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Introduction When Ash Meets Cowhide The Aerodynamics of Baseball The Art of Pitching Summary

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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Introduction When Ash Meets Cowhide The Aerodynamics of Baseball The Art of Pitching Summary

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  1. 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

  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 • http://www.npl.uiuc.edu/~a-nathan/pob

  3. 1927 Yankees: Greatest baseball team ever assembled 1927 Solvay Conference: Greatest physicsteam ever assembled Baseball and Physics: Murderers Rows of 1927

  4. #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

  5. Here’s Why….. (Courtesy of Robert K. Adair)

  6. correct 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

  7. 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?

  8. 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

  9. 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 Conclusion: Bat Speed Matters Much More! Question: What properties of ball/bat determine ?

  10. . CM . recoil What Determines Batted Ball Speed? • Mass of bat

  11. . . CM rotation recoil What Determines Batted Ball Speed? • Mass of bat Mass distribution of bat

  12. (½ mv2) What is the Ideal Bat Weight? Conclusion: More data needed to determine optimum bat weight.

  13. Trivia Timeout • Who is this guy and what was his number? Eddie Gaedel…1/8

  14. 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”?

  15. COR and the “Juiced Ball” Issue MLB:COR=0.546  0.032 @ 58 mph on massive rigid surface

  16. 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: COReffective/COR new NCAA rules:<.228

  17. correct Trivia Timeout • Who is this guy? A) Joe Torre B) Don Zimmer C) Lou Skizas D) Roger Maris

  18. Effect of Bat on COR: Bat Vibrations • Collision excites bending vibrations in bat • Ouch!! Thud!! • Sometimes broken bat • Energy lost  lower COR

  19. f1 = 177 Hz 1st mode nodes 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!

  20. nodes Center of mass Putting it all together….

  21. 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”?

  22. 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

  23. correct 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

  24. 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

  25. The Flight of the BallReal Baseball vs. Physics 101 Baseball • Role of Drag • Role of Spin • Atmospheric conditions • Temperature • Humidity • Altitude • Air pressure • Wind

  26. 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

  27. 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!

  28. “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

  29. 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 correct Trivia Timeout

  30. 7 6 Vertical Position of Ball (feet) 5 90 mph Fastball 4 3 0 10 20 30 40 50 60 Distance from Pitcher (feet) 1.2 1 75 mph Curveball 0.8 Horizontal Deflection of Ball (feet) 0.6 0.4 0.2 0 0 10 20 30 40 50 60 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

  31. Example 1: Fastball 85-95 mph 1600 rpm (back) 12 revolutions 0.46 sec M/W~0.1

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

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

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

  35. 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

  36. 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."

  37. 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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