Why ------ 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

A Brief Outline Introduction How does a baseball bat work? Why is aluminum better than wood? And what’s the deal with a corked 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

How Does a Bat Work? When Ash Meets Cowhide A violent collision! 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! ©Champaign News-Gazette, April 19, 2003

baseball softball

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? speed of pitched ball speed of bat weight and weight distribution of bat “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

What does hit ball speed depend on? Weight and weight distribution of bat heavier bat is better …or is it? what is ideal bat weight? ….weight distribution? Bounciness of ball is it “juiced”? does it matter much? Impact location along bat “sweet spot”

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

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

Why Aluminum Outperforms Wood thin shell & plus weights on each end mass and balance point adjustable generally lighter and BP closer to hands easier to swing: higher bat speed, more control  but less effective at transferring energy  “trampoline” effect this is the principal advantage  net result: higher batted ball speed  higher batting average 

“Trampoline” Effect tennis ball/racket strings Softball/bat DEMO: DEAD BALL ON FLOOR, bongo paddle SUPERBALL ON FLOOR,bongo paddle The issue: springiness of surface. Bat compresses ball, ball compresses bat--same size force--which one gives depends on how easily compressed. NCAA: e<.228 Wood bat, for given force, compresses 2% of ball. Or…only 2% of energy in collision is stored in bat, rest is in ball. Makes no difference how much of energy stored in bat is returned Al bat: 10% in COR==>7 mph==>35’ or more Just like tennis racket....looser strings gives a higher ball speed! All sorts of tricks.....thinner wall..etc. More later. new rule changes in NCAA: e<.228 Better bat: a tennis racket Better ball: spherical metallic shell Golf: “spring-like” effect on drivers

So What’s the Deal with Corked Bats? ~1” diameter hole ~10” deep; fill with whatever similar to aluminum bat easier to swing and control  but less effective at transferring energy  Is there a “trampoline” effect from hole or filler? probably not  Net result: little or no effect for home run hitter  possible advantage for “contact” hitter 

Summary Lots of physics in baseball Knowledge of physics helps understanding and appreciation of the game And you get invited to fun things like this!