Category Aircraft Flight

Lift from rotating wings

In the helicopter the rotor blades are, in effect, long rotating wings of small chord. The blades are mounted on an engine-driven shaft. As they move through the air, they generate lift in the same way as a fixed wing. The obvious advantage over a fixed-wing aircraft is that the rest of the aircraft does not need to move relative to the air, and it can therefore hover.

The torque reaction of the motor tends to rotate the fuselage in the opposite direction to that of the rotor, and on a conventional single rotor helicopter, a tail mounted propeller or fan is used to counteract this effect. The tail pro­peller, which is normally referred to as the tail rotor, wastes power, and is one cause of the poor efficiency of simple helicopters. A recent innovation is the so-called no-tail rotor (NOTAR) design in which the tail rotor is replaced by a jet of air which interacts with the main rotor downflow to produce the required torque. The NOTAR configuration has a number of operational advantages including reduced noise.

When two rotors are used, they can be arranged to rotate in opposite direc­tions, thus cancelling out the unwanted torque reaction, and removing the need for a tail rotor. The two rotors are normally arranged at opposite ends of the fuselage, but sometimes, particularly in Russian designs, they may be arranged so as to counter-rotate on concentric shafts as illustrated in Fig. 1.25. The use of two rotors considerably increases the cost and complexity of the aircraft. There are also problems due to interference between the two rotor wakes.

On a simple single rotor helicopter, direct control of the amount of lift gen­erated by the main rotor blades is provided by the collective pitch mechanism which changes the incidence or ‘pitch angle’ of all of the blades by the same amount simultaneously. In addition, a cyclic pitch mechanism is provided. This causes the incidence of the blades to increase and decrease once per cycle. The cyclic pitch control is used to control both the nose-up (or nose-down) attitude of the helicopter, and the roll motion about the longitudinal axis. The small tail rotor is also provided with a mechanism which can be used to vary the incidence of its blades, thus altering the amount of thrust produced. This allows it to be used to yaw the aircraft.

Lift from rotating wings

Fig. 1.25 A pair of co-axial counter-rotating rotor blades removes the need for a tail rotor on this Kamov Ka-50. Note the considerable complexity of the rotor heads however

On conventional helicopters, particularly older designs, the rotor blades are hinged about two axes at the point where they are joined to the hub, in such a way that they are free both to swing back and forth, and to flap up and down (within limits). The swinging motion is primarily intended to damp out cyclic variations in drag, and this hinge is called the drag (or lag) hinge. A damper is fitted to prevent unwanted oscillations. The flapping motion is resisted by strong centripetal forces, which tend to keep the blades nearly at right angles to the axis of rotation. The lift forces on the blades are always very much smaller than the centripetal forces, but they nevertheless pull the blades up slightly, so that in flight, their rotational path describes a very shallow cone rather than a flat disc.

When the cyclic pitch control is used to vary the incidence cyclically, the blades will tend to flap up and down cyclically in response to the lift variation. If the blades are caused to flap up at the rear, as shown in Fig. 1.27, the effect is to tilt the axis of tip rotation forwards. This generates a horizontal thrust force component, as illustrated, and the helicopter is thus propelled forwards. The flapping hinges are normally offset from the centre of the hub axis, and as the axis of blade rotation is inclined relative to the shaft axis, the centripetal forces produce moments which tend to tilt the rotor axis (and hence the whole aircraft) nose-down. By suitably adjusting the cyclic pitch control, the hori­zontal propulsion force can be arranged to occur in any desired direction, not just forwards, and it is thus possible to fly a helicopter sideways or backwards.

Lift from rotating wings

Fig. 1.26 On the so-called rigid rotor design, flapping is provided by flexible members and compliant joints which replace the hinges of older designs. Note the compactness and simplicity relative to the Kamov design shown in Fig. 1.25

Lift from rotating wings

Fig. 1.27 Helicopter in forward flight

The blades are caused to flap up at the rear by use of the cyclic pitch control. The resultant force provides both lift and thrust components

When a helicopter flies forwards, the relative air speed on the advancing blade side will be greater than on the retreating side. If no corrective action were taken, this would cause the blades to flap up towards the front and down towards the rear, thereby tilting the axis of the blade rotation backwards: a condition known as blowback. If this were allowed to happen unchecked, the helicopter would simply slow down due to the now rearward thrust com­ponent. This tendency therefore has to be overcome by making use of the cyclic pitch control to reduce the blade angle of attack when advancing, and increase it when retreating. By this means, the lift is equalised on the advancing and retreating sides. If simple rigidly fixed blades were used, as on a propeller, the blades would generate more lift when advancing than when retreating, and the aircraft would tend to roll.

Two-bladed rotors may use a teetering rotor instead of flapping hinges. In this arrangement, the two blades are rigidly connected together, but allowed to tilt about the hub to produce a flapping motion. A teetering rotor is used on the autogyro shown in Fig. 1.31.

Some more recent helicopter designs do not use hinged blades, but rely on carefully controlled flexure of the mounting points: an arrangement that is often misleadingly referred to as a rigid rotor. Figure 1.26 shows a ‘rigid rotor’ head mechanism. Its relative simplicity and compactness may be contrasted with the great complexity of the conventionally-hinged double unit of the Kamov shown in Fig. 1.25.

The rotor head contains not only the hinges or flexures but must also carry the mechanism for the cyclic and collective pitch control of the blades. This unit is thus a very complicated and heavily loaded item, and almost any mechanical failure is likely to be disastrous. The safety record of helicopters is generally inferior to that of fixed-wing aircraft.

It should be noted that the description above applies to conventional heli­copters. Various alternative rotor mechanisms have been tried, including ones with tilting shafts.

Since the rotor provides thrust, lift and the primary means of control, the helicopter can be seen as a good example of a radical departure from Cayley’s classical aeroplane, where each component serves only one specific purpose.

The helicopter also suffers from other problems stemming from the differ­ences in the relative airflow velocities on the advancing and retreating blades. In order for the retreating blade to generate any lift at all, it must be moving faster than the relative airflow. As you can see from Fig. 1.28, this means that the advancing blade must be moving through the air at more than twice the speed of the aircraft. The advancing blade will, therefore, approach the speed of sound, when the aircraft is still only travelling at well below half this speed. Having a blade that continually moves in and out of supersonic flow produces considerable structural and aerodynamic problems, not the least of which is the noise created.

Figure 1.28 also shows a common situation, where the inboard part of the retreating blade is not moving fast enough to overtake the air flow. The

Lift from rotating wings Lift from rotating wings

Resultant

Resultant relative velocity

Fig. 1.28 Relative air flow velocities in forward flight air therefore actually flows backwards relative to the blade on this portion. These factors severely limit the maximum speed of conventional helicopters. Figure 1.29 shows the Westland Lynx, which achieved a record-breaking 249.10 mph in 1986. This is less than half the speed attained by the fastest propeller-driven conventional aircraft.

A complete description of helicopter aerodynamics is beyond the scope of this book, but the above outline gives some idea of why rotating wing aircraft have not displaced fixed wing types, despite the obvious attraction of vertical take-off and landing.

Trailing-edge flaps

In Chapter 1, we described how the lift coefficient of a wing depends on its camber. The wing camber can be changed in flight by deflecting the trailing edge downwards as shown in Fig. 3.13. The hinged trailing edge is known as a flap. The simple hinged flap shown in Fig. 3.13(a) is often used on light aircraft. The split flap shown in Fig. 3.13(b) is an alternative arrangement that was commonly used during and just after the Second World War.

The stalling effect, caused by flow separation, however, limits the maximum value of CL that can be obtained in this way. The key to producing very high

Trailing-edge flaps

Fig. 3.13 Passive high lift devices

The increase in CL depends on the precise geometry of the device and the wing section, but generally, the most complicated devices tend to be the most effective. Increases in CL (max) vary from about 50 per cent for the simple camber flap to more than 100 per cent multi-element devices (a) hinged or camber flap (b) split flap (c) slotted flap (d) slotted extending (e) double slotted extending flap (f) dropped leading edge (g) extending leading-edge slat (h) leading-edge or Kruger flap

lift coefficients is to be found in inhibiting or controlling the separation of the boundary layer.

Since separation is associated with the dissipation of energy in the bound­ary layer, it follows that we can prevent separation either by removing the boundary layer, or by adding energy to it. The slotted flap shown in Fig. 3.13(c) represents one simple method. The slot allows air from the undersurface to blow over the flap, so that a fresh new boundary layer is formed on the flap, helping to maintain attachment. The tired wake from the main wing element may also be re-energised by turbulent mixing with the air emerging from the slot, but this is a secondary effect.

On sophisticated aircraft, it is normal to use a flap element that slides out, thereby increasing the wing area. This type is known as a Fowler flap, and is illustrated in Fig. 3.13(d). For very high lift coefficients, the flaps may be split into two or more elements. A two-element slotted flap is shown deployed on the Tornado in Fig. 3.14, and illustrated in Fig. 3.13(e).

Trailing-edge flaps

Fig. 3.14 Two-element full-span slotted flaps on the Tornado

Note the large slab (variable incidence) horizontal tail surfaces The two horizontal tail surfaces can be moved differentially (one up, one down) to provide roll control, an arrangement known as a taileron. No conventional ailerons are used, so the wing trailing edge can be used entirely for flaps

More about oblique shock waves – turning the flow

Because an oblique shock wave is able to impose a sudden change in the direc­tion of an oncoming air stream (Fig. 5.12), the necessary flow deflection around an aerofoil with a sharp leading edge can be achieved with an attached shock wave system (Fig. 5.13) in which the bow shock waves emanate from the lead­ing edge itself.

More about oblique shock waves - turning the flow

Fig. 5.12 Flow deflection at surface with oblique shock wave

Flow direction can be changed almost instantaneously by shock wave

More about oblique shock waves - turning the flow

Fig. 5.13 Sharp nosed aerofoil with attached shock waves

Because shock waves can change flow direction instantaneously the required directions at the sharp leading edge can be obtained by ‘attached’ shock wave

However, there is a limit to the angle through which a flow can be deflected. This depends on the Mach number of the flow. If this critical angle is exceeded, the shock wave becomes detached (Fig. 5.14) and looks very much like the bow shock wave of the blunt aerofoil described earlier (Fig. 5.1).

So far we have only considered sudden changes in flow direction. If the flow is turned gradually (Fig. 5.15), the picture looks slightly different. Near to the surface the flow compresses and turns without a shock wave, but one is observed further away from the surface. The reason for this is that as the flow compresses its temperature rises. The speed of sound therefore increases and if we draw ‘Mach lines’ to indicate the extent to which each point on the surface can influence the oncoming flow, we see that these get progressively steeper and eventually run together to form the shock wave.

The compression near the surface is known as a ‘shockless compression’ and we will see later how this type of compression can be exploited in practical design as it involves no wave drag.

More about oblique shock waves - turning the flow

Fig. 5.14 High angle of turn

If the maximum angle is exceeded the shock wave detaches from the corner as shown

More about oblique shock waves - turning the flow

Fig. 5.15 Shock free compression

Multi-spool engines

As the air flows through a compressor, its pressure and temperature rise. The rise in temperature means that the speed of sound increases, so without raising the Mach number of the flow, we can afford to let the later (high pressure) stages run at a higher speed than the early (low pressure stages). On modern engines, it is therefore usual to use two or more concentric shafts or spools. Each spool is driven by a separate turbine stage and runs at a different speed. Figure 6.22 shows a two-spool layout based on the Rolls-Royce Olympus 593 fitted to Concorde.

In turbo-prop engines, it is normal to drive the propeller from a separate turbine stage and spool from that of the main or core section of the engine. The propeller and core engine speeds can, therefore, be partially independently controlled.

The Rolls-Royce Gem engine, shown in Fig. 6.21, is described as a turbo­shaft engine, as it is intended to drive a helicopter rotor shaft rather than a propeller. It combines many of the features described above. Three spools are used, one to drive a single stage high pressure centrifugal compressor, one to drive a multi-stage low pressure axial compressor, and one to drive the rotor shaft via a gearbox.

Multi-spool enginesturbine

Hot and cold air

Подпись: Cold airПодпись:Подпись: Low pressure

Multi-spool engines
Multi-spool engines
Подпись: compressor

jets have nearly

the same velocity at the point where they

meet

Fig. 6.23 A two-spool low by-pass ratio jet engine (or low by-pass turbo-fan)

Only part of the air passes through the combustion chamber. The rest is by-passed around the core. This type of engine is quieter and more fuel-efficient than the simple type shown in Fig. 6.2. It is commonly used in high performance military aircraft

Performance in turning flight

So far we have considered the aircraft to be flying in a straight line. We now turn our attention to the important manoeuvre of changing direction; the turn.

We look first at the case in which the turn is made at constant altitude. Any time a turn is made by any vehicle, whether it be a bicycle, car, train or aeroplane, a force must be provided towards the centre of the turn because there is an acceleration directed towards the centre. In the case of a car or bicycle this force is provided by the tyres; in the case of a train it is provided by the rails. For an aircraft some other means must be found and this is done by tilting, or banking the aircraft so that a component of the lift force produced by the wings acts in the required direction (Fig. 7.21). Thus the wings must produce a higher amount of lift than was required for normal straight and level flight.

This extra lift means that, for a given speed, the wing must be operated at a higher angle of attack in the turn and, in addition, the increase in the lift will be accompanied by an increase in drag. This drag will, in turn, mean that the power required to sustain a steady turn is greater than that required for flight in a straight line at the same speed. The angle of bank and increase in lift, drag and required power all increase as the turn is tightened, and it may be that the minimum radius of turn which can be achieved is limited by the amount of power that is available from the engine. Alternatively the demand for extra lift may cause the wing to stall before this point is reached, and stalling may therefore prove to be the limiting factor.

Vertical lift component balances weight

Lift component provides required centripetal force

Fig. 7.21 Forces in turning flight

Lift must increase to provide both the vertical component to balance weight and the required forces for the turn

Recommended further reading

Mair, W. A. and Birdsall, D. L., Aircraft performance, Cambridge University Press, Cambridge, 1996, ISBN 0521568366. A good general text on aircraft performance.

The pilot’s controls

Since the very earliest days, the three primary control actions available to the pilot of a conventional aircraft have been those of pitch, roll, and yaw, as defined in Fig. 10.1. On most military interceptor aircraft, the controls are operated by the same type of control stick or joystick as used on early aircraft. On most other aircraft, some form of handlebars or spectacle grip is provided, either protruding from the instrument panel as in Fig. 10.2, or mounted on a movable control column.

With the introduction of completely electronically operated fly-by-wire sys­tems (described later), where the control column provides no direct mechanical operation of the control surfaces, a new form of control called a sidestick has

Fig. 10.2 Controls and instruments on a well-equipped light aircraft (actually a simulator)

been introduced, as seen in Fig. 10.3. This is a miniature form of joystick designed for one-handed operation, and mounted at the side of the pilot’s seat. The use of a sidestick produces a less cluttered flight deck, as shown in the photograph.

In conventionally controlled aircraft, pulling back on the stick or handlebars produces nose-up pitching action. Note, however, that in a weight-control hang-glider or microlight (Fig. 11.10), the control action is reversed; the pilot pulls on the control bar to transfer his weight forwards, tending to produce a nose-down effect. Pilots of conventional aircraft need to be very careful when converting to microlights, and vice-versa.

Turning the handlebars on a conventional aircraft clockwise, or pushing the stick to the right, produces, as its primary effect, a clockwise roll (and a

Fig. 10.3 Airbus A320 flight deck

The sidestick and display screen produce a much less cluttered arrangement than on older airliners

(Photo courtesy of British Aerospace)

consequential tendency to turn to the right). In this book, by left and right we mean pilot’s left and right.

Yaw control is provided by foot-operated pedals. Pushing on the pedal bar with the right foot causes the aircraft to yaw to the pilot’s right. Most people find this pedal action natural, which is curious, because unlike the other con­trols, the pedals work in the opposite sense to the turning direction required. On a bicycle, pushing the right handlebar would turn the bicycle left.

Note, that the amount of rotation of the handlebars affects the rate of roll, rather than the angle to which the aircraft rolls.

Delta-winged aircraft

Delta wings are effectively swept, and tailless delta-winged types can be stabilised in the same way as other tailless aircraft. However, a major problem arises with supersonic tailless deltas, because the rearward shift of the centre of lift position has to be trimmed by a large up-elevator movement. This significantly reduces the lift, while increasing the drag. On Concorde, the prob­lem is mainly solved by rapidly pumping fuel from a front tank to a rear one, so as to move the centre of gravity back for high speed flight. The movements of fuel during any flight have to be carefully calculated before take-off. This method of stability control, though complicated, does result in efficient flight with little or no trim drag.

In addition, the shape of the camber line may be used to control movement of the centre of lift. In Chapter 1 we explained how the lift due to angle of attack, and lift due to camber, were almost independent. At low speeds, the lift coefficient and angle of attack are large, so the lift force is dominated by the angle of attack. The centre of lift will be about – of the way back from the leading edge (- chord position). At high speed, the lift coefficient and angle of attack are low, and the lift is dominated by the camber. By suitable shaping of the camber line, the centre of lift at high speed (low angle of attack) can be arranged to be at about the same position as at low speed (high angle of attack). The very pronounced droop of the leading edge of Concorde’s wing produced by the camber may be seen in Fig. 2.23.

Because of the problems of control and stability of tailless deltas, many delta-winged aircraft have a small tail, or a foreplane.

Dynamic cases

Structural flutter

Flutter is the name given to a form of structural vibration that normally involves a combination of motions; typically bending and twisting. It is most likely to occur on wings, but tailplane flutter is not uncommon. The Handley Page 0/400 bomber produced an early, well documented, case of tailplane flutter, during the First World War.

Figure 14.4 illustrates one flutter mode. In this example, the wing is oscil­lating in torsion (twisting) as well as bending. As it bends upwards as in position-1 in Fig. 14.4, it is twisting in a nose-down sense. When it passes the limit of upward travel and starts to spring back down, it presents a negative (nose-down) angle of attack as in position-4. As the lift force is now down­wards, it aids the motion.

Near the bottom limit of travel, the wing starts to twist nose-up, so that when it springs upwards (position-9), the angle of attack has become positive,

Fig. 14.4 Flutter

The wing twists as it flaps up and down. The changes in angle of attack mean that the aerodynamic force is always tending to help the motion, which does not, therefore, damp out

and the lift force again aids the motion. Because the lift force is assisting the movement, the motion does not damp out like a normal vibration, and it can continue, sometimes with the amplitude increasing until failure occurs.

It will be seen, that in the case described above, the torsional and bending oscillations are 90° out of phase; that is, the bending deflection reaches its max­imum as the twist approaches its mid-position.

The normal remedy is to increase the torsional stiffness of the wing, but flutter can also occur by a coupling of the wing flexure with a pitching oscillation of the whole aircraft. This problem was encountered on some tailless aircraft, for which the pitching inertia was low. In such cases, increasing the torsional stiff­ness would not help, and it was the flexural stiffness that had to be increased.

The mass distribution also critically affects the flutter behaviour of the wing, and the location of wing-mounted engines is an important factor.

As with divergence, the onset of flutter depends on the aircraft speed. The lowest speed at which flutter occurs, is known as the critical flutter speed, and again, it is necessary to ensure that the aircraft speed never reaches the critical value.

Optimum economy with the jet engine

The fuel flow rate in a gas-turbine engine depends only on the throttle set­ting and is approximately proportional to the thrust produced by the engine rather than the power. Unlike the piston engine the efficiency of the turbo-jet engine (Chapter 6) improves with increasing dynamic pressure and reducing temperature. For optimum engine efficiency we therefore need to fly fast and high.

Because the engine efficiency increases with speed, the best speed to fly at is a compromise between the requirements of the airframe and the engine. Thus, unlike the piston engined aircraft, the best cruising speed will be somewhat higher than the minimum drag speed (Fig. 7.4).

Because of the way in which the engine behaves, we now need the dynamic pressure (and hence operating speed) to be as high as possible. Thus we need to design and operate the aircraft so that the best airframe performance is obtained at as high a speed as possible. The requirement for high speed is good news for the commercial operator, as we will see shortly. The aircraft should also be operated at high altitude so that the temperature of the air is low, to further improve engine performance.

As we have seen, reducing the wing area enables us to increase the dynamic pressure to compensate. In order to fly at high speed we therefore need an air­craft with the smallest possible wing area, consistent with acceptable low speed performance.

Flying high, too, has its limitations. The lower the air density the higher the stalling speed of the aircraft (Chapter 2). The maximum speed, for a conventional transonic airliner, will be dictated by the onset of problems associated with high Mach number (the buffet boundary Chapter 9), and so flight becomes possible over an increasingly restricted speed range as height is increased (Fig. 7.8). From an operational viewpoint a safety margin must be allowed to allow for accidental speed changes and for manoeuvres

Fig. 7.8 Effect of weight on stall and buffet boundary

A reduction in aircraft weight as fuel is used means that the intersection between stall and buffet boundaries occurs at a greater height

such as making turns which make extra demands on the wing lift as will be seen later.

Wing plan shape

The way in which the lift per metre of span varies along the span, depends on (among other things) the way in which the chord varies along the span. For untapered rectangular planform wings, most of the trailing vorticity is shed near the tips. In this case, the downwash will be greatest near the tips. If a tapered wing is used, the lift is increased at the centre, and trailing vorticity is produced more evenly along the span.

Theoretical analysis indicates that for a given amount of lift, the smallest amount of trailing vortex (induced) drag will be produced when the downwash is constant along the span. The same analysis also shows that the constant downwash condition is obtained if the lift per metre of span varies from zero at the tips, to a maximum at the centre, following an elliptical relationship, as indicated in Fig. 2.11. An elliptical spanwise variation of lift thus represents a theoretical ideal case for minimum trailing vortex drag.

On aircraft with unswept wings, an elliptical variation of lift can be produced by using a wing where the chord varies elliptically with distance along the span. Such wings have rarely been built, but one notable example

Wing plan shapeConstant downwash

Подпись: < Ml

Подпись: Lift at centre (maximum)

Lift/metre of span at distance у from centre = Lift at centre

Fig. 2.11 Elliptical variation of lift along the span

This variation gives a constant downwash along the span, and the minimum amount of trailing vortex (induced) drag shown in Fig. 2.12 is the Spitfire wing, which has a precise elliptical variation of chord.

There are manufacturing problems associated with an elliptical planform and furthermore, this shape is not ideal from a structural point of view. The structural designer would prefer the lift forces to be concentrated near the centre or root of the wing, so as to reduce bending moments. He would also like the depth of the wing spars to reduce towards the tips to maintain a con­stant level of bending stress. If the wing section shape were then to be the same at all positions, the chord would have to reduce accordingly. This would lead to the form of wing shown by the dashed lines of Fig. 2.13. The trailing vortex drag depends on the lift required, which in turn depends on the aircraft weight. A wing of this better structural shape should be lighter than the elliptical wing. The elliptical planform would only represent the shape for minimum induced drag if the weight of the wing structure were negligible. This is never the case, and by using a more efficient structural shape, it is possible to save weight. It therefore follows that for a real aircraft, the lowest drag would be given by a planform shape that was somewhere between the two extremes shown in Fig. 2.13; a compromise between the aerodynamic and structural ideals. In fact, a straight taper gives a good compromise, and has the advantage of being easy to construct. This factor shows the importance of integrating all aspects of aircraft design, and not trying to optimise any one feature in isolation.

The fact that an elliptical planform does not represent the true minimum drag shape for a practical aircraft was shown by Prandtl in 1933. It should be noted that the Spitfire was originally conceived with a simple tapered wing. The elliptical planform was adopted largely because of a need to increase the

Wing plan shape

Wing plan shape

Fig. 2.12 Elliptical and tapered planforms

The Spitfire (upper) had a wing with an elliptical variation of chord along the span. This theoretically gives the minimum amount of trailing vortex drag for a given wing area The Mustang (lower) used a wing with conventional taper, but improved aerofoil section. Merlin-engined versions of the two aircraft had similar performance, the Mustang being in some respects superior

The Spitfire shown in the photograph is actually a late Griffon-engined Mk-14

Wing plan shapePreferred planform for purely structural considerations

Elliptical planform for minimum trailing vortex (induced) drag

Fig. 2.13 Wing shapes for minimum trailing vortex (induced) drag and for structural efficiency. A straight taper gives a good compromise and is easier to manufacture The elliptical planform shown is that of the Spitfire section depth around mid-span to accommodate ammunition boxes and the undercarriage mechanism.

When engines are mounted on the wings, their weight reduces the bending stresses on the inboard sections of the wing. Little or no taper is thus required for the inboard sections. When an untapered centre section with tapered outer sections is used, the overall wing planform approximates roughly to the ellipt­ical aerodynamic ideal. Designers rarely seem to have taken advantage of this, but the DH Canada Dash-8 (Fig. 13.4) is one example.

On a straight-tapered or untapered wing, an elliptical distribution of lift may be produced by using a variation of incidence along the span; in other words, by twisting the wing. Spanwise variation of wing-section camber is also used in some designs.

For a given aircraft weight and flight altitude, the use of a fixed amount of twist or camber variation can only produce a truly elliptical lift distribution at one speed. This is not necessarily a major objection, however, as many other aspects of aircraft design are optimised for a preferred combination of speed, height and weight, or cruise condition.