Baseball: It's Not Nuclear Physics (or is it?!)
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Transcript Baseball: It's Not Nuclear Physics (or is it?!)
The Physics of Baseball
(or…Just How Did McGwire Hit 70?)
Alan M. Nathan
University of Illinois
February 5, 1999
Introduction
Hitting the Baseball
The Flight of the Baseball
Pitching the Baseball
Summary
Physics of Baseball: Page 1
REFERENCES
The Physics of Baseball, Robert K. Adair (Harper
Collins, New York, 1990), ISBN 0-06-096461-8
The Sporting Life, Davis and Stephens (Henry Holt and
Company, New York, 1997), ISBN 0-8050-4540-6
http://www.exploratorium.edu/sports
ME!
» [email protected]
» www.npl.uiuc.edu/~nathan
Physics of Baseball: Page 2
Hitting the Baseball
“...the most difficult thing to
do in sports”
--Ted Williams,
Professor Emeritus of
Hitting
Physics of Baseball: Page 3
Speed of Hit Ball:
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
Physics of Baseball: Page 4
What Determines Batted Ball Speed?
How does batted ball speed depend on ...
pitched ball speed?
bat speed?
V = 0.25 Vball + 1.25 Vbat
Conclusion:
Bat Speed Matters More!
Physics of Baseball: Page 5
What Determines Batted Ball Speed?
Mass of bat
Conclusion:
mass of bat matters
...but not a lot
Physics of Baseball: Page 6
Dynamics of Ball-Bat Collision
Ball compresses
kinetic energy stored in “spring”
Ball expands
kinetic 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!
Physics of Baseball: Page 7
Dynamics of Ball-Bat Collision
after
Ball compresses
kinetic energy stored in “spring”
Ball expands
kinetic energy restored but...
during
before
70% of energy is lost!
(heat, deformation,vibrations,...)
Forces are large (>5000 lbs!)
Time is short (<1/1000 sec!)
The hands don’t matter!
Physics of Baseball: Page 8
The Coefficient of Restitution
COR measures “bounciness” of ball
Final speed/Initial speed
For baseball, COR=.52-.58
Changing COR by .05 changes V by 7 mph (35 ft!)
How to measure?
This is square of COR------->
Physics of Baseball: Page 9
What About the Bat?
(or, it takes two to tango!)
Wood Bat
Efficiently restores energy
But only 2% energy stored
Bat Performance Factor (BPF) ~1 .02
Aluminum Bat
Stores ~ 20% energy
Efficiently restores energy
Result: “trampoline effect”
» BPF ~ 1.2
» Ball flies off the bat!
A more efficient bat and/or ball
Physics of Baseball: Page 10
Properties 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
vibrational nodes and frequencies
Physics of Baseball: Page 11
Sweet Spot #1: Center of Percussion
When ball strikes bat...
Linear recoil
» conservation of momentum
Rotation about center of mass
» conservation of angular momentum
When CP hit
The two motions cancel at handle
No reaction force felt at handle
Physics of Baseball: Page 12
Sweet Spot #2: Maximum Energy Transfer
Barrel end of bat maximizes
bat speed
Center of Mass minimizes
angular impulse
MET must be in between
Not on COP!
CM COP
Aluminum bat more effective
for inside pitches
Physics of Baseball: Page 13
Sweet Spot #3: “Node” of Vibration
Collision excites bending
vibrations in bat
Ouch!!
Energy lost ==>lower COR
Sometimes broken bat
Reduced considerably if collision
is a node of fundamental mode
Fundamental node easy to find
For an interesting discussion, see
www.physics.usyd.edu.au/~cross
Physics of Baseball: Page 14
So you think bats cannot bend…..
Physics of Baseball: Page 15
So you think bats cannot bend…..
Physics of Baseball: Page 16
How Would a Physicist Design a Bat?
Wood Bat
already optimally designed
» highly constrained by rules!
a marvel of evolution!
Aluminum Bat
lots of possibilities exist
but not much scientific research
a great opportunity for ...
» fame
» fortune
Physics of Baseball: Page 17
Advantages of Aluminum
Length and weight “decoupled”
Can adjust shell thickness
More compressible => “springier”
Trampoline effect
More of weight closer to hands
Easier to swing
Less rotational energy transferred to bat
More forgiving on inside pitches
Stiffer for bending
Less energy lost due to vibrations
Physics of Baseball: Page 18
Aerodynamics of a Baseball
Forces on Moving Baseball
No Spin
Boundary layer separation
DRAG!
Grows with v2
With Spin
Ball deflects wake
action/reaction==>Magnus force
» Force grows with rpm
Pop
Pbot tom
» Force in direction front of ball is
turning
Physics of Baseball: Page 19
The Flight of the Balll
Role of Drag
Role of Spin
Atmospheric conditions
Temperature
Humidity
Altitude
Air pressure
Wind
Physics of Baseball: Page 20
The Home Run Swing
• Ball arrives on 100 downward trajectory
• Big Mac swings up at 250
• Ball takes off at 350
•The optimum home run angle!
Physics of Baseball: Page 21
Physics of Baseball: Page 22
The Role of Friction
Friction induces spin for
oblique collisions
Spin => Magnus force
Results
Balls hit to left/right
break toward foul line
Backspin keeps fly ball
in air longer
Topspin gives tricky
bounces in infield
Pop fouls behind the
plate curve back toward
field
Physics of Baseball: Page 23
Pitching the Baseball
“Hitting is timing. Pitching is
upsetting timing”
---Warren Spahn
Don Larsen, 1956 World Series
Last pitch of perfect game
vary speeds
manipulate air flow
orient stitches
Physics of Baseball: Page 24
Drag/Weight or Magnus/Weight
Let’s Get Quantitative!
I. How Large are the Forces?
2
1.5
Drag/Weight
1
Magnus/Weight
0.5
0
0
25
50
75
100
Speed in mph
125
150
• Drag is comparable to weight
• Magnus force < 1/4 weight)
Physics of Baseball: Page 25
Depends on…
Magnitude and direction of force
Time over which force acts
Calibration
90 mph fastball drops 3.5’ due to
gravity alone
Ball reaches home plate in ~0.45
seconds
Half of deflection occurs in last 15’
Drag reduces fastball by about 8
mph
Examples:
Hop of 90 mph fastball: ~4”
Break of 70 mph curveball ~16”
» slower
» force larger
Drag/Weight or Magnus/Weight
Let’s Get Quantitative!
II. How Much Does the Ball Break?
2
1.5
Drag/Weight
1
Magnus/Weight
0.5
0
0
25
50
75
100
Speed in mph
125
150
Physics of Baseball: Page 26
Example 1: Fastball
85-95 mph
1600 rpm (back)
12 revolutions
0.46 sec
M/W~0.1
Physics of Baseball: Page 27
Example 2: Split-Finger Fastball
85-90 mph
1300 rpm (top)
12 revolutions
0.46 sec
M/W~0.1
Physics of Baseball: Page 28
Example 3: Curveball
70-80 mph
1900 rpm
(top and side)
17 revolutions
0.55 sec
M/W~0.25
Physics of Baseball: Page 29
Example 4: Slider
75-85 mph
1700 rpm (side)
14 revolutions
0.51 sec
M/W~0.15
Physics of Baseball: Page 30
Vertical Position of Ball (feet)
Examples of Trajectories
7
6
5
90 mph Fastball
4
3
0
10
20
30
40
50
60
Horizontal Deflection of Ball (feet)
Distance from Pitcher (feet)
1.2
1
75 mph Curveball
0.8
0.6
0.4
0.2
0
0
10
20
30
40
50
60
Distance from Pitcher (feet)
Physics of Baseball: Page 31
Effect of the Stitches
Obstructions cause turbulance
Turbulance reduces drag
Dimples on golf ball
Stitches on baseball
Asymmetric obstructions
Knuckleball
Two-seam vs. four-seam delivery
Scuffball and “juiced” ball
Physics of Baseball: Page 32
Summary
Much of baseball can be understood with
basic principles of physics
Conservation of momentum, angular momentum, energy
Dynamics of collisions
Trajectories under influence of forces
» gravity, drag, Magnus,….
There is probably much more that we don’t understand
Don’t let either of these interfere with your
enjoyment of the game!
Physics of Baseball: Page 33