Basic Aerodynamic Theory and Lift ATC Chapter 1. Aim To review principals of aerodynamic forces.
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Transcript of 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 =
2. Define energy and 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
2. Define energy and pressure
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
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
Bernoulli's theorem
5. State the principles of lift production
• 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
Pressure Distributions Vs. Angle of Attack
6. Pressure Distributions
• 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
Pressure Distributions Vs. Angle of Attack
6. Pressure Distributions
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
7. State the aerofoil terminology and designs
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
7. State the aerofoil terminology and designs
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
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%
7. State the aerofoil terminology and designs
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. 26% of chord
Approx. 3% of chord
7. State the aerofoil terminology and designs
Location of Maximum Thickness
Maximum Camber
Approx. 11% of chord
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
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
Chord Line
TE
LE
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
7. State the aerofoil terminology and designs
• 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
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
RAF
Chord Line
AoA
Lift
L.E.
T.E.
L = CL . 1/2.ρ.V2 . S
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
RAF
Chord Line
AoA
LiftLine of mean camber
L = CL . 1/2.ρ.V2 . S
8. State the lift equation and its properties
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
8. State the lift equation and its properties
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
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
Lift Equation
L = CL . 1/2.ρ.V2 . S
8. State the lift equation and its properties
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
8. State the lift equation and its properties
L = CL . 1/2.ρ.V2 . S
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
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
8. State the lift equation and its properties
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°
10. State the change of CL vs. angle of attack
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
10. State the change of CL vs. angle of attack
4 °AoA10° AoA
L
D
L
D
CL Graph• 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
10. State the change of CL vs. angle of attack
10° AoA
L
D
L
D
>16° AoA
CL Graph• 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
10. State the change of CL vs. angle of attack
Questions?