UBC Colloquium 10/5/06 1 Thanks to J. J. Crisco & R. M. Greenwald Medicine & Science in Sports &...

UBC Colloquium 10/5/06 1

Thanks to J. J. Crisco & R. M. GreenwaldMedicine & Science in Sports & Exercise

34(10): 1675-1684; Oct 2002

Alan M. Nathan,University of Illinoiswww.npl.uiuc.edu/~a-nathan/pob

a-nathan @uiuc.edu

The Physics of Hitting a Home Run

http://ipsapp002.lwwonline.com/content/getfile/2320/1359/21/abstract.htm

http://ipsapp002.lwwonline.com/content/getfile/2320/1359/21/abstract.htm


1927 Solvay Conference:

Greatest physics team ever assembled

Baseball and Physics

1927 Yankees:Greatest baseball team

ever assembled

MVP’s


Adair’s Book: An Excellent Reference

“Our goal is not to reform the game but to understand it.

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


1. How does a baseball bat work?

2. Aerodynamics: flight of a baseball

3. Leaving the no-spin zone

4. Putting it all together

The Physics of Hitting a Home Run


“You can observe a lot by watching”

Champaign News-Gazette

CE Composites

--Yogi Berra

Easton Sports


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

– >8000 lbs, <1 ms• ball compresses, stops, expands

– KEPEKE– bat recoils

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

• to hit home run….– large hit ball speed (100 mph~400 ft)– optimum take-off angle (300-350)– lots of backspin


vf = q vball + (1+q) vbat

Conclusion:

vbat matters much more than vball

• q “Collision Efficiency” • Joint property of ball & bat

independent of reference frame ~independent of “end conditions”—more later weakly dependent on vrel

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

vf 0.2 vball + 1.2 vbat

vball vbat

vf

Kinematics of Ball-Bat Collision


Kinematics of Ball-Bat Collision

f ball bat

e-rq = 1+r

e-r 1+ev = v v1+r 1+r

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

---heavier is better but…

e: “coefficient of restitution” 0.50 (energy dissipation—mainly in ball, some in bat)

vball vbat

vf

q=0.20


Collision Efficiency q Can Be Measured• Air cannon to fire ball onto stationary bat• q = vout/vin

• Used by NCAA, ASA, … to regulate/limit performance of bats

Sports Sciences Lab @ WSU


Accounting for COR:Dynamic Model for Ball-Bat Collision

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

• Collision excites bending vibrations in bat– hurts! breaks bats– dissipates energy

• lower COR, vf

• Dynamic model of collision– Treat bat as nonuniform beam– Treat ball as damped spring


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


Vibrations, COR, and the “Sweet Spot”

Evib

vf

e

Node of 1nd mode

+

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

-30.00

-20.00

-10.00

0.00

10.00

20.00

30.00

0 1 2 3 4 5

v (m/s)

t (ms)

Strike bat here Measure response here


• handle moves only after ~0.6 ms delay

• collision nearly over by then

• nothing on knob end matters• size, shape• boundary conditions• hands!

• confirmed experimentally

-30.00

-20.00

-10.00

0.00

10.00

20.00

30.00

0 1 2 3 4 5

v (m/s)

t (ms)

Independence of End Conditions


q independent of end conditions:experimental proof

0

0.05

0.1

0.15

0.2

0.25

25 26 27 28 29 30 31 32

Collision Efficiency

distance from knob (inches)

"normal" bat

normal + 3 oz in knob

Conclusion: mass added in knob has no effect on collision efficiency (q)


• Aluminum has thin shell • Hoop modes give “trampoline” effect

– larger COR, vf

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”

• Also seen in golf, tennis, …

The “Trampoline” Effect:A Simple Physical Picture


The Trampoline Effect: A Closer Look

“hoop” modes: cos(2)

“ping”

Thanks to Dan Russell


Wood vs. Aluminum: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)


The Trampoline Effect: A Closer Look

to optimize….kbat//kball small and fhoop > 1

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

Bending Modes vs. Shell Modes


0.40

0.45

0.50

0.55

0.60

0.65

0.70

500 1000 1500 2000

COR-modelCOR-expt

COR

fhoop

(Hz)

Softball Data and Model

essential physics understood


Aerodynamics of a Baseball

Drag: Fd = ½ CDAv2

-v direction

“Magnus” or “Lift”: FL = ½ CLAv2

(ω v) direction

v

ω

mg

Fd

FL (Magnus)

CD~ 0.2-0.5CL ~ R/v

(in direction leading edge is turning)


Effect of Drag and Lift on Trajectories

• drag effect is huge

• lift effect is smaller but significant

0

20

40

60

80

100

120

0 100 200 300 400 500 600 700distance (ft)

no drag or lift

drag, no lift drag and lift

v

ω

mg

Fd

FL (Magnus)


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

Some Effects of Drag

• Reduced distance on fly ball

• Reduction of pitched ball speed by ~10%

• Asymmetric trajectory:– Total Distance 1.7 x

distance at apex

• Optimum home run angle ~30o-35o

0

20

40

60

80

100

120

0 100 200 300 400 500 600 700distance (ft)

no drag or lift

drag, no lift


Some Effects of Lift

0

20

40

60

80

100

120

0 100 200 300 400 500 600 700distance (ft)

no drag or lift

drag, no lift drag and lift

v

ω

mg

Fd

FL (Magnus)

• Backspin makes ball rise

– “hop” of fastball– undercut balls: increased distance, reduced

optimum angle of home run

• Topspin makes ball drop– “12-6” curveball– topped balls nose-dive

• Breaking pitches due to spin– Cutters, sliders, etc.


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


Typical Motion Capture Datameasure spin, CM trajectory

61

62

63

64

65

66

0 5 10 15distance (ft)

94 mph3000 rpm topspin1.8g

Note: topspin ay > g

CM trajectory


Results for Lift Coefficient CL

FL= 1/2ACLv2

S=r/v100 mph, 2000 rpm

S=0.17

Conclusion: data qualitatively consistent (~20%)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

present

Alaways 2-Seam

Alaways 4-Seam

Watts & Ferrer

Briggs

0.0 0.2 0.4 0.6 0.8 1.0

CL

S


Baseball Aerodynamics:Things I would like to know better

• Better data on drag– “drag crisis”?– Spin-dependent drag?– Drag for v>100 mph

• Dependence of drag/lift on seam orientation

• Is the spin constant?


Oblique Collisions:Leaving the No-Spin Zone

Oblique friction spintransverse velocity reducedspin increased

Familiar Results:• Balls hit to left/right break toward foul line• Topspin gives tricky bounces in infield• Backspin keeps fly ball in air longer• Tricky popups to infield

demo


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 backspin

Ball100 downward

Bat 100 upward

D = center-to-center offset

trajectories

“vertical sweet spot”


• Bat-Ball Collision Dynamics– A fastball will be hit faster– A curveball will be hit with more backspin

Putting it all Together:Can curveball be hit farther

than fastball?

UBC Colloquium 10/5/06 33Net effect: backspin larger for curveball

Fastball: spin must reverse

curveball can be hit with more backspin: WHY?

Fastball with backspin

Curveball: spin doesn’t reverse

Curveball with topspin


• Bat-Ball Collision Dynamics– A fastball will be hit faster– A curveball will be hit with more backspin

• Aerodynamics– A ball hit faster will travel farther– Backspin increases distance

• Which effect wins?• Curveball, by a hair!

Can Curveball Travel Farther than Fastball?


Work in Progress

• Collision experiments & calculations to elucidate trampoline effect

• New studies of aerodynamics• Experiments on oblique collisions

– No data!


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!

UBC Colloquium 10/5/06 1 Thanks to J. J. Crisco & R. M. Greenwald Medicine & Science in Sports &...

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Transcript of UBC Colloquium 10/5/06 1 Thanks to J. J. Crisco & R. M. Greenwald Medicine & Science in Sports &...