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AF 202 – Chris Dimoulis. Advanced Aerodynamics 2. Objectives. Review Vectors Forces in climbs and turns Stability Vg diagram. Force. Force: Any influence to an object that causes a change in speed, direction, or shape. The 4 forces of flight Weight Lift Thrust Drag.

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Af 202 chris dimoulis

AF 202 – Chris Dimoulis

Advanced Aerodynamics 2




Forces in climbs and turns


Vg diagram



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

The 4 forces of flight





To accelerate or not
To Accelerate or not…?


A change in speed OR direction which requires an unbalanced forces

Straight, level, and constant speed flight required an equilibrium balance of the forces

Opposing forces are equal

Lift = Weight, Thrust = Drag


Weight is a force

In F=ma, the acceleration is the pull of gravity

As long as an object has mass (and is on earth) there is the downward force of gravity.

Advanced aerodynamics 2

Opposes Weight

Must EQUAL weight for level flight

2 principles cause lift:


Newton’s 3rd law

Advanced aerodynamics 2

Four ways to control lift

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)

V = √2L/ (CL Ρ A)

CL = 2L/(V² Ρ A)

Lift equation
Lift Equation

L - Total lift

CL - Coefficient of lift increases as Angle of attack increases

V – Magnitude of velocity (speed)

A – Area of the Wing

P – Air Density

Uses of the lift equation
Uses of the Lift Equation

To simulate level flight, keep L the same value

We can see how the angle of attack MUST increases as speed slows

We see that as angle of attack decreases we must increase speed to maintain lift.

Advanced aerodynamics 2

Opposes Thrust

2 Types

Parasite Drag

Induced Drag

Parasite drag
Parasite Drag

3 Types




Parasite drag INCREASES as speed increases

Induced drag
Induced Drag

Inherently created when lift is produced by use of angle of attack

As angle of attack increases, induced drag increases

Since angle of attack increases when speed degreases, induced drag ALSO increases when speed decreases.

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)


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.

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

Adverse yaw
Adverse Yaw

When rolling into a bank…

Lift is increased on the outside wing

Lift is decreased on the inside wing

When lift changes so does drag

Drag is increased on the outside wing

Drag is decreased on the inside wing

The aircraft pulls outside of the turn

Vectors forces in climbs
VectorsForces in Climbs


Remember that a force can be considered a vector

Vectors consist of magnitude and direction

They can be broken down into components


The components are PERPENDICULAR to each other

You can add 2 vectors together by adding the horizontal vectors and vertical vectors

Forces in a climb
Forces in a Climb

As a climb begins, lift BRIEFLY exceeds weight.

Forces in a climb1
Forces in a Climb

The brief increase in lift increases drag

If you do not add power you will slow down

Once established, angle of attack decreases which decreases drag

Total drag still remains higher. It does not return to normal…WHY?

Forces in a climb2
Forces in a Climb

Weight now has a rearward component

Forces in a climb3
Forces in a Climb

Total drag now equals the Drag vector PLUS the rearward component of weight

This is why adding power is needed to MAINTAIN airspeed in a climb

Thrust = drag + the rearward component of weight.

Forces in a climb4
Forces in a Climb

Thrust and Lift now have vertical and horizontal components

Forces in a climb5
Forces in a climb

Therefore you can say…

The vertical component of lift PLUS…

The vertical component of thrust EQUALS…

The total weight

Forces in a climb6
Forces in a climb

Or more simply that the OPPOSING forces in a constant rate constant speed climb are equal.

But lift does NOT necessarily = weight and thrust does NOT necessarily = drag

Thought the values of some of the forces may be generally lower than in straight and level flight.

Forces in turns1
Forces in Turns

Lift remains perpendicular to the wings

When the aircraft is banked, lift can be broken down into components

Forces in turns2
Forces in Turns

Once in a turn, the horizontal component is responsible for turning.

The vertical component is opposing weight and responsible for pitch.

Forces in turns3
Forces in Turns

For the vertical component of lift to equal weight, Total Lift must be increased.

This is done by increasing angle of attack

This increases induced drag which will slow us down

And so we need to add power to maintain speed.

The math of turns
The Math of Turns

The angle of bank EQUALS the angle between the Total lift and Vertical Component of lift.

30 bank

45 bank



The math of turns1
The Math of Turns

Right Triangles:

cos θ = A/H

sin θ = O/H

H = Hypotenuse

A = Side adjacent to θ

O = Side opposite to θ

The math of turns2
The Math of Turns

So we can say this

cos θ = Vertical Lift / Total Lift

sin θ = Horizontal Lift / Total Lift

Total Lift x cos θ = Vertical Lift

Vertical Lift / cos θ = Total Lift

Total Lift x Sin θ = Horizontal Lift

Horizontal Lift / sin θ = Total Lift

θ = The angle of Bank.



Forces in turns4
Forces in Turns

What happens when we bank without increasing lift (Use 1.0g for lift)

Total Lift x cos θ = Vertical Lift

1.0g x cos 15 = .96g

1.0g x cos 30 = .86g

1.0g x cos 45 = .70g

Vertical Lift does NOT equal weight

Forces in turns5
Forces in Turns

Vertical Lift must equal weight. Make vertical lift = 1.0g and see what total lift you get.

Vertical Lift / cos θ = Total Lift

1.0g/cos 15 = 1.03g

1.0g/cos 30 = 1.15g

1.0g/cos 45 = 1.41g

Forces in turns6
Forces in Turns

So we can see that as the angle of bank increases, the more TOTAL LIFT we need to remain level

So as bank angle increases, angle of attack must increase also.

Load factor
Load Factor

Opposing total lift is something called Load Factor.

Load Factor is measured in g’s. If the load on the airplane is Xg’s then the load factor is X times it’s weight.

The ratio between total load on wings and the gross weight of aircraft

Load factor1
Load Factor

LF = Wing Loading/Gross Weight

Wing loading = 4800 lbs

Gross Weight = 2400 lbs

Load Factor = 4800/2400 = 2g

BASICALLY – LF = Lift/Weight

Load factor2
Load Factor

In a turn, Load Factor is equal to the Total Lift.

Load factor3
Load Factor

So using our formula for Total lift, we also know the Load Factor

Load Factor at 60 degrees?

1.0g/cos 60 = 2.0g

1.0g/cos 70 = 2.9g


The axes of an airplane





Stability about the lateral axis affects pitch

Stability about the longitudinal axis affects roll

Stability about the vertical axis affects yaw

Types of stability
Types of Stability

Static Stability – The initial tendency back to equilibrium

Dynamic Stability – The tendency over time of the aircraft to return to equilibrium

Types of stability1
Types of Stability

Positive Stability – Tendency to return to equilibrium

Neutral Stability– Tendency to remain in new condition

Negative Stability – Tendency to continue to away from equilibrium

e.g. – Negative Static or Positive Dynamic


Stability effects:


The quality of an aircraft that permits it to be maneuvered easily and to withstand the stresses imposed by maneuvers


The quality of the aircraft’s response to the pilot’s control application when maneuvering the aircraft.

Longitudinal stability
Longitudinal Stability

Longitudinal stability is about the lateral axis

Longitudinal stability1
Longitudinal Stability

Three things affect Longitudinal Stability

Location of Wing with respect to CG

Location of the Horizontal Stabilizer with respect to CG

Area of size of the tail surface

Longitudinal stability2
Longitudinal Stability

Downwash of air from the wings strikes the top of the horizontal stabilizer producing downward pressure.

Lateral stability roll
Lateral Stability (Roll)

Lateral stability is about the Longitudinal axis.

Lateral Stability is most commonly attained by adding a dihedral to the wings


Wings are built 1-3 degrees above perpendicular to the longitudinal axis

Wind striking the plane may cause one wing to rise putting the plane in a bank.

With Dihedral the wind strikes the lower wing with a higher Angle of Attack

Vertical stability yaw
Vertical Stability (Yaw)

Vertical Stability is about the vertical axis.

It is the vertical stabilizer that gives the aircraft stability

Like a weather vane

Like the keel on a ship