The Aerodynamics
of
Baseball
April 18, 2009
Outline
• Background
• Basic Physics of Flight
• Fly Ball
• Pitched Ball
• Questions
Glenn
Research
Why NASA? Center
Computational Fluid Dynamics
Glenn
Research
Why NASA? Center
Educational Outreach
Beginner’s Guide to Aeronautics
Glenn
Research
Why NASA? Center
Glenn
Research
Physics of Flight Center
Objects Respond Newton’s Laws
to External Forces of Motion
Glenn
Forces Research
Center
A Force is a Push or a Pull
A Force is a Vector Quantity
Direction
Vectors Scalars
Magnitude
Magnitude only
(Size)
Vectors: Velocity, Acceleration, Displacement, Force
Scalars: Temperature, Pressure, Density, Mass
Volume, Length, Area, Kinetic Energy, …
Glenn
Forces in Flight Research
Center
Aerodynamics
Drag
Lift
Flight
Center of Gravity Velocity
Center of Pressure
Weight
Glenn
Weight Research
Center
Baseball Rule Book
Weight = 5 oz
(actually 5/16 lb)
W = m g
Diameter = 2.875 to 3 inches
Weight
Glenn
Motion in Flight Research
Center
Neglect Aerodynamics
Newton’s 2nd Law
Flight
Velocity
F = m a (constant mass)
F = W = m g
F
a = = g
m
v = g t + v0
Weight
d = g t2 + v 0t + d 0
2
Vo = VL cos (a)
Uo = VL sin (a)
a
VL
HitModeler
http://www.grc.nasa.gov/WWW/K-12/airplane/hitmod.html
Glenn
Fly Ball Results Research
Center
Speed Angle Location Temp Press Wind Drag Distance
100 45 - - - - 0 669
Glenn
Air Research
Center
Mixture of Gases
Nitrogen N2 78%
Oxygen O 2 21%
Traces - CO 2 - H 2 O - …
Properties
Molecules in constant motion
Collide with each other and container
Mass (m) -> Density
Momentum (m V) -> Pressure
2
Kinetic Energy (m V ) -> Temperature
Viscosity , Compressibility
Glenn
Aerodynamic Drag Research
Center
Air Density r Sir George Cayley
Viscosity m 2
F ~ r V A
Size - Area A
Shape - Inclination - Viscosity
Velocity Modern Drag Equation
V 2
D = Cd r V A
2
Shape Cd = Coefficient contains effects of
Shape – Viscosity
Aerodynamic
Drag r V2 Dynamic Pressure
= depends on state of the gas
2
(pressure & temperature)
Glenn
Motion in Flight Research
Center
Include Aerodynamic Drag
Problem #1 Flow past a ball is highly unsteady
and can become chaotic
Drag
Time
Solution: Slight rotation of the ball pins
the separation point
Glenn
Motion in Flight Research
Center
Include Aerodynamics
Problem #2 Drag Coefficient for a Spinning Ball
Depends on Viscosity & Surface Details
,5 Smooth Ball
,3
Baseball
Cd Baseball Cd = .3
,1
1.0 Re x 10 -5 10.0
r V d
Reynolds Number = Re = Viscous Force = m
Inertial Forces
Glenn
Motion in Flight Research
Center
Include Aerodynamic Drag
Problem #3 Can’t use simplified Newton’s 2nd Law
D = function of V 2
F = W-D = m a
V = a t + V0
dV = F
Must Solve: m
dt
dV = 2 W - C d r V 2 A
dt 2 m
HitModeler
http://www.grc.nasa.gov/WWW/K-12/airplane/hitmod.html
Glenn
Fly Ball Results Research
Center
Speed Angle Location Temp Press Wind Drag Distance
100 45 - - - - 0 669
100 45 Cleve 60 29 0 .3 378
Glenn
Fly Ball Results Research
Center
Speed Angle Location Temp Press Wind Drag Distance
100 45 - - - - 0 669
100 45 Cleve 60 29 0 .3 378
100 45 Cleve 80 29 0 .3 385
Glenn
Fly Ball Results Research
Center
Speed Angle Location Temp Press Wind Drag Distance
100 45 - - - - 0 669
100 45 Cleve 60 29 0 .3 378
100 45 Cleve 80 29 0 .3 385
100 45 Cleve 32 29 0 .3 370
Glenn
Fly Ball Results Research
Center
Speed Angle Location Temp Press Wind Drag Distance
100 45 - - - - 0 669
100 45 Cleve 60 29 0 .3 378
100 45 Cleve 80 29 0 .3 385
100 45 Cleve 32 29 0 .3 370
100 45 Cleve 60 28 0 .3 384
Glenn
Fly Ball Results Research
Center
Speed Angle Location Temp Press Wind Drag Distance
100 45 - - - - 0 669
100 45 Cleve 60 29 0 .3 378
100 45 Cleve 80 29 0 .3 385
100 45 Cleve 32 29 0 .3 370
100 45 Cleve 60 28 0 .3 384
100 45 Cleve 60 29 +5 .3 410
Glenn
Fly Ball Results Research
Center
Speed Angle Location Temp Press Wind Drag Distance
100 45 - - - - 0 669
100 45 Cleve 60 29 0 .3 378
100 45 Cleve 80 29 0 .3 385
100 45 Cleve 32 29 0 .3 370
100 45 Cleve 60 28 0 .3 384
100 45 Cleve 60 29 +5 .3 410
100 45 Cleve 60 29 -5 .3 338
Glenn
Fly Ball Results Research
Center
Speed Angle Location Temp Press Wind Drag Distance
100 45 - - - - 0 669
100 45 Cleve 60 29 0 .3 378
100 45 Cleve 80 29 0 .3 385
100 45 Cleve 32 29 0 .3 370
100 45 Cleve 60 28 0 .3 384
100 45 Cleve 60 29 +5 .3 410
100 45 Cleve 60 29 -5 .3 338
100 45 Denver 60 24 0 .3 404
Glenn
Aerodynamic Lift Research
Center
Air Density r Sir George Cayley
Viscosity m 2
F ~ r V A
Size - Area A
Shape - Inclination - Viscosity
Velocity Modern Lift Equation
V 2
L = Cl r V A
Shape 2
Cl = Coefficient contains effects of
Spin Shape – Spin - Viscosity
Aerodynamic
r V2 Dynamic Pressure
Lift = depends on state of the gas
2
(pressure & temperature)
Moving with ball
Flow
Glenn
Aerodynamic Lift Research
Center
Air Density r Ideal Lift
Viscosity m 2
L ideal = N d d s r V
Size - Diameter d
N = numerical factor
Velocity Lift Equation
V
L = Cl L ideal
Shape
Cl = Coefficient contains effects of
Shape - Viscosity
Spin - s
Aerodynamic
Lift
Cl = .15
Ideal Trajectory
http://www.grc.nasa.gov/WWW/K-12/airplane/foilb.html
Glenn
Some Curve Ball Results Research
Center
A) 100 mph fast ball crosses plate in .44 sec
drops almost 3 feet from the pitcher’s hand
B) Curve ball (80 mph – 2000 rpm – axis vertical – Cleveland)
.54 sec - 20 inches side-to-side - drops 4.5 feet
C) Same as B except Hot Day (90 degrees) – loses 1.1 inch
Same as B except Cold Day (34 degrees) – adds 1.2 inch
D) Same as B except axis horizontal – no side-to side
ball drops 3 feet or 6 feet depending on orientation
No rising fastball (would need about 5000 rpm)
E) Changing axis between B & D gives large variation
Glenn
Some Curve Ball Results Research
Center
A) Curve ball (80 mph – 2000 rpm – axis vertical – Cleveland)
.54 sec - 20 inches side-to-side - drops 4.5 feet
B) Same as A except Denver (25 in Hg vs 29 in Hg)
loses 3.1 inches side-to-side
Denver is a bad place to pitch and a good place to hit!
C) A 100 mph fastball crosses the plate at
94 mph in Cleveland, 96 mph in Denver
Glenn
Conclusions Research
Center
A) Aerodynamics has a big effect on the game of baseball
B) Understanding these effects explain observations about
different ballparks and different pitchers / hitters at
various times during the season and post-season
C) Software is available for you to learn some more about
baseball and aerodynamics. You can play on-line or
download the software (Java source is supplied).
Search on “ NASA Baseball”
D) GO TRIBE !!
Glenn
Advertisements Research
Center
A) May 13 and May 28 - WKYC Weather Days
B) June 27 – 28 NASA Days with the Tribe
special Kid’s events and exhibits
C) GO TRIBE !!
Questions?
Backups
Drag
Time
Drag of a smooth ball ---- Knuckle Ball
Glenn
Fly Ball Results Research
Center
Speed Angle Location Temp Press Wind Drag Distance
100 45 - - - - 0 669
100 45 Cleve 60 29 0 .3 378
100 45 Cleve 90 29 0 .3 387
100 45 Cleve 35 29 0 .3 370
100 45 Cleve 60 28 0 .3 384
100 45 Cleve 60 29 +5 .3 417
100 45 Cleve 60 29 -5 .3 338
100 45 Denver 60 24 0 .3 405