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**Basic Aerodynamic Theory**

ATC Chapters 1 & 6

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Aim To introduce basic aerodynamic theory to a sufficient level to be able to understand chapter 6 of ATC BAK

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**Objectives State the how lift is produced**

State the lift formula and its proportional values Name the control surfaces and the axis around which the aircraft rotates Show arrangement of forces during S & L State the meaning of, and factors affecting stability

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**P+V=C 1. Lift Bernoulli's Theorem**

“In the streamlined flow of an ideal fluid, the sum of all the energies remains constant” At low airspeeds air acts like a fluid therefore we can say… Static pressure + Dynamic pressure = Constant Dynamic pressure is caused by movement of an object therefore we can say… Pressure (pressure energy) + Velocity (Kinetic energy) = Constant P+V=C

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**1. Lift Bernoulli's Theorem P+V=C P+V=C P+V=C**

To prove the theory we can look at a venturi. A venturi is a converging, diverging duct As air flows through a venturi it’s speed increases. Since energy is being conserved it’s pressure decreases. As it passes into the divergent duct pressure increases, velocity decreases If we look at the shape of the bottom half of the venturi it looks like the top of our wing P+V=C P+V=C P+V=C

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**1. Lift Bernoulli's Theorem**

As air flows over the top surface of an aerofoil it is accelerated, therefore pressure is… Reduced The pressure difference between the low pressure on the top of the wing and relatively higher pressure on the bottom of the wing creates an aerodynamic force that we call Lift

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2. Lift Formula The factors that affect the aerodynamic force (Lift) produced by our aircraft can be seen in the lift formula L = CL . 1/2.ρ.V2 . S Where: CL - Co-efficient of lift ρ (Rho) – Free stream air density V – True airspeed (TAS) S – Plan view wing surface area

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**2. Lift Formula CL - Co-Efficient of lift L = CL . 1/2.ρ.V2 . S**

CL refers to the lifting ability of the wing Its made up of a number of factors including: Angle of Attack (AoA) Camber Aspect Ratio Surface condition L = CL . 1/2.ρ.V2 . S

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**2. Lift Formula Angle of Attack L = CL . 1/2.ρ.V2 . S**

Is defined as the angle between the relative airflow (RAF) and chord line of an aerofoil Lift Chord Line L.E. AoA T.E. RAF As AoA increases lift increases L = CL . 1/2.ρ.V2 . S

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**2. Lift Formula Camber L = CL . 1/2.ρ.V2 . S**

Mean Camber is the curvature of a line drawn equidistant between the upper and lower surfaces of the wing Lift Chord Line Line of mean camber AoA RAF As camber increases lift increases L = CL . 1/2.ρ.V2 . S

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**2. Lift Formula Camber L = CL . 1/2.ρ.V2 . S**

High camber aerofoils can be found on aircraft that require high lift at low airspeeds Medium camber (general purpose) aerofoils can be found on light training aircraft Low camber aerofoils can be found on aircraft that travel at high airspeeds L = CL . 1/2.ρ.V2 . S

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**2. Lift Formula Aspect Ratio L = CL . 1/2.ρ.V2 . S**

Aspect ratio is the ratio of wing span to chord Its is measured by: As Aspect Ratio increases lift increases High aspect ratio wings can be seen on gliding aircraft Light training aircraft typically have medium Aspect Ratio wings Low aspect ratio wings can be seen on aerobatic aircraft L = CL . 1/2.ρ.V2 . S

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**2. Lift Formula ρ - Air density L = CL . 1/2.ρ.V2 . S**

Ambient density of the free stream air (air not being disturbed by the passage of the aircraft) If density is increased, lift will increase L = CL . 1/2.ρ.V2 . S

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**2. Lift Formula V - True Airspeed (TAS) L = CL . 1/2.ρ.V2 . S**

The aerodynamic force produced is directly proportional to the airspeed squared The faster the airspeed, the more lift produced L = CL . 1/2.ρ.V2 . S

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**3. Control Surfaces S - Plan surface area L = CL . 1/2.ρ.V2 . S**

The size of wing area is directly proportional to the aerodynamic force produced A larger wing area, will interact with a larger volume of air and therefore produce more lift L = CL . 1/2.ρ.V2 . S

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**3. Control Surfaces Control Surfaces**

The three primary control surfaces are: Ailerons Ailerons

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**3. Control Surfaces Control Surfaces**

The three primary control surfaces are: Elevator

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**3. Control Surfaces Control Surfaces**

The three primary control surfaces are: Rudder

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3. Control Surfaces The control surfaces work by deflecting the trailing edge of the surface, increasing the effective AoA, therefore increasing… Lift Lift RAF Chord Line Chord Line Chord Line RAF Lift RAF

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**3. Control Surfaces The three axes the aircraft rotates about are:**

1. Lateral axis - Pitch Lateral axis

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**3. Control Surfaces The three axes the aircraft rotates about are:**

Longitudinal axis - Roll Longitudinal axis

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**3. Control Surfaces The three axes the aircraft rotates about are:**

3. Normal axis - Yaw Normal axis

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**4. Forces in Straight and Level**

Straight and level flight is defined as flight at a constant heading altitude and power setting with the aircraft in balance. In this state, the motion will not change. Therefore, it must have a constant ... velocity. Constant velocity means nil acceleration therefore all forces must be in a state of ... equilibrium.

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**4. Forces in Straight and Level**

There are four main forces acting in S & L flight: LIFT THRUST DRAG WEIGHT

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**4. Forces in Straight and Level**

These forces do not act from the same point Lift - Is produced by the wings and acts upwards through the centre of pressure. LIFT Weight - Acts straight down through the centre of gravity to the centre of the earth. Thrust - Is provided by the engine through the propeller. CoG DRAG THRUST CoP Drag - Is the resistance to motion felt by all bodies within the atmosphere. WEIGHT

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**4. Forces in Straight and Level**

Because the forces are not acting from the same point they create a couple A couple is two equal and opposite forces acting about a pivot point creating a torque or turning moment The two couple’s generate opposing pitching moments LIFT L / W Couple = Nose DOWN moment T / D Couple = Nose UP moment DRAG THRUST WEIGHT

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**4. Forces in Straight and Level**

We said that the forces must be in equilibrium, therefore: LIFT = WEIGHT (L / W Couple) THRUST = DRAG (T / D Couple) For the aircraft to fly S & L the nose down moment must equal... the nose up moment.

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**4. Forces in Straight and Level**

WEIGHT LIFT DRAG THRUST If the moments are not equal, the tailplane makes up the difference. In a correctly loaded aircraft the tail plane will create a small force… Downwards Force The forces are now in equilibrium

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5. Stability Stability describes the properties of a body’s motion after it is displaced from equilibrium. Static Stability refers to the initial reaction of a body after being displaced from a position of equilibrium Dynamic Stability becomes apparent after a body shows static stability. It refers to the subsequent motion of the disturbed body

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5. Stability Positive Static Stability refers to a body which will return to equilibrium after being displaced.

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5. Stability Neutral Static Stability refers to a body which will maintain its displacement from equilibrium.

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5. Stability Negative Static Stability refers to a body which will increase its displacement from equilibrium.

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5. Stability To have dynamic stability the body must have Static Stability If an aircraft has Positive Static and Positive Dynamic Stability it will eventually return to its original attitude without pilot input Positive static stability Positive Dynamic Stability Returns to original attitude Aircraft is disturbed Original attitude

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5. Stability If an aircraft has Positive Static and Neutral Dynamic Stability it will oscillate about the original attitude without pilot input Positive static stability Neutral Dynamic Stability Aircraft is disturbed Original attitude Will continue to oscillate about original attitude

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5. Stability If an aircraft has Positive Static and Negative Dynamic Stability it will diverge from its original attitude without pilot input Positive static stability Diverges from original attitude Aircraft is disturbed Original attitude Negative Dynamic Stability

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**5. Stability Longitudinal stability**

Stability along the longitudinal axis Stability about the lateral axis Design features that affect longitudinal stability include longitudinal dihedral 4˚ 2˚

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**5. Stability Lateral stability Stability along the lateral axis**

Stability about the longitudinal axis Design features that affect lateral stability include tail/fin surface area, wing position, pendulum effect and lateral dihedral

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**5. Stability Directional stability Stability along the normal axis**

Stability about the normal axis Most important factor affecting is surface area aft of CoG

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