Physics of Baseball: Page 1 The Physics of Baseball (or…Just How Did McGwire Hit 70?) Alan M. Nathan University of Illinois February 5, 1999 l Introduction l Hitting the Baseball l The Flight of the Baseball l Pitching the Baseball l Summary

Physics of Baseball: Page 2 REFERENCES l The Physics of Baseball, Robert K. Adair (Harper Collins, New York, 1990), ISBN l The Sporting Life, Davis and Stephens (Henry Holt and Company, New York, 1997), ISBN l l ME! »

Physics of Baseball: Page 3 Hitting the Baseball “...the most difficult thing to do in sports” --Ted Williams, Professor Emeritus of Hitting

Physics of Baseball: Page 4 Speed of Hit Ball: What does it depend on? l Speed is important: ç105 mph gives 400 ft çeach mph is worth 5 ft l The basic stuff (“kinematics”) çspeed of pitched ball çspeed of bat çweight of bat l The really interesting stuff (“dynamics”) ç“bounciness” of ball and bat çweight distribution of bat çvibrations of bat

Physics of Baseball: Page 5 What Determines Batted Ball Speed? l How does batted ball speed depend on... çpitched ball speed? çbat speed? V = 0.25 V ball V bat Conclusion: Bat Speed Matters More!

Physics of Baseball: Page 6 What Determines Batted Ball Speed? l Mass of bat l Conclusion: çmass of bat matters ç...but not a lot

Physics of Baseball: Page 7 Dynamics of Ball-Bat Collision l Ball compresses çkinetic energy stored in “spring” l Ball expands çkinetic energy restored but... ç70% of energy is lost! (heat, deformation,vibrations,...) l Forces are large (>5000 lbs!) l Time is short (<1/1000 sec!) l The hands don’t matter!

Physics of Baseball: Page 8 Dynamics of Ball-Bat Collision l Ball compresses çkinetic energy stored in “spring” l Ball expands çkinetic energy restored but... ç70% of energy is lost! (heat, deformation,vibrations,...) l Forces are large (>5000 lbs!) l Time is short (<1/1000 sec!) l The hands don’t matter!

Physics of Baseball: Page 9 The Coefficient of Restitution l COR measures “bounciness” of ball l Final speed/Initial speed l For baseball, COR= l Changing COR by.05 changes V by 7 mph (35 ft!) l How to measure? This is square of COR >

Physics of Baseball: Page 10 What About the Bat? (or, it takes two to tango!) l Wood Bat çEfficiently restores energy çBut only 2% energy stored çBat Performance Factor (BPF) ~1.02 l Aluminum Bat çStores ~ 20% energy çEfficiently restores energy çResult: “trampoline effect” »BPF ~ 1.2 »Ball flies off the bat! l A more efficient bat and/or ball

Physics of Baseball: Page 11 Properties of Bats l length, diameter l weight l position of center of gravity where does it balance? l distribution of weight “moment of inertia” l center of percussion l stiffness and elasticity vibrational nodes and frequencies

Physics of Baseball: Page 12 Sweet Spot #1: Center of Percussion l When ball strikes bat... çLinear recoil »conservation of momentum çRotation about center of mass »conservation of angular momentum l When CP hit çThe two motions cancel at handle çNo reaction force felt at handle

Physics of Baseball: Page 13 Sweet Spot #2: Maximum Energy Transfer l Barrel end of bat maximizes bat speed l Center of Mass minimizes angular impulse l MET must be in between l Not on COP! Aluminum bat more effective for inside pitches CM COP

Physics of Baseball: Page 14 Sweet Spot #3: “Node” of Vibration l Collision excites bending vibrations in bat çOuch!! çEnergy lost ==>lower COR çSometimes broken bat l Reduced considerably if collision is a node of fundamental mode l Fundamental node easy to find l For an interesting discussion, see

Physics of Baseball: Page 15 So you think bats cannot bend…..

Physics of Baseball: Page 16 So you think bats cannot bend…..

Physics of Baseball: Page 17 How Would a Physicist Design a Bat? l Wood Bat çalready optimally designed »highly constrained by rules! ça marvel of evolution! l Aluminum Bat çlots of possibilities exist çbut not much scientific research ça great opportunity for... »fame »fortune

Physics of Baseball: Page 18 Advantages of Aluminum l Length and weight “decoupled” çCan adjust shell thickness l More compressible => “springier” çTrampoline effect l More of weight closer to hands çEasier to swing çLess rotational energy transferred to bat çMore forgiving on inside pitches l Stiffer for bending çLess energy lost due to vibrations

Physics of Baseball: Page 19 Aerodynamics of a Baseball Forces on Moving Baseball No Spin  Boundary layer separation  DRAG!  Grows with v 2 With Spin  Ball deflects wake  action/reaction==>Magnus force »Force grows with rpm »Force in direction front of ball is turning

Physics of Baseball: Page 20 The Flight of the Balll l Role of Drag l Role of Spin l Atmospheric conditions çTemperature çHumidity çAltitude çAir pressure çWind

Physics of Baseball: Page 21 The Home Run Swing Ball arrives on 10 0 downward trajectory Big Mac swings up at 25 0 Ball takes off at 35 0 The optimum home run angle!

Physics of Baseball: Page 22

Physics of Baseball: Page 23 The Role of Friction l Friction induces spin for oblique collisions l Spin => Magnus force l Results çBalls hit to left/right break toward foul line çBackspin keeps fly ball in air longer çTopspin gives tricky bounces in infield çPop fouls behind the plate curve back toward field

Physics of Baseball: Page 24 Pitching the Baseball “Hitting is timing. Pitching is upsetting timing” ---Warren Spahn l vary speeds l manipulate air flow l orient stitches l Don Larsen, 1956 World Series l Last pitch of perfect game

Physics of Baseball: Page 25 Let’s Get Quantitative! I. How Large are the Forces? Drag is comparable to weight Magnus force < 1/4 weight)

Physics of Baseball: Page 26 Let’s Get Quantitative! II. How Much Does the Ball Break? l Depends on… çMagnitude and direction of force çTime over which force acts l Calibration ç90 mph fastball drops 3.5’ due to gravity alone çBall reaches home plate in ~0.45 seconds l Half of deflection occurs in last 15’ l Drag reduces fastball by about 8 mph l Examples: çHop of 90 mph fastball: ~4” çBreak of 70 mph curveball ~16” »slower »force larger

Physics of Baseball: Page 27 Example 1: Fastball mph 1600 rpm (back) 12 revolutions 0.46 sec M/W~0.1

Physics of Baseball: Page 28 Example 2: Split-Finger Fastball mph 1300 rpm (top) 12 revolutions 0.46 sec M/W~0.1

Physics of Baseball: Page 29 Example 3: Curveball mph 1900 rpm (top and side) 17 revolutions 0.55 sec M/W~0.25

Physics of Baseball: Page 30 Example 4: Slider mph 1700 rpm (side) 14 revolutions 0.51 sec M/W~0.15

Physics of Baseball: Page 31 Examples of Trajectories Vertical Position of Ball (feet) Distance from Pitcher (feet) 90 mph Fastball Horizontal Deflection of Ball (feet ) Distance from Pitcher (feet) 75 mph Curveball

Physics of Baseball: Page 32 Effect of the Stitches l Obstructions cause turbulance l Turbulance reduces drag çDimples on golf ball çStitches on baseball l Asymmetric obstructions çKnuckleball çTwo-seam vs. four-seam delivery çScuffball and “juiced” ball

Physics of Baseball: Page 33 Summary l Much of baseball can be understood with basic principles of physics çConservation of momentum, angular momentum, energy çDynamics of collisions çTrajectories under influence of forces »gravity, drag, Magnus,…. l There is probably much more that we don’t understand l Don’t let either of these interfere with your enjoyment of the game!