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The Physics of Hitting a Home Run

The Physics of Hitting a Home Run. web site: www.npl.uiuc.edu/~a-nathan/pob e-mail: a-nathan@uiuc.edu. Alan M. Nathan Department of Physics University of Illinois. Photo courtesy of the Champaign News-Gazette. A Brief Introduction…. My day job… experimental nuclear/particle physics

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The Physics of Hitting a Home Run

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  1. The Physics of Hitting a Home Run web site: www.npl.uiuc.edu/~a-nathan/pob e-mail: a-nathan@uiuc.edu Alan M. Nathan Department of Physics University of Illinois Photo courtesy of the Champaign News-Gazette Maine IEEE, Portland, 8/3/06

  2. A Brief Introduction…. • My day job… • experimental nuclear/particle physics • high-speed collisions between subatomic particles • Nights and weekends... • physics of baseball • high-speed collision between baseball and bat • many of the same principles apply Maine IEEE, Portland, 8/3/06

  3. Some Topics I Will Cover • Why is hitting a baseball so hard? • How does a baseball bat work? • Does aluminum outperform wood? • How does spin affect flight of baseball? • Can a curveball be hit farther than a fastball? • How far did that home run go? Maine IEEE, Portland, 8/3/06

  4. “Hitting is timing; pitching is upsetting timing” “Hitting is fifty percent above the shoulders” Hitting the Baseball: the most difficult feat in sports 1955 Topps cards from my personal collection Maine IEEE, Portland, 8/3/06

  5. Why Hitting is Difficult Here’s Why….. • 90 mph fastball takes about 0.40 sec to reach batter • ~0.20 sec needed to “observe, process, decide” • ~0.15 sec needed for swing • half of “break” occurs in last 0.10 sec • if batter overestimates speed by 3 mph (0.013 sec) • swing will be early by 1’ foul ball • ball topped by 1.6” weak grounder • backspin/topspin makes ball fall less/more Maine IEEE, Portland, 8/3/06

  6. Why hitting is so difficult Maine IEEE, Portland, 8/3/06

  7. Example: Tim Wakefield’s Knuckleball Maine IEEE, Portland, 8/3/06

  8. How Does a Baseball Bat Work? • forces large, time short • >8000 lbs, <1 ms • ball compresses, stops, expands • KEPEKE • bat bends & compresses • lots of energy dissipated (“COR”) • distortion of ball • vibrations in bat • hands don’t matter • more later Courtesy of CEComposites Maine IEEE, Portland, 8/3/06

  9. To Hit a Home Run…. • Large hit ball speed • vhit 105 mph  D  400 ft • each additional mph gives 4-5 ft • Lots of backspin • Proper takeoff angle • 250-350—depending on backspin Maine IEEE, Portland, 8/3/06

  10. vpitch vswing vhit How to Get Large Hit Ball Speed ,my only formula: • q = “collision efficiency” • Joint property of ball and bat • For “typical” collision, q~0.2 • vpitch=90, vswing=70  vhit=102 (~400 ft) • Collision very inefficient • For superball on rigid wall, q=1 • vswingmuch more important than vpitch • 1 mph vpitch 1 ft • 1 mph vswing  5 ft Maine IEEE, Portland, 8/3/06

  11. What Does q Depend On? • e = coefficient of restitution (COR) • Bounciness of ball • Typically ~0.5 • e2=hf/hi • Superball has e=1 • Bat matters too—more later • r = bat recoil factor=mball/mbat • Momentum conservation • Want r small  mbat large Maine IEEE, Portland, 8/3/06

  12. The Ideal Bat Weight vhit = q vpitch + (1+q) vswing • Heavier bat  more efficient collision • q larger • Heavier bat  smaller vswing • What about vhit? Maine IEEE, Portland, 8/3/06

  13. The Ideal Bat Weight hit ball speed • batters prefer lighter bats—more control • corking doesn’t help vhit • actually, weight distribution matters more than weight Maine IEEE, Portland, 8/3/06

  14. Thanks to J. J. Crisco & R. M. Greenwald Medicine & Science in Sports & Exercise 34(10): 1675-1684; Oct 2002 • High-Speed Video • track bat and ball • measure collision efficiency • measure bat speed Maine IEEE, Portland, 8/3/06

  15. The Ball-Bat COR: Dynamic Model for Ball-Bat Collision AMN,Am. J. Phys, 68, 979 (2000) • Collision excites bending vibrations in bat • hurts! • breaks bats • dissipates energy • lower COR • lower vf • Solve numerically as non-uniform beam demo Maine IEEE, Portland, 8/3/06

  16. f1 = 179 Hz f3 = 1181 Hz f2 = 582 Hz f4 = 1830 Hz frequency time “Modal Analysis” of a Baseball Bat www.kettering.edu/~drussell/bats.html Maine IEEE, Portland, 8/3/06

  17. Some Interesting Insights:Bat Recoil, Vibrations, COR, and “Sweet Spot” Node of 1nd mode + e vf Evib Maine IEEE, Portland, 8/3/06

  18. The Hands Don’t Matter! • handle moves only after ~0.6 ms delay • collision nearly over by then • nothing on knob end matters • size, shape • boundary conditions • hands, grip • confirmed experimentally Maine IEEE, Portland, 8/3/06

  19. pitcher catcher Vibrations and Broken Bats inside outside node Maine IEEE, Portland, 8/3/06

  20. Does Aluminum Outperform Wood? Aluminum has thin shell • Less mass in barrel • easier to swing and control  • but less effective at transferring energy  • for many bats  cancels  • just like corked wood bat • Hoop modes • trampoline effect • larger COR  Maine IEEE, Portland, 8/3/06

  21. The “Trampoline” Effect: A Simple Physical Picture • Two springs mutually compress each other • KE  PE  KE • PE shared between “ball spring” and “bat spring” • PE in ball mostly dissipated(~80%!) • PE in bat mostly restored • Net effect: less overall energy dissipated • ...and therefore higher ball-bat COR • …more “bounce”—confirmed by experiment • Also seen in golf, tennis, … demo Maine IEEE, Portland, 8/3/06

  22. Effect of Drag and Lift on Trajectories FL(Magnus)  Fd mg • drag effect is huge • lift effect is smaller but significant Maine IEEE, Portland, 8/3/06

  23. Some Effects of Drag • Reduced distance on fly ball • Reduction of pitched ball speed by ~10% • Asymmetric trajectory: • Total Distance  1.7 x distance at apex • Optimum home run angle ~350 Maine IEEE, Portland, 8/3/06

  24. FL(Magnus)  Fd mg Some Effects of Lift • Backspin makes ball rise • “hop” of fastball • undercut balls: increased distance, reduced optimum angle of home run • Topspin makes ball drop • “12-6” curveball • topped balls nose-dive • Breaking pitches due to spin • Cutters, sliders, etc. Maine IEEE, Portland, 8/3/06

  25. Motion Capture System Two-wheel pitching machine Baseball with reflecting dot Measuring the Lift:Motion Capture Experiment @ IllinoisJoe Hopkins, Lance Chong, Hank Kaczmarski, AMN Maine IEEE, Portland, 8/3/06

  26. ~15 ft Joe Hopkins Motion Capture Geometry Maine IEEE, Portland, 8/3/06

  27. Motion Capture System: • 10 cameras • 700 frames/sec • 1/2000 shutter • very fancy software • www.motionanalysis.com • Pitching Machine: • project horizontally • 50-110 mph • 1500-4500 rpm Maine IEEE, Portland, 8/3/06

  28. Typical Data Typical Data Note: topspin  ay > g Maine IEEE, Portland, 8/3/06

  29. Things we would like to know better: • Better data on drag • “drag crisis” • spin-dependent drag? • drag for v>100 mph • Dependence of drag/lift on seam orientation? • Is the spin constant? Maine IEEE, Portland, 8/3/06

  30. Oblique Collisions:Leaving the No-Spin Zone Oblique  friction  spin Familiar Results: • Balls hit to left/right break toward foul line • Topspin gives tricky bounces in infield • Backspin keeps fly ball in air longer • Tricky popups to infield Maine IEEE, Portland, 8/3/06

  31. Ball100 downward D = center-to-center offset Bat 100 upward Undercutting the ball  backspin trajectories Maine IEEE, Portland, 8/3/06

  32. Can Curveball Travel Farther than Fastball? • Bat-Ball Collision Dynamics • A fastball will be hit faster • A curveball will be hit with more backspin Maine IEEE, Portland, 8/3/06

  33. Fastball: spin reverses Curveball: spin doesn’t reverse  backspin larger for curveball Maine IEEE, Portland, 8/3/06

  34. Can Curveball Travel Farther than Fastball? • Bat-Ball Collision Dynamics • A fastball will be hit faster • A curveball will be hit with more backspin • Aerodynamics • A ball hit faster will travel farther • Backspin increases distance • Which effect wins? • Curveball, by a hair! Maine IEEE, Portland, 8/3/06

  35. How Far Did That Home Run Travel? • Ball leaves bat • Hits stands D from home plate, H above ground • How far would it have gone if no obstruction? Maine IEEE, Portland, 8/3/06

  36. 400 ft/30 ft Range=415-455 Time can determine Maine IEEE, Portland, 8/3/06

  37. Final Summary • Physics of baseball is a fun application of basic (and not-so-basic) physics • Check out my web site if you want to know more • www.npl.uiuc.edu/~a-nathan/pob • a-nathan@uiuc.edu • Thanks for the invitation and go Red Sox! Maine IEEE, Portland, 8/3/06

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