081 01 00 00 SUBSONIC AERODYNAMICS

Mass = kg = kilograms

Acceleration = ms^-2 = Metres per second squared

Weight = N = Newtons (Weight Force = ma where acceleration is gravity)

Velocity = ms^-1 = Metres per second.

Energy = J = Joules (Kinetic Energy = 1/2mv²)

Density = kgm^-3 = kg per metres cubed.

Temperature = K

Pressure = Nm^-2 = Newtons per metres squared.

Force = N = Newtons (F = ma)

Wing Loading = kgm^-2

Power = W = Watts (Power=Work/Time = FxD/T = F x Speed) (Work=Fd in J) Power is proportional to speed.

Mass = Is the amount of matter a body has and is the same regardless of gravity.

Force = Push or a pull. If an object is in equilibrium is experiences no acceleration, ie it keeps moving or it keeps still.

Acceleration = The rate of change of velocity.

Weight = F = ma. Weight is the value when gravity influences mass

1- Body remains at rest or uniform motion unless acted on by an external force.

2- Acceleration in a straight line is proportional to the applied force and inversely proportional to the mass.

3- Every action there is equal and opposite reaction.

Density is the mass of air molecules per unit volume. It is proportional to ρ/T (In Kelvin)

Pressure, temperature and humidity, in order of significance.

Air density ∝ p/T

Air density is proportional to pressure but inversely proportional to Temperature.

Air is a fluid so like being in water, pressure is felt from all directions, unlike water, static air pressure decreases with height.

N/m²

 

Static pressure is still and has no kinetic energy. Dynamic pressure has mass therefore possesses kinetic energy when in motion.

 

Dynamic pressure = 1/2 ρ V²  or q

With reference to the formula above, if air density half, so will dynamic pressure. If IAS doubles, the dynamic pressure becomes 4 times larger (the square).

Dynamic pressure (q) describes kinetic energy in the context of moving air.

In a flow of an ideal fluid, the sum of pressure and kinetic energy per unit volume remains constant.

Ps + Dynamic = Total pressure (constant)

Ps + 1/2 ρ V² = Constant

Ps + q = Constant

 

Total pressure is static plus dynamic and varies according to energy in the gas, so whatever the ambient pressure happens to be.

Basically the total pressure varies according to the amount of energy in the gas.

Imagine an old egg timer.

As the air flows into the narrow part of the tube, dynamic increases, the air flows faster, and therefore static must reduce. To keep the system in equilibrium or balance the equation.

 

IAS closely related to dynamic pressure.

Static pressure must be subtracted from total air pressure.

Total air pressure is fed into a capsule which expands in proportion to the total pressure. Static pressure is introduced to the ambient space around the capsule.

q + s = s

q + s = s

Air density = p/T

V = Velocity, ρ = density, A = Area

Through the three stages of a Venturi, 1,2,3, the equation balances in various proportions.

VρA 1 = VρA2 = VρA3

The mass flow remains the same throughout which in turn increases the velocity through the narrow part of the Venturi.

 

Because air is assumed to be incompressible below 300 kt TAS ρ can be ignored at this stage.

As the mass must remain the same, V must increase when A reduces and vice versa.

 

IAS = Indicated Airspeed = Indicated on the ASI (Errors; Instrument, Pressure, Compressibility)

CAS = Calibrated Airspeed = IAS corrected for Instrument and Pressure error.

EAS = Equivalent Airspeed = Corrected for compressibility.

TAS = True Airspeed = Actual speed through the air.

Steady is a smooth uninterrupted flow around a body whereas unsteady or turbulent airflow is when the air is unable to flow smoothly due to the shape of the body creating a sort of vacuum behind and allowing air to move in a chaotic or turbulent way.

Streamline represents one small flow of air. A stream tube represents flow in one specific direction, like a flow through an imaginary pipe. Patlines are basically the same as streamlines.

As above, it behaves as though it is flowing through a pipe.

2D flow is sufficient to describe the flow around a cross section of a wing, but not around a complete wing.

3D flow includes vortex flow which follows a helical path and therefore must be 3D.

The is the centre of pressure. The total reaction is up and back or lift and drag.

Lift acts up perpendicular to the free stream flow and drag acts backwards in the same direction as the free stream flow.

As above Lift up, drag back.

The centre of pressure moves around with alpha, the aerodynamic centre does not.

On a non-symmetrical wing there is a torque force between the sum of the reactive forces on either side of the wing. A moment between two centres of pressure if you like.

Luckily, the aerodynamic centre stays broadly in one place across all alphas. The position affects the size of the aerodynamic moment.

The shape of the aerofoil, the distance between the AC and the CG.

• Zero at all angles of attack for a symmetrical wing.
• Isn’t zero for a thin aerofoil with a camber.
• Is negative for a positively cambered aerofoil (pitch down).

Above

Above

It is the angle between the relative inflow (can be affected by up draughts etc.) and the aerofoil’s zero lift line

This is where the aerofoil first hits the airflow.

Very very back of the pointy aerofoil

The chord line is the line between the leading and trailing edge

Is the ratio between point of maximum aerofoil thickness and the chord length.

Point where the aerofoil is thickest, usually within the first third from the leading edge.

Is a line that is draw at a constant distance from the upper and lower surfaces.

Describes the distance between the camber line and the chord line. It is above the chord line for an aerofoil with positive camber.

It is the radius to the circle of the leading edge.

Um…

The distance between the wingtips, i.e. both wings.

These two chords can be different, giving us a……..

tip chord : root chord

Or gross wing area and is the total area of both wigs including the part under the fuselage.

The outline of the wings as seen from above.

Or average chord. It is the mean of the chord of the wing ! No shit !

Based on a theoretical, rectangular wing that has similar longitudinal stability as the actual wing. Rarely in the same place or the same length as the mean chord.

The wingspan to the average chord. Short and thick wing has a low aspect ratio whereas a long and skinny wing has a high aspect ratio.

Is the gradual bending up of the wing from the fuselage to the tip. It helps with stability in rolling.

The angle inclined relative to the lateral axis. i.e. zero degrees is perpendicular to the fuselage.

Possibly referring to washout. Is the twist at the end to change the angle of attack. Is to reduce the lift at the tips.

Yep…

It is smooth and predictable like John Travolta’s hair in Grease The Movie

Where the flow lines get closer and faster or further and slower.

Upwash is the process of the air being lifted upwards over the top of the aerofoil. Downwash is the downward flow running off the back of the trailing edge.

Is the point is where the air is neither going above or below the aerofoil and is stationary. Dynamic pressure is zero. Static pressure is maximum but exceeds atmospheric pressure.

A alpha increases, the stagnation point moves down

As the aerofoil thickens the airflow speeds up and its pressure drops, Venturi styleee. Airflow below is higher pressure and slightly slower.

Minimum static is when maximum dynamic is as total pressure remains the same. Normally at the thickest point.

Centre of Pressure – The average point from which the forces act. Does not move for a symmetrical wing, but due to changing lift, does for an asymmetrical wing.

Aerodynamic Centre – Where the wing moment remains about constant. About 25% Chord, 50% for supersonic flight.

Skin friction and Form

Like a spotty teenager, a rough surface that slows the airflow.

The form of the aircraft through the air. Air has mass so it can resist a force.

Energy transfer to the chaotic turbulent air, air has mass so uses energy to be turbulent, taken ultimately from the engines.

An increase in alpha forces the air to travel faster over the top of the aerofoil because it is presenting a larger barrier to the air so increasing the pressure differential.  This increases the lift

Shows lift factor against angle of attack. It is linear from the origin (symmetrical aerofoil) until C_L max where it drops off abruptly at about 16% AoA, which is the stall. 

1 – No Lift at all, not flying.

2 – The can still be lift at 0 AoA. A cambered aerofoil for example.

3 – The stall

To define lift or drag potential without using specific values.

Lift = C_L  1/2  ρ  V²   S

Lift is a force. Lift depends on dynamic pressure or kinetic energy, the area of the aerofoil and its lift coefficient. The formula for kinetic energy is:

Kinetic Energy = 1/2  m  V²

In the lift equation density is the mass.

The lift coefficient depends on the aerofoil’s camber and angle of attack.

 

 

Because a cambered aerofoil generates lift at a negative angle of attack the line is offset to the left of that for a symmetrical aerofoil.

 

A negative camber is basically an upside down aerofoil. The graph looks the same as it does not account for orientation, only lift to alpha.

A high speed aerofoil generates left lift for a given angle of attack because it is compensated for by a hight IAS.

CL Max is the stalling angle of attack and the angle for which most lift is generated.

αCRIT is the highest angle at which the aerofoil does NOT stall, just below the stalling angle if you like.

 

Angle of attack, aerofoil camber and the thickness of the aerofoil.

 

Drag = C_D  1/2  ρ  V²   S

TAS 120kt 63 m/s

S = 16m²

C_D = 0.03

Density = 1.2 kg/m³

 

Answer in Newtons

 

 

Form drag is the result of the body and cross sectional area. Increased size and shape will generally increase the coefficient.

Surface friction and increased drag is related to the condition of the skin. The airflow shears over the surface in increasingly faster layers.

 

Not very clear.

The angle of attack is the angle between the aerofoil’s chord line and the relative airflow for 2D.

 

For 3d, longitudinal axis of what? The aircraft?

 

The angle of attack is the angle between the aerofoil’s chord line and the relative airflow for 2D.

The attitude is the aircrafts angle relative to the horizon, but AoA changes with the relative airflow.

 

Best with a picture but the flow increases and decreases with thickness because of pressure differences. Laminar flow is nice and smooth and turbulent flow is chaotic and contains Eddie currents.

Because of higher pressure below the aerofoil and lower pressure above, the airflow tries to equalise. Air flows towards the fuselage above and away below the aerofoil.

 

The above has the effect of creating vortices as the pressure differential creates a circular motion.

A higher angle of attack provides more lift and more pressure differential therefore the vortices get stronger.  

A different platform will have varying lift distribution, from the root to the tip for example.

Elliptical wings taper outwards so the lift reduces and so do the vorticies .

Wake turbulence is caused by the wing tip vortices, it flows downwards and can extend several miles behind and last and number of minutes depending on the below factors.

Flaps reduce wing tip vortices.

Pressure differential and the time the wing spends influencing any given mass of air.

 

Induced drag comes directly from the production of lift.

Induced drag reduces as speed increases but parasite drag increases more and therefore increases total drag.

Lift must equal drag so if more lift is needed for more mass, then induced drag must also increase.

 

— aspect ratio; Reduces the wing tip vortices.
— winglets; Restricts vortices but adds parasite drag.
— tip tanks; Similar effect to winglets.
— wing twist; A gradual reduction of lift towards the tips, reducing lift and therefore vortices and drag.

Any design which reduces lift at the tips helps reduce induced drag. Elliptical wings being good.

Charges the airflow by reducing the effective angle of attack.

Induced is the angle between effective and relative airflow.

Effective is the angle between the effective airflow and the chord of the wing.

Tips it backwards.

— speed; Less as speed increases.
— aspect ratio; High aspect ratio (long and thin) produces more lift over drag compared to low aspect ratio.
— wing planform; An elliptical wing will reduce, induced drag.
— bank angle in a horizontal coordinated turn – At a level bank angle in a horizontal turn, more lift is needed and therefore induced drag.

 

Induced drag is inversely proportional to aspect ratio. The higher the aspect ratio – wide and small chord – the less vortices and less induced drag. Induced drag is directly proportional to the lift coefficient- the more lift the more induced or lift induced drag.

 

Mathematically then, CDI is proportional to CL^2 / Aspect Ratio

, where CD = coefficient of drag and CPD = coefficient of parasite drag.”]

— the CL–α graph; Lower drag because a higher aspect ratio gives the same lift for a smaller AoA.

— the CL–CD (aeroplane polar); Induced drag coefficient varies with coefficient of lift squared. A more efficient wing will have less drag for a given amount of lift.

— the parabolic aeroplane polar in a graph and as a formula; Parasite drag doesn’t vary much so induced drag is the main influence. CDI = CL^2 / Aspect Ratio

 

Lift and drag act at right angles to each other. There comes a point where CD continues to increase with no increase in CL.

The best L/D ratio is the tangent to the curve from the origin. 

Fuel efficiency

??

It does…

Form, skin friction and interference.

Comes from the pressure differential between the front and the back of the aircraft.

Local vortices and airflows at the junction of different parts of the aircraft. Un-aerodynamic features increase interference drag.

Is the shear force created between layers of air as it flows over the surfaces. A higher speed gives a steeper differential and higher drag. A large surface obviously creates more. A turbulent boundary layer also. Finally, surface roughness.

It increases with the square of the speed.

Total drag graph is a U-shape. Induced drag is high to begin then reduces. Parasite drag is low to begin then increases.

Where induced and parasite drag are both at their lowest.

It moves up and to the right. Parasite drag doesn’t change much but induced does.

— drag–IAS graph; – Does not change as it is an indication of dynamic pressure.
— drag–TAS graph – For the same IAS the TAS increase with altitude. The curve moves right when plotted against TAS.

On the Left side of the curve a reduction of speed increases drag so degrease speed further. On the right side a decrease in speed gives a decrease in drag also causing the speed to increase again.

Stability above VM, instability below VMD. Neutral is either side of VMD.

Slow down and stall as more thrust is needed.

wing tip vortices and downwash, the surface constrains them so is reduced or shallowed.

Effective airflow pattern changes because of reduced downwash across the tail plane causing a pitch down moment.

Lift increases because drag is reduced.

Induced drag decreases due to the reduced induced angle of attack.

The is a smaller induced AoA because of the flattening of the effective airflow relative the relative airflow.

Entering at 1 wingspan from the ground;

• alpha – Induced A0A reduces and so does induced drag = more lift.
• induced drag dominates total drag at low speed so has a big effect on total drag.
• Vortices are flattened or shallowed by the ground reducing the…
• Effective airflow
• IAS – Under reads because the dynamic pressure reduces slightly.

It is reduced because the effective angle of attack increases as the effective airflow flattens out. From 16deg to 12deg for example.

As the effective alpha increases so does CL.

Drag, lift and ASI explained above. There are also pitching moments, a nose down when entering and nose up when leaving. It’s because of the change in effective airflow across the tailplane. When entering GE, the EAF flattens out reducing the effective AoA on the tailplane, reducing its downforce giving a pitch down because the CofG is forward of the CofP. High tails not effected so much.  

High wings are less prone to ground effect as the reduction in drag over the height above the ground is not linear. The largest reduction is when the aircraft is below about 0.3 to 0.2 wingspans which a high wing may new get into. This helps on short runways.

 

CL is proportional to velocity squared and the lift equation shows that the lift will increase x4 for a doubling in speed.

Ok, do it.

— split flaps; Reduces airflow disturbance on the top side of the wing relative to simple flaps and gives a slightly higher CLmax but a higher drag penalty.
— plain flaps; Similar to the other primary control surfaces.
— slotted flaps; The gap helps re-energise the airflow above the wing delaying separation allowing a higher alpha and therefore CLmax. When at the leading edge, is called a slot.
— Fowler flaps. Extends the chord and therefore surface area adding lift and also induced drag. Can extend out to add a slot to the party.

By lowering flaps, you lower the chord and therefore the camber, increasing the pressure differential increasing both lift and drag. More lift means slower approach and take off speeds, more drag means a steeper approach angle and pitch down attitude (good for visibility).

— the location of CP moves aft as more lift is created further back.
— nose down pitching moments (due to wing CP movement);
— stall speed is reduced, the curve moves up and left, you get more lift for less alpha.

— indicate the variation in CL at any given α; Flaps move the line up, trailing edge more so.
— indicate their effect on CLMAX; Is increased in all cases.
— indicate their effect on critical α; Reduced with simple flaps, the same with leading edge, increased with slats.
— indicate their effect on the α at a given CL. Allows a lower alpha for given lift.

More lift and drag.

Steepens it due to drag, simple flaps present quite a high area to the airflow.

 

Can cause uncontrollable roll.

1 – Better view of the runway.

2 – More lift at a lower speed. More drag slows for landing.

— take-off and landing distance and speeds; Increased
— climb and descent performance; Lack of lift
— stall buffet margins. Stall speed increased.

— Krueger flaps; At the front, folds out.
— variable camber flaps; A droop at the leading edge and trailing edge flaps change the shape of the wing.
— slats. At the leading edge.

Called slats at the leading edge, smooth the airflow on the top side of the wing delaying separation to a higher AoA.

The chord lowers increasing the distance to the mean camber.

Peak suction doesn’t move as much as it does with trailing edge flaps so the CP doesn’t really move.

1 – Does not increase CL for a given AoA like trailing edge device do.

2 – Generally linearly increase the aCRIT.

In reverse order of lift increase over drag increase;

Plain

Split

Slotted

Fowler

Different aCRIT on each side.

They don’t change the position of the CP and increase the stalling angle. Nose up, less visibility. Distances reduced due to extra lift.

Pull down higher energy airflow into a limp boundary layer.

 

Improves the CLmax and critical angle for extra drag.

Increases parasite drag.

— roll spoilers; Decreases CL
— flight spoilers (speed brakes); Reduce airspeed, increase descent angle and rate. Control speed.
— ground spoilers (lift dumpers). Exactly that.

Lowers the line.

Gives the same lift for a higher alpha.

Increase drag, explained above.

Lots more drag for a given aloha.

Increase exposed area for no lift benefit.

Decreases Vmd because total drag is increased.

Increases both.

Leading edges

— lift (maximum CL); Reduce
— drag; Increase
— stall speed; Increase
— αCRIT; Reduction
— stability and controllability. Reduction.

Just wrong ! Unpredictability everywhere.

Boundary layer can be disturbed increasing skin friction drag. Less fuel efficient.

Generally less aerodynamically efficient.