page 1 imac xxiv, january 30, 2006 effect of spin on flight of baseball joe hopkins a, lance chong...
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Page 2IMAC XXIV, January 30, 2006
Introduction:Forces on a Moving, Spinning
Baseball
Fd=½ CDAv2
-v direction
FM = ½ CLAv2
(ω v) direction
v
ω
mg
Fd
FM
Page 3IMAC XXIV, January 30, 2006
Lift: What do we know?
• Hubbard (SHS, AJP 71, 1151, 2003):
CL = 1.5S (S = R/v <0.1)
= 0.09 + 0.6S (S>0.1)
• Adair (The Physics of Baseball):
CL = 2CDS {1 + 0.5(v/CD)dCD/dv}
Page 4IMAC XXIV, January 30, 2006
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Alaways 2-Seam
Alaways 4-Seam
Watts & Ferrer
Briggs
SHS
RKA-100
RKA-50
0.0 0.2 0.4 0.6 0.8 1.0
CL
S
0
0.2
0.4
0.6
0.8
1
0 20 40 60 80 100 120V (mph)
=1800 rpm SHS
RKA
S~0.15
• Factor of ~3 difference at 100 mph, 1800 rpm
• Serious implications for flight of fly ball
50
100
150
200
250
300
350
400
450
0 10 20 30 40 50 (deg)
SHS
RKA
Page 5IMAC XXIV, January 30, 2006
Experiment Fire baseball horizontally from pitching
machine Use motion capture to determine
initial conditions (x0,y0,vx,vy,)track trajectory over ~5m to get CL, CD
Measure horizontal distance D traversed (and sometimes flight time) as ball drops through y0 (~5 ft)ay = 2y0 <vx>2/D2
Page 6IMAC XXIV, January 30, 2006
Experiment: The Equipment
ATEC 2-wheel pitching machine
Motion Capture System
Baseball with reflecting dot
Page 7IMAC XXIV, January 30, 2006
Joe
Page 8IMAC XXIV, January 30, 2006
Motion Capture System:
(www.motionanalysis.com)
• Ten Eagle-4 cameras
• EVaRT4.0 software
Page 9IMAC XXIV, January 30, 2006
Experiment: Some Details Motion capture:
700 fps, 1/2000 s shutter Track over ~5 m y 0.5 mm; z 13 mm
• with some caveats only 1 reflectorassume horizontal spin axis
Pitching machine: Speeds: 50-110 mph Spins: 1500-4800 rpm Mainly topspin, some backspin All trials “two-seam” Initial angle ~0o
Distances: 40-100 feet Calibrations and cross-checks
Simple ball toss gets a=g to 2%
Page 10IMAC XXIV, January 30, 2006
Typical Data
-3000
-2000
-1000
0
1000
2000
3000
1400
1420
1440
1460
1480
1500
1520
0.00 0.04 0.08 0.12 0.16t (s)
z
y
y
z
Page 11IMAC XXIV, January 30, 2006
Data Analysis
Nonlinear least-squares fit y(t) = yCM(t) + Acos(t+)
z(t) = zcm(t) Asin(t+)
cm trajectory calculated numericallyRK4
nine free parameters• ycm(0), zcm(0), vy,cm(0), vz,cm(0)
• A, , • CL, CD
z
y
Page 12IMAC XXIV, January 30, 2006
Typical Data and Fit
-3000
-2000
-1000
0
1000
2000
3000
1400
1420
1440
1460
1480
1500
1520
0.00 0.04 0.08 0.12 0.16t (s)
z
y
<v>=72 mph =4900 rpm
ay=1.58g
y
z
Page 13IMAC XXIV, January 30, 2006
Results of Analysis: CL
0.0
0.1
0.2
0.3
0.4
0.0 0.1 0.2 0.3 0.4 0.5 0.6
CL
S
Page 14IMAC XXIV, January 30, 2006
0.0
0.1
0.2
0.3
0.4
0.0 0.1 0.2 0.3 0.4 0.5 0.6
CL
S
55
65
75
85
95
105
0.0 0.1 0.2 0.3 0.4 0.5 0.6
v (mph)
S
Conclusion:
No strong v-dependence at fixed S 0.2
Page 15IMAC XXIV, January 30, 2006
CL: Comparison with Previous Data
0.0
0.1
0.2
0.3
0.4
0.5
0.6
present
Alaways 2-Seam
Alaways 4-Seam
Watts & Ferrer
Briggs
SHS
RKA-100
0.0 0.2 0.4 0.6 0.8 1.0
CL
S
Conclusion: SHS parametrization looks good
Page 16IMAC XXIV, January 30, 2006
Results of Analysis: CD
0.0
0.2
0.4
0.6
0.8
60 70 80 90 100 110
CD
v (mph)
SHSRKA
present
Alaways
Conclusion: RKA looks better than SHS
Caveat: CD inherently less precise than CL
Page 17IMAC XXIV, January 30, 2006
Implications for Trajectory
50
100
150
200
250
300
350
400
450
0 10 20 30 40 50 (deg)
SHS
RKA
Black curve:SHS LiftRKA drag
Page 18IMAC XXIV, January 30, 2006
Summary and Outlook
Even with the limited precision of the present data, there is a clear preference for the lift coefficients of Hubbard than those of Adair
We learned enough from our initial measurements to know how to do better.
New experiments are planned to provide improved determinations of lift and drag coefficients