Baseball Aerodynamics

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


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


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


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


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

…prior to 2 yrs ago


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


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


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


New Technologies

• The PITCHf/x system

• The TrackMan Doppler radar system


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


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


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


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


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


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


Compare with knuckleball pitcher Tim WakefieldFB

CB


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


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


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


The “carry” of a fly ball819 home runs from April 2009


Fly ball trajectory from TrackMan(Safeco Field experiment)

Conclusion:Simple prescription for drag and Magnus fits data beautifully.

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Cd

v (mph)

CD

0

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300

-20

0

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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


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?

Documents

Baseball Aerodynamics