FSU Colloquium 9/1/05 1 Thanks to J. J. Crisco & R. M. Greenwald Medicine & Science in Sports & Exercise 34(10): ; Oct 2002 Alan M. Nathan,University of Illinois Some Topics in the Physics of Baseball

FSU Colloquium 9/1/ Solvay Conference: Greatest physics team ever assembled Baseball and Physics 1927 Yankees: Greatest baseball team ever assembled MVP’s

FSU Colloquium 9/1/ How does a baseball bat work? 2.Why does aluminum outperform wood? 3.Effect of spin on flight of baseball? 4.Can a curveball be hit farther than a fastball? Some Topics in the Physics of Baseball

FSU Colloquium 9/1/05 4 Brief Description of Ball-Bat Collision 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 to hit home run…. –large hit ball speed –optimum take-off angle –backspin Courtesy of CE Composites

FSU Colloquium 9/1/05 5 Kinematics of Ball-Bat Collision v ball v bat vfvf r = m ball /M bat,eff : bat recoil factor =  0.25 (momentum and angular momentum conservation) e: “coefficient of restitution”  0.50 (energy dissipation) typical numbers: v f = 0.2 v ball v bat  v bat matters much more than v ball

FSU Colloquium 9/1/05 6 Kinematics of Ball-Bat Collision r = m ball /M bat,eff : bat recoil factor =  0.25 (momentum and angular momentum conservation) heavier bat better but…

FSU Colloquium 9/1/05 7 Crisco/Greenwald Batting Cage Study v bat  I -0.3 v bat  I -0.5

FSU Colloquium 9/1/05 8 Collision excites bending vibrations in bat –Ouch!! Thud!! Sometimes broken bat –Energy lost  lower COR, v f Reduced if … –Impact is at a node –f n  >1, where  ~ ms Calculate as non-uniform beam Accounting for COR: Dynamic Model for Ball-Bat Collision AMN, Am. J. Phys, 68, 979 (2000)

FSU Colloquium 9/1/05 9 Modal Analysis of a Baseball Bat frequency time f 1 = 179 Hz f 2 = 582 Hz f 3 = 1181 Hz f 4 = 1830 Hz

FSU Colloquium 9/1/05 10

FSU Colloquium 9/1/05 11 E vib vfvf e Vibrations, COR, and Sweet Spot Center of percussion (~27”) Node of fundamental (~27”) Maximum e (~29”) Minimum E vib (~29”) Maximum v f (29”) Don’t feel a thing (?) Node of 2 nd mode

FSU Colloquium 9/1/05 12 Experimental Data ball incident on bat at rest Conclusion: essential physics understood

FSU Colloquium 9/1/05 13 Boundary Conditions handle moves after ~0.6 ms ball leaves bat after ~0.6 ms  ball doesn’t “know” about far end of bat nothing on knob end matters: size, shape boundary conditions batter’s hands!

FSU Colloquium 9/1/05 14 Aluminum has thin shell –Less mass in barrel –easier to swing and control –but less effective at transferring energy  –Hoop modes –trampoline effect –larger COR Why Does Aluminum Outperform Wood?

FSU Colloquium 9/1/05 15 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” The “Trampoline” Effect: A Simple Physical Picture

FSU Colloquium 9/1/05 16 The Trampoline Effect: A Closer Look “hoop” modes: cos(n  ) k  (t/R) 3 : hoop mode largest in barrel f 2 (1-3 kHz) < 1/   energy mostly restored (unlike bending modes) “ping” Thanks to Dan Russell

FSU Colloquium 9/1/05 17 Verification from Crisco/Greenwald Study V f correlated with COR COR main factor for v f –inertial factors “cancel out” COR correlated with f hoop – f hoop main factor for v f wood

FSU Colloquium 9/1/05 18 Effect of Spin on Baseball Trajectory Drag: F d = ½ C D  Av 2 “Lift”: F L = C M  AR  v mg FdFd F L (Magnus)  C D, C M ~ (in direction leading edge is turning)

FSU Colloquium 9/1/05 19 Who is right? Hubbard vs. Adair: Large difference in F M at 100 mph 1.Hubbard (AJP, 71, 1152, 2003) 2.Adair, The Physics of Baseball, 3 rd Ed.

FSU Colloquium 9/1/05 20 New Experiment at Illinois Fire baseball horizontally from pitching machine Use motion capture to track ball over ~5m of flight and determine x 0,y 0,v x,v y, ,a y Use a y to determine Magnus force as function of v, 

FSU Colloquium 9/1/05 21 Motion Capture Experiment Joe Hopkins, Lance Chong, Hank Kaczmarski, AMN Two-wheel pitching machine Baseball with reflecting dot Motion Capture System

FSU Colloquium 9/1/05 22 Experiment: Sample MoCap Data y z topspin  a y > g y = ½ a y t 2

FSU Colloquium 9/1/05 23 (PRELIMINARY) Results Present data support Hubbard, not Adair --spin plays important role in flight of baseball More extensive experiment planned for early 2006

FSU Colloquium 9/1/05 24 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? Can Curveball Travel Farther than Fastball?

FSU Colloquium 9/1/05 25 Oblique Collisions: Leaving the No-Spin Zone Friction … sliding/rolling vs. gripping transverse velocity reduced, spin increased Familiar Results Balls hit to left/right break toward foul line Topspin gives tricky bounces in infield Pop fouls behind the plate curve back toward field Backspin keeps fly ball in air longer f

FSU Colloquium 9/1/05 26 Undercutting the ball  backspin Ball10 0 downward Bat 10 0 upward D = center-to-center offset trajectories

FSU Colloquium 9/1/05 27   larger for curveball Fastball: spin reverses Curveball: spin doesn’t reverse

FSU Colloquium 9/1/05 28 In summary…. Can a curveball be hit farther than a fastball? Higher pitch speed  higher hit ball speed on fastball But…more backspin on curve ball Net result: curveball goes farther –by a little bit Mont Hubbard, AJP 71, (2003) –See also February 2005 issue of AJP for a debate: Hubbard vs. Adair

FSU Colloquium 9/1/05 29 Work in Progress Collision experiments & calculations to elucidate trampoline effect New measurements of lift and drag Experiments on oblique collisions? –Rod Cross & AMN: rolling almost works at low speed –AMN: studies in progress at high speed

FSU Colloquium 9/1/05 30 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 – Go Red Sox!..and the Quantum Fielders too!