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The Physics of Hitting a Home Run. web site: www.npl.uiuc.edu/~a-nathan/pob e-mail: [email protected] Alan M. Nathan Department of Physics University of Illinois. Photo courtesy of the Champaign News-Gazette. A Brief Introduction…. My day job… experimental nuclear/particle physics

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The physics of hitting a home run l.jpg

The Physics of Hitting a Home Run

web site:

www.npl.uiuc.edu/~a-nathan/pob

e-mail:

[email protected]

Alan M. Nathan

Department of Physics

University of Illinois

Photo courtesy of the Champaign News-Gazette

Maine IEEE, Portland, 8/3/06


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A Brief Introduction….

  • My day job…

    • experimental nuclear/particle physics

    • high-speed collisions between subatomic particles

  • Nights and weekends...

    • physics of baseball

    • high-speed collision between baseball and bat

    • many of the same principles apply

Maine IEEE, Portland, 8/3/06


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Some Topics I Will Cover

  • Why is hitting a baseball so hard?

  • How does a baseball bat work?

  • Does aluminum outperform wood?

  • How does spin affect flight of baseball?

  • Can a curveball be hit farther than a fastball?

  • How far did that home run go?

Maine IEEE, Portland, 8/3/06


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“Hitting is timing; pitching is

upsetting timing”

“Hitting is fifty percent above the shoulders”

Hitting the Baseball:

the most difficult feat in sports

1955 Topps cards from my personal collection

Maine IEEE, Portland, 8/3/06


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Why Hitting is Difficult

Here’s Why…..

  • 90 mph fastball takes about 0.40 sec to reach batter

    • ~0.20 sec needed to “observe, process, decide”

    • ~0.15 sec needed for swing

    • half of “break” occurs in last 0.10 sec

  • if batter overestimates speed by 3 mph (0.013 sec)

    • swing will be early by 1’ foul ball

    • ball topped by 1.6” weak grounder

      • backspin/topspin makes ball fall less/more

Maine IEEE, Portland, 8/3/06


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Why hitting is so difficult

Maine IEEE, Portland, 8/3/06


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Example: Tim Wakefield’s Knuckleball

Maine IEEE, Portland, 8/3/06


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How Does a Baseball Bat Work?

  • forces large, time short

    • >8000 lbs, <1 ms

  • ball compresses, stops, expands

    • KEPEKE

    • bat bends & compresses

  • lots of energy dissipated (“COR”)

    • distortion of ball

    • vibrations in bat

  • hands don’t matter

    • more later

Courtesy of CEComposites

Maine IEEE, Portland, 8/3/06


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To Hit a Home Run….

  • Large hit ball speed

    • vhit 105 mph  D  400 ft

    • each additional mph gives 4-5 ft

  • Lots of backspin

  • Proper takeoff angle

    • 250-350—depending on backspin

Maine IEEE, Portland, 8/3/06


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vpitch

vswing

vhit

How to Get Large Hit Ball Speed

,my only formula:

  • q = “collision efficiency”

    • Joint property of ball and bat

  • For “typical” collision, q~0.2

    • vpitch=90, vswing=70  vhit=102 (~400 ft)

  • Collision very inefficient

    • For superball on rigid wall, q=1

  • vswingmuch more important than vpitch

    • 1 mph vpitch 1 ft

    • 1 mph vswing  5 ft

Maine IEEE, Portland, 8/3/06


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What Does q Depend On?

  • e = coefficient of restitution (COR)

    • Bounciness of ball

    • Typically ~0.5

      • e2=hf/hi

      • Superball has e=1

    • Bat matters too—more later

  • r = bat recoil factor=mball/mbat

    • Momentum conservation

    • Want r small  mbat large

Maine IEEE, Portland, 8/3/06


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The Ideal Bat Weight

vhit = q vpitch + (1+q) vswing

  • Heavier bat  more efficient collision

    • q larger

  • Heavier bat  smaller vswing

  • What about vhit?

Maine IEEE, Portland, 8/3/06


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The Ideal Bat Weight

hit ball speed

  • batters prefer lighter bats—more control

  • corking doesn’t help vhit

  • actually, weight distribution matters more than weight

Maine IEEE, Portland, 8/3/06


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Thanks to J. J. Crisco & R. M. Greenwald

Medicine & Science in Sports & Exercise 34(10): 1675-1684; Oct 2002

  • High-Speed Video

  • track bat and ball

  • measure collision efficiency

  • measure bat speed

Maine IEEE, Portland, 8/3/06


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The Ball-Bat 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

      • lower vf

  • Solve numerically as non-uniform beam

demo

Maine IEEE, Portland, 8/3/06


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f1 = 179 Hz

f3 = 1181 Hz

f2 = 582 Hz

f4 = 1830 Hz

frequency

time

“Modal Analysis” of a Baseball Bat

www.kettering.edu/~drussell/bats.html

Maine IEEE, Portland, 8/3/06


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Some Interesting Insights:Bat Recoil, Vibrations, COR, and “Sweet Spot”

Node of 1nd mode

+

e

vf

Evib

Maine IEEE, Portland, 8/3/06


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The Hands Don’t Matter!

  • handle moves only after ~0.6 ms delay

  • collision nearly over by then

  • nothing on knob end matters

    • size, shape

    • boundary conditions

    • hands, grip

  • confirmed experimentally

  • Maine IEEE, Portland, 8/3/06


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    pitcher

    catcher

    Vibrations and Broken Bats

    inside

    outside

    node

    Maine IEEE, Portland, 8/3/06


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    Does Aluminum Outperform Wood?

    Aluminum has thin shell

    • Less mass in barrel

      • easier to swing and control 

      • but less effective at transferring energy 

      • for many bats  cancels 

        • just like corked wood bat

  • Hoop modes

    • trampoline effect

    • larger COR 

  • Maine IEEE, Portland, 8/3/06


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    The “Trampoline” Effect:

    A Simple Physical Picture

    • 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”—confirmed by experiment

    • Also seen in golf, tennis, …

    demo

    Maine IEEE, Portland, 8/3/06


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    Effect of Drag and Lift on Trajectories

    FL(Magnus)

    Fd

    mg

    • drag effect is huge

    • lift effect is smaller but significant

    Maine IEEE, Portland, 8/3/06


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    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 ~350

    Maine IEEE, Portland, 8/3/06


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    FL(Magnus)

    Fd

    mg

    Some Effects of Lift

    • 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.

    Maine IEEE, Portland, 8/3/06


    Measuring the lift motion capture experiment @ illinois joe hopkins lance chong hank kaczmarski amn l.jpg

    Motion Capture System

    Two-wheel pitching machine

    Baseball with reflecting dot

    Measuring the Lift:Motion Capture Experiment @ IllinoisJoe Hopkins, Lance Chong, Hank Kaczmarski, AMN

    Maine IEEE, Portland, 8/3/06


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    ~15 ft

    Joe Hopkins

    Motion Capture Geometry

    Maine IEEE, Portland, 8/3/06


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    • Pitching Machine:

    • project horizontally

    • 50-110 mph

    • 1500-4500 rpm

    Maine IEEE, Portland, 8/3/06


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    Typical Data

    Typical Data

    Note: topspin  ay > g

    Maine IEEE, Portland, 8/3/06


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    Things we 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?

    Maine IEEE, Portland, 8/3/06


    Oblique collisions leaving the no spin zone l.jpg
    Oblique Collisions:Leaving the No-Spin Zone

    Oblique  friction  spin

    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

    Maine IEEE, Portland, 8/3/06


    Undercutting the ball backspin l.jpg

    Ball100 downward

    D = center-to-center offset

    Bat 100 upward

    Undercutting the ball  backspin

    trajectories

    Maine IEEE, Portland, 8/3/06


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    Can Curveball Travel Farther than Fastball?

    • Bat-Ball Collision Dynamics

      • A fastball will be hit faster

      • A curveball will be hit with more backspin

    Maine IEEE, Portland, 8/3/06


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    Fastball: spin reverses

    Curveball: spin doesn’t reverse

     backspin larger for curveball

    Maine IEEE, Portland, 8/3/06


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    Can Curveball Travel Farther than Fastball?

    • 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!

    Maine IEEE, Portland, 8/3/06


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    How Far Did That Home Run Travel?

    • Ball leaves bat

    • Hits stands D from home plate, H above ground

    • How far would it have gone if no obstruction?

    Maine IEEE, Portland, 8/3/06


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    400 ft/30 ft

    Range=415-455

    Time can determine

    Maine IEEE, Portland, 8/3/06


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    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

    • Thanks for the invitation and go Red Sox!

    Maine IEEE, Portland, 8/3/06


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