2. Baseball 101: A Primer on the Physics of Baseball Page 1 l Introduction l When Ash Meets Cowhide l The Aerodynamics of Baseball l The Art of Pitching l Summary Baseball 101: A Primer on the Physics of Baseball Alan M. Nathan Saturday Physics Honors Lecture October 21, 2000

3. Baseball 101: A Primer on the 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 »http://www.npl.uiuc.edu/~a-nathan/pobhttp://www.npl.uiuc.edu/~a-nathan/pob

4. Baseball 101: A Primer on the Physics of Baseball Page 3 1927 Yankees: Greatest baseball team ever assembled Baseball and Physics: Murderers Rows of 1927 1927 Solvay Conference: Greatest physics team ever assembled

5. Baseball 101: A Primer on the Physics of Baseball Page 4 Hitting the Baseball “...the most difficult thing to do in sports” --Ted Williams, Professor of Hitting BA:.344 SA:.634 OBP:.483 HR: 521 #521, September 28, 1960 all time leader

6. Baseball 101: A Primer on the Physics of Baseball Page 5 Here’s Why…..(Courtesy of Robert K. Adair)

7. Baseball 101: A Primer on the Physics of Baseball Page 6 Trivia Timeout l 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 correct

8. Baseball 101: A Primer on the Physics of Baseball Page 7 When Ash Meets Cowhide l A violent collision! çforces large (>8000 lbs!) çtime is short (<1/1000 sec!) çball compresses, stops, expands çkinetic energy  potential energy çlots of energy dissipated (friction) l hands don’t matter! l GOAL: maximize ball exit speed v f v f  105 mph  x  400 ft  x/  v f = 4-5 ft/mph What aspects of collision lead to large v f ?

9. Baseball 101: A Primer on the Physics of Baseball Page 8 Speed of Hit Ball: What does it depend on? l The basic stuff (“kinematics”) çspeed of pitched ball çspeed of bat çweight and weight distribution of bat l The really interesting stuff (“dynamics”) ç“bounciness” of ball çvibrations of bat

10. Baseball 101: A Primer on the Physics of Baseball Page 9 What Determines Batted Ball Speed? Conclusion: Bat Speed Matters Much More! For typical collision on fat part of bat,  =0.2 1+  = 1.2 Question: What properties of ball/bat determine  ? v f =  v ball + (1+  ) v bat collision efficiency (property of ball/bat) l How does batted ball speed depend on... çpitched ball speed? çbat speed?

11. Baseball 101: A Primer on the Physics of Baseball Page 10 What Determines Batted Ball Speed? l Mass of bat. recoil CM.

12. Baseball 101: A Primer on the Physics of Baseball Page 11 What Determines Batted Ball Speed? l Mass of bat.. CM recoil rotation l Mass distribution of bat

13. Baseball 101: A Primer on the Physics of Baseball Page 12 What is the Ideal Bat Weight? (½ mv 2 ) Conclusion: More data needed to determine optimum bat weight.

14. Baseball 101: A Primer on the Physics of Baseball Page 13 l Who is this guy and what was his number? Trivia Timeout Eddie Gaedel…1/8

15. Baseball 101: A Primer on the Physics of Baseball Page 14 The Coefficient of Restitution: Energy Dissipation in Ball l COR measures “bounciness” of ball l Final speed/Initial speed l For baseball, COR  0.5 çh f /h i = 3/4 ç3/4 energy lost! l Is the ball “juiced ”? This is COR 2

16. Baseball 101: A Primer on the Physics of Baseball Page 15 COR and the “Juiced Ball” Issue MLB: COR= 0.546  0.032 @ 58 mph on massive rigid surface

17. Baseball 101: A Primer on the Physics of Baseball Page 16 Effect of Bat on COR: “Trampoline” Effect l Energy shared between ball and bat l Wood Bat: nearly incompressible ç~ 2% of energy stored in bat çEfficiently restored to ball »BPF ~ 1 l Aluminum Bat ç~ 10-20% energy stored in bat çEfficiently restored to ball çResult: “trampoline effect” »BPF ~ 1.1-1.2 »Ball flies off the bat! tennis ball/racket Bat Performance Factor: COR effective /COR new NCAA rules:  <.228

18. Baseball 101: A Primer on the Physics of Baseball Page 17 l Who is this guy? A) Joe Torre B) Don Zimmer C) Lou Skizas D) Roger Maris Trivia Timeout correct

19. Baseball 101: A Primer on the Physics of Baseball Page 18 Effect of Bat on COR: Bat Vibrations l Collision excites bending vibrations in bat çOuch!! Thud!! çSometimes broken bat çEnergy lost  lower COR

20. Baseball 101: A Primer on the Physics of Baseball Page 19 Vibrational Modes of Bat Louisville Slugger R161 (33”, 31 oz) Shape of vibration Time profile of vibration f 1 = 177 Hz f 2 = 583 Hz nodes 1st mode 2nd mode 0-20 ms This can be measured!

21. Baseball 101: A Primer on the Physics of Baseball Page 20 Putting it all together…. nodes Center of mass

22. Baseball 101: A Primer on the Physics of Baseball Page 21 Possible “Physics Sweet Spots” l Center of Percussion (~6”) l Node of lowest vibration (~6”) l Maximum hit ball speed (~5”) l Minimum total vibrations (~5”) Question: Where is “batters sweet spot”?

23. Baseball 101: A Primer on the Physics of Baseball Page 22 Advantages of Aluminum l Length and weight “decoupled” çCan adjust shell thickness çFatter barrel, thinner handle çLighter »Higher bat speed çMore of weight closer to hands »Easier to swing »Less rotational recoil »More forgiving on inside pitches l More compressible => “springier” çTrampoline effect, higher COR l Stiffer for bending çLess energy lost due to vibrations

24. Baseball 101: A Primer on the Physics of Baseball Page 23 Trivia Timeout l Who is the only player to steal five bases in one game? A) Ricky Henderson B) Lou Brock C) Tony Gwynn D) Ty Cobb correct

25. Baseball 101: A Primer on the Physics of Baseball Page 24 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

26. Baseball 101: A Primer on the Physics of Baseball Page 25 The Flight of the Ball Real Baseball vs. Physics 101 Baseball l Role of Drag l Role of Spin l Atmospheric conditions çTemperature çHumidity çAltitude çAir pressure çWind

27. Baseball 101: A Primer on the Physics of Baseball Page 26 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

28. Baseball 101: A Primer on the Physics of Baseball Page 27 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!

29. Baseball 101: A Primer on the Physics of Baseball Page 28 The Art of Pitching “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

30. Baseball 101: A Primer on the Physics of Baseball Page 29 Trivia Timeout Who is standing behind Don Larsen? A) Bobby Richardson B) Tony Kubek C) Billy Martin D) Yogi Berra l Don Larsen, 1956 World Series l Last pitch of perfect game correct

31. Baseball 101: A Primer on the Physics of Baseball Page 30 How Much Does the Ball Break? 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 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

32. Baseball 101: A Primer on the Physics of Baseball Page 31 Example 1: Fastball 85-95 mph 1600 rpm (back) 12 revolutions 0.46 sec M/W~0.1

33. Baseball 101: A Primer on the Physics of Baseball Page 32 Example 2: Split-Finger Fastball 85-90 mph 1300 rpm (top) 12 revolutions 0.46 sec M/W~0.1

34. Baseball 101: A Primer on the Physics of Baseball Page 33 Example 3: Curveball 70-80 mph 1900 rpm (top and side) 17 revolutions 0.55 sec M/W~0.25

35. Baseball 101: A Primer on the Physics of Baseball Page 34 Example 4: Slider 75-85 mph 1700 rpm (side) 14 revolutions 0.51 sec M/W~0.15

36. Baseball 101: A Primer on the Physics of Baseball Page 35 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

37. Baseball 101: A Primer on the Physics of Baseball Page 36 Trivia Timeout l "Baseball is 90% mental. The other half is physical." l "You can observe a lot by watching." l "If the people don’t want to come out to the park, nobody’s going to stop them." l "No one ever goes to that restaurant any more. It’s too crowded." Who said...

38. Baseball 101: A Primer on the Physics of Baseball Page 37 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!