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**Basic Aerodynamic Theory and Lift**

ATC Chapter 1

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Aim To review principals of aerodynamic forces

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**Objectives Define motion and equilibrium Define energy and pressure**

State the four main forces Define weight State the principles of lift production (Bernoulli’s Theorem) State the pressure distributions over an aerofoil State the aerofoil terminology and designs State the lift equation and its properties Define total reaction and centre of pressure movement State the change of CL vs. angle of attack

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**1. Define motion and equilibrium**

Motion is defined as: The action or process of moving or being moved Every object on the earths surface is in motion around the Earth’s axis, in addition to orbiting the sun Relative motion is defined as: The calculation of the motion of an object with regard to some other moving object When we discuss aircraft motion we are referring to relative motion and change of motion Equilibrium is defined as: A state in which opposing forces or influences are balanced

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**1. Define motion and equilibrium**

Aeroplane Motion When the four forces acting on the aircraft are balanced the aircraft is in a state of equilibrium Weight is balanced by lift Drag is balanced with thrust When the aeroplane is in a state equilibrium it will neither accelerate, decelerate or change its direction Situation of equilibrium are: Flying straight and level In a steady climb In a steady descent

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**2. Define energy and pressure**

Kinetic Energy Kinetic energy is defined as: Energy that a body possesses by virtue of being in motion Kinetic Energy = ½.m.v2 For an aeroplane to have kinetic energy it must be in motion When the kinetic energy formula with relation to an aeroplane in motion is directly related to the air and its motion, therefore: m = the mass of the air V = the velocity at which the air flows around the aircraft Therefore this can be referred to as the aeroplane’s true airspeed (TAS)

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**2. Define energy and pressure**

Air is made up of a mixture of gasses Each gas contains millions of molecules which act in a state of random motion Each molecule has a mass When the molecules collide with a surface, such as an aerofoil a very small force is created The created force, when measured over the surface in which it acts is known as pressure Total Pressure = Force Area

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**2. Define energy and pressure**

Total pressure is made up of two components: Static pressure & Dynamic pressure Static pressure is pressure at a nominated point in a fluid Dynamic Pressure is the kinetic energy per unit volume of a fluid particle q = ½.ρ.v2 Where q = dynamic pressure ρ = density v = Velocity of the fluid When discussing aerodynamics we can say the airflow below 300kts acts the same as a fluid

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**3. State the four main forces**

The four forces during S&L LIFT DRAG THRUST WEIGHT

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4. Define weight Weight Newton’s second law states that a force(F) is equal to mass(m) multiplied by acceleration(a) F = ma Therefore the force of weight(W) must equal the mass of an object(m) multiplied acceleration due to gravity(g) W = mg The total weight of an aeroplane always acts directly towards the centre of the Earth and through a single point, called the centre of gravity CoG WEIGHT

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**P+V=C Bernoulli's theorem 5. State the principles of lift production**

In the streamlined flow of an ideal fluid, the sum of all the energies remains constant An ideal fluid is an imaginary fluid that has no viscosity, thermal conductivity and is not influenced by friction At airspeeds lower than 300kts air acts like a fluid therefore we can say… Total pressure is always constant ∴ Total pressure = dynamic pressure + static pressure Dynamic pressure is caused by movement of an object therefore we can say… Pressure (static pressure) + Velocity (dynamic pressure) = Constant P+V=C

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**Bernoulli's theorem 5. State the principles of lift production 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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**Bernoulli's theorem 5. State the principles of lift production**

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

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**Pressure Distributions Vs. Angle of Attack**

In normal flight the air is accelerated over the top surface of a wing, which causes a reduction in static pressure (Bernoulli’s Theorem) The rate of acceleration increases with any increase in angle of attack, up to the stalling angle As the velocity increases the static pressure reduces At the point of highest velocity = least amount of static pressure At small angles of attack there are static pressure reductions over both the top and bottom surface of the wing Lift is created from the pressure differential between the top and bottom surfaces of a wing

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**Pressure Distributions Vs. Angle of Attack**

As the static pressure is reduced by increasing the angle of attack On the bottom of the wing the static pressure increases above the static pressure of the free stream air As the angle of attack is increased and the static pressure on the top of the wing, the area in which the velocity is the highest moves forward This results in the wings center of pressure to move forward with an increased angle of attack

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**Pressure Distributions Vs. Angle of Attack**

Beyond the stalling angle the streamline flow over the top surface of the wing reduces This results in an increase in static pressure Thus resulting in Less lift being produced The center of pressure moving aft

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**Aerofoil Terminology 7. State the aerofoil terminology and designs**

Wingspan – is the length from one wing tip to the other Wingspan

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**Aerofoil Terminology 7. State the aerofoil terminology and designs**

Chord line – is a theoretical straight line drawn from the leading edge of the aerofoil to the trailing edge LE Chord Line TE

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**Aerofoil Terminology 7. State the aerofoil terminology and designs**

Mean camber – is a theoretical line drawn from the leading edge of the aerofoil to the trailing edge This differs from the chord line as it must also be at an equal distance from the top and bottom surface of the aerofoil Line of mean camber LE Chord Line TE

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**Aerofoil Terminology 7. State the aerofoil terminology and designs**

Maximum camber – is at the location where the difference in distance between the chord line and the mean chamber line is at a maximum Maximum camber Line of mean camber LE Chord Line TE

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**Location of Maximum Camber**

7. State the aerofoil terminology and designs Aerofoil Terminology Maximum thickness – is at the location where the distance between the top and bottom of the aerofoil is at a maximum The location of this point is measured as a percentage of the chord I.e. the maximum chamber is approximately 3% occurring at approximately 30% Location of Maximum Thickness Maximum Thickness Maximum Camber LE Line of mean camber TE Chord Line Location of Maximum Camber

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**Aerofoil Terminology 7. State the aerofoil terminology and designs**

Maximum Camber Maximum Thickness Location of Maximum Thickness Location of Maximum Camber Chord Line Approx. 3% of chord Approx. 36% of chord Approx. 11% of chord Approx. 26% of chord

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**Aerofoil Designs – Cambered Aerofoils**

7. State the aerofoil terminology and designs Aerofoil Designs – Cambered Aerofoils An aerofoil is cambered when the chord line does not equal the mean camber line Aerofoils can be either positively or negatively cambered A cambered aerofoil at 0° AofA will create some lift as the air has to flow faster over the top surface compared to the bottom surface in the same time, creating a pressure gradient Line of mean camber LE Chord Line TE

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**Aerofoil Designs – Symmetrical Aerofoils**

7. State the aerofoil terminology and designs Aerofoil Designs – Symmetrical Aerofoils An aerofoil is symmetrical when the chord line equals the mean chamber line A symmetrical aerofoil at 0 ° AoA will create no lift as the air flows at the same speed over both the top and bottom surface of the aerofoil, creating no pressure gradient Line of mean camber TE Chord Line LE

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**Aerofoil Designs – Laminar-flow aerofoils**

7. State the aerofoil terminology and designs Aerofoil Designs – Laminar-flow aerofoils A laminar-flow aerofoil is slightly chambered However the maximum chamber is further aft creating a larger amount of laminar flow air prior to the transition point Laminar flow aerofoils create less parasite drag at low angles of attack These aerofoils are used for high performance aeroplanes The downside to a laminar-flow aerofoil is that only a small amount of lift is created at slow speeds and AofA’s These are found on jet aeroplanes and the extra lift is created by high life devices such as slats, slots and flaps

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

8. State the lift equation and its properties Lift Equation 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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**Lift Equation 8. State the lift equation and its properties**

CL - Co-Efficient of lift 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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**Lift Equation 8. State the lift equation and its properties**

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

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**Lift Equation 8. State the lift equation and its properties**

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

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**Lift Equation 8. State the lift equation and its properties**

Camber 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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**Lift Equation 8. State the lift equation and its properties**

Aspect Ratio Aspect ratio is the ratio of wing span to chord Its is measured by: Span 2 Gross wing area 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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**Lift Equation 8. State the lift equation and its properties**

ρ - Air density 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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**Lift Equation 8. State the lift equation and its properties**

V - True Airspeed (TAS) V – is the speed in which the aeroplane moves through the air (TAS) 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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**Lift Equation 8. State the lift equation and its properties**

1/2.ρ.V2 – Indicated Airspeed (IAS) The indicated airspeed is a measure of dynamic pressure The Airspeed Indicator displays the dynamic pressure in a measurement of knots (NM/hr) The IAS also is dependent on density, pressure and temperature As IAS is measured with respect to dynamic pressure, IAS is a function of the lift equation L = CL . 1/2.ρ.V2 . S

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**Lift Equation 8. State the lift equation and its properties**

S - Plan surface area 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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**CL Graph 10. State the change of CL vs. angle of attack**

From the lift equation we know that: Lift is proportional to the angle of attack (CL) and Lift is proportional to IAS L AoA . IAS Therefore, at a constant IAS if the angle of attack is increased then lift must increase Lift will continue to increase up until the critical point, at which the stall occurs, and then decreases CL Cambered Aerofoil Symmetrical Aerofoil -4° 0° 16° AoA

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**CL Graph 10. State the change of CL vs. angle of attack**

As the angle of attack in increased up to the critical angle (stall) CL increases The centre of pressure moves forward The pressure above the wing decreases, causing a greater gradient The transition point moves forward CL Cambered Aerofoil Symmetrical Aerofoil -4° 0° 16° AoA

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**9. Define total reaction and centre of pressure movement**

We know: Lift always acts perpendicular to the relative airflow Drag always acts parallel to the relative airflow, opposing thrust Using vector addition was can create one resultant force, this is called the total reaction Lift Total Reaction Chord Line L.E. Drag AoA T.E. RAF

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**CL Graph L D 10. State the change of CL vs. angle of attack 4 °AoA**

Airflow Over The Wing At low angles of attack there is relatively little disturbance to the airflow as the aerofoil travels through it CoP is typically around 1/3 chord length L 4 °AoA D

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**CL Graph L L D D 10. State the change of CL vs. angle of attack**

Airflow Over The Wing As AoA increases the airflow must increasingly deviate from its path and accelerate to follow the contour of the wing The air toward the aft of the aerofoil begins to separate As AoA increases CoP moves forward L L 10° AoA 4 °AoA D D

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**CL Graph L L D D 10. State the change of CL vs. angle of attack**

Airflow Over The Wing As AoA increases the airflow must increasingly deviate from its path Beyond an AoA of around 16 ° the change in direction and speed is too great, the airflow can no longer conform to the shape of the aerofoil and becomes turbulent CoP moves rapidly rewards Lift reduces A large increase in drag occurs L >16° AoA 10° AoA L D D

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