Introduction:
Forces on a Spinning Baseball in Flight
FM
v
ω
Fd
mg
• gravity: “physics 101”
• drag: “wind resistance”
• lift: Magnus force on spinning baseball
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Introduction:
Forces on a Spinning Baseball in Flight
FM
v
ω
Fd
mg
• drag is opposite to direction of motion
• “lift” is in direction that leading edge is turning
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Effect of Drag and Lift on Trajectories
120
100
no drag or lift
80
60
40
drag, no lift
drag and lift
20
0
0
100
200
300
400
500
600
700
distance (ft)
• drag effect is huge
• lift effect is smaller but significant
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Some Effects of Drag
120

Reduced distance on fly ball
100
no drag or lift
80


Reduction of pitched ball
speed by ~10%
Asymmetric trajectory:
60
40
drag, no lift
20
0
0
 Total Distance  1.7 x distance atRange (ft)
400
apex
100
200
300
Optimum home run angle
~350
500
600
700
distance (ft)
2000 rpm
350

400
300
0 rpm
250
200
150
100
Range vs. 
50
0
10
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20
30
40
50 60
 (deg)
70
80
90
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Some Effects of Lift

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

120
100
no drag or lift
80
60
Breaking pitches due to spin
40
Cutters, sliders, etc.
drag, no lift
drag and lift
20
0
0
100
200
300
400
500
600
700
distance (ft)
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Some Effects of Lift
Balls hit to left/right
curve toward foul pole
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Some Effects of Lift
Tricky popups with lots of backspin
200
150
100
50
0
0
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10
20
30
40
distance (ft)
50
60
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Let’s Get Quantitative:
Measurements of Drag and Lift
What do we know?
 How do we know it?
 How well do we know it?


Two types of experiments:
Wind tunnel
• Measure forces directly
Video tracking of trajectory
• “You can observe a lot by watching”
• Infer forces from measured acceleration
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Experiment #1: Tracking Trajectory
(UC/Davis; Illinois)
Motion Capture System
ATEC 2-wheel pitching machine
Baseball with reflecting dot
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Motion Capture Geometry
~15 ft
Joe Hopkins
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Motion Capture System:
• 10 cameras
• 700 frames/sec
• 1/2000 shutter
• very fancy software
www.motionanalysis.com
Pitching Machine:
• project horizontally
• 50-110 mph
• 1500-4500 rpm
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Typical Data
66
94 mph
3000 rpm topspin
1.8g
65
64
63
62
61
0
5
10
15
distance (ft)
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Results for Lift Coefficient CL
present
C
L
Alaways 2-Seam
0.6
Alaways 4-Seam
0.5
FL= 1/2ACLv2
Watts & Ferrer
S=r/v
Briggs
0.4
100 mph, 2000 rpm
0.3
S=0.17
0.2
0.1
0.0
0.0
0.2
0.4
0.6
0.8
1.0
S
Conclusion: data qualitatively consistent (~20%)
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Results for Drag Coefficient CD
0.8
present
0.6
C
FD= 1/2ACDv2
Alaways
D
0.4
RKA
0.2
SHS
0.0
60
70
80
90
v (mph)
100
110
Conclusion:
Major disagreements for v= 70-100 mph
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Experiment #2: Sportvision—
A Potential New Tool

Track pitched baseballs with 2 cameras
High-speed not necessary
Tracking of MLB game pitches
Used by ESPN for K-Zone

From trajectory, determine
lift,drag,spin axis

Spin rate not measured
Thanks to Marv White, CTO, for providing a
wealth of data
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Sportvision Data
dx or dz vs. 
batter’s view
15.00
dx
dz
10.00
5.00
0.00
225o
-5.00
Backspin:
-10.00
-15.00
0
50
100
150
 (deg)
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200
250
300
up and in to
RHH
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Sportvision Data
dx or dz vs. 
batter’s view
15.00
dx
dz
10.00
135o
5.00
0.00
Backspin:
-5.00
up and away
to RHH
-10.00
-15.00
0
50
100
150
200
250
300
 (deg)
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Sportvision Data
1.2
warmup game pitches
Drag/Weight
1
0.8
0.6
Lift/Weight
0.4
0.2
0
50
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60
70
80
V (mph)
90
100
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Synthesis of Results
2
1.5
Drag/Weight
1
Lift/Weight
@1800 rpm
0.5
0
0
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25
50
75
100
Speed in mph
125
150
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Synthesis of Results
120
100
80
60
40
20
0
0
100
200
300
distance (ft)
400
500
Uncertainty in drag  50 ft!
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Summary

We have much empirical knowledge of lift
and drag
…and some promising new tools for future
research

Things we 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?
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