The Aerodynamicsof

Baseball

April 18, 2009

Outline

• Background

• Basic Physics of Flight

• Fly Ball

• Pitched Ball

• Questions

Why NASA?

Computational Fluid Dynamics

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Why NASA?

Educational OutreachBeginner’s Guide to Aeronautics

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Why NASA?GlennResearchCenter

Physics of Flight

Objects Respond to External Forces

Newton’s Laws of Motion

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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

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Forces in Flight

Flight Velocity

Weight

LiftDrag

Aerodynamics

Center of GravityCenter of Pressure

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Weight

Weight

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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

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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

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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

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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

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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

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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

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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

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Speed Angle DistanceDragLocation Temp Press

100 45 - - - 0

Wind- 669

100 45 Cleve 60 29 0 .3 378

Fly Ball Results

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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

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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

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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

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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

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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 !!

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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

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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