EASA ATPL TRAINING: Principles of flight
Subsonic aerodynamics
Principles, laws and definitions
The SI system of units
Quantities SI designation Example
Lengths Meter Inch, foot, yard, nm
Speed Meters per second Km per second, knots
Acceleration Meter per second squared g, feet per square second
Areas Squared meters Square kilometer, hectare
Volume Cubic meters Cubic centimeter, liter
Mass/weight Kilogram Tons, gram, grain
Force Newton force Pound-force, decanewton
Pressure Pascal Bar, millimeters of mercury
Power Watt Kilowatt, horse power
Temperature Kelvin Degree Celsius/Fahrenheit
Density Kilograms per cubic meter Pounds per cubic inch/foot
Surface stress Kilograms per cubic meter Pounds per cubic inch/foot
important physical quantities
- Mass: the matter contained in an object > no weight
• expressed in Kilogram
- Force: strength or energy as an attribute of physical action or movement
• expressed in kilogram per meter/seconde
- Acceleration: a chance in speed of an object > increase or decrease in speed
• The speed is expressed in meters per second squared
• The acceleration is known as factor a
- Weight: vertical and downwards action force to which an object is subjected to acceleration
due to the gravitation force
• Expressed in kilograms or tons
Laws of newton
- First law of newton: an object in motion will remain in motion unless another force acts on it
> an object in rest will remain in rest unless a force acts on it
- Second law of newton: force = mass x acceleration
- Third law of newton: for each action performed > there will be an opposite reaction
Density: the amount of air molecules per unit of volume
- Is directly proportional to pressure
• The higher the altitude = the lower the pressure = density decreases
• The higher the temperature = the lower the pressure = density decrease
• Pressure increases = density increases
- Formula: density (Kg/ 3 squared m) = mass (kg) / volume (3 squared m)
• Pressure (p) x volume (squared m) = mass x R (gas constant) x temperature
• Pressure x volume / temperature = constant
- The density at 18.000ft is equal to half the density at 0ft
,Static pressure (q): extorted equally on the whole aircraft
- Comes from the pulling and the weight of air particles
• Is constant present
• Decreases with increasing altitude
- Standard pressure at sea level is 1013,25 hPa
- Formula: pressure (ps) = density (p) x gravitation force (8.9) x height (m) = force (f) / area
(a)
Dynamic pressure (Q): extorted on the leading edge surfaces of the aircraft due to motion
- Formula: dynamic pressure (q) = density (p) / 2 x squared velocity (squared v)
Total pressure: the sum of the dynamic and static pressure
- Formula: total pressure (Pt) = dynamic pressure (Pq) + static pressure (Ps)
Continuity: the mass flow of air is constant in a flow through a duct
- the density remains constant
- Subsonic flow is at approximately 200kts
- Formula: density x area x velocity = constant
• Area x velocity = constant
equation of Bernoulli: for a steady flow of air > the sum of its kinetic potential and pressure energy is
constant
- higher speed causes a higher kinetic energy and a lower potential energy
• kinetic energy = dynamic pressure > potential energy = static pressure
- formula: dynamic pressure + static pressure = total pressure = constant
definition of the various speed concepts in aviation: different types of airspeeds must be correct to
get the wanted true airspeed
- ICE Tea is a PrItty Cool Drink
- Indicated airspeed (Vias): the indication of the airspeed on speed gauge
- Calibrated airspeed (Vcas): Vias corrected for position and instrument error
- Equivalent airspeed (Veas): Vcas corrected for compressibility error
- True airspeed (Vtas): Veas corrected for density error
Principles of airflow: stream lines in the 2D plane represent the direction of the airflow
- The closer the lines of the flow are to each other > the faster the air will move in that plane
- The further the lines of the flow are to each other > the slower the air will move in that plane
- A steady or laminar airflow = the air molecules follow each other without any diversions
- Unsteady airflow = each air molecule has its own path > chaos between the molecules
- 2D airflow: air above the aerofoil will move faster > because the air molecules are pressed
against each other
• Low pressure on the upper side of the aerofoil > 2/3 of the air
• High pressure on the lower side of the aerofoil > 1/3 of air
- 3D airflow: spanwise flow
Aerofoils: the shape of any aerofoil is defined by:
- The leading edge: the front edge of an aerofoil
- The trailing edge: the back part of an aerofoil
- The chord line: straight line joining the leading and trailing edge
• The chord: the distance between the leading and trailing edge
,- The camber line: a line joining the leading edge and trailing > drawn between the upper and
lower side (divides the aerofoil always in two even parts)
- The camber: distance between the chord line and the mean camber line
• If the camber line is above the chord line > positive camber
▪ Positive camber gives lift at small negative and 0° angle of attack
• If the camber line is below the chord line > negative camber
▪ Negative camber gives negative lift at positive angles of attack
• If the camber line comes together with the chord line > neutral camber
▪ Neutral camber gives no lift at 0° angle of attack
• Aerofoils with a negative or positive camber are known as asymmetric aerofoils
• Aerofoils with a neutral camber are known as symmetric aerofoils
- Thickness: the maximum distance between the upper and lower side of an aerofoil
- Nose radius: a circle who gives the indication of the thickness of the leading edge
- Thickness to chord ratio: T/C ratio = maximum thickness / chord x 100 (for percentage)
- Wing root: located at the junction of the wing to the fuselage
- Wing tip: the outer edge of the wing
- Wingspan: the distance from the wing tip to the wing tip
- Chord lengths: the chord lengths are different between the tip and root > average length is
the difference between those
- Taper ratio: taper ratio = tip chord / root chord
- Mean geometric chord: the average chord of the wing
- Wing area: the area of a wing = wingspan x mean geometric chord
- Mean aerodynamic chord: imaginary chord to compare different wing profiles with each
other
• The mean aerodynamic chord will form a rectangle shaped wing > this wing has the
same properties as the wing of the aircraft
▪ The rectangle is formed by connecting the tip and root to each other with
the use of a constant chord (geometric chord)
• Used as a reference line for the center of gravity
- 25% chord line: is a chord line which is used to determine the sweep angle of the wing
• 25% of the chord (seen from the leading edge) is connect throughout the whole wing
▪ This line will form a diagonal and the angle between the fuselage and the
diagonal is the chord angle
• We can use that angle to determine if the wing is dihedral or anhedral
▪ Angle positive = dihedral > angel negative = anhedral
- Aspect ratio: is the ratio between wingspan and wing surface > aspect radio = squared
wingspan / wing surface
- Angle of incidence: is the angle between the chord line of the wing and the longitudinal axis
of the aircraft
- Angle of attack: is the angle between the chord line of the wing and the relative airflow of
the air
- two types of wing twists: the twist of the wing influences the angel or thickness of the wing
with the propose the maintain lateral control (ailerons) during a stall
• geometric twist: bending of the wing from the root towards the tip
▪ The chord will be at a different angle towards the tip > this will chance the
angle of attack at the tip vs at the root
• Angle of attack at the tip decreases in comparison with the angle of
attack at the root
▪ This causes a delayed stall at the tip of the wing > thus the ailerons remain
functional during stall recovery
• Aerodynamic twist: changing the camber of the wing
, ▪ The root will be thicker > will have a more positive camber then the tip
• This will cause the root to stall earlier in comparison to the tip
▪ Eventually the aerodynamic twist will remain to maintain the same functions
as the geometric twist
Two-dimensional airflow around an aerofoil
Stream line: on the upper side of the wing > acceleration of the airflow
- Causes a formation of a low pressure zone (suction zone) on the upper side and a high
pressure zone on the lower side
• Upwash ahead of the wing and a downwash behind > the flow goes from underneath
the wing to the upper side
Stagnation point: the very first point where the air will be divided (towards the upper or lower side)
and where it will come to a rest
- No motion in air = low dynamic energy and high static energy
- The smaller the stagnation point is > the less drag your wing will produce
- The stagnation point is dependent of the angle of attack:
• AoA increase = stagnation point moves aft = point of lowest pressure moves forward
= more drag
• AoA decreases = stagnation point moves forward = point of lowest pressure moves
aft = less drag
- The stagnation point is also used for the stall system
Pressure distribution: is dependent of the angle of attack and the camber of the wing
- Effect of AoA: higher AoA mean a higher suction force due to the production of more low
pressure on the upper side of the wing > the air must accelerate faster through a smaller
area
- Effect of camber: the positivity of the camber can create more or lift at lower angles of attack
> opposite for negative cambered wings
Center of pressure (aerodynamic center): is a point on the wing where all the forces will act > it
moves relevant to the angle of attack (see stagnation point)
Aerodynamic center: corresponds to the aerodynamic center of gravity of all pressure points along a
wing = independent of AoA
- In subsonic aerodynamics this point will be at the 25% chord
Relationship between lift and downwash: the amount of deflected air behind the earofoil
(downwash) corresponds to the total lift produced
- The higher the airspeed = more air deflected downwards (due to mass flow)
- The lager the angle of attack = the more air deflected downwards (due to change of angle)
Coefficients
- Lift coefficient CL: the lift coefficient will continue to increase with increasing angle of attack
until it reaches a critical point > stall
• For symmetrical aerofoils is the CL max normal for each AoA
▪ For cambered aerofoils is the CL max greater compared for each AoA
(compared to symmetrical aerofoils)
• Wings with a higher lift coefficient > high aspect ratio wings will produce higher lift at
small AoA but require a smaller AoA for the stall
Subsonic aerodynamics
Principles, laws and definitions
The SI system of units
Quantities SI designation Example
Lengths Meter Inch, foot, yard, nm
Speed Meters per second Km per second, knots
Acceleration Meter per second squared g, feet per square second
Areas Squared meters Square kilometer, hectare
Volume Cubic meters Cubic centimeter, liter
Mass/weight Kilogram Tons, gram, grain
Force Newton force Pound-force, decanewton
Pressure Pascal Bar, millimeters of mercury
Power Watt Kilowatt, horse power
Temperature Kelvin Degree Celsius/Fahrenheit
Density Kilograms per cubic meter Pounds per cubic inch/foot
Surface stress Kilograms per cubic meter Pounds per cubic inch/foot
important physical quantities
- Mass: the matter contained in an object > no weight
• expressed in Kilogram
- Force: strength or energy as an attribute of physical action or movement
• expressed in kilogram per meter/seconde
- Acceleration: a chance in speed of an object > increase or decrease in speed
• The speed is expressed in meters per second squared
• The acceleration is known as factor a
- Weight: vertical and downwards action force to which an object is subjected to acceleration
due to the gravitation force
• Expressed in kilograms or tons
Laws of newton
- First law of newton: an object in motion will remain in motion unless another force acts on it
> an object in rest will remain in rest unless a force acts on it
- Second law of newton: force = mass x acceleration
- Third law of newton: for each action performed > there will be an opposite reaction
Density: the amount of air molecules per unit of volume
- Is directly proportional to pressure
• The higher the altitude = the lower the pressure = density decreases
• The higher the temperature = the lower the pressure = density decrease
• Pressure increases = density increases
- Formula: density (Kg/ 3 squared m) = mass (kg) / volume (3 squared m)
• Pressure (p) x volume (squared m) = mass x R (gas constant) x temperature
• Pressure x volume / temperature = constant
- The density at 18.000ft is equal to half the density at 0ft
,Static pressure (q): extorted equally on the whole aircraft
- Comes from the pulling and the weight of air particles
• Is constant present
• Decreases with increasing altitude
- Standard pressure at sea level is 1013,25 hPa
- Formula: pressure (ps) = density (p) x gravitation force (8.9) x height (m) = force (f) / area
(a)
Dynamic pressure (Q): extorted on the leading edge surfaces of the aircraft due to motion
- Formula: dynamic pressure (q) = density (p) / 2 x squared velocity (squared v)
Total pressure: the sum of the dynamic and static pressure
- Formula: total pressure (Pt) = dynamic pressure (Pq) + static pressure (Ps)
Continuity: the mass flow of air is constant in a flow through a duct
- the density remains constant
- Subsonic flow is at approximately 200kts
- Formula: density x area x velocity = constant
• Area x velocity = constant
equation of Bernoulli: for a steady flow of air > the sum of its kinetic potential and pressure energy is
constant
- higher speed causes a higher kinetic energy and a lower potential energy
• kinetic energy = dynamic pressure > potential energy = static pressure
- formula: dynamic pressure + static pressure = total pressure = constant
definition of the various speed concepts in aviation: different types of airspeeds must be correct to
get the wanted true airspeed
- ICE Tea is a PrItty Cool Drink
- Indicated airspeed (Vias): the indication of the airspeed on speed gauge
- Calibrated airspeed (Vcas): Vias corrected for position and instrument error
- Equivalent airspeed (Veas): Vcas corrected for compressibility error
- True airspeed (Vtas): Veas corrected for density error
Principles of airflow: stream lines in the 2D plane represent the direction of the airflow
- The closer the lines of the flow are to each other > the faster the air will move in that plane
- The further the lines of the flow are to each other > the slower the air will move in that plane
- A steady or laminar airflow = the air molecules follow each other without any diversions
- Unsteady airflow = each air molecule has its own path > chaos between the molecules
- 2D airflow: air above the aerofoil will move faster > because the air molecules are pressed
against each other
• Low pressure on the upper side of the aerofoil > 2/3 of the air
• High pressure on the lower side of the aerofoil > 1/3 of air
- 3D airflow: spanwise flow
Aerofoils: the shape of any aerofoil is defined by:
- The leading edge: the front edge of an aerofoil
- The trailing edge: the back part of an aerofoil
- The chord line: straight line joining the leading and trailing edge
• The chord: the distance between the leading and trailing edge
,- The camber line: a line joining the leading edge and trailing > drawn between the upper and
lower side (divides the aerofoil always in two even parts)
- The camber: distance between the chord line and the mean camber line
• If the camber line is above the chord line > positive camber
▪ Positive camber gives lift at small negative and 0° angle of attack
• If the camber line is below the chord line > negative camber
▪ Negative camber gives negative lift at positive angles of attack
• If the camber line comes together with the chord line > neutral camber
▪ Neutral camber gives no lift at 0° angle of attack
• Aerofoils with a negative or positive camber are known as asymmetric aerofoils
• Aerofoils with a neutral camber are known as symmetric aerofoils
- Thickness: the maximum distance between the upper and lower side of an aerofoil
- Nose radius: a circle who gives the indication of the thickness of the leading edge
- Thickness to chord ratio: T/C ratio = maximum thickness / chord x 100 (for percentage)
- Wing root: located at the junction of the wing to the fuselage
- Wing tip: the outer edge of the wing
- Wingspan: the distance from the wing tip to the wing tip
- Chord lengths: the chord lengths are different between the tip and root > average length is
the difference between those
- Taper ratio: taper ratio = tip chord / root chord
- Mean geometric chord: the average chord of the wing
- Wing area: the area of a wing = wingspan x mean geometric chord
- Mean aerodynamic chord: imaginary chord to compare different wing profiles with each
other
• The mean aerodynamic chord will form a rectangle shaped wing > this wing has the
same properties as the wing of the aircraft
▪ The rectangle is formed by connecting the tip and root to each other with
the use of a constant chord (geometric chord)
• Used as a reference line for the center of gravity
- 25% chord line: is a chord line which is used to determine the sweep angle of the wing
• 25% of the chord (seen from the leading edge) is connect throughout the whole wing
▪ This line will form a diagonal and the angle between the fuselage and the
diagonal is the chord angle
• We can use that angle to determine if the wing is dihedral or anhedral
▪ Angle positive = dihedral > angel negative = anhedral
- Aspect ratio: is the ratio between wingspan and wing surface > aspect radio = squared
wingspan / wing surface
- Angle of incidence: is the angle between the chord line of the wing and the longitudinal axis
of the aircraft
- Angle of attack: is the angle between the chord line of the wing and the relative airflow of
the air
- two types of wing twists: the twist of the wing influences the angel or thickness of the wing
with the propose the maintain lateral control (ailerons) during a stall
• geometric twist: bending of the wing from the root towards the tip
▪ The chord will be at a different angle towards the tip > this will chance the
angle of attack at the tip vs at the root
• Angle of attack at the tip decreases in comparison with the angle of
attack at the root
▪ This causes a delayed stall at the tip of the wing > thus the ailerons remain
functional during stall recovery
• Aerodynamic twist: changing the camber of the wing
, ▪ The root will be thicker > will have a more positive camber then the tip
• This will cause the root to stall earlier in comparison to the tip
▪ Eventually the aerodynamic twist will remain to maintain the same functions
as the geometric twist
Two-dimensional airflow around an aerofoil
Stream line: on the upper side of the wing > acceleration of the airflow
- Causes a formation of a low pressure zone (suction zone) on the upper side and a high
pressure zone on the lower side
• Upwash ahead of the wing and a downwash behind > the flow goes from underneath
the wing to the upper side
Stagnation point: the very first point where the air will be divided (towards the upper or lower side)
and where it will come to a rest
- No motion in air = low dynamic energy and high static energy
- The smaller the stagnation point is > the less drag your wing will produce
- The stagnation point is dependent of the angle of attack:
• AoA increase = stagnation point moves aft = point of lowest pressure moves forward
= more drag
• AoA decreases = stagnation point moves forward = point of lowest pressure moves
aft = less drag
- The stagnation point is also used for the stall system
Pressure distribution: is dependent of the angle of attack and the camber of the wing
- Effect of AoA: higher AoA mean a higher suction force due to the production of more low
pressure on the upper side of the wing > the air must accelerate faster through a smaller
area
- Effect of camber: the positivity of the camber can create more or lift at lower angles of attack
> opposite for negative cambered wings
Center of pressure (aerodynamic center): is a point on the wing where all the forces will act > it
moves relevant to the angle of attack (see stagnation point)
Aerodynamic center: corresponds to the aerodynamic center of gravity of all pressure points along a
wing = independent of AoA
- In subsonic aerodynamics this point will be at the 25% chord
Relationship between lift and downwash: the amount of deflected air behind the earofoil
(downwash) corresponds to the total lift produced
- The higher the airspeed = more air deflected downwards (due to mass flow)
- The lager the angle of attack = the more air deflected downwards (due to change of angle)
Coefficients
- Lift coefficient CL: the lift coefficient will continue to increase with increasing angle of attack
until it reaches a critical point > stall
• For symmetrical aerofoils is the CL max normal for each AoA
▪ For cambered aerofoils is the CL max greater compared for each AoA
(compared to symmetrical aerofoils)
• Wings with a higher lift coefficient > high aspect ratio wings will produce higher lift at
small AoA but require a smaller AoA for the stall
