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Baseball (Its Not Nuclear Physics) PowerPoint Presentation

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Slide 1 -

The Physics of Baseball (or…Just How Did McGwire Hit 70?) Alan M. Nathan University of Illinois February 5, 1999 Introduction Hitting the Baseball The Flight of the Baseball Pitching the Baseball Summary

Slide 2 -

REFERENCES 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 http://www.exploratorium.edu/sports ME! a-nathan@uiuc.edu www.npl.uiuc.edu/~nathan

Slide 3 -

Hitting the Baseball “...the most difficult thing to do in sports” --Ted Williams, Professor Emeritus of Hitting

Slide 4 -

Speed of Hit Ball: What does it depend on? Speed is important: 105 mph gives 400 ft each mph is worth 5 ft The basic stuff (“kinematics”) speed of pitched ball speed of bat weight of bat The really interesting stuff (“dynamics”) “bounciness” of ball and bat weight distribution of bat vibrations of bat

Slide 5 -

What Determines Batted Ball Speed? How does batted ball speed depend on ... pitched ball speed? bat speed? V = 0.25 Vball + 1.25 Vbat Conclusion: Bat Speed Matters More!

Slide 6 -

What Determines Batted Ball Speed? Mass of bat Conclusion: mass of bat matters ...but not a lot

Slide 7 -

Dynamics of Ball-Bat Collision Ball compresses kinetic energy stored in “spring” Ball expands kinetic energy restored but... 70% of energy is lost! (heat, deformation,vibrations,...) Forces are large (>5000 lbs!) Time is short (<1/1000 sec!) The hands don’t matter!

Slide 8 -

Slide 9 -

The Coefficient of Restitution COR measures “bounciness” of ball Final speed/Initial speed For baseball, COR=.52-.58 Changing COR by .05 changes V by 7 mph (35 ft!) How to measure? This is square of COR------->

Slide 10 -

What About the Bat? (or, it takes two to tango!) Wood Bat Efficiently restores energy But only 2% energy stored Bat Performance Factor (BPF) ~1 .02 Aluminum Bat Stores ~ 20% energy Efficiently restores energy Result: “trampoline effect” BPF ~ 1.2 Ball flies off the bat! A more efficient bat and/or ball

Slide 11 -

Properties of Bats length, diameter weight position of center of gravity where does it balance? distribution of weight “moment of inertia” center of percussion stiffness and elasticity vibrational nodes and frequencies

Slide 12 -

Sweet Spot #1: Center of Percussion When ball strikes bat... Linear recoil conservation of momentum Rotation about center of mass conservation of angular momentum When CP hit The two motions cancel at handle No reaction force felt at handle

Slide 13 -

Sweet Spot #2: Maximum Energy Transfer Barrel end of bat maximizes bat speed Center of Mass minimizes angular impulse MET must be in between Not on COP! Aluminum bat more effective for inside pitches

Slide 14 -

Sweet Spot #3: “Node” of Vibration Collision excites bending vibrations in bat Ouch!! Energy lost ==>lower COR Sometimes broken bat Reduced considerably if collision is a node of fundamental mode Fundamental node easy to find For an interesting discussion, see www.physics.usyd.edu.au/~cross

Slide 15 -

So you think bats cannot bend…..

Slide 16 -

So you think bats cannot bend…..

Slide 17 -

How Would a Physicist Design a Bat? Wood Bat already optimally designed highly constrained by rules! a marvel of evolution! Aluminum Bat lots of possibilities exist but not much scientific research a great opportunity for ... fame fortune

Slide 18 -

Advantages of Aluminum Length and weight “decoupled” Can adjust shell thickness More compressible => “springier” Trampoline effect More of weight closer to hands Easier to swing Less rotational energy transferred to bat More forgiving on inside pitches Stiffer for bending Less energy lost due to vibrations

Slide 19 -

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

Slide 20 -

The Flight of the Balll Role of Drag Role of Spin Atmospheric conditions Temperature Humidity Altitude Air pressure Wind

Slide 21 -

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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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

Slide 24 -

Pitching the Baseball “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

Slide 25 -

Let’s Get Quantitative! I. How Large are the Forces? Drag is comparable to weight Magnus force < 1/4 weight)

Slide 26 -

Let’s Get Quantitative! II. 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 M/W~0.1

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Example 2: Split-Finger Fastball 85-90 mph 1300 rpm (top) 12 revolutions 0.46 sec M/W~0.1

Slide 29 -

Example 3: Curveball 70-80 mph 1900 rpm (top and side) 17 revolutions 0.55 sec M/W~0.25

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Example 4: Slider 75-85 mph 1700 rpm (side) 14 revolutions 0.51 sec M/W~0.15

Slide 31 -

Examples of Trajectories

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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

Slide 33 -

Summary 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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