baseball aerodynamics
DESCRIPTION
Alan M. Nathan, University of Illinois [email protected] webusers.npl.uiuc.edu/~a-nathan/pob. Baseball Aerodynamics. Introduction State of our previous knowledge What we are learning from newer technologies… --about baseball aerodynamics --about the game itself Summary. F M. F d. - PowerPoint PPT PresentationTRANSCRIPT
APS/DFD, Nov. 2009 1
Baseball AerodynamicsAlan M. Nathan, University of Illinois
[email protected]/~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 2
Forces and Torques on a Spinning Baseball in Flight
2D D
Drag:1
ˆF = - C ρAv v2
2LM
Magnus:1
ˆ ˆF = ρAv (ω v)2
C
M2
Torque:ˆN = C- RρAv ω
The goal: determine the coefficients of drag, lift, and moment
v
ω
mg
Fd
FM
APS/DFD, Nov. 2009 3
Real vs. “Physics 101” Trajectory: Effect of Drag and Magnus
• Reduced distance on fly ball
• Reduction of pitched ball speed by ~10%
• Asymmetric trajectory
• Optimum fly ball angle~30o 0
20
40
60
80
100
120
0 100 200 300 400 500 600 700
distance (ft)
no drag or lift
drag, no lift
APS/DFD, Nov. 2009 4
Some Effects of Spin
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
• Backspin makes ball rise– “hop” of fastball
– increased distance of fly ball
– tricky popups
• Topspin makes ball drop– “12-6” curveball
– topspin line drives nose-dive
• Sidespin makes ball break toward foul pole
• Breaking pitches due to spin– curveballs, sliders, cutters, etc.
v
ω
mg
Fd
FM
APS/DFD, Nov. 2009 5
So what do we know about CD, CL, and CM?
…prior to 2 yrs ago
APS/DFD, Nov. 2009 6
What do we know about CD?
Depends on ….• Reynold’s Number
– Re= Dv/– Re~1x105 @ 45 mph
• surface “roughness”• seam orientation?• spin?
0.00
0.20
0.40
0.60
0.80
40 50 60 70 80 90 100 110
Cd-AtlantaCd-MehtaCd-BriggsCd-Alaways2Cd-Alaways4Cd-SHSCd-RKAC
d
v (mph)
Summary: • Existing data show factor of ~2 discrepencies• Character of the “drag crisis” not well determined• CD above ~100 mph not well determined
APS/DFD, Nov. 2009 7
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
0.0
0.1
0.2
0.3
0.4
0.5
0.6
presentAlaways 2-SeamAlaways 4-SeamWatts & FerrerBriggsCl-JinjiSHSRKA-100
0.0 0.2 0.4 0.6 0.8 1.0
CL
S
In region of importance for baseball (S=0.05-0.30), data are consistent at 20% level
APS/DFD, Nov. 2009 9
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 10
New Technologies
• The PITCHf/x system
• The TrackMan Doppler radar system
APS/DFD, Nov. 2009 11
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-by- frame in real time full trajectory
• Installed in every MLB ballpark
Image, courtesy of Sportvision
APS/DFD, Nov. 2009 12
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 1360
65
70
75
80
85
90
70 75 80 85 90 95 100v
0 (mph)
y = m1 * M0
ErrorValue
0.000868580.89296m1
NA56.865Chisq
NA0.98879R
• Pitched ball loses about 10% of speed between pitcher and batter• Average speed <v> is ~95% of release speed
Example: Pitch Speed--PITCHf/x vs. the gun
v0
vf
Do
f ρCv
v
APS/DFD, Nov. 2009 14
Example: Pitching at High Altitude
10%
loss of velocity
total movement12”
7.5%
8”
PITCHf/x data contain a wealth of information about drag and lift!
Toronto
Toronto
Denver
Denver
APS/DFD, Nov. 2009 15
20k pitches from Anaheim, 2007:Fluctuations consistent with x1 inch!
Cd vs. v0 <Cd> vs. v0 in 2 mph bins
Example: CD from Pitchf/x
APS/DFD, Nov. 2009 16
Drag Coefficient:no evidence for “drag crisis”
0.00
0.10
0.20
0.30
0.40
0.50
0.60
60 65 70 75 80 85 90 95 100
Cd
v (mph)
wind tunnel
Adair
older pitch tracking
Pitchf/x Anaheim 2007
Briggs
Good approximation: Cd = 0.35±0.05 in range 70-100 mph
APS/DFD, Nov. 2009 17
Example: Pitch Classification: LHP Jon Lester, 8/4/07
catcher’s view
pitches fall into neat clusters:I: 4-seam FBII: 2-seam FBIII: slider (note the reduced spin)IV: CB
APS/DFD, Nov. 2009 18
Compare with knuckleball pitcher Tim WakefieldFB
CB
APS/DFD, Nov. 2009 19
Josh Kalk, THT, 5/22/08
What makes an effective slider?—C. C. Sabathia
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”).
0
1
2
3
4
5
6
7
0 10 20 30 40 50
C. C. Sabathia: FB vs. Slider
Distance from home plate (ft)
95 mph fastball
82 mph slider
~4 inches
~12 inches
side view
APS/DFD, Nov. 2009 20
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
• Possibly spin decay
APS/DFD, Nov. 2009 21
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)
for same initial conditions
APS/DFD, Nov. 2009 22
The “carry” of a fly ball819 home runs from April 2009
APS/DFD, Nov. 2009 23
Fly ball trajectory from TrackMan(Safeco Field experiment)
Conclusion:Simple prescription for drag and Magnus fits data beautifully.
0.00
0.10
0.20
0.30
0.40
0.50
0.60
50 60 70 80 90 100 110
Cd
v (mph)
CD
0
50
100
150
200
250
300
-20
0
20
40
60
80
100
0.0 1.0 2.0 3.0 4.0 5.0
t (sec)
yz
x
Trial 27:v
0=76 mph; standard Cd
2413 rpm backspin; 237 rpm sidespin
v
New TrackMan pitch data
APS/DFD, Nov. 2009 24
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?