Af 202 chris dimoulis
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AF 202 – Chris Dimoulis. Advanced Aerodynamics. Objectives. A little bit of Theory A little bit of Physics A little bit of Math A whole lot of fun!. Definitions. Leading edge Trailing edge Chord Line. Definitions. Relative Wind Angle of Attack. Aerodynamic Forces. What is a force?

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Advanced Aerodynamics

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Af 202 chris dimoulis

AF 202 – Chris Dimoulis

Advanced Aerodynamics


Objectives

Objectives

A little bit of Theory

A little bit of Physics

A little bit of Math

A whole lot of fun!


Definitions

Definitions

Leading edge

Trailing edge

Chord Line


Definitions1

Definitions

Relative Wind

Angle of Attack


Aerodynamic forces

Aerodynamic Forces

What is a force?

Any influence to an object that causes a change in speed, direction, or shape.

What is acceleration?

A change in velocity (speed and direction)

An unbalanced force is required for an acceleration.

Force, acceleration, velocity are ‘vectors’


Aerodynamic forces1

Aerodynamic Forces

The most known force formula:

Force = Mass x Acceleration

You can rewrite this to say that:

Acceleration = Force/Mass


Forces on airplanes

Forces on Airplanes

The 4 Airplane Forces are:

Weight

Lift

Thrust

Drag


Level constant speed flight

Level/Constant Speed Flight

Remember what an acceleration is

Change of speed and/or direction

Requires and unbalanced force

Opposing forces must be equal

Thrust = Drag

Lift = Weight


Unbalanced forces

Unbalanced Forces

If weight and lift are not balanced…

Weight > Lift = Airplane decends

Lift > Weight = Airplane pitches up (NOT CLIMB!!!!)

If thrust and drag are not balanced…

Thrust > Drag = Aircraft speeds up

Drag > Thrust = Aircraft slows down


The mathematical way

The Mathematical Way

It is simply a matter of adding the vectors together…

The resulting force is…

This will produce an acceleration in the direction of that force.

-90

100

10


Weight

Weight

Weight is a force

The acceleration in F=ma is the pull of gravity (9.8 m/s2)

The total weight of your plane is the downward force applied at the center of gravity (CG).


Weight1

Weight

We feel weight

It is equally opposed by the ground.

Therefore there is no acceleration


Advanced aerodynamics

Lift

Opposes weight

Acts perpendicular to the flight path

Occurs at the center of lift/pressure


Advanced aerodynamics

Lift

Two principles are used to explain lift:

Bernoulli’s Principle

Newton’s 3rd law of motion


Bernoulli s principle

Bernoulli’s Principle

When the velocity increases the pressure decreases


Bernoulli s principle1

Bernoulli’s Principle

High pressure always seeks a low pressure

High pressure below the wing applies a force upward


Newton s 3 rd law

Newton’s 3rd Law

For every action there is an equal and opposite reaction


Advanced aerodynamics

Lift

What ways can lift be changed?

Pilot Controlled:

Change Speed

Change Angle of Attack

Non-Pilot Controlled

Change Wing Surface Area

Change Air Density


The lift equation

The Lift Equation

L=1/2 (CL V² Ρ A)

CL= Coefficient of Lift

V = Velocity (ft per sec)

1 knot = 6076 ft/hr = 1.68527 ft/sec

P = Air Density

A = Wing Surface Area (sq.ft.)


The coefficient of lift

The Coefficient of Lift

The coefficient of Lift increase as Angle of Attack increases


Lift equation

Lift Equation

Velocity also has a great impact.

Velocity increases – Lift Increases

Air density and the design of the wing have an affect, but cannot be changed by the pilot


Air density table

Air Density Table

Altitude Density Speed of Sound

(Feet) (d) (Knots)

0 .002377 661.7

1,000 .002308 659.5

2,000 .002241 657.2

3,000 .002175 654.9

4,000 .002111 652.6

5,000 .002048 650.3


Lift equation example

Lift Equation Example

Angle of Attack = 5 degrees

Coefficient of lift = .4

Airspeed = 100 knots = 607600 ft/hr = 168.7 ft per sec

Air density = .002175 (3000 feet)

Wing surface area of 172 = 174 sq.ft.

L = .5(.4 x 168.72 x .002175 x 174)

Lift = 2154 lbs


A little change

A little change…

Increase the speed to say… 150 knots and let’s see what happens

150 knots = 253.167 ft/sec

L = .5(.4 x 253.1672 x .002175 x 174)

L = 4853 lbs

THAT’S 2G’S AT FULL WEIGHT


How great an equation

How great an equation!!!

With just a little rearranging we can learn other wonderful things about lift

Rearrange for velocity and we can see what angle of attack will do to it (assuming you remain level)

Rearrange for Coefficient of Lift to see what Angle of Attack you need for a given Air speed


Velocity vs angle of attack

Velocity vs Angle of Attack

Keep L = 2154 lbs. for level flight

V = SqRt(2L/ (CL Ρ A))

Make the Angle of Attack 10 degrees

Coefficient of lift = .8

V = SqRt(4308/(.8 x .002175 x 174))

V = 119.2 ft/sec

V = 70 knots


Angle of attack vs velocity

Angle of Attack vs Velocity

Once again keep lift at 2154 lbs.

CL = 2L/(V² Ρ A)

Slow airspeed from 100 to 80 knots

80 knots = 135 ft/sec

CL= 4308/(1352 x .002175 x 174)

CL = .62

Angle = 8 degrees


So we can see a pattern

So we can see a pattern

ASSUMING LEVEL FLIGHT IS MAINTAINED

VelocityAngle of Attack

1005 degrees

906 degrees

808 degrees

7010 degrees

6013 degrees

5016 degrees


Velocity and angle of attack

Velocity and Angle of Attack

As Angle of Attack increases we decrease speed

As speed decreases we need to increase angle of attack to maintain lift

As speed increases we must decrease angle of attack.


Critical angle of attack

Critical Angle of Attack

Airplane stalls at Critical Angle of Attack

An airplane can stall at any airspeed

Why then do we have Vso and Vs?


Stalls

Stalls

The Airplane will stall at the critical angle of attack regardless of

Speed

Pitch

Angle of Bank

Below Vso and Vs you the required angle of attack to produce lift is beyond the critical angle of attack


On the topic of stalls

On the topic of stalls…

Types of stalls

Landing

Takeoff

Trim

Cross-Control

Secondary

Accelerated


Advanced aerodynamics

Drag

Drag is the rearward acting force opposing thrust

Two types

Parasite

Induced


Parasite drag

Parasite Drag

Three Types of Parasite Drag

Form Drag

Skin Friction

Interference

Increases when speedincreases (exponential)


Induced drag

Induced Drag

Inherent whenever a wing produces lift

Increases when speed decreases

WHY??????


Induced drag1

Induced Drag

As speed decreases we need to increase angle of attack

Induced drag increases as AOA increases


Induced drag2

Induced Drag

Induced Drag is also caused by wingtip vortices

High pressure below the wing is pulled toward the low pressure above the wing.


Drag formula

Drag Formula

D =1/2 (Cd V² Ρ A)

Cd = Coefficient of Drag

V = Velocity (ft per sec)

P = Air Density

A = Wing Area (Sq.Ft.)


So let s test it

So let’s test it

Speed = 100 knots = 168 ft/sec

Air Density = .002175

Wing Area = 174 sq.ft.

Angle of Attack = 2 degrees

Coefficient of Drag= .03

D = .5(.03 x 1682 x 174 x .002175)

D = 160 lbs of Drag


Parasite vs induced drag

Parasite vs. Induced Drag


Region of reverse command

Region of Reverse Command

After a certain speed drag increases and so the required thrust increases.

Region of reverse command refers to the need for MORE power to fly SLOWER speeds

This is reversed from normal (hopefully that is obvious to you)


Ground effect

Ground Effect

As one enters ground effect, much of the downwash, upwash, and wingtip vortices are reduced effectively increasing your Coefficient of Lift


Thrust

Thrust

Forward force pulling/pushing plane through the air.


Thrust1

Thrust

Thrust is most easily described as lift in the horizontal direction

The propeller aerodynamically functions similar to a wing

By spinning it creates its own relative wind.

Why does the propeller have a twist in it?


Thrust2

Thrust

Just like with lift, thrust on the propeller increases with angle of attack and with speed.

The outside of the propeller spins faster thus requiring a smaller pitch


Thrust3

Thrust


Propeller efficiency

Propeller Efficiency

No Propeller is 100% Efficient

Effecitve Pitch

Geometric Pitch

Slippage


Turning tendencies

Turning Tendencies

Asymmetrical Thrust (P-Factor)

Gyroscopic Precession

Spiraling Slipstream

Torque from the engine


Asymmetrical thrust

Asymmetrical Thrust

When pitching up, the angle on the DOWNWARD moving blade is greater than that on the upward moving blade. Causes a left yaw.


Gyroscopic precession

Gyroscopic Precession

A gyroscope is basically something that spins

A force applied to a spinning object is felt 90 degrees in the direction of rotation.

Pitch up – right yaw

Pitch down – left yaw


Gyroscopic precession1

Gyroscopic Precession


Spiraling slipstream

Spiraling Slipstream

The slipstream strikes the left side of the rudder yawing tail right and the nose left


Torque of the engine

Torque of the Engine

The engine is rotating Clockwise from a pilot’s view. The opposing reaction makes the plane want to bank left


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