Hitting Home Runs: How a Physicist Thinks About Baseball Alan M Hitting Home Runs: How a Physicist Thinks About Baseball Alan M. Nathan University of Illinois at Urbana-Champaign a-nathan@uiuc.edu http://www.npl.uiuc.edu/~a-nathan/pob 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 PROPS: wood bat aluminum bat baseball happy/sad balls bongo paddle flexible meter stick tennis racket

Hitting the Baseball “...the most difficult thing in sports” #521, last at-bat September 28, 1960 “...the most difficult thing in sports” --Ted Williams BA: .344 SA: .634 HR: 521 OBP: .483

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 mis-estimates speed by 1.5 mph (0.007 sec) swing will be early/late by 1’ elevation of ball misjudged by 1” backspin/topspin makes ball fall less/more Warren Spahn (greatest lefthander?) said: “Hitting is timing. Pitching is upsetting timing.” 30% success rate gets you in Hall of Fame! 400 ms travel time but only about 100 ms to observe

When Ash Meets Cowhide A violent collision! hands don’t matter! forces large (>8000 lbs!) time is short (<1/1000 sec!) ball compresses, stops, expands kinetic energy  potential energy lots of energy dissipated distortion of ball and bat hands don’t matter!

To Hit a Home Run…. Large hit ball speed Proper takeoff angle vhit  105 mph  D  400 ft each additional mph gives 4-5 ft Proper takeoff angle about 350 Lots of backspin

Speed of Hit Ball: What does it depend on? The basic stuff (“kinematics”) speed of pitched ball speed of bat weight and weight distribution of bat The really interesting stuff (“dynamics”) “bounciness” of ball impact location on bat (“sweet spot”)

Pitched Ball and Bat Speeds My only formula vhit = 0.2 vball + 1.2 vbat example: 90 + 70 gives 102 mph (~400”) Bat speed matters much more! Each mph of bat speed worth 5 ft Each mph of pitch speed worth 1 ft Collision is very inefficient perfect efficiency: 0.2/1.21.0/2.0

Weight and Weight Distribution of Bat vhit = 0.2 vball + 1.2 vbat CM recoil rotation For given bat speed, heavier bat is better 0.2/1.2 0.5/1.5 But….

The Coefficient Of Restitution: Energy Dissipation in Ball COR measures “bounciness” of ball Final speed/Initial speed (from massive rigid surface) For baseball, COR 0.5 hf/hi = 3/4 3/4 energy lost! Is the ball “juiced”? 10% change  30’

The Sweet Spot of the Bat Bat Vibrations Collision excites bending vibrations in bat Ouch!! Thud!! Sometimes broken bat Energy lost  lower COR

Effect of Vibrations on Hit Ball Speed nodes Center of mass “sweet spot” zone

Wood versus Aluminum thin shell & added mass mass, mass distribution, length independent lighter and CG closer to hands …easier to swing fatter barrel, thinner handle more forgiving on mis-hits “trampoline” effect golf drivers tennis rackets corked bats? Net result: higher batted ball speed

Aerodynamics of Ball in Flight Forces on Moving Baseball Without Spin: Ball pushes air out of way Low-pressure wake  DRAG! Grows with square of velocity With Spin: Ball deflects wake action/reaction  “Magnus force” Force grows with rpm Force in direction front of ball is turning Curveball fastball SFFB

The Flight of the Ball Real Baseball vs. Physics 101 Baseball ROLE OF DRAG: factor of 2 in distance optimum angle from 45 deg to 35 deg not parabolic orbit (outfielders know this! ball goes up, then “dies” and just sort of falls MAGNUS: keeps ball in air longer. Esp impt for golf. 100’ altitude +7’ 10 deg air temp +4’ 10 deg ball temp +4’ 1” drop in barometer +6’ 1 mph following wind +3’ ball at 100% humidity -30’ hit along foul line +11’

Friction between ball and bat Spin on the Hit Ball Friction between ball and bat  spin on ball Bat undercuts ball  ball goes up backspin

Friction between ball and bat Spin on the Hit Ball Friction between ball and bat  spin on ball Bat overcuts ball  ball goes down topspin

Friction between ball and bat Spin on the Hit Ball Friction between ball and bat  spin on ball Swing early/late  ball goes left/right sidespin

Spin and the Magnus Force 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

Spin and the Magnus Force Backspin (RPM) optimum angle distance 0 360 355 ft 500 350 361 ft 1000 340 368 ft 1500 320 375 ft 2000 310 382 ft 2500 290 389 ft

The Home Run Swing Ball arrives on 8.5o downward trajectory Big Mac swings up at 8.5o Undercuts ball by ~1” Ball takes off at 35o with lots of backspin The optimum home run swing! So how does he do it? Strong==>ability to get high bat speed quickly; good technique Show movie of #70 NOTE: 10o is ideal “contact” angle

Summary Lots of physics in baseball Knowledge of physics helps understanding of game And it’s fun too….