THE
PILOT
Principles
of flight
ATPL
STUDENT
pilot
resume
all info you need to pass atpl exams
, POF
General:
Bernoulli: Sum of all energy constant
3
Temperature ~ density(rho)[kg/m ]
Density ∝ mass
Density ∝ pressure
Density does not vary in venturi
Density decrease as humidity increase
Temp ↑ mass flow ↓
2
Dynamic pressure [q]( N/m )
1 2
= / 2 ρV(TAS)
Dynamic press = 0 when speed = 0
Static + dynamic = constant
p/(rho*T) = Constant
• SI units:
- Weight (Newton) = Force = Mass(kg) x acceleration
- Power (Nm/s) = Watts (W) Force x distance ÷ time (J/s) [There is time]
- Work = Joule
2
- Force [kg.m/s ]= m x a
2
- Wing loading[W/S](N/m ): Weight of aircraft ÷ area of the wings
• Density decrease with increase in humidity (Dry air = better performance)
• Mean geometric chord: Wing area ÷ wing span
Difference between MAC & mean camber line
Relative thickness: Expressed in % chord
Symmetrical airfoil: 0 camber, mean camber line = chord line
& lift characteristics as the actual wing
• Aeroplane AOA: Angle between speed vector & longitudinal axis
Wing AOA: Angle between longitudinal axis & wing root chord line
Angle of incidence: Angle between wing root chord line & longitudinal axis
Dihedral angle:
- Angle between wing plane & the horizontal with aeroplane in an unbanked , level condition
- Angle between the 0.25 chord line of the wing and the lateral axis
• Lift & drag forces depend on the pressure distribuition around the aerofoil cross section
• Lift = Component of total aerodynamic force perpendicular to the undisturbed airflow
2D airflow over an aerofoil
o
• Typical C L /C D ratio: Max at angle of attack of 4
• Lift:
- Upwash ahead of the wing & downwash behind
- Downwash increase: Lift generated by the aerofoil increases
- Upper surface produces greatest proportion of lift at all speeds
- Generated when the flow direction of a certain mass of air is changed
• Stagnation point:
- Static pressure maximum value
- Relative velocity = 0
• AOA
- Decrease: Stagnation point moves forward /up, lowest pressure(CP) moves aft, COP moves aft
- Increase: Stagnation point moves down, lowest pressure(CP) moves forward, COP moves forward until crit AOA
• Aerodynamic centre of an aerofoil:
- Approx 25% chord irrespective/independent of AOA
- Assume no flow separation, pitching moment coefficient does not change with carying angle of attack
, - Where instantaneous variation in wing lift acts
- Don’t mix up aerodynamic centre with centre of pressure
• Centre of pressure:
- Does not change on symmetric airfoils
- Moves forward as AOA increase
• Streamlines:
- Speed increases: Area of condensed streamlines moves to the back (In the direction of trailing edge), COP moves aft
- Speed decreases: COP moves forward & total lift force is constant
- Streamlines converge: Static pressure decreases & velocity increases
- Streamlines diverge: Stati pressure increases & velocity decreases
- Airflow accelerates over wing when generating lift
• Drag:
- Total drag: Pressure drag & skin friction drag
- Profile drag proportional to square of the relative velocity of the air & drag coefficient
Coefficients:
• Positively cambered airfoil: C L = 0, pitching moment down, negative AOA
Negatively cambered airfoil: C L = 0, pitching moment up, positive AOA
Symmetric airfoil: AOA = 0, pitching moment = 0, there is only drag but no lift
• Swept vs unswept: Swept has less lift at AOA
• Lift/aerodynamic force:
1 2
- / 2 ρV SC L Above & left of origin
- q(dynamic pressure) x S x C L
2 2
- (V S ) C LMAX = (V) C L [V = actual speed & C L = actual lift coefficient]
2 1 2
- When speed increases by a ratio = Lift = ratio , C L = / ratio
- C L is directly affected by AOA Below & right of origin
1 2
• Drag = / 2 ρV SC D [S = reference area, C D = Drag coefficient]
- Minimum when C L /C D ratio is maximum
• Coefficient of lifts & drag affected by camber & AOA only
• Parabolic curve: Minimum glide angle & parasite drag coefficient
• Aerofoil polar graph: C L /C D , shows max ratio(Total drag lowest) & max C L
• AOA is unaffected by density
IAS & TAS:
• Assuming no compressibility effects & straight & level flight with same AOA:
- TAS is higher at higher altitudes
- IAS is constant with altitude, C L must be constant as density is changed hence AOA the same
3D airflow over an aeroplane
• Spanwise component
- Added compared to 2D airflow
- Airflow on the upper surface flows to root, lower surface to wingtip
• Wing tip vortices:
- Increase as AOA increase
- Descrease as aspect ratio increase
- Highest at take-off
- Vortex waves gradually descends to a lower level
- Vortex forms on rotation & ends when noswheel touches down
• Aspect ratio:
- Increase: Induced drag & crit AOA decrease
- Increase: Max lift lift/drag ratio increase
- Decreases: when flaps are deployed
• Induced drag:
- Induced AOA: A result of downwash due to tip vortices
- Caused by wing tip vortices & downwash
- Reduced by installing wing tip tank
- Strongest at wing tips
- Increases as AOA increase
- Increases airplane mass increase (Higher mass = higher AOA)
- Decreases as speed increases (See curve)
- Decreases when flaps are deployed
2
- C Di = (C L ) ÷ π x AR
2
- C Di = 1 ÷ V
1 2
- D i = / 2 ρV SC Di
PILOT
Principles
of flight
ATPL
STUDENT
pilot
resume
all info you need to pass atpl exams
, POF
General:
Bernoulli: Sum of all energy constant
3
Temperature ~ density(rho)[kg/m ]
Density ∝ mass
Density ∝ pressure
Density does not vary in venturi
Density decrease as humidity increase
Temp ↑ mass flow ↓
2
Dynamic pressure [q]( N/m )
1 2
= / 2 ρV(TAS)
Dynamic press = 0 when speed = 0
Static + dynamic = constant
p/(rho*T) = Constant
• SI units:
- Weight (Newton) = Force = Mass(kg) x acceleration
- Power (Nm/s) = Watts (W) Force x distance ÷ time (J/s) [There is time]
- Work = Joule
2
- Force [kg.m/s ]= m x a
2
- Wing loading[W/S](N/m ): Weight of aircraft ÷ area of the wings
• Density decrease with increase in humidity (Dry air = better performance)
• Mean geometric chord: Wing area ÷ wing span
Difference between MAC & mean camber line
Relative thickness: Expressed in % chord
Symmetrical airfoil: 0 camber, mean camber line = chord line
& lift characteristics as the actual wing
• Aeroplane AOA: Angle between speed vector & longitudinal axis
Wing AOA: Angle between longitudinal axis & wing root chord line
Angle of incidence: Angle between wing root chord line & longitudinal axis
Dihedral angle:
- Angle between wing plane & the horizontal with aeroplane in an unbanked , level condition
- Angle between the 0.25 chord line of the wing and the lateral axis
• Lift & drag forces depend on the pressure distribuition around the aerofoil cross section
• Lift = Component of total aerodynamic force perpendicular to the undisturbed airflow
2D airflow over an aerofoil
o
• Typical C L /C D ratio: Max at angle of attack of 4
• Lift:
- Upwash ahead of the wing & downwash behind
- Downwash increase: Lift generated by the aerofoil increases
- Upper surface produces greatest proportion of lift at all speeds
- Generated when the flow direction of a certain mass of air is changed
• Stagnation point:
- Static pressure maximum value
- Relative velocity = 0
• AOA
- Decrease: Stagnation point moves forward /up, lowest pressure(CP) moves aft, COP moves aft
- Increase: Stagnation point moves down, lowest pressure(CP) moves forward, COP moves forward until crit AOA
• Aerodynamic centre of an aerofoil:
- Approx 25% chord irrespective/independent of AOA
- Assume no flow separation, pitching moment coefficient does not change with carying angle of attack
, - Where instantaneous variation in wing lift acts
- Don’t mix up aerodynamic centre with centre of pressure
• Centre of pressure:
- Does not change on symmetric airfoils
- Moves forward as AOA increase
• Streamlines:
- Speed increases: Area of condensed streamlines moves to the back (In the direction of trailing edge), COP moves aft
- Speed decreases: COP moves forward & total lift force is constant
- Streamlines converge: Static pressure decreases & velocity increases
- Streamlines diverge: Stati pressure increases & velocity decreases
- Airflow accelerates over wing when generating lift
• Drag:
- Total drag: Pressure drag & skin friction drag
- Profile drag proportional to square of the relative velocity of the air & drag coefficient
Coefficients:
• Positively cambered airfoil: C L = 0, pitching moment down, negative AOA
Negatively cambered airfoil: C L = 0, pitching moment up, positive AOA
Symmetric airfoil: AOA = 0, pitching moment = 0, there is only drag but no lift
• Swept vs unswept: Swept has less lift at AOA
• Lift/aerodynamic force:
1 2
- / 2 ρV SC L Above & left of origin
- q(dynamic pressure) x S x C L
2 2
- (V S ) C LMAX = (V) C L [V = actual speed & C L = actual lift coefficient]
2 1 2
- When speed increases by a ratio = Lift = ratio , C L = / ratio
- C L is directly affected by AOA Below & right of origin
1 2
• Drag = / 2 ρV SC D [S = reference area, C D = Drag coefficient]
- Minimum when C L /C D ratio is maximum
• Coefficient of lifts & drag affected by camber & AOA only
• Parabolic curve: Minimum glide angle & parasite drag coefficient
• Aerofoil polar graph: C L /C D , shows max ratio(Total drag lowest) & max C L
• AOA is unaffected by density
IAS & TAS:
• Assuming no compressibility effects & straight & level flight with same AOA:
- TAS is higher at higher altitudes
- IAS is constant with altitude, C L must be constant as density is changed hence AOA the same
3D airflow over an aeroplane
• Spanwise component
- Added compared to 2D airflow
- Airflow on the upper surface flows to root, lower surface to wingtip
• Wing tip vortices:
- Increase as AOA increase
- Descrease as aspect ratio increase
- Highest at take-off
- Vortex waves gradually descends to a lower level
- Vortex forms on rotation & ends when noswheel touches down
• Aspect ratio:
- Increase: Induced drag & crit AOA decrease
- Increase: Max lift lift/drag ratio increase
- Decreases: when flaps are deployed
• Induced drag:
- Induced AOA: A result of downwash due to tip vortices
- Caused by wing tip vortices & downwash
- Reduced by installing wing tip tank
- Strongest at wing tips
- Increases as AOA increase
- Increases airplane mass increase (Higher mass = higher AOA)
- Decreases as speed increases (See curve)
- Decreases when flaps are deployed
2
- C Di = (C L ) ÷ π x AR
2
- C Di = 1 ÷ V
1 2
- D i = / 2 ρV SC Di
