Category Aircraft Flight

A major breakthrough in the development of theoretical aerodynamics came when it was realised that a wing or lifting surface thus behaves rather like a rotating vortex placed in an air stream. This apparently odd conceptual jump was important, because it was relatively easy to mathematically analyse the effect of a simple vortex placed in a uniform flow of air.

In the simplest version of the theory, the wing is represented by a single vortex, which is known as the wing-bound vortex. In later developments, the wing is considered to be replaced by a set of vortices, as described further in Chapter 2. In Chapter 2 we also show how this vortex concept is very helpful in understanding the flow around a wing, and in analysing the influences of wing planform and general geometry.

One of the most important advances in the study of aerodynamics was the discovery of the influence of the ‘boundary layer’. This is a very thin layer of air adjacent to the surface of the aircraft. Despite its thinness, it holds the key to understanding how air flows behave, and in particular how lift is generated.

In this chapter we shall show how a knowledge of the behaviour of the boundary layer can enable us to improve the lift, drag and general handling characteristics of aircraft.

A major breakthrough

At the time of the Wright brothers’ first flight, a significant part of the basis of modern aerodynamic theory already existed in the form of the so-called clas­sical theory of fluid mechanics. In the early stages of its development, this theory took no account of the effects of viscosity (the stickiness of the air), with the unfortunate result that lift and drag forces were not predicted. For some time, therefore, it was little more than a toy for mathematicians. Equations which correctly took account of viscosity had been derived, but these ‘Navier-Stokes’ equations are extremely complex, and in their complete form they were of little practical use, until invention of the digital computer.

A big breakthrough occurred a few years after the Wright Brothers’ historic flight, when Prandtl found that the effects of viscosity were only important and apparent in a very thin layer adjacent to the surface. He called this the boundary layer. For an aircraft wing in cruising flight, it is, at most, only a few centimetres thick.

Although an exact analysis of the flow in the boundary layer was not possible, approximate methods based on experimental observation were developed. Outside the boundary layer, the effects of viscosity are negligible, and develop­ments of the classical theory can be used. By combining boundary layer theory

with the classical theory, it eventually became possible to produce results that were of real practical use.

There are several wing-tip devices that have been shown to produce significant reductions in drag. One of these is the wing-tip sail shown in Fig. 4.15. This device has been around for millions of years in the form of the tip feathers on some birds’ wings. At the tip of the wing, there is a strong upflow, as the air spills over from the underside. The feathers, or sails, are angled so that they generate a forward component of force, or negative drag, as illustrated in Fig. 4.16. For optimum effect, the feather angles need to be altered accord­ing to the flight condition. Curiously, quite a bit of research work had been conducted on this idea before anyone spotted that birds were already using the principle. It has been found that beneficial interference effects occur when

several sails (usually three) are used, as in Fig. 4.15. Birds also use several tip feathers; interestingly, always an odd number.

The sudden increase in fuel costs that occurred in the mid-1970s, caused man­ufacturers to look again at the possibility of designing propellers suitable for flight at high subsonic Mach numbers.

The primary approach to solving the problem of supersonic tips, is the same as that used for transonic wing design, as described in Chapter 12. Essentially, it is necessary to keep the maximum relative velocity on the blade surface as small as possible. Thin ‘transonic’ blade sections may be used, and the blades may be swept back producing the characteristic scimitar shape shown in Fig. 6.9.

Accurate control of pitch, enables high lift/drag ratio sections to be employed, and this in turn allows the use of large helix angles, so that the resultant relative flow speed past the blade is minimised.

A large number of blades is used, in order to reduce the thrust force per blade. As with wing lift, blade thrust is related to the circulation strength. By reducing the thrust per blade, the circulation is reduced, and hence the maximum relative speed on the upper surface is lowered.

Figure 6.9 shows a typical design for a contra-rotating configuration. Such propellers are variously described as prop-fans or unducted fans, and though

they may look very different from older designs, they are, in principle, still propellers. Although not providing such efficient propulsion as low speed pro­peller designs, unducted fan propulsion is more efficient than the turbo-fan system that it is intended to replace.

The relative airflow speed at the tips of such propellers is designed to be supersonic in high speed flight, and they are therefore very noisy. This is the major obstacle to their use in civil transport aircraft.

It should be noted, that reducing the propeller diameter will not reduce the tip Mach number, because in order to produce the same amount of thrust, the smaller diameter propeller will have to rotate at a higher speed.

The fuel flow rate required by a piston engine driving a propeller is approxim­ately proportional to the power produced (Chapter 6). Over a typical range of cruising speeds below about M = 0.65 we find that the engine/propeller combination can be designed to have roughly the same efficiency irrespective of the selected cruising speed of the aircraft.

Thus, if we look at Fig. 7.5 again for a moment, and select as our operat­ing point the minimum drag speed for any wing loading curve, we can design a piston/propeller combination which will operate at the same efficiency irre­spective of the particular wing loading chosen.

The main thing that will change in the engine design as we alter the wing loading will be the engine size. If we select a wing of small area the loading will be large and the minimum drag speed high. We already know that the min­imum drag value for the airframe will be the same for all the curves in Fig. 7.5, so the increase in operating speed means that the power (equal to drag times speed) required will be greater; hence the need for a larger engine.

If we double the engine size to double the power, we also double the fuel flow rate. Thus, if we select a smaller wing area and double the minimum drag speed, we will double the engine size and use fuel at twice the previous rate. However, we shall complete the journey in half the time so the same total amount of fuel will have been used.

We have, of course, been guilty of over-simplification once more. The larger engine will increase the weight of the aircraft which we have assumed to be constant. If we recall that a large wing implied an increase in structural weight we can now see the design compromise which must be made. If we choose a high operating speed then the engine weight will be high. If, on the other hand we choose a low speed the wing will be large and the structure heavy. The designer has, therefore, to seek an optimum point between the two extremes.

Figure 7.5 also shows that an increase in altitude also means an increase in the minimum drag speed. This means a more powerful engine once again. This means an increase in weight – a good reason for limiting the cruising altitude of piston-engined aircraft. In addition, piston engines do not work particularly well at high altitude, although supercharging helps (see Chapter 6).

So far we have considered the size of the required engine only from the standpoint of cruise performance. In the real aircraft a somewhat larger engine will be required since matching the engine to the minimum drag speed at low altitude would permit the aircraft to fly only over a very limited speed range (Fig. 7.7), and extra power is required to give the aircraft an acceptable speed range and ceiling.

In order to get full benefit from the engine for a given weight it should be operated near the maximum throttle opening. Because of the reducing air density the power output of the engine falls with increasing altitude. Thus a cruising altitude is selected where the available engine power matches the required power near minimum drag.

There will be other operational requirements, such as the need to keep above severe weather, which will influence the actual choice of cruising altitude, but in general, the type of piston driven airliner of a few decades ago cruised at a comparatively low altitude compared with today’s turbo-jet driven airliners. We shall now examine reasons for the increased cruising altitude for this latter type of aircraft.

In designing a wing it is necessary to consider not only one specific design point in the cruise, but off design conditions as well. We have already discussed this with reference to low speed requirements at landing or take-off, and the air­craft must also be able to accelerate safely through the entire speed range to the cruising condition. The idea of an aircraft having a single ‘design point’ is in itself somewhat misleading. A typical transport aircraft will have to operate over a number of different routes and hence ranges. It will also be required to carry a variety of different payloads. A military aircraft (Fig. 9.8) may, for example, also be required to carry a variety of underwing ‘stores’ such as mis­siles, bombs or fuel tanks for extended range. It must be able to perform these

tasks safely and inadvertent excursions from the cruise condition, such as gusts or a reasonable degree of pilot error, must not put it in danger.

One of the problems with transonic aircraft is that the speed margin for safe operation is fairly small. For example the difference between the stalling speed and cruising speed for a large airliner (Fig. 9.9) may be as little as 60 m/s. This may seem surprisingly small, but it must be remembered that we are talking about the aircraft in the ‘clean’, flaps up, condition. Because the aircraft usu­ally cruises at a considerable altitude the density is low, which means that the stalling speed will be increased (Chapter 2). Furthermore, because the temper­ature of the air is also low, the speed of sound will be reduced, and the speed at which the cruise Mach number occurs will be lower than we might expect (Chapter 5).

If we inadvertently impose an extra load on the wing, say due to a gust, or allow the Mach number to rise, we encounter another factor which limits the speed range in the upwards direction, not because of lack of power and excess­ive drag, but because of a potentially dangerous ‘buffeting’ effect.

We have seen that one of the design features of a supercritical aerofoil is that the supersonic flow over the top surface is recompressed by, at worst, a relat­ively weak shock wave. Provided that this shock wave is not too far back on the section, it will not produce any extensive separation of the boundary layer, although a small separation bubble may form. If the intersection point is nearer

Air speed

Fig. 9.11 Stall and buffet boundaries

As the aircraft flies higher its speed range gets smaller as it is squeezed between the two boundaries

the trailing edge, however, extensive separation may occur (Fig. 9.10). This can lead to unsteady flow in which the shock wave moves rapidly backwards and forwards over the section – clearly not a desirable state of affairs. The loading on the section then fluctuates significantly and buffet is said to occur.

Thus, as well as the need for good characteristics at the design point, it is necessary to ensure that there is adequate margin before buffet occurs, and that its onset will not be sudden and catastrophic. Usually the presence of a weak shock wave at a point in front of, or at least not too far downstream of the maximum thickness point on the aerofoil, is helpful in giving reasonably good buffet behaviour.

An idea of the restricted operating range of a typical transonic aerofoil is given by Fig. 9.11 where both stall and buffet boundaries are shown.

Buffet behaviour can be improved by devices other than section design. One way of doing this on the three-dimensional wing is to introduce a series of

bodies starting near the point of maximum thickness and extending beyond the trailing edge (Fig. 9.12). These are colloquially known as Kuchemann carrots or Whitcomb bumps after the two people who first, independently, suggested their use. The local flow fields produced by these bodies break up the shock wave when it moves towards the trailing edge, thus improving the buffet behaviour.

At low speeds, where the angle of the wing is high, and the aircraft is flying in a nose-up attitude, the tail surfaces may be partially immersed in the wake of the wing. To prevent this, the horizontal tail surface may either be mounted low so that it is out of the wake, as on the Tornado (Fig. 3.14), or high, as on the C-17 (Fig. 10.20). When the high option is chosen, the tail may need to be

WING TIP ROLL REACTION CONTROL VALVE

Fig. 10.21 Reaction controls are necessary on the VTOL Harrier (Diagrams courtesy of Rolls-Royce pic)

mounted very high indeed, as on the C-17, otherwise it may come under the influence of wing wash just before the stall. This creates a very dangerous con­dition known as superstall, where not only is the aircraft stalled, but the lack of control means that the pilot can do nothing about it. The stall is likely to deepen, and recovery at low altitude is impossible; a situation that has caused a number of fatal accidents.

Because of the dangers of stalling, particularly at low altitude, a number of automatic devices may be fitted to warn, or otherwise help the pilot to avoid a stall. These include a flashing light, and an audible warning that is triggered off if the angle of attack is sensed to be too high.

On small aircraft, the onset of a stall can often be sensed by the shaking of the control stick, caused by buffeting of the control surfaces by the turbulent separated flow. On aircraft with powered controls, this buffeting may not be transmitted, and a stick shaker mechanism can be fitted to shake the stick artificially, and thus provoke the required conditioned response from the pilot.

In some cases, particularly on large airliners, a stick pusher may be incor­porated. This is a device that automatically pushes the stick forwards to reduce

the angle of attack when it is sensed to be too high. A good description of such devices is again given by Davies (1971).

The use of reliable fly-by-wire systems enables aircraft to be flown much closer to the stall than was previously considered either possible or advisable. Some control systems may even allow the aircraft to be flown in a partially stalled condition.

Take-off and landing present a particularly hazardous part of the flight of an aircraft. During take-off the aircraft will be heavily loaded with fuel for the journey and the engines will be working at high rating in order to take off in as short a distance as possible. The take-off for a commercial airliner is further complicated by the need to adhere to appropriate noise abatement procedures. This may typically involve an initial climb at high angle in order to put the maximum distance between the aircraft and the ground at the boundary of the airfield. This may then be followed by the need to reduce throttle setting as a populated area is reached.

Landing, too, has its difficulties. The pilot has to manoeuvre the aircraft to a precise touch-down point in three-dimensional space. Furthermore when touch-down is achieved the aircraft must be flying in the correct direction, aligned with the runway, and must be at a low air speed to facilitate bringing it to a halt in a reasonable distance while retaining a safe margin over the stalling speed.

Take-off and landing have common features; for instance the object of the exercise is to transfer the weight from wheels to wings (or vice versa) in as short a distance as possible. However the conditions of weight are considerably different because most of the fuel will generally have been used on landing. Also the engine power output used will differ considerably in the two cases. For these reasons we consider them in separate sections.

Gas turbine engines are capable of producing a maximum thrust of more than twenty times their own weight. It is therefore possible to dispense with wing­generated lift, and use engine thrust instead, by directing the jet downwards. This method of lift production was successfully demonstrated on a skeletal rig aptly known as the ‘Flying Bedstead’, shown in Fig. 1.24.

The British Aerospace Harrier (manufactured under licence in the USA as the McDonnell Douglas AV-8) shown in Fig. 7.12, was the first operational aircraft to use this method of generating lift, and employs rotatable nozzles to direct or ‘vector’ the engine jets. Two sets of nozzles are used; one pair for the exhaust jet, and the other for a jet of air bled from the compressor. For ver­tical take-off and landing (VTOL), the jets are directed vertically downwards. For forward flight, the nozzles are rotated to direct the jets aft. As the air-speed increases, a conventional wing gradually takes over the job of providing lift. Intermediate nozzle positions can be used for low speed flight, and for short take-off and landing (STOL). A broadly similar approach is used on the (STOVL) version of the F35, but an engine-driven fan is used at the front.

An alternative, which was used on the YAK-36, is to employ auxiliary lift engines to supplement the vectored lift from the main propulsion engines.

Using engine thrust to produce lift directly in this way is extremely in­efficient, as it requires in the order of fifteen to twenty times more thrust than is necessary with conventional wing-generated lift. Another problem is, that in the vertical motion, hover and transition stages, the aircraft cannot be stabil­ised or controlled by normal aerodynamic means. In the case of the Harrier, auxiliary ‘puffer’ jets are mounted on the nose, tail and wing tips to provide stability and control (Fig. 10.21). The aircraft is, therefore, very vulnerable to failures in the propulsion and stability system during vertical flight. In practice, this has not been a major problem. Landing a conventional interceptor aircraft is if anything more hazardous. The disadvantages of direct lift are largely out­weighed by the operational advantages of vertical take-off and landing, as was well demonstrated by the Harriers during the Falklands conflict.

For efficient flight, the wing must produce a good ratio of lift to drag at the designed cruising speed. This requires the use of a wing section with only a modest amount of camber. The wing should also be as small as possible, so as to minimise the weight and the surface area, since both of these factors affect the drag.

Remembering that for level flight,

Lift = Weight = – pV2 (Area) CL,

it can be seen, that as the aircraft slows down, the lift coefficient required increases, so for landing, it is necessary to generate very large values of CL. Simply increasing the angle of attack may be insufficient if the aircraft is designed for a cruising speed that is much higher than its landing speed, and it may be necessary to use other methods of increasing CL for landing.