The Physics of Hitting a Home Run St. Marys University Colloquium October 4, 2002 Page 1 The Physics of Hitting a Home Run Colloquium, St. Marys University Halifax, October 4, 2002 Alan M. Nathan University of Illinois at Urbana-Champaignl Introduction l Model for colinear ball-bat collisions some applicatons l Beginners guide to aerodynamics l Model for oblique ball-bat collisions some applications l Summary & Conclusions The Physics of Hitting a Home Run St. Marys University Colloquium October 4, 2002 Page Solvay Conference: Greatest physics team ever assembled Baseball and Physics 1927 Yankees: Greatest baseball team ever assembled MVPs The Physics of Hitting a Home Run St. Marys University Colloquium October 4, 2002 Page 3 Hitting the Baseball ... the most difficult thing to do in sports -- Ted Williams: BA:.344 SA:.634 OBP:.483 HR: 521 #521, September 28, 1960 The Physics of Hitting a Home Run St. Marys University Colloquium October 4, 2002 Page 4 Introduction: Description of Ball-Bat Collision l forces large (>8000 lbs!) l time short ( T N see AMN, Am. J. Phys, 68, 979 (2000) Accounting for Energy Dissipation: Dynamic Model for Ball-Bat Colllision The Physics of Hitting a Home Run St. Marys University Colloquium October 4, 2002 Page 12 ball bat Mass= >> 1 m on M a +M b (1 on 6) 1 to minimize retained energy Conclusion: there is an optimum The Physics of Hitting a Home Run St. Marys University Colloquium October 4, 2002 Page 25 Where Does the Energy Go? The Physics of Hitting a Home Run St. Marys University Colloquium October 4, 2002 Page 26 Corking a Wood Bat (illegal!) Drill ~1 diameter hole along axis to depth of ~10 Smaller mass larger recoil factor (bad) higher bat speed (good) Is there a trampoline effect? The Physics of Hitting a Home Run St. Marys University Colloquium October 4, 2002 Page 27 Not Corked DATA Corked COR: Conclusions: no tramopline effect! corked bat is WORSE even with higher v bat Baseball Research Center, UML, Sherwood & amn, Aug calculation The Physics of Hitting a Home Run St. Marys University Colloquium October 4, 2002 Page 28 Aerodynamics of a Baseball Forces on Moving Baseball No Spin Boundary layer separation DRAG! F D = C D Av 2 With Spin Ball deflects wake ==>lift F M ~ RdF D /dv Force in direction front of ball is turning Drawing courtesty of Peter Brancazio The Physics of Hitting a Home Run St. Marys University Colloquium October 4, 2002 Page 29 The Physics of Hitting a Home Run St. Marys University Colloquium October 4, 2002 Page 30 approx linear: The Flight of the Ball: Real Baseball vs. Physics 101 Baseball The Physics of Hitting a Home Run St. Marys University Colloquium October 4, 2002 Page 31 Summary of Aerodynamics l 108 mph ~400 ft l each mph ~5 ft l optimum angle ~35 0 l 2000 rpm backspin Increases range ~27 ft Decreases optimum angle ~3 0 l these number are only estimates! The Physics of Hitting a Home Run St. Marys University Colloquium October 4, 2002 Page 32 Oblique Collisions: The Role of Friction l Friction halts v T spin, lift l 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 The Physics of Hitting a Home Run St. Marys University Colloquium October 4, 2002 Page 33 Model for Oblique Collisions: v N treated as before v Nf = e A (v ball +v bat ) N + v bat,N Angular momentum conserved about contact point (!) Friction reduces v T, increases Rolls when v T = R Horizontal: v Tf (5/7)v T Vertical: a bit more complicated Not the way a superball works! vNvN vTvT vN|vN| vT|vT| The Physics of Hitting a Home Run St. Marys University Colloquium October 4, 2002 Page 34 Oblique Collisions: Horizontal Plane Initial takeoff angle down the line power alley The Physics of Hitting a Home Run St. Marys University Colloquium October 4, 2002 Page 35 Oblique Collisions: Vertical Plane optimum: D 0.75 3000 rpm 33 0 Ball10 0 downward Bat 10 0 upward D = center-to-center offset The Physics of Hitting a Home Run St. Marys University Colloquium October 4, 2002 Page 36 Typical Trajectories Ball10 0 downward Bat 10 0 upward D = center-to-center offset The Physics of Hitting a Home Run St. Marys University Colloquium October 4, 2002 Page 37 Some Practical/Interesting Questions l Does more friction help? l Can a curveball be hit further than a fastball? The Physics of Hitting a Home Run St. Marys University Colloquium October 4, 2002 Page 38 Summary and Conclusions l Some aspects of baseball are amenable to physics analysis Kinematic and dynamics of ball-bat collision Trajectory of a ball with drag and lift l Can understanding these things improve our ability to play the game? Almost surely NOT l Can understanding these things enhance our own enjoyment of the game For me, a resounding YES I hope for you also