GWU Colloquium, October 21, 1999 Page 1 Baseball: It’s Not Nuclear Baseball: It’s Not Nuclear Physics Physics (or is it?!) (or is it?!) Alan M. Nathan Alan M. Nathan University of Illinois University of Illinois GWU Colloquium, October 21, 1999 GWU Colloquium, October 21, 1999 Introduction Introduction Hitting the Baseball Hitting the Baseball The Flight of the Baseball The Flight of the Baseball Pitching the Baseball Pitching the Baseball Summary
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GWU Colloquium, October 21, 1999 Page 1 Baseball: It’s Not Nuclear Physics (or is it?!) Alan M. Nathan University of Illinois GWU Colloquium, October 21,
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GWU Colloquium, October 21, 1999 Page 1
Baseball: It’s Not Nuclear PhysicsBaseball: It’s Not Nuclear Physics(or is it?!)(or is it?!)
Alan M. Nathan Alan M. Nathan
University of IllinoisUniversity of IllinoisGWU Colloquium, October 21, 1999GWU Colloquium, October 21, 1999
IntroductionIntroduction
Hitting the BaseballHitting the Baseball
The Flight of the BaseballThe Flight of the Baseball
Pitching the BaseballPitching the Baseball
Summary
GWU Colloquium, October 21, 1999 Page 2
REFERENCESREFERENCES
The Physics of Baseball, Robert K. Adair (Harper Collins,
New York, 1990), ISBN 0-06-096461-8
The Physics of Sports, Angelo Armenti (American Institute of Physics, New York, 1992), ISBN 0-88318-946-1
www.physics.usyd.edu.au/~cross
L. L. Van Zandt, AJP 60, 72 (1991)
www.npl.uiuc.edu/~a-nathan
GWU Colloquium, October 21, 1999 Page 3
Hitting the BaseballHitting the Baseball
“...the most difficult thing to do in sports”
--Ted Williams
BA: .344SA: .634OBP: .483HR: 521
GWU Colloquium, October 21, 1999 Page 4
Speed of Hit Ball:Speed of Hit Ball:What does it depend on?What does it depend on?
Speed is important: 105 mph gives ~400 ft each mph is worth 5 ft
The basic stuff (“kinematics”)
speed of pitched ball
speed of bat
weight of bat The really interesting stuff (“dynamics”)
“bounciness” of ball and bat
weight distribution of bat
vibrations of bat
GWU Colloquium, October 21, 1999 Page 5
What Determines Batted Ball Speed?What Determines Batted Ball Speed?
1. pitched ball speed
2. bat speed
Rigid-Body Kinematics:
Conclusion:Bat Speed Matters More!
V = 0.25 Vball + 1.25 Vbat
20
40
60
80
100
120
140
160
180
0 20 40 60 80 100speed of pitched ball or bat (mph)
vary pitched ball speed
vary bat speed
GWU Colloquium, October 21, 1999 Page 6
40
50
60
70
80
90
100
20 30 40 50 60
mass of bat (oz)
constant bat energy
constant bat+batter energy
60
70
80
90
100
110
120
20 30 40 50 60
mass of bat (oz)
constant bat energy
constant bat speed
constant bat+batter energy
What Determines Batted Ball Speed?What Determines Batted Ball Speed?
3. Mass of bat larger mass lower bat speed
Conclusion:mass of bat matters….but not a lot
bat speed vs mass
ball speed vs mass
GWU Colloquium, October 21, 1999 Page 7
What Determines Batted Ball Speed? What Determines Batted Ball Speed?
4. Inelasticity Ball compresses
kinetic energy stored in “spring”
Ball expandskinetic energy restored but...
70% of energy is lost!
(heat, deformation,vibrations,...)
Forces are large (>5000 lbs!)
Time is short (<1/1000 sec!)
The hands don’t matter!
0
1000
2000
3000
4000
5000
6000
0 0.2 0.4 0.6 0.8 1
Time in milliseconds
0
2000
4000
6000
8000
1 104
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
force (pounds)
compression (inches)
approx quadratic
GWU Colloquium, October 21, 1999 Page 8
Inelasticity: The Inelasticity: The CCoefficient oefficient oof f RRestitutionestitution
COR = Vrel,f/Vrel,I COR2 = KEcm,f /KEcm,i
For baseball, COR=.52-.58 Changing COR by .05 changes V by 7 mph (35 ft!)
How to measure? Bounce ball off hard surface COR2 = hf/hi
0
50
100
150
200
0 0.2 0.4 0.6 0.8 1COR
GWU Colloquium, October 21, 1999 Page 9
Energy shared between ball and bat
Ball is inefficient: 25% returned
Wood Bat r~0.02 80% restored
COReff = 0.50-0.51
Aluminum Bat
r~0.10 80% restored COReff = 0.55-0.58
“trampoline effect”
ball flies off the bat!
What About the Bat?What About the Bat?(or, it takes two to tango!)(or, it takes two to tango!)
r Ebat/Eball kball/kbat xbat/ xball
>10% larger!
GWU Colloquium, October 21, 1999 Page 10
Properties of BatsProperties of Bats
length, diameter weight position of center of gravity
where does it balance? distribution of weight
moment of inertia center of percussion stiffness and elasticity