strike bat here Measure response here
UBC Colloquium 10/5/06 13
• handle moves only after ~0.6 ms delay
• collision nearly over by then
• nothing on knob end matters• size, shape• boundary conditions• hands!
• confirmed experimentally
-30.00
-20.00
-10.00
0.00
10.00
20.00
30.00
0 1 2 3 4 5
v (m/s)
t (ms)
Independence of End Conditions
UBC Colloquium 10/5/06 14
q independent of end conditions:experimental proof
0
0.05
0.1
0.15
0.2
0.25
25 26 27 28 29 30 31 32
Collision Efficiency
distance from knob (inches)
"normal" bat
normal + 3 oz in knob
Conclusion: mass added in knob has no effect on collision efficiency (q)
UBC Colloquium 10/5/06 15
• Aluminum has thin shell • Hoop modes give “trampoline” effect
– larger COR, vf
Why Does Aluminum Outperform Wood?
UBC Colloquium 10/5/06 16
•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”
• Also seen in golf, tennis, …
The “Trampoline” Effect:A Simple Physical Picture
UBC Colloquium 10/5/06 17
The Trampoline Effect: A Closer Look
“hoop” modes: cos(2)
“ping”
Thanks to Dan Russell
UBC Colloquium 10/5/06 18
Wood vs. Aluminum:Where Does the Energy Go?
0
50
100
150
200
250
300
350
400
0 0.2 0.4 0.6 0.8 1
Wood Bat
Ball KE
Ball PE
Bat Recoil KE
Bat Vibrational E
Energy (J)
t (ms)
0
50
100
150
200
250
300
350
400
0 0.2 0.4 0.6 0.8 1
Aluminum Bat
Ball KE
Ball PE
Bat Recoil KE
Bat Vibrational E
Energy (J)
t (ms)
UBC Colloquium 10/5/06 19
The Trampoline Effect: A Closer Look
to optimize….kbat//kball small and fhoop > 1
k R4: large in barrel little energy stored
f (170 Hz, etc) > 1/ energy goes into
vibrations
k (t/R)3: small in barrel
more energy stored
f (2-3 kHz) < 1/ energy mostly restored
Bending Modes vs. Shell Modes
UBC Colloquium 10/5/06 20
0.40
0.45
0.50
0.55
0.60
0.65
0.70
500 1000 1500 2000
COR-modelCOR-expt
COR
fhoop
(Hz)
Softball Data and Model
essential physics understood
UBC Colloquium 10/5/06 21
Aerodynamics of a Baseball
Drag: Fd = ½ CDAv2
-v direction
“Magnus” or “Lift”: FL = ½ CLAv2
(ω v) direction
v
ω
mg
Fd
FL (Magnus)
CD~ 0.2-0.5CL ~ R/v
(in direction leading edge is turning)
UBC Colloquium 10/5/06 22
Effect of Drag and Lift on Trajectories
• drag effect is huge
• lift effect is smaller but significant
0
20
40
60
80
100
120
0 100 200 300 400 500 600 700distance (ft)
no drag or lift
drag, no lift drag and lift
v
ω
mg
Fd
FL (Magnus)
UBC Colloquium 10/5/06 23
0
50
100
150
200
250
300
350
400
10 20 30 40 50 60 70 80 90
Range (ft)
(deg)
Range vs.
2000 rpm
0 rpm
Some Effects of Drag
• Reduced distance on fly ball
• Reduction of pitched ball speed by ~10%
• Asymmetric trajectory:– Total Distance 1.7 x
distance at apex
• Optimum home run angle ~30o-35o
0
20
40
60
80
100
120
0 100 200 300 400 500 600 700distance (ft)
no drag or lift
drag, no lift
UBC Colloquium 10/5/06 24
Some Effects of Lift
0
20
40
60
80
100
120
0 100 200 300 400 500 600 700distance (ft)
no drag or lift
drag, no lift drag and lift
v
ω
mg
Fd
FL (Magnus)
• Backspin makes ball rise
– “hop” of fastball– undercut balls: increased distance, reduced
optimum angle of home run
• Topspin makes ball drop– “12-6” curveball– topped balls nose-dive
• Breaking pitches due to spin– Cutters, sliders, etc.
UBC Colloquium 10/5/06 25
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,
UBC Colloquium 10/5/06 26
Motion Capture ExperimentJoe Hopkins, Lance Chong, Hank Kaczmarski, AMN
Two-wheel pitching machine
Baseball with reflecting dot
Motion Capture System
UBC Colloquium 10/5/06 27
Typical Motion Capture Datameasure spin, CM trajectory
61
62
63
64
65
66
0 5 10 15distance (ft)
94 mph3000 rpm topspin1.8g
Note: topspin ay > g
CM trajectory
UBC Colloquium 10/5/06 28
Results for Lift Coefficient CL
FL= 1/2ACLv2
S=r/v100 mph, 2000 rpm
S=0.17
Conclusion: data qualitatively consistent (~20%)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
present
Alaways 2-Seam
Alaways 4-Seam
Watts & Ferrer
Briggs
0.0 0.2 0.4 0.6 0.8 1.0
CL
S
UBC Colloquium 10/5/06 29
Baseball Aerodynamics:Things I would like to know better
• Better data on drag– “drag crisis”?– Spin-dependent drag?– Drag for v>100 mph
• Dependence of drag/lift on seam orientation
• Is the spin constant?
UBC Colloquium 10/5/06 30
Oblique Collisions:Leaving the No-Spin Zone
Oblique friction spintransverse velocity reducedspin increased
Familiar Results:• Balls hit to left/right break toward foul line• Topspin gives tricky bounces in infield• Backspin keeps fly ball in air longer• Tricky popups to infield
demo
UBC Colloquium 10/5/06 31
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 backspin
Ball100 downward
Bat 100 upward
D = center-to-center offset
trajectories
“vertical sweet spot”
UBC Colloquium 10/5/06 32
• Bat-Ball Collision Dynamics– A fastball will be hit faster– A curveball will be hit with more backspin
Putting it all Together:Can curveball be hit farther
than fastball?
UBC Colloquium 10/5/06 33Net effect: backspin larger for curveball
Fastball: spin must reverse
curveball can be hit with more backspin: WHY?
Fastball with backspin
Curveball: spin doesn’t reverse
Curveball with topspin
UBC Colloquium 10/5/06 34
• Bat-Ball Collision Dynamics– A fastball will be hit faster– A curveball will be hit with more backspin
• Aerodynamics– A ball hit faster will travel farther– Backspin increases distance
• Which effect wins?• Curveball, by a hair!
Can Curveball Travel Farther than Fastball?
UBC Colloquium 10/5/06 35
Work in Progress
• Collision experiments & calculations to elucidate trampoline effect
• New studies of aerodynamics• Experiments on oblique collisions
– No data!
UBC Colloquium 10/5/06 36
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!