1. 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
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. 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

3. 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

4. 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!

5. 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

6. 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”)

7. 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
Collision is very inefficient
perfect efficiency: 0.2/1.21.0/2.0

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

9. 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’

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

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

12. 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

13. 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

14. 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’

15. 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

16. 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

17. 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

18. 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

19. Spin and the Magnus Force
Backspin (RPM) optimum angle distance ft ft ft ft ft ft

20. 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

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