1. can a curveball be hit farther than a fastball? some aerodynamics
DESCRIPTION
F L (Magnus). . Drag: F d = ½ C D Av 2. “Lift”: F L = C M ARv. F d. mg. 1. Can a curveball be hit farther than a fastball? Some Aerodynamics. (in direction leading edge is turning). C D , C M ~ 0.2-0.5. Motion Capture System. Two-wheel pitching machine. - PowerPoint PPT PresentationTRANSCRIPT
NSBP Meeting, February 18, 2005
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1. Can a curveball be hit farther than a fastball?Some Aerodynamics
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)
NSBP Meeting, February 18, 2005
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Measurements of Lift and DragJoe Hopkins, Lance Chong, Hank Kaczmarski, AMN
Two-wheel pitching machine
Motion Capture System
Baseball with reflecting dot
NSBP Meeting, February 18, 2005
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Experiment: MoCap Data
y
z
-20
0
20
40
60
80
100
120
140
0.00 0.02 0.04 0.06 0.08 0.10 0.12-5
0
5
10
y (mm)
t (sec)
93.6 mph/3040 rpm/1.83g
topspinay>gy = ½ ayt2
NSBP Meeting, February 18, 2005
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Effect of Spin on Baseball Trajectory
0
20
40
60
80
100
0 100 200 300 400 500
y (ft)
x (ft)
=2000 rpm
=0 rpm
77’
-0.5
0
0.5
1
1.5
2
0 20 40 60 80 100 120
(drag or lift)/wt
v (mph)
drag/wt
lift/wt
2000 rpm
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
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
NSBP Meeting, February 18, 2005
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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)
NSBP Meeting, February 18, 2005
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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
NSBP Meeting, February 18, 2005
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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?
Courtesy of CE Composites
NSBP Meeting, February 18, 2005
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NSBP Meeting, February 18, 2005
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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
Wood versus Aluminum
NSBP Meeting, February 18, 2005
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•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
NSBP Meeting, February 18, 2005
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“Trampoline” Effect
tennis ball/racket strings
Softball/bat
NSBP Meeting, February 18, 2005
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Experimental Modal Analysis
Impact hammer (force transducer)35 points along length
FFT Analyzer
Frequency Response Function (accel / force)
Accelerometer fixed location on barrel
Dan Russell, Kettering U.
NSBP Meeting, February 18, 2005
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Lowest hoop mode… --that annoying “ping” --“trampoline effect”
Hoop Modes of Hollow Bats
NSBP Meeting, February 18, 2005
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COR correlated with fhoop
0.40
0.45
0.50
0.55
0.60
0.65
0.70
500 1000 1500 2000
COR-modelCOR-expt
COR
fhoop
(Hz)
Energy left in hoop vibrations...
Courtesy of Dan Russell www.kettering.edu/~drussell/bats
Wood bat~30’ on long fly ball
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– [email protected]
• Go Red Sox!