FSU Colloquium 9/1/05 1 Thanks to J. J. Crisco & R. M. Greenwald Medicine & Science in Sports &...

FSU Colloquium 9/1/05 2

1927

Solvay Conference:

Greatest physics team

ever assembled

Baseball and Physics

1927 Yankees:

Greatest baseball team

ever assembled

MVP’s


Brief Description of Ball-Bat Collision• forces large, time short

– >8000 lbs, <1 ms

• ball compresses, stops, expands– KEPEKE

– bat bends & compresses

• lots of energy dissipated (“COR”)– distortion of ball

– vibrations in bat

• to hit home run….– large hit ball speed

– optimum take-off angle

– backspin

Courtesy of CE Composites


Kinematics of Ball-Bat Collisionvball vbat

vff ball bat

e-r 1+ev = v v

1+r 1+r

r = mball /Mbat,eff : bat recoil factor = 0.25(momentum and angular momentum conservation)

e: “coefficient of restitution” 0.50 (energy dissipation)

typical numbers: vf = 0.2 vball + 1.2 vbat

vbat matters much more than vball


Kinematics of Ball-Bat Collision

f ball bat

e-r 1+ev = v v

1+r 1+r

• r = mball /Mbat,eff: bat recoil factor = 0.25(momentum and angular momentum conservation)

• heavier bat better but…


Crisco/Greenwald Batting Cage Study

40

42

44

46

48

50

1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9

Iknob

(104 oz-in2)

knob

(rad/s)

Crisco/Greenwald Batting Cage Study

vbat I-0.3

vbat I-0.5

60

70

80

90

100

110

120

20 30 40 50 60

n=0constant v

bat

n=0.5constant bat KE

vbat

= 65 mph x (32/Mbat

)n

Mbat

(oz)

vf (mph)

n=0.31 (expt)


• Collision excites bending vibrations

in bat– Ouch!! Thud!! Sometimes broken bat

– Energy lost lower COR, vf

• Reduced if …

– Impact is at a node

– fn>1, where ~ 0.5-1.0 ms

• Calculate as non-uniform beam

Accounting for COR:

Dynamic Model for Ball-Bat CollisionAMN, Am. J. Phys, 68, 979 (2000)


Modal Analysis of a Baseball Batwww.kettering.edu/~drussell/bats.html

0

0.05

0.1

0.15

0 500 1000 1500 2000 2500

FFT(R)

frequency (Hz)

179

582

1181

1830

2400

frequency

-1.5

-1

-0.5

0

0.5

1

0 5 10 15 20

R

t (ms)

time

0 5 10 15 20 25 30 35

f1 = 179 Hz

f2 = 582 Hz

f3 = 1181 Hz

f4 = 1830 Hz


-40.0

-20.0

0.0

20.0

40.0

0 2 4 6 8 10

v (m/s)

t (ms)

0.1

0.2

0.2

0.3

0.3

0.4

0.4

0.5

0

20

40

60

80

100

120

0 5 10 15

e

vf (mph)

distance from tip (inches)

nodes4 3 2 1

Evib

vf

e

Vibrations, COR, and Sweet Spot

• Center of percussion (~27”)• Node of fundamental (~27”)• Maximum e (~29”)

• Minimum Evib (~29”)

• Maximum vf (29”)

• Don’t feel a thing (?)

Node of 2nd mode


Experimental Data

ball incident on bat at rest

Conclusion: essential physics understood

0.25

0.30

0.35

0.40

0.45

0.50

0.55

23 24 25 26 27 28 29 30 31

e

distance from knob (inches)

flexible bat

rigid bat

Louisville Slugger R161 Wood Batv

i=100 mph


Boundary Conditions

• handle moves after ~0.6 ms

• ball leaves bat after ~0.6 ms

• ball doesn’t “know” about far end of bat

nothing on knob end matters:• size, shape• boundary conditions

• batter’s hands!

-40.0

-20.0

0.0

20.0

40.0

0 2 4 6 8 10

v (m/s)

t (ms)


Aluminum has thin shell – Less mass in barrel

–easier to swing and control –but less effective at transferring energy

– Hoop modes –trampoline effect –larger COR

Why Does Aluminum Outperform Wood?


•Two springs mutually compress each other KE PE KE

• PE shared between “ball spring” and “bat spring”

• PE in ball mostly dissipated (~80%!)

• PE in bat mostly restored

• Net effect: less overall energy dissipated...and therefore higher ball-bat COR

…more “bounce”

The “Trampoline” Effect:A Simple Physical Picture


The Trampoline Effect: A Closer Look

“hoop” modes: cos(n)k (t/R)3: hoop mode largest in barrel

f2 (1-3 kHz) < 1/ energy mostly restored

(unlike bending modes)

“ping”

Thanks to Dan Russell


Verification from Crisco/Greenwald Study

90

92

94

96

98

100

90 92 94 96 98 100 102

vf

' (mph)

vf (mph)

W

M2

M1

M4M5

M3

• Vf correlated with COR

• COR main factor for vf

–inertial factors “cancel out”

• COR correlated with fhoop

– fhoop main factor for vf

wood


Effect of Spin on Baseball Trajectory

Drag: Fd = ½ CDAv2

-v direction

“Lift”: FL = CMARv(ω v) direction

v

ω

mg

Fd

FL (Magnus)

CD, CM ~ 0.2-0.5

(in direction leading edge is turning)


0

20

40

60

80

100

0 100 200 300 400

y (ft)

x (ft)

Hubbard

100 mph, 2000 rpm backspin, 25o

Adair

444'367'

77'

Who is right?

Hubbard vs. Adair:

Large difference in FM at 100 mph

0

0.5

1

1.5

2

0 25 50 75 100 125 150Speed in mph

Drag/Weight

Lift/Weight@1800 rpm

solid: Hubbarddashed: Adair-3

1. Hubbard (AJP, 71, 1152, 2003)

2. Adair, The Physics of Baseball, 3rd Ed.


New Experiment at Illinois

• Fire baseball horizontally from pitching

machine

• Use motion capture to track ball over ~5m

of flight and determine x0,y0,vx,vy,,ay

• Use ay to determine Magnus force as

function of v,


Motion Capture ExperimentJoe Hopkins, Lance Chong, Hank Kaczmarski, AMN

Two-wheel pitching machine

Baseball with reflecting dot

Motion Capture System


Experiment: Sample MoCap Datay

z

topspin ay > g

-3000

-2000

-1000

0

1000

2000

-20

0

20

40

60

80

100

120

140

0.00 0.02 0.04 0.06 0.08 0.10 0.12

z (mm)y (mm)

time (sec)

93.6 mph/3040 rpm/1.83g

Z

y

y = ½ ayt2


0

0.1

0.2

0.3

0.4

0.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

CL

presentexperiment

Hubbardparametrization

(PRELIMINARY) Results

0

20

40

60

80

100

0 100 200 300 400

y (ft)

x (ft)

Hubbard

100 mph, 2000 rpm backspin, 25o

Adair

444'367'

77'

present

• Present data support Hubbard, not Adair--spin plays important role in flight of baseball

• More extensive experiment planned for early 2006


Oblique Collisions:Leaving the No-Spin Zone

Friction … • sliding/rolling vs. gripping• transverse velocity reduced, spin increased

Familiar Results• Balls hit to left/right break toward foul line

• Topspin gives tricky bounces in infield

• Pop fouls behind the plate curve back toward field

• Backspin keeps fly ball in air longer

f


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

Undercutting the ball backspinBall100 downward

Bat 100 upward

D = center-to-center offset

trajectories

-5000

0

5000

10000

15000

-50

0

50

100

150

-0.5 0 0.5 1 1.5 2 2.5 3

vertical (rpm) (deg)

D (inches)D (inches)


larger for curveball

-1000

0

1000

2000

3000

4000

5000

6000

0 0.2 0.4 0.6 0.8 1A

2000 rpm topspin

2000 rpm backspin

D (in)

(rpm)

Fastball: spin reverses

Curveball: spin doesn’t reverse


In summary….Can a curveball be hit farther than a fastball?

• Higher pitch speed higher hit ball speed on fastball

• But…more backspin on curve ball

• Net result: curveball goes farther– by a little bit

• Mont Hubbard, AJP 71, 1152-1162 (2003) – See also February 2005 issue of AJP for a debate: Hubbard vs. Adair


Work in Progress

• Collision experiments & calculations to elucidate trampoline effect

• New measurements of lift and drag

• Experiments on oblique collisions?– Rod Cross & AMN: rolling almost works at

low speed– AMN: studies in progress at high speed


Final Summary

• Physics of baseball is a fun application of basic (and not-so-basic) physics

• Check out my web site if you want to know more– www.npl.uiuc.edu/~a-nathan/pob– [email protected]

• Go Red Sox!..and the Quantum Fielders too!

FSU Colloquium 9/1/05 1 Thanks to J. J. Crisco & R. M. Greenwald Medicine & Science in Sports &...

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Transcript of FSU Colloquium 9/1/05 1 Thanks to J. J. Crisco & R. M. Greenwald Medicine & Science in Sports &...