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The Aerodynamicsof
Baseball
April 18, 2009
Outline
• Background
• Basic Physics of Flight
• Fly Ball
• Pitched Ball
• Questions
Why NASA?
Computational Fluid Dynamics
GlennResearchCenter
Why NASA?
Educational OutreachBeginner’s Guide to Aeronautics
GlennResearchCenter
Why NASA?GlennResearchCenter
Physics of Flight
Objects Respond to External Forces
Newton’s Laws of Motion
GlennResearchCenter
Forces
A Force is a Push or a Pull A Force is a Vector Quantity
Vectors: Velocity, Acceleration, Displacement, Force
Scalars: Temperature, Pressure, Density, Mass Volume, Length, Area, Kinetic Energy, …
Magnitude (Size)
Direction
Vectors
Scalars
Magnitude only
GlennResearchCenter
Forces in Flight
Flight Velocity
Weight
LiftDrag
Aerodynamics
Center of GravityCenter of Pressure
GlennResearchCenter
Weight
Weight
GlennResearchCenter
W = m g
Baseball Rule Book
Weight = 5 oz
(actually 5/16 lb)
Diameter = 2.875 to 3 inches
Motion in Flight
Flight Velocity
Weight
Neglect Aerodynamics
GlennResearchCenter
F = m a
a = F m
v = g t + v 0
d = g t + v t + d 0 0 2
2
Newton’s 2nd Law
F = W = m g
(constant mass)
= g
VL
V = V cos (a)Lo
a
U = V sin (a)o L
HitModeler
http://www.grc.nasa.gov/WWW/K-12/airplane/hitmod.html
Fly Ball ResultsGlennResearchCenter
Speed Angle DistanceDragLocation Temp Press
100 45 - - - 0
Wind- 669
Properties
GlennResearchCenter
Air
Nitrogen N 78%Oxygen O 21%Traces - CO - H O - …
Mixture of Gases 2
2
2 2
Molecules in constant motionCollide with each other and container
Mass (m) -> Density
Momentum (m V) -> Pressure
Kinetic Energy (m V ) -> Temperature 2
Viscosity , Compressibility
Aerodynamic Drag
Velocity V
Aerodynamic Drag
Sir George Cayley
GlennResearchCenter
2
2
D = Cd V A
F ~ V A
Shape - Inclination - Viscosity Size - Area A
Air Density Viscosity
Shape
Modern Drag Equation 2
Cd = Coefficient contains effects of Shape – Viscosity
Dynamic Pressure depends on state of the gas (pressure & temperature)
V
2
2 =
Motion in FlightInclude Aerodynamic Drag
GlennResearchCenter
Problem #1
Solution: Slight rotation of the ball pins the separation point
Time
Drag
Flow past a ball is highly unsteady and can become chaotic
Motion in FlightInclude Aerodynamics
GlennResearchCenter
Problem #2 Drag Coefficient for a Spinning Ball Depends on Viscosity & Surface Details
Re x 101.0 10.0
Reynolds Number = Re = Viscous Force Inertial Forces
= V d
Cd
,5
,3
,1
Smooth Ball
Baseball
-5
Cd = .3 Baseball
Motion in FlightInclude Aerodynamic Drag
GlennResearchCenter
V = a t + V 0
Problem #3
F = W - D = m a
Can’t use simplified Newton’s 2nd Law
D = function of V 2
Must Solve:
dV 2 W C V A dt 2 m
= - 2 d
dV dt
= F m
HitModeler
http://www.grc.nasa.gov/WWW/K-12/airplane/hitmod.html
GlennResearchCenter
Speed Angle DistanceDragLocation Temp Press
100 45 - - - 0
Wind- 669
100 45 Cleve 60 29 0 .3 378
Fly Ball Results
GlennResearchCenter
Speed Angle DistanceDragLocation Temp Press
100 45 - - - 0
Wind- 669
100 45 Cleve 60 29 0 .3 378100 45 Cleve 80 29 0 .3 385
Fly Ball Results
GlennResearchCenter
Speed Angle DistanceDragLocation Temp Press
100 45 - - - 0
Wind- 669
100 45 Cleve 60 29 0 .3 378100 45 Cleve 80 29 0 .3 385100 45 Cleve 32 29 0 .3 370
Fly Ball Results
GlennResearchCenter
Speed Angle DistanceDragLocation Temp Press
100 45 - - - 0
Wind- 669
100 45 Cleve 60 29 0 .3 378100 45 Cleve 80 29 0 .3 385100 45 Cleve 32 29 0 .3 370
100 45 Cleve 60 28 0 .3 384
Fly Ball Results
GlennResearchCenter
Speed Angle DistanceDragLocation Temp Press
100 45 - - - 0
Wind- 669
100 45 Cleve 60 29 0 .3 378100 45 Cleve 80 29 0 .3 385100 45 Cleve 32 29 0 .3 370
100 45 Cleve 60 28 0 .3 384
100 45 Cleve 60 29 +5 .3 410
Fly Ball Results
GlennResearchCenter
Speed Angle DistanceDragLocation Temp Press
100 45 - - - 0
Wind- 669
100 45 Cleve 60 29 0 .3 378100 45 Cleve 80 29 0 .3 385100 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
Fly Ball Results
GlennResearchCenter
Speed Angle DistanceDragLocation Temp Press
100 45 - - - 0
Wind- 669
100 45 Cleve 60 29 0 .3 378100 45 Cleve 80 29 0 .3 385100 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
Fly Ball Results
Aerodynamic Lift
Velocity V
Aerodynamic Lift
Sir George Cayley
GlennResearchCenter
2
2
L = Cl V A
F ~ V A
Shape - Inclination - Viscosity Size - Area A
Air Density Viscosity
Shape
Modern Lift Equation 2
Cl = Coefficient contains effects of Shape – Spin - Viscosity
Dynamic Pressure depends on state of the gas (pressure & temperature)
V
2
2 =
Spin
Flow
Moving with ball
Aerodynamic Lift
Velocity V
Ideal Lift
GlennResearchCenter
2
L = Cl L ideal
L ideal = N d d s V Size - Diameter d
Air Density Viscosity
Shape
Lift Equation
Cl = Coefficient contains effects of Shape - Viscosity
Spin - sAerodynamic Lift Cl = .15
N = numerical factor
Ideal Trajectory
http://www.grc.nasa.gov/WWW/K-12/airplane/foilb.html
Some Curve Ball ResultsGlennResearchCenter
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
Some Curve Ball ResultsGlennResearchCenter
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
ConclusionsGlennResearchCenter
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 !!
AdvertisementsGlennResearchCenter
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
Time
Drag
Drag of a smooth ball ---- Knuckle Ball
GlennResearchCenter
Speed Angle DistanceDragLocation Temp Press
100 45 - - - 0
Wind- 669
100 45 Cleve 60 29 0 .3 378100 45 Cleve 90 29 0 .3 387100 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
Fly Ball Results