1. Can a curveball be hit farther than a fastball?
Some Aerodynamics
FL (Magnus)
v

ω
Fd
mg
Drag: Fd = ½ CDAv2
-v direction
“Lift”: FL = CMARv
(ω  v) direction
(in direction leading edge is turning)
CD, CM ~ 0.2-0.5
NSBP Meeting, February 18, 2005
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Measurements of Lift and Drag
Joe Hopkins, Lance Chong, Hank Kaczmarski, AMN
Motion Capture System
Two-wheel pitching machine
NSBP Meeting, February 18, 2005
Baseball with reflecting dot
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Experiment: MoCap Data
93.6 mph/3040 rpm/1.83g
10
140
y
120
100
5
z
80
y (mm) 60
40
20
0
y = ½ ayt2
topspinay>g
0
-20
0.00
0.02
NSBP Meeting, February 18, 2005
0.04
0.06
t (sec)
0.08
0.10
-5
0.12
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Effect of Spin on Baseball Trajectory
(drag or lift)/wt
2
100
1.5
2000 rpm
60
1
y (ft)
lift/wt
0.5
40
=0 rpm
20
0
0
-0.50
=2000 rpm
80
drag/wt
20
40
60
v (mph)
80
100
120
77’
0
100
200
300
400
500
x (ft)
Lift …
• scales approx. linearly with 
• has major effect on trajectory
NSBP Meeting, February 18, 2005
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Oblique Collisions:
Putting Spin on the Ball
Sliding friction …
• reduces transverse velocity
• increases 
• sliding-to-rolling transition
f
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
NSBP Meeting, February 18, 2005
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Undercutting the ball  backspin
Ball100 downward
D = center-to-center offset
Bat 100 upward
 (rpm)
 (deg)
vertical
15000
150
100
10000
trajectories
250
200
150
50
5000
1.5
1.0
2.0
100
0.5
0
0
50
-5000
-0.5
0
0.5
1
1.5
D (inches)
D (inches)
NSBP Meeting, February 18, 2005
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2.5
3
0.25
-50
0
-100
0.75
0.75
0
100
0
200
300
400
8
Fastball: spin reverses
Curveball: spin doesn’t reverse
 (rpm)
6000
5000
  larger for curveball
4000
2000 rpm topspin
3000
2000
1000
2000 rpm backspin
0
-1000
NSBP Meeting, February 18, 2005
0
0.2
0.4
0.6
DA (in)
0.8
1
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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
NSBP Meeting, February 18, 2005
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Physics Description of Ball-Bat Collision
• forces large (>8000 lbs!)
• time is short (<1/1000 sec!)
• ball compresses, stops, expands
– bat compresses ball
– ball bends/compresses bat
• lots of energy dissipated
– distortion of ball
– vibrations in bat
• ball-bat COR related to energy dissipation
– why is aluminum better?
NSBP Meeting, February 18, 2005
Courtesy of CE Composites
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NSBP Meeting, February 18, 2005
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Wood versus Aluminum
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 
NSBP Meeting, February 18, 2005
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The “Trampoline” Effect:
A Simple Physical Picture
•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”
NSBP Meeting, February 18, 2005
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“Trampoline” Effect
tennis ball/racket strings
NSBP Meeting, February 18, 2005
Softball/bat
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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, Kettering U.
NSBP Meeting, February 18, 2005
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Hoop Modes of Hollow Bats
Lowest hoop mode…
--that annoying “ping”
--“trampoline effect”
NSBP Meeting, February 18, 2005
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COR correlated with fhoop
COR
0.70
Energy left in hoop vibrations...
0.65
COR-model
COR-expt
0.60
0.55
Wood bat
0.50
~30’ on long fly ball
0.45
0.40
500
1000
1500
f
hoop
2000
(Hz)
Courtesy of Dan Russell
www.kettering.edu/~drussell/bats
NSBP Meeting, February 18, 2005
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Summary:
Why Does Aluminum Outperform Wood?
Trampoline effect reduces energy dissipation
– More pop
– Longer fly ball
NSBP Meeting, February 18, 2005
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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
– a-nathan@uiuc.edu
• Go Red Sox!
NSBP Meeting, February 18, 2005
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