Page 1 Did Sammy Sosa Take Physics 101 Alan M. Nathan University of Illinois at Urbana-Champaign Georgetown Colloquium, April 6, 2004 June 3, 2003

Page 2 Is There an Advantage to “Corking” a Bat?...or is the cork better left in the wine bottle?

Page 3 Does Corking the Bat Give an Advantage? A Physicist’s Approach l Introduction: The Ball-Bat Collision l Kinematics l Dynamics: a long (but interesting) detour l Kinematics revisited l Hitting the Ball Squarely...or not Pitching and Hitting, Thinking and Guessing l Summary/Conclusions

Page Solvay Conference: Greatest physics team ever assembled Baseball and Physics 1927 Yankees: Greatest baseball team ever assembled MVP’s

Page 5 Introduction: Description of Ball-Bat Collision l forces large (>8000 lbs!) l time short (<1/1000 sec!) l ball compresses, stops, expands  kinetic energy  potential energy  lots of energy lost l bat is flexible  it compresses too l to hit a home run...  large hit ball speed  optimum take-off angle  backspin Courtesy of CE Composites

Page 6 Kinematics of Ball-Bat Collision v ball v bat vfvf r: bat recoil factor = m ball /M bat,eff  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 eAeA 1+ e A

Page 7 Kinematics of Ball-Bat Collision For maximum v f : r = m ball /M bat,eff small  M bat,eff large M bat,eff  I h /z 2 v bat large v bat ~ (I h ) -x e large v ball v bat vfvf Z a tradeoff

Page 8 The v bat -M bat tradeoff: General Considerations 0  n  0.5 are physically sensible bounds

Page 9 Swinging the Bat

Page 10 Thanks to J. J. Crisco & R. Greenwald Medicine & Science in Sports & Exercise 34(10): ; Oct 2002 Experimental Swing Speed Studies

Page 11 z x Crisco/Greenwald Batting Cage Study: College Baseball Z 0.8” X 3”  45 rad/s v bat vs. z  70 28”

Page 12   I -n knob n = 0.31  % reduction in I gives ~4% increase in bat speed bat speed versus MOI v bat  I -0.3 v bat  I -0.5

Page 13 Recent ASA Slow-Pitch Softball Field Tests ( L. V. Smith, J. Broker, AMN) Conclusions: bat speed more a function of mass distribution than mass n~ 0.25 fixed M fixed MOI knob

Page 14 The v bat -M bat tradeoff revisited Looks like corking reduces v f ! More later...

Page 15 Kinematics of Ball-Bat Collision For maximum v f : r = m ball /M bat,eff small  M bat,eff large M bat,eff  I h /z 2 v bat large v bat ~ (I h ) -x v ball v bat vfvf Z a wash—at best e large  what about this?

Page 16 l Collision excites bending vibrations in bat  Ouch!! Thud!! Sometimes broken bat  Energy lost  lower e, v f l Find lowest mode by tapping l Reduced considerably if  Impact is at a node  Collision time (~0.6 ms) > T N Accounting for Energy Dissipation: Dynamics of Ball-Bat Colllision

Page y z y A Dynamic Model of the Bat-Ball Collision Solve eigenvalue problem for free oscillations (F=0)  normal modes (y n,  n ) Model ball-bat force F Expand y in normal modes Solve coupled equations of motion for ball, bat ‡ Note for experts: full Timoshenko (nonuniform) beam theory used Euler-Bernoulli Beam Theory ‡

Modal Analysis of a Baseball Bat frequency time f 1 = 179 Hz f 2 = 582 Hz f 3 = 1181 Hz f 4 = 1830 Hz

Page 19 f 1 = 179 Hz f 2 = 582 Hz Effect of Bat Vibrations on COR COR depends strongly on impact location E vib vfvf COR

Page 20 Relation to Reality: Experimental Data Ball incident on bat at rest Conclusion: essential physics understood only lowest mode excited lowest 4 modes excited

Page 21 time evolution of bat rigid-body motion develops only after few ms far end of bat has no effect on ball  knob moves after >0.6 ms  collision over after 0.6 ms  nothing on knob end matters size, shape boundary conditions hands

Page 22 Why is Aluminum Different (Better)? Inertial differences Hollow shell  more uniform mass distribution  effectively, less mass near impact location swing speed higher  ~cancels for many bats   definite advantage for “contact” hitter Dynamic differences Ball-Bat COR significantly larger for aluminum (“trampoline effect”)

Page 23 Aluminum Bats: The “Trampoline” Effect: l Ball and bat mutually compress each other  Compressional energy shared  Essential parameter: k bat /k ball large for wood; smaller for Al l Ball inefficient, bat efficient at returning energy l Net effect: less overall energy dissipation l Effect occurs in tennis, golf, aluminum bats,...  >20% increase in COR! Demo

Page 24 “Corking” a Wood Bat (illegal!) ~1” hole, 10” deep + filler Is there a trampoline effect? MOVIE

Page 25 Conclusion: no trampoline effect! COR Measurements Lloyd Smith,Dan Russell, AMN, July %

Page 26 Kinematics and Swing Speed, Revisted V bat dependence on I: ~ I -n : purely phenomenological ~ (I+I 0 ) -1/2 : fixed energy shared between bat (I) and batter (I 0 ) Sosa   Nomar Conclusions: under most swing speed scenarios, increased swing speed does not compensate for reduced e A “anti-corking” is probably better

Page 27 “Hitting is timing; pitching is upsetting timing” Subtle Effects where Corking May Help Bat Control Hitting and Pitching, Thinking and Guessing “Hitting is fifty percent above the shoulders” 1955 Topps cards from my personal collection

Page 28 Graphic courtesy of Bob Adair and NYT Hitting, Pitching, and Thinking

Page 29 Quick Guide to Aerodynamics: Effect of Spin on Trajectory Drag Force opposite to velocity vector Magnus Force in direction the leading edge is turning --curve balls break --backspin keeps fly ball in air longer

Page 30 Oblique Collisions: Leaving the No-Spin Zone --Oblique collisions and friction cause hit ball to spin --Early or later: sidespin --Undercut: backspin --Overcut: topspin f

Page 31 Application: Swinging Early or Late Initial takeoff angle down the line Balls hit to left or right curve towards foul line 90 mph pitch misjudged by 3 mph (!) over last 30’ --swing is early or late by ~7 ms --ball goes down the line and curves foul

Page 32 Application: Hitting Strategies and Undercutting the Ball Ball10 0 downward Bat 10 0 upward D = center-to-center offset fastball Can a curveball be hit farther than a fastball?

Page 33 And Finally.... fastball Ball10 0 downward Bat 10 0 upward D = center-to-center offset

Page 34 Summary l Kinematic factors do not favor corked bat  Higher swing speed does not compensate reduced collision efficiency l No evidence for trampoline effect in corked bat l Corked bat can help in subtle ways  bat control  bat acceleration Sammy probably didn’t take Physics 101!...but he may have taken Biology 101!