1. Why
Hitting Home Runs: How a Physicist Thinks About Baseball Alan M. Nathan University of Illinois at Urbana-Champaign
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

2. 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

3. 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:
OBP: .483

4. 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

5. 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

6. baseball
softball

7. 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

8. 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”)

9. Pitched Ball and Bat Speeds
My only formula
vhit = 0.2 vball vbat
example: 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

10. 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”

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

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

13. 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 

14. “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

15. 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 

16. 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!