basic aerodynamic theory and lift atc chapter 1. aim to review principals of aerodynamic forces

Basic Aerodynamic Theory and Lift

ATC Chapter 1

Aim

To review principals of aerodynamic forces

Objectives1. Define motion and equilibrium2. Define energy and pressure3. State the four main forces 4. Define weight5. State the principles of lift production (Bernoulli’s

Theorem)6. State the pressure distributions over an aerofoil7. State the aerofoil terminology and designs8. State the lift equation and its properties9. Define total reaction and centre of pressure movement10. State the change of CL vs. angle of attack

1. Define motion and equilibriumMotion

• 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

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

1. Define motion and equilibrium

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)

2. Define energy and pressure

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 =


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


3. State the four main forces The four forces during S&L

LIFT

WEIGHT

DRAGTHRUST

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

4. Define weight

WEIGHT

CoG

P+V=C

Bernoulli's theorem• 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

5. State the principles of lift production

• 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

P+V=C P+V=C P+V=C• If we look at the shape

of the bottom half of the venturi it looks like the top of our wing

Bernoulli's theorem


• 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

Bernoulli's theorem


• 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

Pressure Distributions Vs. Angle of Attack

6. Pressure Distributions

• 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



• 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



Aerofoil Terminology• Wingspan – is the length from one wing tip to the other

Wingspan

7. State the aerofoil terminology and designs

Aerofoil Terminology• Chord line – is a theoretical straight line drawn from the leading edge of the

aerofoil to the trailing edge

Chord Line TE

LE


Aerofoil Terminology• 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

Chord Line TE

LE


Aerofoil Terminology• Maximum camber – is at the location where the difference in distance

between the chord line and the mean chamber line is at a maximum

Line of mean camber

Chord Line TE

LE

Maximum camber


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

Chord Line

Line of mean camber

TE

LE

Maximum Camber

Location of Maximum Camber

Maximum Thickness

Approx. 36% of chord

Aerofoil Terminology

Location of Maximum Camber

Maximum Thickness

Chord Line


Approx. 3% of chord


Location of Maximum Thickness

Maximum Camber


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

Chord Line

LE

TE


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

Chord Line

TE

LE


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


• 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 . SWhere: CL - Co-efficient of lift

ρ (Rho) – Free stream air density

V – True airspeed (TAS)

S – Plan view wing surface area

8. State the lift equation and its properties

Lift Equation

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

Lift Equation


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

RAF

Chord Line

AoA

Lift

L.E.

T.E.

L = CL . 1/2.ρ.V2 . S

Lift Equation


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

RAF

Chord Line

AoA

LiftLine of mean camber

L = CL . 1/2.ρ.V2 . S


Lift Equation

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

Lift Equation


Aspect Ratio• 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

Lift Equation


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

Lift Equation

L = CL . 1/2.ρ.V2 . S


L = CL . 1/2.ρ.V2 . S

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

Lift Equation


L = CL . 1/2.ρ.V2 . S


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

Lift Equation

L = CL . 1/2.ρ.V2 . S

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

Lift Equation


CL Graph• 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

AoA

CL

Symmetrical Aerofoil

Cambered Aerofoil

16°-4° 0°

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

CL Graph• 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

AoA

CL

Symmetrical Aerofoil

16°-4° 0°


Cambered Aerofoil

• 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

Total reaction

Chord Line

AoA

Lift

L.E.

T.E.

Drag

Total Reaction

RAF

9. Define total reaction and centre of pressure movement

L

D

4 °AoA

CL Graph• 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


4 °AoA10° AoA

L

D

L

D


• 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


10° AoA

L

D

L

D

>16° AoA


• 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


Questions?

basic aerodynamic theory and lift atc chapter 1. aim to review principals of aerodynamic forces

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