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