Introduction When Ash Meets Cowhide The Aerodynamics of Baseball The Art of Pitching Summary - PowerPoint PPT Presentation

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Baseball 101: A Primer on the Physics of Baseball Alan M. Nathan Saturday Physics Honors Lecture October 21, 2000. Introduction When Ash Meets Cowhide The Aerodynamics of Baseball The Art of Pitching Summary. REFERENCES.

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Baseball 101: A Primer on the Physics of BaseballAlan M. NathanSaturday Physics Honors LectureOctober 21, 2000

  • Introduction

  • When Ash Meets Cowhide

  • The Aerodynamics of Baseball

  • The Art of Pitching

  • Summary

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  • The Physics of Baseball, Robert K. Adair (Harper Collins, New York, 1990), ISBN 0-06-096461-8

  • The Sporting Life, Davis and Stephens (Henry Holt and Company, New York, 1997), ISBN 0-8050-4540-6


  • ME!



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1927 Yankees:

Greatest baseball team

ever assembled


Solvay Conference:

Greatest physicsteam

ever assembled

Baseball and Physics: Murderers Rows of 1927

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#521, September 28, 1960

Hitting the Baseball

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

--Ted Williams,

Professor of Hitting

BA: .344

SA: .634

OBP: .483

HR: 521

all time leader

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Here’s Why…..

(Courtesy of Robert K. Adair)

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Trivia Timeout

  • Rogers Hornsby is one of only two players to have won the Triple Crown twice. Who is the other player?

    A) Hank Aaron

    B) Mickey Mantle

    C) Carl Yastrzemski

    D) Ted Williams

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When Ash Meets Cowhide

  • A violent collision!

    • forces large (>8000 lbs!)

    • time is short (<1/1000 sec!)

    • ball compresses, stops, expands

    • kinetic energy  potential energy

    • lots of energy dissipated (friction)

  • hands don’t matter!

  • GOAL: maximize ball exit speed vf

    vf 105 mph  x  400 ft x/vf = 4-5 ft/mph

What aspects of collision lead to large vf?

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Speed of Hit Ball:What does it depend on?

  • The basic stuff (“kinematics”)

    • speed of pitched ball

    • speed of bat

    • weight and weight distribution of bat

  • The really interesting stuff (“dynamics”)

    • “bounciness” of ball

    • vibrations of bat

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collision efficiency

(property of ball/bat)

vf =  vball + (1+) vbat

What Determines Batted Ball Speed?

  • How does batted ball speed depend on ...

    • pitched ball speed?

    • bat speed?

For typical collision on fat part of bat,

=0.2 1+ = 1.2


Bat Speed Matters Much More!

Question: What properties of ball/bat determine ?

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What Determines Batted Ball Speed?

  • Mass of bat

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What Determines Batted Ball Speed?

  • Mass of bat

Mass distribution of bat

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(½ mv2)

What is the Ideal Bat Weight?

Conclusion: More data needed to determine optimum bat weight.

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Trivia Timeout

  • Who is this guy and what was his number?

Eddie Gaedel…1/8

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This is COR2

The Coefficient of Restitution:Energy Dissipation in Ball

  • COR measures “bounciness” of ball

  • Final speed/Initial speed

  • For baseball, COR 0.5

    • hf/hi = 3/4

    • 3/4 energy lost!

  • Is the ball “juiced”?

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COR and the “Juiced Ball” Issue

MLB:COR=0.546  0.032

@ 58 mph on massive rigid surface

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tennis ball/racket

Effect of Bat on COR:“Trampoline” Effect

  • Energy shared between ball and bat

  • Wood Bat: nearly incompressible

    • ~ 2% of energy stored in bat

    • Efficiently restored to ball

      • BPF~ 1

  • Aluminum Bat

    • ~ 10-20% energy stored in bat

    • Efficiently restored to ball

    • Result: “trampoline effect”

      • BPF ~ 1.1-1.2

      • Ball fliesoff the bat!

Bat Performance Factor:


new NCAA rules:<.228

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Trivia Timeout

  • Who is this guy?

    A) Joe Torre

    B) Don Zimmer

    C) Lou Skizas

    D) Roger Maris

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Effect of Bat on COR: Bat Vibrations

  • Collision excites bending vibrations in bat

    • Ouch!! Thud!!

    • Sometimes broken bat

    • Energy lost  lower COR

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f1 = 177 Hz

1st mode


2nd mode

f2 = 583 Hz

0-20 ms

Shape of vibration

Time profile of vibration

Vibrational Modes of Bat

Louisville Slugger R161 (33”, 31 oz)

This can be measured!

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Center of mass

Putting it all together….

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Possible “Physics Sweet Spots”

  • Center of Percussion (~6”)

  • Node of lowest vibration (~6”)

  • Maximum hit ball speed (~5”)

  • Minimum total vibrations (~5”)

Question: Where is “batters sweet spot”?

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Advantages of Aluminum

  • Length and weight “decoupled”

    • Can adjust shell thickness

    • Fatter barrel, thinner handle

    • Lighter

      • Higher bat speed

    • More of weight closer to hands

      • Easier to swing

      • Less rotational recoil

      • More forgiving on inside pitches

  • More compressible => “springier”

    • Trampoline effect, higher COR

  • Stiffer for bending

    • Less energy lost due to vibrations

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Trivia Timeout

  • Who is the only player to steal five bases in one game?

    A) Ricky Henderson

    B) Lou Brock

    C) Tony Gwynn

    D) Ty Cobb

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Aerodynamics of a Baseball

Forces on Moving Baseball

  • No Spin

    • Boundary layer separation

    • DRAG!

    • Grows with v2

  • With Spin

    • Ball deflects wake

    • action/reaction  Magnus force

      • Force grows with rpm

      • Force in direction front of ball is turning

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The Flight of the BallReal Baseball vs. Physics 101 Baseball

  • Role of Drag

  • Role of Spin

  • Atmospheric conditions

    • Temperature

    • Humidity

    • Altitude

    • Air pressure

    • Wind

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The Role of Friction

  • Friction induces spin for oblique collisions

  • Spin => Magnus force

  • 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

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The Home Run Swing

  • Ball arrives on 100 downward trajectory

  • Big Mac swings up at 250

  • Ball takes off at 350

    • The optimum home run angle!

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“Hitting is timing. Pitching is upsetting timing”

---Warren Spahn

vary speeds

manipulate air flow

orient stitches

Don Larsen, 1956 World Series

Last pitch of perfect game

The Art of Pitching

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Who is standing behind Don Larsen?

A) Bobby Richardson

B) Tony Kubek

C) Billy Martin

D) Yogi Berra

Don Larsen, 1956 World Series

Last pitch of perfect game


Trivia Timeout

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Vertical Position of Ball (feet)


90 mph Fastball










Distance from Pitcher (feet)



75 mph Curveball


Horizontal Deflection of Ball (feet)












Distance from Pitcher (feet)

How Much Does the Ball Break?

  • Depends on…

    • Magnitude and direction of force

    • Time over which force acts

  • Calibration

    • 90 mph fastball drops 3.5’ due to gravity alone

    • Ball reaches home plate in ~0.45 seconds

  • Half of deflection occurs in last 15’

  • Drag reduces fastball by about 8 mph

  • Examples:

    • Hop of 90 mph fastball: ~4”

    • Break of 70 mph curveball ~16”

      • slower

      • force larger

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Example 1: Fastball

85-95 mph

1600 rpm (back)

12 revolutions

0.46 sec


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Example 2: Split-Finger Fastball

85-90 mph

1300 rpm (top)

12 revolutions

0.46 sec


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Example 3: Curveball

70-80 mph

1900 rpm

(top and side)

17 revolutions

0.55 sec


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Example 4: Slider

75-85 mph

1700 rpm (side)

14 revolutions

0.51 sec


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Effect of the Stitches

  • Obstructions cause turbulance

  • Turbulance reduces drag

    • Dimples on golf ball

    • Stitches on baseball

  • Asymmetric obstructions

    • Knuckleball

    • Two-seam vs. four-seam delivery

    • Scuffball and “juiced” ball

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Trivia Timeout

Who said...

  • "Baseball is 90% mental. The other half is physical."

  • "You can observe a lot by watching."

  • "If the people don’t want to come out to the park, nobody’s going to stop them."

  • "No one ever goes to that restaurant any more. It’s too crowded."

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  • Much of baseball can be understood with

    basic principles of physics

    • Conservation of momentum, angular momentum, energy

    • Dynamics of collisions

    • Trajectories under influence of forces

      • gravity, drag, Magnus,….

  • There is probably much more that we don’t understand

  • Don’t let either of these interfere with your

    enjoyment of the game!

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