1. Basic Aerodynamic Theory and Lift
ATC Chapter 1

2. Aim
To review principals of aerodynamic forces

3. 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

4. 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

5. 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

6. 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)

7. 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

8. 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

9. 3. State the four main forces
The four forces during S&L
LIFT
DRAG
THRUST
WEIGHT

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. Aerofoil Terminology 7. State the aerofoil terminology and designs
Wingspan – is the length from one wing tip to the other
Wingspan

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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

35. 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

36. 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

37. 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

38. 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

39. 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

40. 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

41. 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

42. Questions?