We have examined the way in which the flow changes as the speed of sound is exceeded and in Chapter 8 we will look at the way aircraft have developed to operate at speeds up to about twice the speed of sound (Mach 2). Some aircraft, however, have to operate at very much higher Mach numbers, particularly re-entering satellites and space shuttles. We find that a number of problems are associated with flight at these very high Mach numbers (up to about 27). Some of these are direct aerodynamic problems associated with the extreme speeds. Some are primarily structural and material problems caused by the high temperature induced by the flow. The SR-71 spy-plane used expansion joints in the structure, which lead to conspicuous, but not dangerous, leakage of fuel when on the ground. Other problems are due to the height at which such flight conditions are most likely to be made and are caused by the very low density encountered. For realistic flight conditions these problems begin to be felt at Mach numbers above about six, and so flight above this rather imprecise demarcation line is known as hypersonic.
What, then, are the aerodynamic problems associated with this flight regime? Initially nothing particularly dramatic occurs. All the main features of the supersonic flow are there, such as the bow shock wave and expansions. As would be expected from the increase in Mach number, the bow shock wave is more acutely swept to the free-stream direction. It is when we come to look at the details of the flow that we find the important changes that have taken place.
We have already seen that the shock wave is quite a traumatic experience for the flow passing through it. Pressure, density and temperature all increase dramatically over a very short distance. However, the basic composition of the air passing through the wave does not change in supersonic flow. It still consists of a mixture of roughly 70 per cent nitrogen, 20 per cent oxygen, 9 per cent carbon dioxide, with a few rare gases thrown in for good measure. The molecules of each of the various constituents are in their usual form with the nitrogen and oxygen molecules both being diatomic (i. e. with two atoms to each molecule). All the constituents are also electrically neutral, the electrons in each molecule exactly balancing the charge in the molecular nucleus.
As the Mach number increases and the shock wave gets stronger this situation changes and the so-called real gas effects become important. The relatively simple relationships between gas properties which occur under moderate conditions of temperature and pressure break down. The two atoms in the gas molecules become detached from each other, a process known as dissociation and energy is released into the flow. This dissociation may also be present in the high temperature regions of the boundary layer near the surface of the vehicle.
A further problem occurs due to the fact that molecules may become electrically charged, or ionised. This means that electrical forces may further complicate the fluid motion. This may not necessarily be a bad thing, and schemes have been suggested to use this feature to control the flow or even provide a propulsion system.
Yet another complication arises when we consider flight at extreme altitude. For normal aircraft operation, the air molecules are very close together. The average distance between molecular impacts (the mean free path at sea level) is about 6.6 x 10-5 mm. At 120 km altitude, this distance increases to 7 m, a distance that is quite large when compared with the size of the vehicle travelling through the air. In this case we can no longer think of the air as being a continuous fluid, but must consider the action of individual molecules, and average their effect.
From the above, it will be appreciated that the theoretical prediction of such flows becomes very difficult. Experimental work under such extreme conditions is also an arduous and costly undertaking. For further information, the interested reader is referred to Cox and Crabtree (1965).
An early problem with turbo-jet propulsion was that the high speed aircraft that it produced tended to have a high landing speed. As there was no propeller drag to help slow them down, they needed very long runways. One solution to this problem is to fit thrust reversers in the form of a movable device to deflect the exhaust jet forwards. Thrust reversers take many forms, and may either use cold air from the compressor, or the hot exhaust gases. Two typical hot-jet
deflector designs are shown in Fig. 6.31. The louvred cascade for the hot-jet deflector used on Concorde may be seen in Fig. 6.32.
Despite the added cost and weight penalty, thrust reversers are now popular even on small executive jets. Apart from reducing the landing run, the feature enables the aircraft to manoeuvre more easily on the ground under its own power.
A more detailed description of jet engine components is given in the well – illustrated Rolls-Royce publication The Jet Engine (1986).
Any real swept wing with subsonic leading edges will not behave in quite the same way as it would at subsonic speed because of the fact that there must be a limit to its span. For simplicity we will first examine the simple case of a swept wing without a fuselage separating the two halves (Fig. 8.11).
In this case the flow can only be influenced at a finite distance upstream and for very thin wings at small angles of incidence the appropriate zone of influence will be approximately defined by the Mach waves at the apex of the wing (Fig. 8.11(a)). If the disturbance to the flow is bigger, because of increased wing thickness or angle of attack, then a shock wave forms at the apex (Fig. 8.11(b)) and, because of its higher propagation speed, the zone of influence of the wing will be extended slightly in the upstream direction.
We now see that for a real swept wing we will still generate wave drag due to this bow shock wave. However we have gained one important advantage and that is due to the fact that the wing now works in much the same way at both sub – and supersonic speeds over most of the span. This means that the problem of choosing a wing section which is a suitable compromise between high and low speed has been made very much easier than before.
If we now introduce a fuselage the overall picture does not look very different, although some clever aerodynamic design at the wing fuselage junction may well prove very worthwhile – but more of that later.
The tip region
Unlike the unswept wing which we discussed earlier in this chapter, the tip region lies within the Mach cone of all the upstream wing sections. This region thus again behaves in a manner very similar to its subsonic counterpart (Chapter 2) and a trailing vortex sheet will be generated along the trailing edge of the wing and this will roll up into two large vortices which stream downstream of the wing in a position close to the tips.
A final variant of tailplane design is the vee-tail, illustrated in Fig. 10.9. The hinged trailing-edge control surfaces are moved differentially (one up and the other down) to provide a sideforce component like a rudder, and collectively (both up or down together) to provide a vertical component like a conventional tail. The claimed advantage of the vee-tail is that the number of surfaces is reduced, with consequential reductions in drag and weight. The F117A stealth fighter Fig. 6.34 uses a vee-tail which avoids the right-angles that cause large radar reflections.
Flying an aircraft in a neutrally or slightly unstable condition is not necessarily difficult or dangerous, but it involves hard work for the pilot, who cannot take his hands off the controls, and must make continuous control adjustments. The Wright brothers’ original aircraft was unstable, which made it more responsive and controllable than many of its contemporary rivals. There are, however, other more important advantages in moving the centre of gravity aft. By moving it to the neutral point, the position where the aircraft is neutrally stable, the tail has to produce no trimming force, and hence there is no trim drag. By moving it even further aft to an unstable position (negative CG margin) we can arrive at a position where the wing and the tail are both producing lift at an efficient positive angle of attack. This considerably improves the lift-to-drag ratio of the aircraft, and can dramatically improve its performance. An unstable aircraft will also respond more quickly to control inputs, making it highly manoeuvrable.
Aviation safety regulations traditionally took a dim view of flying in an unstable condition, but for military applications, the performance advantages are considerable. With the development of increasingly reliable electronic control systems it became practical to build aircraft that could be flown in a naturally unstable condition, relying entirely on automatic systems to maintain artificial stability. Most high performance military aircraft are in any case
totally unflyable in the event of a major electrical failure, so further dependence on electrical systems does not significantly reduce their safety. The X-29 (Fig. 9.20), and Typhoon (Fig. 10.8) are both designed to be inherently unstable at subsonic speeds. For civil aircraft, some reduction in stability may be tolerated, if the overall system can be shown to be capable of coping safely with failures in individual elements. This normally entails duplicate or multiple components, and rapid automatic fault diagnosis.
The introduction of new materials has opened up a range of possibilities for the design of more efficient aircraft, and even new types of aircraft. Man-powered flight would probably not have been possible using traditional materials.
Since the First World War, aluminium alloys have been almost universally used as the primary structural material, even for supersonic aircraft capable of Mach numbers up to about 2.2, such as Concorde. However, for sustained flight at Mach numbers above about 2.5, the effects of kinetic heating render conventional aluminium alloys unsuitable. Instead titanium and steel alloys may be employed. Unfortunately, their use presents something of an economic barrier. Apart from the higher cost of these materials, the fabrication techniques required tend to be more expensive. It is this economic barrier, rather than any purely aerodynamic problem, that has limited the maximum Mach number to around 2.5 for all but a handful of experimental aircraft. Rare exceptions are the MiG-25 combat aircraft, which is capable of Mach 3, and the even faster specialised Lockheed SR-71 reconnaissance aircraft.
Since the 1950s, gradually increasing use has been made of fibre reinforced materials. Originally, glass fibres were used, but a major advance came with the introduction of carbon (graphite) fibres. Carbon fibres can be produced in a number of forms, and can be optimised either for high strength, or for high stiffness (high modulus). It is the high stiffness of carbon fibres that make them a particularly attractive alternative to metals in aircraft construction. Boron fibres show even better properties, but are less cost effective than carbon fibres, and have only been used in experimental or highly specialised applications.
Although fibre reinforced or composite materials can have a higher strength – to-weight or stiffness-to-weight ratio than metals, they cannot simply be used as a direct replacement. The main problem is that they do not deform plastically like metals, and cannot be joined by conventional types of bolts or rivets, since this causes local cracking. The general adoption of fibre reinforced materials
was, therefore, slowed down by the need to develop suitable fastenings and construction techniques. Increasing use of composites is now being made, particularly in military combat aircraft and helicopters. The Beech Starship (Fig. 4.10) was one of the first civil transport aircraft designed for large-scale production, to use composites for its primary structure.
In addition to high strength and stiffness, fibre reinforced materials have some other important special properties. By aligning the fibres in particular patterns within a structure, it is possible to control the relationship between bending and torsional stiffness. This technique is one of the methods that can be used to reduce the tendency to structural divergence of forward-swept wings, and gives us another example of the way in which the development of materials can influence aerodynamic design judgements.
The use of moulded composite structures has also made it economically practical to produce complex aerodynamically optimised shapes, even for light aircraft.
Because fibre reinforced materials are built-up, rather than being cut or bent out of solid block and sheet, they can be produced in much more complex, ‘organic’ forms, with continuous variations in thickness, curvature and stiffness. Such structures begin to resemble the highly efficient optimised shapes found in the bones of birds.
Composite structures were initially restricted to smaller components such as control surfaces, but more recent aircraft employ composite materials for the main structural components, as on the Airbus A350XWB shown in Fig. 14.6, and also the A400 heavy lifter, and the Boeing Dreamliner. The weight saving allows for significant improvement in fuel consumption, or enhanced payload capacity.
Further discussion of aircraft structural design is beyond the intended scope of this book, but Megson (2007) gives a good introduction.
Recommended further reading
Megson, T. H. G., Aircraft structures for engineering students, 4th edn, Butterworth – Heinemann, 2007, ISBN 9780750667395. A well-respected standard undergraduate textbook. Includes examples. Solutions manual available.
Stinton, Darrol, The anatomy of the aeroplane, 2nd edn, Blackwell Science, Oxford, 1998, ISBN 0632040297. A classic introduction to aircraft design.
Wilkinson, R., Aircraft structures and systems, 2nd edn, Mechaero Publishing, St Albans, UK, 2001, ISBN 095407341X. A good easily read introductory text with a non-mathematical approach.
This concludes our introduction to the subject of aircraft flight. We have tried to include all of the important basic principles, and one or two items of interest. Inevitably we will have omitted something important, but the references given in this book should lead you to most of the missing information.
Air molecules are always in a state of rapid random motion. When they strike a surface, they bounce off, and in doing so, produce a force, just as you could
produce a force on a wall by throwing handfuls of pebbles against it. We describe the magnitude of pressure in terms of the force that the molecular impacts would produce per square metre (or square foot) of surface.
The air density (p) is the mass (quantity) of air in each cubic metre and the density therefore depends on how many air molecules are contained in that volume. If we increase the number of molecules in a given volume without altering their rate of movement, the force due to pressure will increase, since there will be more impacts per square metre.
The rate at which air molecules move is determined by the temperature. Raising the temperature increases the rate of molecular movement, and hence tends to increase the pressure.
It will be seen, therefore, that the air pressure is related to its density and temperature. Students of engineering may care to note that the relationship is given by the gas law p = pRT, where R is a constant.
The pressure, temperature and density of the atmospheric air all reduce significantly with increasing altitude. The variation is described more fully in Chapter 7. The reduction in density is a particularly important factor in aircraft flight, since aerodynamic forces such as lift and drag are directly related to the air density.
Highly swept wings tend to produce the stable separated conical vortex type flow described in Chapter 1, at relatively low angles of attack. For aircraft
designed to fly at twice the speed of sound or more, it becomes possible to use this type of flow for all flight conditions. On the slender-delta-winged Concorde, the leading edge was made very sharp to provoke separation even at the low angles of attack required at cruising speed. It was also warped along its length in such a way as to ensure that the vortices grew evenly along the leading edge. Figure 2.23 gives some idea of the complexity of this wing. In addition to the leading edge warp, the wing has spanwise variations in camber for reasons that will be explained later.
The conical leading edge vortices extend downstream, and the usual trailing vortices are formed, as illustrated in Fig. 1.21. One advantage of this type of flow is that tip stalling does not occur, since the flow is already separated and stable.
From the plan view of Fig. 2.24 it will be seen that the wings of Concorde were not a true delta, but had curved leading edges; a shape that is known as an ogive. The ogive shape has the effect of moving the position of centre of lift rearwards and also reduces the variation of the position of the centre of lift with angle of attack and speed.
Concorde was originally envisaged as flying with conventional attached flow in cruise, but it was found that the optimum cruise condition was obtained with a small amount of leading edge vortex flow.
Highly swept wing root strakes are used on some aircraft to provide a combination of separated conical vortex flow inboard, and conventional flow outboard. Wing root strakes may be seen on the F-18 in Fig. 2.25. With this arrangement, at high angles of attack, the loss of lift on the outboard wing sections may be more than compensated for by the extra conical vortex-lift generated by the strakes. The vortex produced by the strakes also helps maintain flow attachment on the wing, as described in Chapter 3.
Another way of increasing the proportion of laminar boundary layer on a wing of given area, is to reduce the chord of the section, while increasing the wing span: in other words, by increasing the aspect ratio. Thus, high-aspect-ratio wings can be beneficial in reducing both trailing vortex and surface-friction drag.
Artificially induced laminar flow
In order to preserve a low-drag laminar boundary layer over an even larger proportion of the surface of an aircraft, the engines can be used to provide suction to remove the boundary layer through slots, as described in the previous chapter, or through a porous skin. Several research aircraft have been flown with experimental porous or slotted surfaces. A good description of early postwar experiments is given by Lachmann (1961). Although very low drag values were often obtained, it was discovered that there were considerable practical difficulties, particularly in keeping the holes free of debris and suicidal insects. A boundary layer suction system would increase the cost, complexity and weight of the aircraft. The engine performance, and the aircraft handling properties may also be adversely affected. Thus far, there has been no widespread application of suction-induced laminar flow in production aircraft.
For many years, the main concession to the idea of using engine suction in this way, has been the occasional use of a pusher propeller situated at the rear of the fuselage or engine nacelle, as in the Beech Starship shown in Fig. 4.10. The rear-mounted propellers ensure that there is a favourable
pressure gradient (air moving towards a lower pressure) over the nacelles, and a large area of the wing. This in turn delays the transition to a turbulent flow, and inhibits separation. Proponents of the aft-mounted pusher propeller claim considerable reductions in drag by this method, but this may be partially offset by a deterioration in propeller efficiency. A more significant advantage of this arrangement is the reduction in cabin noise.
As with wings, increasing the aspect ratio of the propeller blades reduces the drag or resistance. However, the amount of thrust that can be produced, depends on the total blade area, so the use of high aspect ratio blades may result in an unacceptably large propeller diameter. Large high-powered propeller-driven aircraft often have low-aspect-ratio ‘paddle’ blades.
A small number of blades is preferable as it reduces the mutual interference effect between blades. However, maintaining sufficient total blade area to transmit the required power through a given diameter may necessitate a compromise between aspect ratio and number of blades. The Spitfire, which started life with only two blades and 1000 bhp, ended up as the Seafire 47 with six blades (on two co-axial contra-rotating propellers) and 2350 bhp. The diameter was limited by ground clearance. The Lockheed Super Hercules, shown in Fig. 6.6 uses high-aspect-ratio six-bladed 4.11 m diameter propellers.
Increasing the number of blades also reduces the amount of thrust that has to be produced by each blade, which is an advantage in high speed operation, as it lowers the maximum local Mach number on the blades. The importance of limiting the Mach number is described later.