The Physics of Hitting a Home Run ANL Colloquium, September 20, 2002 Alan M. Nat
Green, G. Richard, Food & Wine Editor has reference to this Academic Journal, PHwiki organized this Journal The Physics of Hitting a Home Run ANL Colloquium, September 20, 2002 Alan M. Nathan University of Illinois at Urbana-Champaign email@example.com Introduction Model as long as colinear ball-bat collisions some applicatons Beginners guide to aerodynamics Model as long as oblique ball-bat collisions some applications Summary & Conclusions http://www.npl.uiuc.edu/~a-nathan/pob Baseball in addition to Physics As smart as he was, Albert Einstein could not figure out how to h in addition to le those tricky bounces at third base.
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Philosophical Notes: the physics of baseball is not the clean, well-defined physics of fundamental matters but the ill-defined physics of the complex world in which we live, where elements are not ideally simple in addition to the physicist must make best judgments on matters that are not simply calculable Hence conclusions about the physics of baseball must depend on approximations in addition to estimates .But estimates are part of the physicists repertoire a competent physicist should be able to estimate anything –Bob Adair in The Physics of Baseball, May, 1995 issue of Physics Today The physicists model of the game must fit the game. Our aim is not to re as long as m baseball but to underst in addition to it. Hitting the Baseball the most difficult thing to do in sports -Ted Williams: 1918-2002 BA: .344 SA: .634 OBP: .483 HR: 521 Introduction: Description of Ball-Bat Collision as long as ces large (>8000 lbs!) time short (<1/1000 sec!) ball compresses, stops, exp in addition to s kinetic energy potential energy lots of energy lost bat is flexible h in addition to s dont matter to hit a home run large hit ball speed optimum take-off angle backspin The Ball-Bat Collision: Kinematics vf = eA vball + (1+eA) vbat Conclusion: vbat matters much more than vball eA Collision Efficiency property of ball & bat weakly dependent on vrel Superball-wall: eA 1 Ball-Bat near sweet spot: eA 0.2 vf 0.2 vball + 1.2 vbat What Does eA Depend On Heavier bat is better but . What is Ideal Bat Weight Note: Batters seem to prefer lighter bats! Actually, Scaling with Iknob better vBAT(6) = 1.2 mph/(1000 oz-in2) (vf=1.5 0.3 mph) Energy Dissipation: the ball-bat COR (e) Coefficient Of Restitution in CM frame: Ef/Ei = e2 ball on hard floor: e2 = hf/hi 0.25 e 0.5 (note: r=0.25, e=0.5 eA =0.2) ~3/4 CM energy dissipated! depends (weakly) on impact speed the bat matters too! vibrations trampoline effect Aside: Effect of Juiced Ball MLB: e = 0.546 0.032 @ 58 mph on massive rigid surface 10% increase in COR ~30-35 ft increase in distance Collision excites bending vibrations in bat Ouch!! Thud!! Sometimes broken bat Energy lost lower e, vf Find lowest mode by tapping Reduced considerably if Impact is at a node Collision time (~0.6 ms) > TN see AMN, Am. J. Phys, 68, 979 (2000) Accounting as long as Energy Dissipation: Dynamic Model as long as Ball-Bat Colllision Dynamic Model Normal Modes of the Bat Louisville Slugger R161 (33, 31 oz) Can easily be measured: Modal Analysis
frequency barrel node Expt Calc Expt Calc 179 177 26.5 26.6 582 583 27.8 28.2 1181 1179 29.0 29.2 1830 1821 30.0 29.9 Measurements via Modal Analysis Louisville Slugger R161 (33, 31 oz) Conclusion: free vibrations of bat can be well characterized FFT Theory vs. Experiment: Louisville Slugger R161 33-inch/31-oz. wood bat Conclusion: essential physics understood only lowest mode excited lowest 4 modes excited Time evolution of the bat 0.6 ms h in addition to s dont matter
Effect of Bat on COR: Vibrations COR maximum near 2nd node Putting Everything Together sweet spot depends on collision efficiency recoil factor COR how bat is swung vf = eA vball + (1+eA) vbat Conclusion: ideal ball-bat collision can be simulated
Wood versus Aluminum Kinematics Length, weight, MOI decoupled shell thickness, added weight fatter barrel, thinner h in addition to le weight distribution more uni as long as m CM closer to h in addition to le less mass at contact point easier to swing Dynamics Stiffer as long as bending Less vibrational energy More compressible COR larger The Trampoline Effect Compressional energy shared between ball in addition to bat PEbat/PEball = kball/kbat 1 PEball mostly dissipated (75%) Wood Bat hard to compress little effect on COR: BPF 1 Aluminum Bat compressible through shell modes kball/kbat ~ 0.10 (more or less) PEbat mostly restored (more on this later) COR larger: BPF 1.1 (more or less) The Trampoline Effect: A Closer Look Bending Modes vs. Shell Modes k R4: large in barrel little energy stored f (170 Hz, etc) > 1/ energy goes into vibrations k (t/R)3: small in barrel more energy stored f (2-3 kHz) < 1/ energy mostly restored
Wood versus Aluminum: Dynamics of Trampoline Effect bell modes: ping of bat Want k small to maximize stored energy Want >>1 to minimize retained energy Conclusion: there is an optimum Where Does the Energy Go 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
Not Corked DATA Corked COR: 0.445 0.005 0.444 0.005 Conclusions: no tramopline effect! corked bat is WORSE even with higher vbat Baseball Research Center, UML, Sherwood & amn, Aug. 2001 calculation Aerodynamics of a Baseball Forces on Moving Baseball No Spin Boundary layer separation DRAG! FD=½ CDAv2 With Spin Ball deflects wake ==>lift FM ~ RdFD/dv Force in direction front of ball is turning Drawing courtesty of Peter Brancazio
Typical Trajectories Some Practical/Interesting Questions Does more friction help Can a curveball be hit further than a fastball Summary in addition to Conclusions Some aspects of baseball are amenable to physics analysis Kinematic in addition to dynamics of ball-bat collision Trajectory of a ball with drag in addition to lift Can underst in addition to ing these things improve our ability to play the game Almost surely NOT Can underst in addition to ing these things enhance our own enjoyment of the game For me, a resounding YES I hope as long as you also
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