APS/DFD, Nov. 20091 The Flight of a Baseball Alan M. Nathan, University of Illinois [email protected] Introduction

APS/DFD, Nov. 2009 1

The Flight of a BaseballAlan M. Nathan, University of Illinois

[email protected]://go.illinois.edu/physicsofbaseball

• Introduction

• PITCHf/x and HITf/x

• Using baseball to learn about physics

• Using physics to learn about baseball

-how pitchers do what they do

-how batters do what they do


Forces on a Spinning Baseball in Flight

D2

D C1

ˆF = - ρAv v2

2LM

1ˆ ˆF = ρAv (ωC v)

2

v

ω

mg

FD

FM

• Drag slows ball down

• Magnus + mg deflects ball from straight line


Real vs. “Physics 101” Trajectory: Effect of Drag and Magnus


PITCHf/x and HITf/x• Two video cameras @60 fps

– “high home” and “high first”– tracks every pitch in every MLB ballpark

• all data publicly available on web!

– tracks initial trajectory of batted ball

• Used for analysis, TV broadcasts, MLB Gameday, etc.

Image, courtesy of Sportvision


• Minimal parametrization of the trajectory– Constant acceleration works very well for pitched

ball – Batted balls: ???

• Determining Magnus acceleration– “spin movement” important for studying pitching

• Dealing with noisy data, miscalibrations, etc.• Keeping everyone honest

– Measurements have uncertainties!

So what good is a physicist in all this?

0 0(r , v ,a)


Baseball Analysis:Using PITCHf/x to discover how

pitchers do what they do

“Hitting is timing. Pitching is upsetting timing.”


home plate

Ex 1: Mariano Rivera: Why is he so good??

Three Reasons: Location, Location, Location

Home Runs


Ex 2: “Late Break”: Truth or MythMariano Rivera’s Cut Fastball

View from above:actual trajectory --------linear extrapolation - - - -


Josh Kalk, THT, 5/22/08

Ex 2a: What makes an effective slider

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


>90 mph

80-90 mph

<80 mph

Ex 3: A Pitcher’s RepertoireLHP Jon Lester, August 2007

4-seam fastball

2-seam fastball

curveball

slider

Catcher’s View

4-seam fastball

2-seam fastball

curveball

slider


Ex 4 Jon Lester vs. Brandon Webb

Brandon Webb is a “sinkerball” pitcher:Almost no rise on his fastball

15 inches


Ex 5 The Knuckleball

Tim Wakefield is a knuckleball pitcher:Chaotic Movement


Studies of Batted Balls• HITf/x v0,,

• Hittracker (Greg Rybarczyk)– Landing point– Flight time

• Together these constrain the full trajectory


Hitting a Long Fly Ball

R vs. v0 R vs. 0

USEFUL BENCHMARK400 ft @ 103 mph

~5 ft per mph

peaks @ 25o-35o


What Constitutes a Well-Hit Ball?

w/o home runs

home runs

HR

BABIP V0>90


Putting Spin on Batted Balls

• undercutting/overcutting backspin/topspin– upward/downward Magnus force

• In front or behind sidespin– sideways Magnus force

friction

normal forcevfriction


Some Familiar Effects Due to Spin

• Balls hit to left/right break toward foul line


Extract sidespin vs. from trajectoryCF

RF

break to right

break to left

LF

• Balls break toward foul pole• Break increases with angle• Ball hit to CF slices

LHH/RHH asymmetry Tilt in bat

RF

RHH

LHHLF RF



Some Familiar Effects Due to Spin

• Balls hit to left/right break toward foul line

• Topspin makes line drives nose-dive

• Backspin keeps fly ball in air longer

• Tricky popups to infield

0

50

100

150

200

250

-100 0 100 200 300 400

1.5

0

0.25

0.5 0.75

1.02.0

0.75

???


Paradoxical Popups

Watch for fielder’s confusion and for bounce of ball


HITf/x+hittracker Analysis: The “carry” of a fly ball

• Motivation: does the ball carry especially well in the new Yankee Stadium? • “carry” ≡ (actual distance)/(vacuum distance)

for same initial conditions

(379,20,5.2)


HITf/x + hittracker Analysis:4354 HR from 2009

Denver

Cleveland Yankee Stadium


Summary We are on the verge of major

breakthrough on our ability to track baseballs and determine the aerodynamic effects

The new tools I have discussed are already revolutionizing baseball analysis

And the tools are getting better….

So, fun times ahead for me…

…shown here doing experimental baseball physics

Documents

APS/DFD, Nov. 20091 The Flight of a Baseball Alan M. Nathan, University of Illinois [email protected] Introduction