Aerodynamics

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What are disadvantages of wing sweep?

Sweep reduces a wings coefficient of lift, increases stall speed, thus increasing take off and landing speeds and reducing field performance. Swept wings tend to stall first at the wingtips, which in turn causes the C of P to move forward producing a nose up pitching moment. This can lead to a deep stall, particularly in rear engined, T tailed aircraft

What is Dutch roll?

Dutch roll is a coupled lateral-directional oscillation, which is usually dynamically stable but is objectionable because of the oscillatory nature. The damping of this oscillatory mode may be weak or strong depending on the properties of the aircraft. The response of the aircraft to a disturbance from equilibrium is a combined rolling-yawing oscillation in which the rolling motion is phased to precede the yawing motion. Generally, Dutch roll will occur when the dihedral effect is large when compared to the static directional stability.

Span wise flow

Travels from the root to the tip and produces no lift.

Chord wise flow

The airflow over the wing that is perpendicular [at a right angle to the leading edge of the wing].

The airflow is accelerated over the wing and produces lift.

Where will shockwaves first occur on the wing?

At the point of maximum camber, usually at the wing root an a swept wing.

At what point on an aircraft is the local airflow the fastest?

At the point of greatest curvature. [Top of the 747's hump]

How does sweepback affect Mcrit?

By sweeping a wing significantly the velocity vector normal to the leading edge is made less than the chord wise resultant, thus MCRIT is increased.

What are the advantages and disadvantages of a thin wing?

Advantages:

• Raise Mcrit to a higher value

Buffet, drag rise and control and stability problems are all deferred to a higher Mach number and when they do occur, they are less severe than on a thicker wing.

Wave drag is proportional to thickness/chord [T/C] ratio

Disadvantages

• Structural weaknesses [rigidity/strength]

• Limited storage capacity [fuel and undercarriage]

• Poor low-speed aerodynamic characteristics [low CL, high Vs] and may also be prone to leading edge stall [sudden, no buffet]

What are the advantages and disadvantages of sweepback?

 Advantages:

• Sweep increases spiral stability, as does dihedral.

• Raise Mcrit to a higher value - Mcrit = Mcrit [straight]__

Cosine sweep angle

Eg. Mcrit straight = 0.8 [Now with sweep angle 30º]

Mcrit [swept] = 0.8___

Cos 30

 

= 0.8_

0.87

= 0.92 [in theory, a little less in practice]

This increase in Mcrit means buffet, drag rise and control and stability problems are all deferred to a higher Mach number and when they do occur, they are less severe than on a similar straight wing.

Disadvantages:

• Poor oscillatory stability

• Poor lift at low airspeeds [flatter lift curve]

• Less lift for a given airspeed/AoA [higher stall speed]

• High AoA at stall

• Tendency for the tips to stall first causing a pitch up at stall

• Steep deck angle on approach

• A swept wing has a high Vimd [min drag speed] requiring a large acceleration after rotation to achieve Vy

• Excessive lateral stability [can result in Dutch roll]

• Aero elastic effects such as aileron reversal, reduced tip AoA under G-loading which may cause a pitch up and tightening turn

• Limited visibility [of the wing] from the cockpit

Why are wings swept?

As the air passes over the wing accelerates to near sonic speeds, shock waves form and compressibility effects become apparent; the drag increases, buffeting is felt and changes in lift and C of P occur. The speed at which these compressibility effects first become apparent is the Critical Mach number [MCRIT].

 

 

By sweeping a wing significantly the velocity vector normal to the leading edge is made less than the chord wise resultant. As the wing is only responsive to the velocity vector to the normal leading edge, for a given Mach number the effective chord wise velocity is reduced (in effect the wing is persuaded to believe it is flying slower than it actually is). This means the airspeed can be increased before the effective chord wise component becomes sonic and thus the critical Mach number is raised. [HTBJ]

Why doesn’t the B777 have winglets?

The B777 uses the most aerodynamically efficient wing ever developed for sub-sonic commercial aircraft, allowing it to climb quickly, cruise at higher levels and higher speeds than comparable aircraft. [FTBJ B777]

Define angle of incidence.

Angle between longitudinal axis and the chord line of the wing.

Define AoA...

Angle between the relative wind and the chord line of the wing.

Define pitch attitude...

The angle between longitudinal axis and the horizon.

What is the mean camber line?

Line drawn halfway between the upper and lower surfaces of a wing.

Define chord.

Measure of the width of the wing.

Positive camber, negative camber, symmetrical airfoil definitions.

• Positive camber: mean camber line is above chord line
• Negative camber: mean camber line is below chord line
• Symmetrical airfoil: mean camber line coincides with chord line

If you decrease AoA how does that affect induced drag?

If you decrease AoA that will increase velocity which means that induced drag will decrease.

Define 'Mach number'...

Mach number is the ratio of the speed of an object or flow to the local speed of sound, under the same conditions.

How do you get zero lift in a positive camber wing?

You must go to a negative AOA.

Define Equilibrium

Sum of the forces is equals zero.
Sum of the moments is equals zero.
Aircraft is moving in a straight line at a constant velocity.

Draw the forces acting on an aircraft in a descent.

Draw the forces acting on an aircraft in a climb.

Why do some aircraft have winglets?

Tip devices have become a popular technique to increase the aerodynamic performances of lifting wings, short and slender alike. The idea behind all wingtip devices is to diffuse the strong vortices released at the tip and optimise the span-wise lift distribution, while maintaining the additional moments on the wing within certain limits. Investigations and experiments, indicated that the use of vertical lifting surfaces placed at the wing tips produce a beneficial effect on both lift and drag characteristics. This is found at the cost of increased bending moment. The increase in root bending moment is found to be lower than for an equivalent tip extension. Winglet sections can be airfoils with their own design.

At the tip, due to the pressure differential between the upper and lower surfaces, there is a significant span wise component to the airflow.  On the lower surface, the span wise component of flow is outwards, away from the wing root, and on the upper surface, the span wise component tends to be towards the root. Lift is defined as acting perpendicularly to the flow local of the airfoil and the surface plan form, then with a bit of cunning engineering, the lift on a vertical surface at the wing tip, in a flow with a span wise component toward the root such as occurs on the upper wing surface, could be directed "forward" - in the direction of flight, - and "inward" - toward the wing root.  The forward component of lift manifests itself as a reduction in total aircraft drag.  Of course, the benefit is reduced somewhat by the component of winglet drag acting aft, but nonetheless, the net result is a reduction in total aircraft drag.  And as mentioned elsewhere, winglets will indeed reduce the strength of the shed vortices in the tip region, but only as a consequence of the generation of a lift force on the winglet. For a given angle of attack, installation of winglets can also increase lift, but since aircraft mass is approximately unchanged, the aircraft would have to fly at a decreased angle of attack to maintain the same lift as in the pre-winglet case - which further decreases drag.

Winglets can be used to produce extra lift, besides lower drag. The winglets must be mounted on the rear part of the wing (region of lowest pressure), to minimize interference effects. Drag reduction rates are of the order of 5 %.

Winglets are applied in the latest generation of Boeing 747, MD 11, Airbus, and most executive jets and many sailplanes. Data available for the Boeing 747-400 indicate that without winglets the aircraft. suffers about 2.5 % drag losses, which corresponds to +9.5 tons at take-off.

How is range increased when flying into a headwind?

In a headwind maximum range is achieved by flying faster than 1.32 Vimd to minimise exposure to the headwind.

What is the difference between Max Range Cruise [MRC] and Long Range Cruise [LRC]?

MRC: The speed at which, for a given weight and altitude, the maximum fuel mileage is obtained. It is difficult to establish and maintain stable cruise conditions at max range speeds. 1.32 Vimd constant speed with variable AoA [dependent on weight].  

LRC: Speed slightly faster than MRC at a constant AoA [slightly faster than Vimd] As weight decreases, speed needs to decrease to maintain AoA Reducing speed necessitates reducing thrust, though because best SFC for a given engine occurs at a particular design RPM, you must climb

In the graph below a drag curve has been re-labelled 'Fuel Flow vs. Velocity'. In order to better see the origin of this graph the parasite drag and induced drag curves have been drawn in.

 

Maximum Endurance

Previously we defined SE as 1/FF. in other words an aircraft achieves more endurance when FF is smaller. Therefore, it is obvious that maximum endurance occurs at the bottom of the FF curve as shown above.

Since the above FF curve is exactly the same shape as the Drag curve, the lowest fuel consumption would correspond to the speed for minimum drag, [also known as L/D max AoA].

Maximum Range

As discussed previously, the speed for maximum specific range, in zero wind, will occur where the tangent line drawn from the origin just touches the curve [as shown below]. It is worth noting that maximum range always occurs at a higher speed than maximum endurance.

More correctly best range always occurs at a smaller angle of attack than best endurance. It is critical to remember that best range and best endurance both occur at specific angles of attack, regardless of weight.

 

Effect of wind on Range

A headwind will decrease the range and a tailwind will increase the range. This is only common sense.

However, with a headwind the aircraft must fly faster. In other words at a smaller angle of attack.

The tailwind graph below shows that theoretically the pilot should slow down [fly at a greater angle of attack] with a tailwind.

Note: the tailwind or headwind tangent line is drawn with the headwind or tailwind added. This ensures that the tangent [FF/V] of the line has the correct magnitude.

 

As a rule of thumb the pilot should speed up by half the headwind velocity. You can see from the above graph that this is a reasonable approximation.

Effect of Weight on Endurance and Range

Previously we examined how weight changes affected the total drag curve. You must remember that only the induced drag changes with weight.

In the diagram below the green curve is the original drag curve. The red curve is the total drag after some fuel is consumed [weight reduced].

You can see from the above graph that SE improves with lower weight. In other words the aircraft can fly for longer if it is lighter. However the aircraft must fly slower at the reduced weight. As proven earlier in our discussion of gliding however, the same L/D max angle of attack applies in both cases.

If you draw the tangent line in from the origin to both the green and red curves, you can quickly see that SR also improves at lighter weights. Just as with endurance the aircraft must fly slower as the weight is decreased. However, it should remain at the same angle of attack.

 

 

In summary, there is an optimum angle of attack for endurance. There is another optimum angle of attack (smaller) for range. The aircraft should always be operated at the correct angle of attack, which means that airspeed must be reduced as weight decreases (other factors being equal.)

 

Effect of Altitude on Range and Endurance (Jet)

The graph below shows how the drag curves and Fuel Flow vs. Velocity curves change with altitude. As the aircraft climbs into the less dense air the parasite drag decreases, but the induced drag increases. As a result the total drag curve moves to the right. Remember that the drag curve is exactly the same shape as the FF vs. Velocity graph for a jet.

As you can see in the graphs below there should be no change in the maximum endurance of the aircraft with altitude. However, the required endurance speed will increase. As before maximum endurance always occurs at L/D max. [I.e. always the same angle of attack] On web page 8 we will discuss the effect of engine and propeller efficiency.

For a jet range is significantly affected by altitude. As you can see in the graph below, as the aircraft climbs higher the max SR [V/FF] keeps getting better and better. Therefore, the jet aircraft should always be operated at high altitude unless there is a very strong headwind.

Jet Aircraft range/endurance summary

The TSFC of the jet engine improves up to the altitude for the coldest air temperature. In the ISA this is the tropopause [TSFC holds constant in the stratosphere]. Endurance will increase with altitude as long as temperature decreases with altitude. Maximum endurance will therefore occur at the tropopause. Range will increase with altitude up to the altitude at which Mach effects arise (see Cruise Control.) Endurance does not increase in the stratosphere, but it does not decline either. Therefore, pilots should not descend when holding. Wind will be a factor. But, due to the powerful benefit of altitude a jet will often get better range at altitude even with a moderate headwind.

 

Jet engine fuel consumption

Both jet and propeller engines consume fuel at a certain rate [FF] Jet engines convert the fuel-flow directly into thrust

Specific Fuel Consumption
Specific Fuel Consumption is a measure of the fuel consumed by an engine. There are two types of specific fuel consumption:

1.  Thrust Specific Fuel Consumption [TSFC]
2.  Power Specific Fuel Consumption [SFC]

TSFC is defined as fuel-low per pound of thrust produced [FF/Thrust]
SFC is defined as fuel-flow per horsepower produced [FF/HP]

Fuel-flow should be measured in units of pounds of fuel per hour, rather than gallons per hour. This is because the chemical energy in the fuel is a function of the mass of the fuel. A gallon of fuel expands or contracts with temperature. Therefore, a gallon of cold fuel contains more energy than a gallon of warm fuel.

The units of TSFC and SFC will be:

TSFC = lb per hr/thrust lb
SFC = lb per hr/HP

 

Converting the Drag vs. Velocity Curve

A perfectly accurate conversion of the drag curve into a Fuel-flow vs. Velocity graph must take variations in engine and propeller efficiency into account. However, we will find it easier to break the process into two steps. We will therefore conduct a simple aerodynamic analysis first, in which we will assume that:

• TSFC is constant for a jet
• SFC is constant for piston and turbo-prop engines

 

FF vs. Velocity for a Jet

We will start by converting a Drag vs. Velocity curve into a Fuel-flow vs. Velocity curve for a jet aircraft. This will be very easy because the TSFC is a constant.

Remember the definition of TSFC:
TSFC = FF/Thrust

We will assume that: TSFC = FF/Drag (i.e. we assume thrust = drag)

Therefore: FF = TSFC x Drag

What is the Critical Drag-rise Mach number [Mcdr]?

Mcdr is that free stream Mach number at which, because of compressibility effects the drag co-efficient at a specified angle of attack, has risen by 20% of its low subsonic value.

Define Mach Number Detachment [Mdet]

Mdet is that free stream Mach number at which the bow wave becomes attached to the leading edge.

Explain Compressibility Mach Number [Mcomp]...

Mcomp is that free stream Mach number at which, because of compressibility effects, control of an aircraft becomes difficult and beyond which loss of control is probable.

What is Mach Number?

Mach number is the ratio of the speed of an object or flow to the local speed of sound, under the same conditions.

How do you get zero lift in a positive camber wing?

You must go to a negative AOA.

If you decrease AoA how does that affect induced drag?

If you decrease AoA that will increase velocity which means that induced drag will decrease.

Explain positive camber, negative camber and symmetrical airfoil definitions.

• Positive camber: mean camber line is above chord line
• Negative camber: mean camber line is below chord line
• Symmetrical airfoil: mean camber line coincides with chord line

What is the mean camber line?

A line drawn halfway between the upper and lower surfaces of a wing.

Define chord

This is the measure of the width of the wing.

Define chord line

Infinitely long line drawn through the trailing edge and leading edge of airfoil (wing).

Define angle of incidence.

Angle between longitudinal axis and the chord line of the wing.

Define angle of attack

Angle between the relative wind and the chord line of the wing.

Define pitch attitude

The angle between longitudinal axis and the horizon.

What is the Mean Camber Line?

It's a line drawn between the upper and lower surfaces of the airfoil.

Define relative wind

Airflow the airplane experiences as moves through the air.
Equal in magnitude and opposite in direction to the flight path.

Explain IAS, EAS and TAS

IAS: Indicated airspeed

EAS: Equivalent airspeed-IAS corrected for position and compressibility errors

TAS: True airspeed, EAS corrected for atmospheric conditions

What limits an aircraft climb performance?

The amount of 'excess thrust' available.

How is drag defined?

Drag acts along the dragline of the aircraft
Drag = CD½ρV²S
Induced drag is the by product of the production of lift

Define Thrust

Thrust acts along the average centreline of the engines.
Thrust = Mass air flow x [Vj-V], or [mass x acceleration]

Define aerodynamic lift

Lift acts through the centre of pressure and acts perpendicular to the relative airflow.

Lift = CL½ΡV²S

CL: Co-efficient of lift [Lifting ability for a particular wing design at a given AoA]
Ρ: Rho represents the value of density [If density doubles, lift doubles]
V: Velocity or TAS of the air flowing around the wing [If velocity doubles, lift quadruples]
S: Surface area of the wing [If wing area doubles lift doubles]

What are the forces acting on an aircraft in flight?

Drag, thrust, lift and weight.

If thrust is greater than drag the aircraft will accelerate. If lift and weight are the same, an aircraft will maintain a steady, level attitude.If the aircraft is in a turn, lift is reduced due to the reduction of effective wingspan. The weight of the aircraft though remains the same. To maintain altitude when in a turn, speed and/or angle of attack has to be increased.

What is the Free Stream Mach number [Mfs]

Mfs is the Mach number of the flow sufficiently remote from the aircraft to be unaffected by it.

Explain Local Mach Mumber [Ml]

Ml is the ratio of the speed of the flow at a specified point to the speed of sound at the same point

Define Critical Mac Number [Mcrit]

MCRIT is that free stream Mach number at which the highest local Mach number reaches Mach 1.

What is the definition of Subsonic, Transonic, and Supersonic?

Subsonic
All flow everywhere on the aircraft is less than the speed of sound

Transonic
Some flow is subsonic and some is supersonic

Supersonic
All flow everywhere on the aircraft is supersonic