Post on 14-Jan-2016
Page 2SABR36, June 29, 2006
Introduction:Forces on a Spinning Baseball in Flight
v
ω
mg
Fd
FM
• gravity: “physics 101”
• drag: “wind resistance”
• lift: Magnus force on spinning baseball
Page 3SABR36, June 29, 2006
Introduction:Forces on a Spinning Baseball in Flight
v
ω
mg
Fd
FM
• drag is opposite to direction of motion
• “lift” is in direction that leading edge is turning
Page 4SABR36, June 29, 2006
Effect of Drag and Lift on Trajectories
• drag effect is huge
• lift effect is smaller but significant
0
20
40
60
80
100
120
0 100 200 300 400 500 600 700
distance (ft)
no drag or lift
drag, no lift drag and lift
Page 5SABR36, June 29, 2006
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 ~350
0
20
40
60
80
100
120
0 100 200 300 400 500 600 700
distance (ft)
no drag or lift
drag, no lift
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
Page 6SABR36, June 29, 2006
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
Breaking pitches due to spinCutters, sliders, etc.
0
20
40
60
80
100
120
0 100 200 300 400 500 600 700
distance (ft)
no drag or lift
drag, no lift drag and lift
Page 7SABR36, June 29, 2006
Some Effects of Lift
Balls hit to left/right curve toward foul pole
Page 8SABR36, June 29, 2006
0
50
100
150
200
0 10 20 30 40 50 60
distance (ft)
Some Effects of Lift
Tricky popups with lots of backspin
Page 9SABR36, June 29, 2006
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 directlyVideo tracking of trajectory
• “You can observe a lot by watching”
• Infer forces from measured acceleration
Page 10SABR36, June 29, 2006
Experiment #1: Tracking Trajectory(UC/Davis; Illinois)
ATEC 2-wheel pitching machine
Motion Capture System
Baseball with reflecting dot
Page 11SABR36, June 29, 2006
Joe Hopkins
~15 ft
Motion Capture Geometry
Page 12SABR36, June 29, 2006
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
Page 13SABR36, June 29, 2006
Typical Data
61
62
63
64
65
66
0 5 10 15
distance (ft)
94 mph3000 rpm topspin1.8g
Page 14SABR36, June 29, 2006
Results for Lift Coefficient CL
FL= 1/2ACLv2
S=r/v100 mph, 2000 rpm
S=0.17
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
Conclusion: data qualitatively consistent (~20%)
Page 15SABR36, June 29, 2006
Results for Drag Coefficient CD
FD= 1/2ACDv2
Conclusion:
Major disagreements for v= 70-100 mph
0.0
0.2
0.4
0.6
0.8
60 70 80 90 100 110
CD
v (mph)
SHSRKA
present
Alaways
Page 16SABR36, June 29, 2006
Experiment #2: Sportvision—A Potential New Tool
Track pitched baseballs with 2 camerasHigh-speed not necessaryTracking of MLB game pitchesUsed 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
Page 17SABR36, June 29, 2006
Sportvision Data
-15.00
-10.00
-5.00
0.00
5.00
10.00
15.00
0 50 100 150 200 250 300
dx or dz vs.
dxdz
(deg)
batter’s view
Backspin:
up and in to RHH
225o
Page 18SABR36, June 29, 2006
Sportvision Data
-15.00
-10.00
-5.00
0.00
5.00
10.00
15.00
0 50 100 150 200 250 300
dx or dz vs.
dxdz
(deg)
batter’s view
Backspin:
up and away to RHH
135o
Page 19SABR36, June 29, 2006
Sportvision Data
0
0.2
0.4
0.6
0.8
1
1.2
50 60 70 80 90 100
V (mph)
Drag/Weight
Lift/Weight
warmup game pitches
Page 20SABR36, June 29, 2006
Synthesis of Results
0
0.5
1
1.5
2
0 25 50 75 100 125 150Speed in mph
Drag/Weight
Lift/Weight@1800 rpm
Page 21SABR36, June 29, 2006
Synthesis of Results
0
20
40
60
80
100
120
0 100 200 300 400 500
distance (ft)
Uncertainty in drag 50 ft!
Page 22SABR36, June 29, 2006
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?