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Introduction Hitting the Baseball The Flight of the Baseball Pitching the Baseball Summary

Baseball: It’s Not Nuclear Physics (or is it?!) Alan M. Nathan University of Illinois GWU Colloquium, October 21, 1999. Introduction Hitting the Baseball The Flight of the Baseball Pitching the Baseball Summary. REFERENCES.

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Introduction Hitting the Baseball The Flight of the Baseball Pitching the Baseball Summary

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  1. Baseball: It’s Not Nuclear Physics(or is it?!)Alan M. Nathan University of IllinoisGWU Colloquium, October 21, 1999 • Introduction • Hitting the Baseball • The Flight of the Baseball • Pitching the Baseball • Summary

  2. REFERENCES • The Physics of Baseball, Robert K. Adair (Harper Collins, New York, 1990), ISBN 0-06-096461-8 • The Physics of Sports, Angelo Armenti (American Institute of Physics, New York, 1992), ISBN 0-88318-946-1 • www.physics.usyd.edu.au/~cross • L. L. Van Zandt, AJP 60, 72 (1991) • www.npl.uiuc.edu/~a-nathan

  3. Hitting the Baseball “...the most difficult thing to do in sports” --Ted Williams BA: .344 SA: .634 OBP: .483 HR: 521

  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

  5. What Determines Batted Ball Speed? 1. pitched ball speed 2. bat speed Rigid-Body Kinematics: V = 0.25 Vball + 1.25 Vbat • Conclusion: • Bat Speed Matters More!

  6. What Determines Batted Ball Speed? 3. Mass of bat • larger mass  lower bat speed bat speed vs mass ball speed vs mass • Conclusion: • mass of bat matters….but not a lot

  7. What Determines Batted Ball Speed? 4. Inelasticity • 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!

  8. Inelasticity: The Coefficient of Restitution • COR = Vrel,f/Vrel,ICOR2 = KEcm,f /KEcm,i • For baseball, COR=.52-.58 • Changing COR by .05 changes V by 7 mph(35 ft!) • How to measure? • Bounce ball off hard surface • COR2 = hf/hi

  9. What About the Bat?(or, it takes two to tango!) • Energy shared between ball and bat • Ball is inefficient:  25% returned • Wood Bat • r~0.02 • 80% restored • COReff = 0.50-0.51 • Aluminum Bat • r~0.10 • 80% restored • COReff = 0.55-0.58 • “trampoline effect” • ball flies off the bat! r  Ebat/Eball kball/kbat  xbat/ xball >10% larger!

  10. 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

  11. Sweet Spot #1: Maximum Energy Transfer • Barrel end of bat maximizes bat speed • Center of Mass minimizes angular impulse • MET must be in between • MET  COP @ 5” from knob Aluminum bat more effective for inside pitches CM Alum Wood xcm 21.9” 19.6” kch 9.2” 10.2” kh23.8” 22.1”

  12. x2 x1 Sweet Spot #2: Center of Percussion • When ball strikes bat... • Linear recoil • conservation of momentum • Rotation about center of mass • conservation of angular momentum • When COP hit • The two motions cancel (at conjugate point) • No reaction force felt x1x2=Icm/M

  13. 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

  14. Dynamics of Bat-Ball Collision • Step 1: Solve eigenvalue problem for free vibrations • Step 2: Model force • Step 3: Expand in normal modes and solve

  15. General Results • Excitation of normal mode depends on ... • fnT (or T/Tn) • yn at impact point • For T 1 ms • only lowest 2 or 3 modes important (fn=171, 568, 1178, 1851,…)

  16. RESULTS: typical speed theory vs. experiment (Rod Cross) at low speed

  17. 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

  18. Aerodynamics of a Baseball Forces on Moving Baseball • No Spin • Boundary layer separation • DRAG! • FD=½CDAv2 • With Spin • Ball deflects wake ==>Magnus force • FMRdFD/dv • Force in direction front of ball is turning

  19. How Large are the Forces? =1800 RPM • Drag is comparable to weight • Magnus force < 1/4 weight)

  20. The Flight of the Ball:Real Baseball vs. Physics 101 Baseball • Role of Drag • Role of Spin • Atmospheric conditions • Temperature • Humidity • Altitude • Air pressure • Wind Max @ 350 approxlinear

  21. 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

  22. 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!

  23. “Hitting is timing. Pitching is upsetting timing” ---Warren Spahn vary speeds manipulate air flow orient stitches Pitching the Baseball

  24. 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 0.6 Horizontal Deflection of Ball (feet) 0.4 0.2 0 0 10 20 30 40 50 60 Distance from Pitcher (feet) Let’s Get Quantitative!How Much Does the Ball Break? • Kinematics • z=vT • x=½(F/M)T2 • 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: v  -8 mph • Examples: • “Hop” of 90 mph fastball ~4” • Break of 75 mph curveball ~14” • slower • more rpm • force larger

  25. Examples of Pitches Pitch V(MPH)  (RPM) T M/W fastball 85-95 1600 0.46 0.10 slider 75-85 1700 0.51 0.15 curveball 70-80 1900 0.55 0.25 What about split finger fastball?

  26. 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

  27. Summary • Much of baseball can be understood with basic principles of physics • Conservation of momentum, angular momentum, energy • Dynamics of collisions • Excitation of normal modes • 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!

  28. radius of gyration What Determines Batted Ball Speed?A Simple Formula Conservation of momentum, energy, and angular momentum:

  29. 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

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

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

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

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

  34. Note: both ball and racket compress

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