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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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Af 202 chris dimoulis

AF 202 – Chris Dimoulis

Advanced Aerodynamics


A little bit of Theory

A little bit of Physics

A little bit of Math

A whole lot of fun!


Leading edge

Trailing edge

Chord Line


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:





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.





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).


We feel weight

It is equally opposed by the ground.

Therefore there is no acceleration


Opposes weight

Acts perpendicular to the flight path

Occurs at the center of lift/pressure


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


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


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


Velocity Angle of Attack

100 5 degrees

90 6 degrees

80 8 degrees

70 10 degrees

60 13 degrees

50 16 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?


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



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








Drag is the rearward acting force opposing thrust

Two types



Parasite drag
Parasite Drag

Three Types of Parasite Drag

Form Drag

Skin Friction


Increases when speedincreases (exponential)

Induced drag
Induced Drag

Inherent whenever a wing produces lift

Increases when speed decreases


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

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


Forward force pulling/pushing plane through the air.


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?


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

Propeller efficiency
Propeller Efficiency

No Propeller is 100% Efficient

Effecitve Pitch

Geometric Pitch


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

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