38
ysics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 2 1927 Solvay Conference: Greatest physics team ever assembled Baseball and Physics 1927 Yankees: Greatest baseball team ever assembled MVP’s

1927 Solvay Conference: Greatest physics team ever assembled

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1927 Yankees: Greatest baseball team ever assembled. 1927 Solvay Conference: Greatest physics team ever assembled. MVP’s. Baseball and Physics. As smart as he was, Albert Einstein could not figure out how to handle those tricky bounces at third base. Philosophical Notes:. - PowerPoint PPT Presentation

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Page 1: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 2

1927

Solvay Conference:

Greatest physics team

ever assembled

Baseball and Physics

1927 Yankees:

Greatest baseball team

ever assembled

MVP’s

Page 2: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 3

As smart as he was, Albert Einstein could not figure out how to handle those tricky bounces at third base.

Page 3: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 4

Philosophical Notes:“…the physics of baseball is not the clean, well-defined

physics of fundamental matters but the ill-defined physics of the complex world in which we live, where elements are not ideally simple and the physicist must make best judgments on matters that are not simply calculable…Hence conclusions about the physics of baseball must depend on approximations and estimates….But estimates are part of the physicist’s repertoire…a competent physicist should be able to estimate anything ...”

---Bob Adair in “The Physics of Baseball”, May, 1995 issue of Physics Today

“The physicist’s model of the game must fit the game.”

“Our aim is not to reform baseball but to understand it.”

Page 4: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 5

Hitting the Baseball

“...the most difficult thing to do in sports”

--Ted Williams: 1918-2002

BA: .344SA: .634OBP: .483HR: 521 #521, September 28, 1960

Page 5: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 6

Introduction: Description of Ball-Bat Collision

forces large (>8000 lbs!) time short (<1/1000 sec!) ball compresses, stops, expands

kinetic energy potential energy

lots of energy lost

bat is flexible hands don’t matter

to hit a home run... large hit ball speed

optimum take-off angle

backspin

Page 6: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 7

The Ball-Bat Collision: Kinematics

vf = eA vball + (1+eA) vbat

Conclusion:

vbat matters much more than vball

vball vbat

vf

“Lab” Framevrel

eAvrel

Bat Rest Frame

eA “Collision Efficiency”

• property of ball & bat• weakly dependent on vrel

• Superball-wall: eA 1• Ball-Bat near “sweet spot”: eA 0.2

vf 0.2 vball + 1.2 vbat

Page 7: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 8

What Does eA Depend On?

r1

r-e eA • Kinematics: recoil of bat (r)

• Dynamics: energy dissipation (e)

I

bm

m

m

m

m r

CMbat,

2ball

bat

ball

effbat,

ball

Small r is best

r 0.25 typical…depends on….

• mass of bat

• mass distribution of bat

• impact location

. .CM .

b

= +

Heavier bat is better but….

Page 8: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 9

What is Ideal Bat Weight?

60

70

80

90

100

110

120

20 30 40 50 60

vf (mph)

Mbat

(oz)

vbat

= 65 mph x (32/Mbat

)n

n=0.5constant KE

n=0.31experiment

n=0constant v

bat

Note: Batters seem to prefer lighter bats!

Actually,

Scaling with Iknob better

Page 9: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 10

vBAT(6”) = 1.2 mph/(1000 oz-in2) (vf=1.5 0.3 mph)

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

Page 10: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 11

Energy Dissipation: the ball-bat COR (e)

Coefficient Of Restitution

• in CM frame: Ef/Ei = e2

• ball on hard floor: e2 = hf/hi 0.25

e 0.5 (note: r=0.25, e=0.5 eA =0.2)

~3/4 CM energy dissipated!

• depends (weakly) on impact speed

• the bat matters too! vibrations “trampoline” effect

Page 11: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 12

Aside: Effect of “Juiced” Ball

MLB: e = 0.546 0.032 @ 58 mph on massive rigid surface

320

360

400

440

0.4 0.45 0.5 0.55 0.6

R (ft)

cor

*

*~ 35 '

Distance vs. COR "90+70" collision

0.40

0.45

0.50

0.55

0.60

60 80 100 120 140equivalent impact speed (mph)

COR

Briggs, 1945

UML/BHM

Lansmont

MLB specs

MLB/UML

COR Measurements

Lansmont/CPD

10% increase in COR ~30-35 ft increase in distance

Page 12: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 13

Collision excites bending vibrations in

bat

Ouch!! Thud!! Sometimes broken bat

Energy lost lower e, vf

Find lowest mode by tapping

Reduced considerably if

Impact is at a node

Collision time (~0.6 ms) > TN

see AMN, Am. J. Phys, 68, 979 (2000)

Accounting for Energy Dissipation:

Dynamic Model for Ball-Bat Colllision

Page 13: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 14

Dynamic Model

x

yEI

x - F

t

yA

2

2

2

2

2

2

-2 0

-1 5

-1 0

-5

0

5

10

15

20

0 5 10 15 20 25 30 35

20

y

z

y

Step 1: Solve eigenvalue problem for free vibrations

Step 2: Nonlinear lossy spring for F

Step 3: Expand in normal modes and solve

yA x

yEI

x n

2n2

n2

2

2

A

)t(Fq

dt

qd )(y)(q)y( n

n2n2

n2

nn

n xtx,t

Page 14: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 15

Normal Modes of the Bat

Louisville Slugger R161 (33”, 31 oz)

0 5 10 15 20 25 30 35

f1 = 177 Hz

f2 = 583 Hz

f3 = 1179 Hz

f4 = 1821 Hz

Can easily be measured: Modal Analysis

Page 15: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 16

-1.5

-1

-0.5

0

0.5

1

0 5 10 15 20

R

t (ms)

0

0.05

0.1

0.15

0 500 1000 1500 2000 2500

FFT(R)

frequency (Hz)

179

582

1181

1830

2400

frequency barrel nodeExpt Calc Expt Calc 179 177 26.5 26.6 582 583 27.8 28.21181 1179 29.0 29.21830 1821 30.0 29.9

Measurements via Modal Analysis

Louisville Slugger R161 (33”, 31 oz)

Conclusion: free vibrationsof bat can be well characterized

FFT

Page 16: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 17

Theory vs. Experiment:Louisville Slugger R16133-inch/31-oz. wood bat

Conclusion: essential physics understood

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

23 24 25 26 27 28 29 30 31

vfinal

/vinitial

distance from knob (inches)

data from Lansmont BBVCbat pivoted about 5-3/4"

vinitial

=100 mph

rigid bat

flexible bat

nodes

only lowest mode excited lowest 4 modes excited

0

0.1

0.2

0.3

0.4

16 20 24 28 32

vfinal

/vinitial

distance from knob (inches)

rigid bat

flexible bat

CM node

data from Rod Crossfreely suspended bat

vi = 2.2 mph

Page 17: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 18

Time evolution

of the bat

0.6 ms

hands don’t matter

-4

-2

0

2

4

6

8

10

displacement (mm)

0.1 ms intervals

impact point

pivot point

-50

0

50

100

150

200

0 5 10 15 20 25 30distance from knob (inches)

1 ms intervals

impact point

pivot point

T= 0-1 ms

T= 1-10 ms

Page 18: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 19

Effect of Bat on COR: Vibrations

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12 14

COR % Energy Dissipated

inches from barrel

Ball

Vibrations

Nodes

COR

COR maximum near 2nd node

Page 19: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 20

Putting Everything Together...

“sweet spot” depends on•collision efficiency

*recoil factor*COR

•how bat is swung

20

40

60

80

100

0.00

0.05

0.10

0.15

0.20

0.25

0 2 4 6 8 10 12 14

eAv (mph)

distance from tip (inches)

vf

eA

vbat

CM

vf = eA vball + (1+eA) vbat

Page 20: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 21

60

70

80

90

100

110

0 2 4 6 8 10

Vf (mph)

distance from barrel (inches)

Crisco/Greenwald Data vs. Calculation

Conclusion: ideal ball-bat collision can be simulated

Page 21: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 22

Wood versus Aluminum

Kinematics

Length, weight, MOI “decoupled”

shell thickness, added weight

fatter barrel, thinner handle

weight distribution more uniform

CM closer to handle

less mass at contact point easier to swing

Dynamics

Stiffer for bending

Less vibrational energy

More compressible

COR larger

Page 22: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 23

The “Trampoline” Effect

Compressional energy shared between ball and bat PEbat/PEball = kball/kbat << 1 PEball mostly dissipated (75%)

Wood Bat hard to compress little effect on COR: “BPF” 1

Aluminum Bat

compressible through “shell” modes

kball/kbat ~ 0.10 (more or less)

PEbat mostly restored (more on this later)

COR larger: “BPF” 1.1 (more or less)

Page 23: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 24

The Trampoline Effect: A Closer Look

Bending Modes vs. Shell Modes

k R4: large in barrel little energy stored

f (170 Hz, etc) > 1/ energy goes into

vibrations

k (t/R)3: small in barrel

more energy stored

f (2-3 kHz) < 1/ energy mostly restored

Page 24: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 25

Wood versus Aluminum:

Dynamics of “Trampoline” Effect

“bell” modes: 3

2 R

t k

R

t ω

“ping” of bat

• Want k small to maximize stored energy

• Want >>1 to minimize retained energy

• Conclusion: there is an optimum

0 1000 2000 3000 4000frequency (Hz)

bending modes

bell modes

Page 25: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 26

Where Does the Energy Go?

0

50

100

150

200

250

300

350

400

0 0.2 0.4 0.6 0.8 1

Wood Bat

Ball KE

Ball PE

Bat Recoil KE

Bat Vibrational E

Energy (J)

t (ms)

0

50

100

150

200

250

300

350

400

0 0.2 0.4 0.6 0.8 1

Aluminum Bat

Ball KE

Ball PE

Bat Recoil KE

Bat Vibrational E

Energy (J)

t (ms)

Page 26: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 27

“Corking” a Wood Bat (illegal!)

Drill ~1” diameter hole along axis to depth of ~10”

• Smaller mass

• larger recoil factor (bad)

• higher bat speed (good)

• Is there a trampoline effect?

Page 27: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 28

Not Corked DATA Corked COR: 0.445 0.005 0.444 0.005

Conclusions:

• no tramopline effect!

• corked bat is WORSE even with higher vbat

Baseball Research Center, UML, Sherwood & amn, Aug. 2001

70

80

90

2 3 4 5 6 7 8 9

vf (mph)

distance from knob (inches)

uncorked

corked

calculation

Page 28: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 29

Aerodynamics of a Baseball

Forces on Moving Baseball

No SpinBoundary layer separationDRAG!FD=½ CDAv2

With Spin

Ball deflects wake ==>”lift”FM ~ RdFD/dvForce in direction front of ball

is turning

Pop

Pbottom

Drawing courtesty of Peter Brancazio

Page 29: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 30

0

0.5

1

1.5

2

0 25 50 75 100 125 150Speed in mph

Drag/Weight

Magnus/Weight@1800 rpm

Page 30: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 31

0

50

100

150

200

250

300

350

400

10 20 30 40 50 60 70 80 90

Range (ft)

(deg)

Range vs.

2000 rpm

0 rpm

0

20

40

60

80

100

120

0 100 200 300 400 500 600 700

y (ft)

x (ft)

no drag

with drag

approx linear:100

200

300

400

500

50 60 70 80 90 100 110 120

Range (ft)

vi (mph)

Range vs. v

0

50

100

150

200

250

-100 0 100 200 300 400horizontal distance in feet

200

350

500

750900

The Flight of the Ball:Real Baseball vs. Physics 101 Baseball

Page 31: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 32

Summary of Aerodynamics

108 mph ~400 ft each mph ~5 ft optimum angle ~350

2000 rpm backspinIncreases range ~27 ftDecreases optimum angle ~30

these number are only estimates!

Page 32: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 33

Oblique Collisions:The Role of Friction

Friction halts vT

spin, “lift”

Results

Balls hit to left/right break toward foul line

Backspin keeps fly ball in air longer

Topspin gives tricky bounces in infield

Pop fouls behind the plate curve back toward field

Page 33: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 34

Model for Oblique Collisions:

vN treated as before

vNf = eA(vball+vbat)N + vbat,N

Angular momentum conserved about contact point (!)

Friction reduces vT, increases

Rolls when vT = R

Horizontal: vTf (5/7)vT

Vertical: a bit more complicated Not the way a superball works!

vN

vT

vN|

vT|

Page 34: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 35

Oblique Collisions: Horizontal Plane

0

20

40

60

80

0 2 4 6 8 10 12 14

f (deg)

t (ms)

foul

fair

~11 inches

Initial takeoff angle

down the line

0

20

40

60

80

100

120

0 100 200 300 400

height vs. distance

angle vs. distanze

0

20

40

60

80

100

120

0 100 200 300 400

height vs. distance

angle vs. distanze

power alley

Page 35: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 36

Oblique Collisions: Vertical Plane

-2000

0

2000

4000

6000

8000

10000

12000

-50

0

50

100

150

-0.5 0 0.5 1 1.5 2 2.5 3

(rpm) (deg)

D (inches)

optimum:

D 0.75”

3000 rpm

330

Ball100 downward

Bat 100 upward

D = center-to-center offset

Page 36: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 37

Typical Trajectories

Ball100 downward

Bat 100 upward

D = center-to-center offset

0

50

100

150

200

250

0 50 100 150 200 250 300 350 400

1.5

0

0.25

0.50.75

1.0

Page 37: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 38

Some Practical/Interesting Questions

Does more friction help? Can a curveball be hit further than a

fastball?

Page 38: 1927  Solvay Conference: Greatest  physics team  ever assembled

The Physics of Hitting a Home Run ANL Colloquium September 20, 2002 Page 39

Summary and Conclusions Some aspects of baseball are amenable to

physics analysis Kinematic and dynamics of ball-bat collision Trajectory of a ball with drag and lift

Can understanding these things improve our ability to play the game? Almost surely NOT

Can understanding these things enhance our own enjoyment of the game For me, a resounding YES I hope for you also