# Aerodynamics

Font Size: Larger /Smaller

## 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
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