## Commercial Ground School AVF 221

## Aerodynamics

Lift

1. Airstream velocity V (knots)

2. Air density ratio (sigma)

3. Airfoil planform area square feet

4. Profile shape of the airfoil

5. Viscosity of the air

6. Compressibility effects

7. Angle of attack (degrees)

Lift

We know that lift is produced by low pressure above and high pressure below

We also know that lift is the force acting perpendicular to the relative wind

And that any increase in alpha will generate an increase in drag

Drag acts parallel to the flight path

In all steady state flight lift=weight and thrust=drag

This is true in a descent

Also true in a steady climb

However in initiating a climb an alpha change is needed to change the pitch

Once airspeed stabilizes we are again in steady state

Any given alpha has a corresponding airspeed to achieve steady state

As speed slows, alpha is increased to provide sufficient lift

As altitude increases, a higher TAS is needed to provide sufficient lift

Remember that if the V is doubled it is at the square so lift goes up 4 times as much

Lift

There are 3 basic ways lift is generated on an airfoil:

Bernoulli’s Principle

Deflection (Newton)

Downwash (Newton)

This is a bit of an over simplification of how lift is generated however

Lift generation, the real story

There are 3 concepts to lift generation

Conservation of momentum

Conservation of energy

Conservation of mass

Newton’s laws explain the conservation of momentum

Every action has an opposite and equal reaction

Bernoulli’s equation explains the conservation of energy

Static pressure + Dynamic pressure = Total pressure

Euler equations explain the conservation of mass

This is where it gets messy

Lift generation, the real story

The Euler equations are a series of calculus equations that relate 2 dimensions of velocity along x and y axis along with pressure and density

All equations must be solved simultaneously

This area of study is called Computational Fluid Dynamics

Engineers use this method to determine the conservation of mass airflow around the airfoil

Lift myths

Equal transit theory

Venturi flow

Skipping stone theory

Lift the Coanda effect

The Coanda effect (pronounced cwanda)

This explains the air’s tendency to stick to a surface and bend around the curved portion of the upper surface

Newton’s law then takes over explaining the force generated by the bending of the air stream

As air flows over a curved surface, a negative pressure results which pulls the flow toward the airfoil’s surface

Back to the Lift Equation

Of all the variables in the lift equation, CL is probably the least understood so let’s look at that

A coefficient is defined as a dimensionless number made up of some number of variables

In this case, airfoil shape and angle of attack

The dimensions are worked out as the result of a ratio which eliminates them to keep our formula from getting messy, mathematically speaking

So the CL is a measurement of an airfoils lifting capacity with regards to shape and alpha

CL

The neat thing about CL is we can graph it to get a better handle on it

As you can see CL increases with alpha to the point of CL MAX which is our stall alpha

2 things to note:

Symmetrical airfoils start at 0

The more curvature to the airfoil the sharper CL MAX drops at the point of stall

Practical Application

So just by looking at the airfoil a pilot can get a good idea of what the stall characteristics are

Large thick airfoils give lots of lift at slow speeds but have a high drag penalty at higher speeds

Skinny airfoils give less lift at slow airspeeds and require flaps or slats to generate lift needed to land but have less drag penalties at higher speeds

Airfoils

Pressure patterns on airfoils

Note the difference of pitching moments

Wing Planforms

Wing planforms influence lift patterns

Note the rectangular wing stall pattern

Washout

Any change in alpha influences 3 things:

Lift

Drag

Airspeed

Any change in alpha also controls the distribution of positive and negative pressures along that wing

Wing Design

Wing design is a series of compromises

For example a tapered wing has better high speed performance than the rectangular wing

However, stall characteristics are worse

This may be solved by

Geometric wing twist

Adding slots

Stall strips

Spanwise airfoil variation (like a propeller)

In addition tip tanks may effectively increase aspect ratio (span/chord)

Flaps

In addition to the 4 types of flaps, Kershner adds the zap flap

This is a split flap that slides rearward adding surface area

Remember the main function of flaps is to produce more lift at landing speeds while lowering the stall speed

Since the fowler flap generates the most lift it also generates the most pitching moment when deployed

Slots and Slats

Leading edge slots keep the air smooth at high alphas

They are usually placed near the wingtip to keep the ailerons effective

Slats are moveable leading edge vanes that form slots

Both increase the CL MAX

Spoilers

Found on high speed jets and gliders

They disrupt the airflow over the wing and reduce lift

This in turn makes braking more effective

They may be deployed automatically or manually

Drag

Drag is the component of the aerodynamic force that is parallel to the relative wind and retards the forward motion of the aircraft.

Drag

The Drag equation is:

The coefficient of drag is the ratio of the drag pressure to the dynamic pressure.

Drag like lift is proportional to the dynamic pressure of the air and the area on which it acts.

The equation is much like the lift equation except that it measures the force in the stream-wise direction or parallel to the flow.

The Cd is obtained from wind tunnel testing

Also note that the S is replaced with an A for area

Also note that V occurs at the square, so double V and drag goes up 4 times as much

Induced Drag

Induced drag is drag generated by the production of lift or more accurately by the production of wingtip vortices.

The DI formula is:

or

Induced Drag

Low pressure on top and high pressure underneath induces a vortex to form at each tip, causing a downward push on the air leaving the trailing edge.

This downward component known as downwash, causes the airstream to depart at an angle downward from the incoming air.

The lift vector being perpendicular to the flow, is now tilted backward at half the downwash angle.

Induced Drag

This means some lift is being generated opposite to the flight path this rearward component is by definition drag.

Induced drag is influenced by the CL and aspect ratio.

It increases directly as the square of CL and inversely as the aspect ratio.

This inverse relationship is why long skinny wings generate higher CL

Induced Drag

At low speed and low aspect ratio (short wings) induced drag is greatest.

Induced drag varies inversely with the velocity squared.

Aspect ratio = span (b)/chord (c)

high = glider wing

low = jet fighter wing

Parasite Drag

Parasite drag is the drag caused by protuberances and increases directly with the velocity squared.

The Dp formula is:

Parasite Drag

Ski

n Friction – Drag caused by rivets, dirty surfaces, effects boundary layer

Form Drag – caused by the shape of the surface

Interference – collision of boundary layers of different surfaces

Leakage – pressure differences inside and outside the plane, like cracks in door seals

Profile – drag with regards to moving helicopter rotors

Drag Definitions pg 72

Total drag

Total drag is the sum of induced drag and parasite drag

Ground effect

Ground effect usually happens when within one wingspan of the ground.

The surface actually helps destroy the downwash generated by the wingtip vortices and thus forces the lift vector more to the vertical thereby reducing drag.

Note; span is represented by b and height by h

Ground effect

Above 1 span length there is little or no ground effect

At 3/10 span length there is a reduction of 20% induced drag

For our planes that’s 9 feet up

At 1/10 span length there is a reduction of 50% induced drag

For our planes that’s 3 feet up

Ground effect

There is also a change in the effective angle of attack. Because of the altered downwash, an angle of attack increase is the result

Pitching moments develop downward for an aircraft entering ground effect because of the wings downwash not being able to help the tail generate lift downward.

Ground effect

Pitching moments develop upward for the aircraft leaving ground effect and may cause an increase in angle of attack such that the corresponding increase in drag may cause the aircraft to settle.

The pitch up and down moments are experienced entering and leaving ground effect

Level flight in ground effect results in a significant pitch up requiring a substantial force on the yoke to keep the nose down

Ground Effect

There may be an increase in static pressure if the ports are below the wing. This will result in a decrease of airspeed the closer the plane gets to the ground or water.

Ground Effect Summary

On entering ground effect:

Induced drag is decreased

Nose-down pitching moments occur

Airspeed may indicate slow

On leaving ground effect

Induced drag is increased

Nose-up pitching moments occur

Airspeed may indicate higher

Thrust

There is a difference between aircraft that produce thrust and ones that produce power.

The turbojet, fanjet, ramjet, scramjet and rocket are examples of thrust producing power plants.

Thrust is measured in pounds.

Fuel burn is proportional to thrust

Which in turn affects range and endurance

In turbojet aircraft the engine produces thrust directly.

In prop aircraft, the powerplant does not produce thrust directly.

The engine produces power which turns the prop.

The prop is what produces the thrust.

Thrust

The piston engine and turbo prop are examples of power producing aircraft.

Power is measured in horsepower.

Performance considerations are then based on the amount of thrust or the amount of power respectively.

For example, fuel flow for a turbofan engine would be related to thrust whereas the fuel flow for a piston would be related to power

Each pound of drag requires a pound of thrust to offset

Thrust Required for Jets

Since 1lb of thrust is required to offset 1lb of drag, we may use the Total drag curve as a thrust required (TR) curve for jets

Thrust Required Curve

At stall, drag is about 2000lbs

At 485kts drag is also about 2000lbs

Dmin occurs at L/Dmax about 240kts

Note the sharp increase about 600kts

Mach 1 is 661.5kts sea level standard day

Thrust available and Thrust required

If thrust available is equal to the thrust required, the plane can fly straight and level but cannot accelerate or climb.

This is because drag and thrust are balanced

Power Required Curve for Props

The Thrust required curve or drag curve must be converted into power required using this formula:

Induced drag varies inversely as V2

Induced power varies inversely of the V ratio

Parasite drag varies directly as V2

Ppower varies directly as the V ratio is cubed (V3 )

Power Required Curve

Total power required is Ipower + Ppower

The power required curve is flatter in the low speed region than the Thrust required but steeper in the high speed region.

The intersection of the Ppower and Ipower curves is the L/Dmax

The Prop

For a prop plane the greatest thrust is full power, not moving

Referred to as static condition or static rpm

As airspeed is increased, thrust decreases

Alpha on the prop decreases as forward speed increases

This is due to the change in relative wind

The Prop

Since the prop is a rotating airfoil, it is subject to all the same conditions as wing

Geometric pitch is the distance covered if the prop moved through a medium like jello with no slippage

Effective pitch is the actual distance the prop covers in the air, accounts for slippage

We will cover more about props during systems

The 4 left turning forces

Torque

Action of the engine/prop turning clockwise causes a counterclockwise turn or left bank

Slipstream

Rotational velocity imparted by the prop forces the tail right

Gyroscopic Precession

Force is felt 90° in the direction of rotation

P-Factor

Thrust on the downward blade is more than on the upward blade