Baseball Aerodynamics

1
Baseball Aerodynamics
Alan M. Nathan, University of Illinois a-nathan_at_il
linois.edu 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

2
Forces and Torques on a Spinning Baseball in
Flight
The goal determine the coefficients of drag,
lift, and moment
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 angle30o

4
Some Effects of Spin

• 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.

5
So what do we know about CD, CL, and CM?

• prior to 2 yrs ago

6
What do we know about CD?

• Depends on .
• Reynolds Number
• Re ?Dv/?
• Re1x105 _at_ 45 mph
• surface roughness
• seam orientation?
• spin?

• Summary
• Existing data show factor of 2 discrepencies
• Character of the drag crisis not well
  determined
• CD above 100 mph not well determined

7
What do we know about CL?

• Depends on .
• spin parameter S ? R?/v
• Seam orientation?
• Reynolds number _at_ fixed S?
• best evidence in no, in region of 50-100 mph

In region of importance for baseball
(S0.05-0.30), data are consistent at 20 level
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Dependence of CL on Re at fixed S
Conclusion No strong dependence on Re at fixed
S ? 0.2
9
What do we know about CM?

• Almost nothing experimentally!
• For golf.
• CM ?S ? 0.012S
• ? ? 19-24 sec _at_ 100 mph
• ? ? M/R2/?v (8 larger for baseball)
• Therefore estimate ? ? 20-26 sec _at_ 100 mph

10
New Technologies

• The PITCHf/x system
• The TrackMan Doppler radar system

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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
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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!

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Example Pitch Speed--PITCHf/x vs. the gun

• Pitched ball loses about 10 of speed between
  pitcher and batter
• Average speed ltvgt is 95 of release speed

vf
v0
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Example Pitching at High Altitude
Denver
Toronto
Toronto
Denver
PITCHf/x data contain a wealth of information
about drag and lift!
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Example CD from Pitchf/x
Cd vs. v0
ltCdgt vs. v0 in 2 mph bins
20k pitches from Anaheim, 2007 Fluctuations
consistent with ?x?1 inch!
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Drag Coefficientno evidence for drag crisis
Good approximation Cd 0.350.05 in range
70-100 mph
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Example Pitch Classification LHP Jon Lester,
8/4/07
pitches fall into neat clusters I 4-seam
FB II 2-seam FB III slider (note the reduced
spin) IV CB
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Compare with knuckleball pitcher Tim Wakefield
FB
CB
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What makes an effective slider?C. C. Sabathia
Josh Kalk, THT, 5/22/08
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).
side view
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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

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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

22
The carry of a fly ball819 home runs from
April 2009
23
Fly ball trajectory from TrackMan(Safeco Field
experiment)
New TrackMan pitch data
Conclusion Simple prescription for drag and
Magnus fits data beautifully.
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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 vgt100 mph
• spin-dependent drag?
• dependence of drag Magnus on seam orientation,
  surface roughness,
• time constant for spin decay?