Transcript Baseball Aerodynamics

Baseball Aerodynamics
Alan M. Nathan, University of Illinois
[email protected]
webusers.npl.uiuc.edu/~a-nathan/pob
• Introduction
• State of our previous knowledge
• What we are learning from newer
technologies…
--about baseball aerodynamics
--about the game itself
• Summary
APS/DFD, Nov. 2009
1
Forces and Torques on a
Spinning Baseball in Flight
Drag:
1
2
FD = - CDρAv vˆ
2
FM
v
ω
Magnus:
1
2
ˆ  v)
ˆ
FM = CLρAv (ω
2
Torque:
2
ˆ
N = -CM RρAv ω
Fd
mg
The goal: determine the
coefficients of drag, lift,
and moment
APS/DFD, Nov. 2009
2
Real vs. “Physics 101” Trajectory:
Effect of Drag and Magnus
• Reduced distance on fly ball
• Reduction of pitched ball
speed by ~10%
• Asymmetric trajectory
120
100
no drag or lift
80
60
40
drag, no lift
20
• Optimum fly ball angle~30o
0
0
100
200
300
400
500
600
distance (ft)
APS/DFD, Nov. 2009
3
700
FM
Some Effects of Spin
v
ω
• Backspin makes ball rise
– “hop” of fastball
Fd
– increased distance of fly ball
mg
– tricky popups
• Topspin makes ball drop
– “12-6” curveball
120
100
no drag or lift
80
– topspin line drives nose-dive
60
40
drag, no lift
• Sidespin makes ball break toward foul pole
drag and lift
20
0
• Breaking pitches due to spin
0
100
200
300
400
500
600
distance (ft)
– curveballs, sliders, cutters, etc.
APS/DFD, Nov. 2009
4
700
So what do we know about
CD, CL, and CM?
…prior to 2 yrs ago
APS/DFD, Nov. 2009
5
What do we know about CD?
Depends on ….
• Reynold’s Number
– Re= Dv/
– Re~1x105 @ 45 mph
• surface “roughness”
• seam orientation?
• spin?
0.80
Cd-Atlanta
Cd-Mehta
Cd-Briggs
Cd-Alaways2
Cd-Alaways4
Cd-SHS
Cd-RKA
0.60
C
d
0.40
0.20
0.00
40
50
60
70
80
90
100
110
v (mph)
Summary:
• Existing data show factor of ~2 discrepencies
• Character of the “drag APS/DFD,
crisis”Nov.
not2009
well determined
• CD above ~100 mph not well determined
6
What do we know about CL?
Depends on ….
• spin parameter S  R/v
• Seam orientation?
• Reynold’s number @ fixed S?
• best evidence in “no”, in region of
50-100 mph
In region of importance for
baseball (S=0.05-0.30),
data are consistent at 20%
level
0.6
0.5
0.4
C
L
present
Alaways 2-Seam
Alaways 4-Seam
Watts & Ferrer
Briggs
Cl-Jinji
SHS
RKA-100
0.3
0.2
0.1
APS/DFD, Nov. 2009
0.0
0.0
7
0.2
0.4
0.6
S
0.8
1.0
What do we know about CM?
• Almost nothing experimentally!
• For golf….
CM = S  0.012S
  19-24 sec @ 100 mph
  [M/R2]/v (8% larger for baseball)
• Therefore estimate   20-26 sec @ 100 mph
APS/DFD, Nov. 2009
9
New Technologies
• The PITCHf/x system
• The TrackMan Doppler radar system
APS/DFD, Nov. 2009
10
The PITCHf/x Tracking System
• Two video cameras track baseball in 1/60-sec
intervals (usually “high home” and “high first”)
• Software to identify and track pitch frame-byframe in real time  full trajectory
• Installed in every MLB ballpark
Image, courtesy of Sportvision
APS/DFD, Nov. 2009
11
What kind of “stuff” can one learn?
• Pitch speed to ~0.5 mph
– at release and at home plate
• Pitch location to ~0.5 inches
– at release and at home plate
• “movement” to ~2.0 inches
– both magnitude and direction
• Initial velocity direction
• Pitch classification
– more on this later
• And all these data are freely available online!
APS/DFD, Nov. 2009
12
Example: Pitch Speed--PITCHf/x vs. the gun
• Pitched ball loses about 10% of speed
between pitcher and batter
• Average speed <v> is ~95% of release
speed
vf
y = m1 * M0
90
m1
Chisq
R
85
Value
0.89296
56.865
0.98879
Error
0.00086858
NA
NA
vf
 ρC D
vo
80
75
70
65
v0
APS/DFD, Nov. 2009
60
70
75
80
85
90
95
100
13
Example: Pitching at High Altitude
7.5%
loss of velocity
Denver
Toronto
total movement
8”
Denver
10%
12”
Toronto
PITCHf/x data contain a wealth
of information
about drag and lift!
APS/DFD,
Nov. 2009
14
Example: CD from Pitchf/x
Cd vs. v0
<Cd> vs. v0 in 2 mph bins
20k pitches from Anaheim, 2007:
Fluctuations consistent with x1 inch!
APS/DFD, Nov. 2009
15
Drag Coefficient:
no evidence for “drag crisis”
0.60
0.50
wind tunnel
Adair
0.40
C
d
Pitchf/x Anaheim 2007
0.30
Briggs
0.20
older pitch tracking
0.10
0.00
60
65
70
75
80
85
90
95
100
v (mph)
Good approximation:
Cd = 0.35±0.05APS/DFD,
in range
Nov. 200970-100 mph
16
Example: Pitch Classification: LHP Jon Lester, 8/4/07
catcher’s view
pitches fall into neat clusters:
I: 4-seam FB
II: 2-seam FB
III: slider (note the reduced spin)
IV: CB
APS/DFD, Nov. 2009
17
Compare with knuckleball pitcher
Tim Wakefield
FB
CB
APS/DFD, Nov. 2009
18
What makes an effective slider?—C. C. Sabathia
Josh Kalk, THT, 5/22/08
C. C. Sabathia: FB vs. Slider
7
6
5
95 mph fastball
This slider is very
effective since it looks
like a fastball for over half
the trajectory, then seems
to drop at the last minute
(“late break”).
~4 inches
4
3
82 mph slider
2
side view
1
~12 inches
0
0
10
20
30
40
50
Distance from home plate (ft)
APS/DFD, Nov. 2009
19
New Tools to Study
Trajectories of Batted Balls
• Hitf/x
– Uses Pitchf/x cameras to track initial trajectory
• v0,,
• Hittracker (www.hittrackeronline.com)
– Measure landing point and flight time for home runs
• TrackMan Doppler radar
– Tracks full batted ball trajectory
– Determines initial spin
APS/DFD, Nov. 2009
• Possibly spin decay
20
Example: The “carry” of a fly ball
• How much does a fly ball “carry”?
• Motivation: does the ball carry especially well in
the new Yankee Stadium?
• “carry” ≡ (actual distance)/(vacuum
distance)
APS/DFD, Nov. 2009
for same initial conditions
21
The “carry” of a fly ball
819 home runs from April 2009
APS/DFD, Nov. 2009
22
Fly ball trajectory from TrackMan
(Safeco Field experiment)
Trial 27:
v =76 mph; standard Cd
0.60
0
300 2413 rpm backspin; 237 rpm sidespin 100
CD
0.50
250
0.40
C
d
80
y
z
0.30
200
0.20
150
40
100
20
0.10
0.00
60
v
New TrackMan pitch data
50
60
70
80
90
100
110
50
0
v (mph)
x
0
0.0
1.0
2.0
3.0
4.0
-20
5.0
t (sec)
Conclusion:
Simple prescriptionAPS/DFD,
for drag
and Magnus
Nov. 2009
fits data beautifully.
23
Summary
• We are on the verge of major breakthrough on our
ability to track baseballs and determine the
aerodynamic effects
• In the near future we should be able to address some
outstanding issues:
– more precise values for Cd
• in “crisis” region
• for v>100 mph
– spin-dependent drag?
– dependence of drag & Magnus on seam orientation,
surface roughness, …
– time constant for spin decay?
APS/DFD, Nov. 2009
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