1. 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

2. Physics of Baseball: Page 2 REFERENCES l The Physics of Baseball, Robert K. Adair (Harper Collins, New York, 1990), ISBN 0-06-096461-8 l The Sporting Life, Davis and Stephens (Henry Holt and Company, New York, 1997), ISBN 0-8050-4540-6 l http://www.exploratorium.edu/sports l ME! »a-nathan@uiuc.edu »www.npl.uiuc.edu/~nathan

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

4. 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

5. 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 + 1.25 V bat Conclusion: Bat Speed Matters More!

6. 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

7. 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!

8. 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!

9. Physics of Baseball: Page 9 The Coefficient of Restitution l COR measures “bounciness” of ball l Final speed/Initial speed l For baseball, COR=.52-.58 l Changing COR by.05 changes V by 7 mph (35 ft!) l How to measure? This is square of COR------->

10. 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

11. 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

12. 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

13. 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

14. 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 www.physics.usyd.edu.au/~cross

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

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

17. 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

18. 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

19. 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

20. 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

21. 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!

22. Physics of Baseball: Page 22

23. 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

24. 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

25. 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)

26. 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

27. Physics of Baseball: Page 27 Example 1: Fastball 85-95 mph 1600 rpm (back) 12 revolutions 0.46 sec M/W~0.1

28. Physics of Baseball: Page 28 Example 2: Split-Finger Fastball 85-90 mph 1300 rpm (top) 12 revolutions 0.46 sec M/W~0.1

29. Physics of Baseball: Page 29 Example 3: Curveball 70-80 mph 1900 rpm (top and side) 17 revolutions 0.55 sec M/W~0.25

30. Physics of Baseball: Page 30 Example 4: Slider 75-85 mph 1700 rpm (side) 14 revolutions 0.51 sec M/W~0.15

31. Physics of Baseball: Page 31 Examples of Trajectories 3 4 5 6 7 0102030405060 Vertical Position of Ball (feet) Distance from Pitcher (feet) 90 mph Fastball 0 0.2 0.4 0.6 0.8 1 1.2 0102030405060 Horizontal Deflection of Ball (feet ) Distance from Pitcher (feet) 75 mph Curveball

32. 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

33. 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!