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Advanced Aerodynamics 2

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AF 202 – Chris Dimoulis

Advanced Aerodynamics 2

Review

Vectors

Forces in climbs and turns

Stability

Vg diagram

Force:

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

The 4 forces of flight

Weight

Lift

Thrust

Drag

Acceleration:

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.

Opposes Weight

Must EQUAL weight for level flight

2 principles cause lift:

Bernoulli’s

Newton’s 3rd law

Four ways to control lift

Pilot Controlled:

Change Speed

Change Angle of Attack

Non-Pilot Controlled

Change Wing Surface Area

Change Air Density

L=1/2 (CL V² Ρ A)

V = √2L/ (CL Ρ A)

CL = 2L/(V² Ρ A)

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

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.

Opposes Thrust

2 Types

Parasite Drag

Induced Drag

3 Types

Form

Skin-Friction

Interference

Parasite drag INCREASES as speed increases

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.

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.

No Propeller is 100% Efficient

Effecitve Pitch

Geometric Pitch

Slippage

Asymmetrical Thrust (P-Factor)

Gyroscopic Precession

Spiraling Slipstream

Torque from the engine

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

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

As a climb begins, lift BRIEFLY exceeds weight.

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?

Weight now has a rearward component

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.

Thrust and Lift now have vertical and horizontal components

Therefore you can say…

The vertical component of lift PLUS…

The vertical component of thrust EQUALS…

The total weight

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.

Lift remains perpendicular to the wings

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

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

The vertical component is opposing weight and responsible for pitch.

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

30 bank

45 bank

30

45

Right Triangles:

cos θ = A/H

sin θ = O/H

H = Hypotenuse

A = Side adjacent to θ

O = Side opposite to θ

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.

{

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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

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

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.

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

LF = Wing Loading/Gross Weight

Wing loading = 4800 lbs

Gross Weight = 2400 lbs

Load Factor = 4800/2400 = 2g

BASICALLY – LF = Lift/Weight

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

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

Lateral

Longitudinal

Vertical

Stability about the lateral axis affects pitch

Stability about the longitudinal axis affects roll

Stability about the vertical axis affects yaw

Static Stability – The initial tendency back to equilibrium

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

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:

Maneuverability

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

Controllability

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

Longitudinal stability is about the lateral axis

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

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

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 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