Category Aircraft Flight

In the above section we saw that, in supersonic flow as well as subsonic, boundary layers exist and can separate. There is a great deal of similarity in the behaviour of the boundary layer at both high and low speeds. Chapter 3 is applicable above as well as below the speed of sound. The requirement that the flow is at rest relative to the surface (the no-slip condition) is still applic­able and so somewhere in the boundary layer the flow goes from subsonic to supersonic speed (Fig. 5.20).

One way in which the boundary layer in supersonic flow can be subjected to a severe pressure gradient is when a shock wave, which may be generated by another part of an aircraft, strikes the surface. In this case the shock wave reflects as is shown in Fig. 5.21. It will be observed that the shock wave cannot penetrate right to the surface but only as far as the sonic line (see Fig. 5.21), but the pressure rise is transmitted through the boundary layer and may well cause separation to occur.

Figure 5.21 shows that the reflection process is quite complex. As the flow speed falls within the boundary layer so the shock wave angle becomes steeper to give the same pressure rise, as the local Mach number is reduced. The increase in pressure in the boundary layer will cause it to thicken and may well cause separation. The picture shown in Fig. 5.21 is therefore just one of a number of possibilities.

It should be noted that we have been guilty of some simplification in some of the previous figures. For example the shock wave in Fig. 5.12 has been drawn right down to the surface as if there were no boundary layer present. This may be an acceptable approximation in many cases, but if the boundary layer should separate then the picture may be changed considerably.

Shock wave reflections of this sort are important in determining how the flow behaves, and reflections are by no means always as simple as that shown in Fig. 5.21. The boundary layer at the point of reflection as well as the strength of the shock wave may be complicated by such factors as local separation bubbles or complete boundary layer separation. Three­dimensional effects will also have an important bearing on the nature of the reflection process. A detailed discussion of the various types of reflection which may be encountered is outside the scope of this book, and the interested reader will find a great deal on the subject in the literature, e. g. Cox and Crabtree (1965).

Kinetic heating

In Chapter 2 we saw how the pressure and velocity for a low speed flow could be related by Bernoulli’s equation. This equation is only approximately true, however, and, for a compressible fluid, becomes less accurate as the speed of flow increases. This is because significant changes start to occur not only in the kinetic energy of the fluid but also in the internally stored energy within the gas. This means that, as the speed increases, not only does the pressure fall but so does the temperature. Conversely, when a high speed air stream is slowed down there is an accompanying rise in the temperature.

Again it makes no difference if we consider the aircraft moving through the air rather than the air streaming past the stationary aircraft. The rise in tem­perature is most severe when the air is brought to rest, relative to the aircraft, at a stagnation point. Figure 5.22 shows the air temperatures encountered, at different flight Mach numbers, in such a stagnation region at a cruising height roughly equivalent to that of Concorde. Such temperature rises can have important implications in terms of structural strength and distortion.

We have seen that another way in which the air can be suddenly slowed in supersonic flow is by the presence of a shock wave. Frequently very severe heating problems can be encountered where the flow passes through a local shock wave near the surface. One example of this is provided by the high local heating rates which can occur at a junction between a fin and a fuselage.

The boundary layer provides another mechanism which can raise the air temperature with important structural consequences for high speed aircraft. The boundary layer slows the flow near the surface with a consequential

temperature rise. This temperature increase is only of any significance at high flight speeds.

The state of the boundary layer is also important in determining the rate of heat transfer to the surface. In general a turbulent boundary layer will transmit heat into the structure more readily than a laminar layer because in the turbu­lent layer the regions of the boundary layer close to the surface are continually replenished with high temperature air.

This heat transfer process can also affect the way in which the boundary layer behaves. The extreme temperatures which may be encountered at very high (hypersonic) speed may cause significant changes in the properties of the air itself, as we shall discuss briefly in the next section.

In gas-turbine-propelled aircraft, there is frequently a requirement for short bursts of increased thrust, particularly for high performance military aircraft, which need to accelerate rapidly. Unlike the reciprocating engine, the gas tur­bine only uses, for combustion, a small proportion of the available oxygen in the air that passes through it. It is, therefore, possible to obtain a significant boost in thrust by burning more fuel in an extended tailpipe section known as an afterburner or reheat chamber, as illustrated in Fig. 6.30.

The thrust can be approximately doubled in this way with only a relatively small increase in weight. At low flight speeds, reheat is extremely inefficient, and is normally only used for take-off, and to produce short bursts of rapid acceleration. In supersonic flight, it becomes more efficient. Most modern supersonic aircraft use reheated low by-pass turbo-fans.

Reheat necessitates the use of a variable-area exhaust nozzle, and the extra tailpipe length and burner produce additional friction losses when not in use.

The requirement that the velocity component normal to the leading edge should be subsonic implies that the degree of sweep must be greater than the local Mach angle (Chapter 5). If this is so, we can see from Fig. 8.9 that the sec­tion AA’ on the wing lies within the Mach cone emanating from a point B. Point B will influence not only section AA’ but also the flow approaching the section AA’. The distance ahead of A where the approaching flow is first influenced will increase as the distance between A and B increases and, for a wing of infinite span, the approaching flow and the flow over section AA’ are (ignoring boundary layer effects) precisely equivalent to the flow over AA’ being at the subsonic velocity Vn.

This may, perhaps, seem like a rather tortuous way of repeating what we know already. However, the value of looking at things from this point of view will be apparent when we come to examine the tip and centre section flows shortly.

A wing whose leading edge is swept at an angle greater than the Mach angle is said to have a subsonic leading edge. If the sweep angle is less than this value then the leading edge is said to be supersonic (Fig. 8.10). In this case the flow over the section will be supersonic in nature, albeit at an apparently reduced Mach number as a result of the sweep.

In a tail-first or canard (the French word for a duck) configuration, shown in Fig. 10.8, and Fig. 10.1, a nose-up pitching moment is obtained by using the forward foreplane to lift the nose up. Rotating the foreplane surface to increase its incidence will increase its lift and consequently the overall lift.

Operating the elevator control on a canard configuration produces an immediate increase in lift, and thus, a more favourable response to pitch con­trol. Together with other factors described later, this has led to the adoption of

a canard configuration on many aircraft, particularly delta-winged types, as illustrated in Fig. 10.8, where a slab-type canard foreplane may be seen. The foreplane is capable of a large range of movement.

The experimental X-29, shown in Fig. 9.20, has no fewer than three sets of pitch-control surfaces, resulting in something of a headache for the control system designer.

In the simple cases shown in Figs 11.5 and 11.6 we conveniently had the drag force passing through the centre of gravity. In practice, the line of action of the tailplane drag must move as the aircraft attitude changes. With the aid of sim­ple sketches, it is easy to work out that for a conventional aircraft this produces a stabilising tendency, while for a canard, the influence is destabilising.

In addition to the factors given above, we also have to consider the influence of fuselage, flaps, undercarriage, external stores (armaments) and any other features that can produce either an aerodynamic force or moment, or a change in the centre of gravity position. It is also very important to take account of the flexibility of the aircraft and control system components.

Active load control may also be used to reduce structural loads during man­oeuvres. One method of manoeuvre load control (MLC) is to use inboard flaps to increase the load on the inboard portion of the wing when performing manoeuvres that require a high lift. By concentrating the lift inboard, the bending stresses at the wing root are reduced.

Alternatively, by using a large number of individually adjustable trailing edge flaps or flaperons, it is possible to adjust the spanwise loading to give a low-drag elliptical distribution, even during high-load combat manoeuvres. Again, these techniques require the use of reliable automatic control sytems.

Once again, birds have beaten us to it, and have been using complex forms of active load control for millions of years.

Structural solutions

As we have seen, aeroelastic effects occur as a consequence of insufficient struc­tural stiffness, rather than a lack of strength. Problems of aeroelastic failure are

as old as aviation itself, and a number of early attempts at flight are thought to have failed due to structural divergence.

The biplane arrangement of struts and wires initially provided an acceptable solution. By suitable criss-crossing of the wires, this arrangement could pro­duce a surprisingly stiff structure. In contrast, many early monoplanes suffered aeroelastic failures due to a lack of torsional stiffness.

Early aircraft wings were constructed using a number of spars which, though capable of withstanding large bending moments, produced little torsional resist­ance (Fig. 14.5(a)). The torsional stiffness was initially improved by adding stiffening webs between the spars, but later, it was found that by placing two spars close together and closing them to form a ‘torsion box’, as shown in Fig. 14.5(b), the torsional rigidity could be greatly increased. Closed tubes offer considerably better torsional stiffness than open sections. Try twisting a cardboard tube such as an empty toilet roll tube, and you will find it almost impossible. Now slit the tube from one end to the other, and you will find that it will twist easily.

With the adoption of metal skins for wings, instead of doped canvas, the torsional rigidity increased considerably. In Fig. 14.5(b), it will be seen that the leading and trailing-edge sections themselves form closed tubes, in addition to the central box. Figure 14.5(b) thus illustrates a torsion box construction with two additional closed cells.

For transonic and supersonic aircraft it is advantageous to use thin wing sec­tions. This in turn requires the use of very thick skins in order to provide the necessary stiffness. Consequently it has become practical to machine the skin out of solid plates of metal. Stiffening elements and details can be machined integrally with the skin, eliminating the need for rivets. By this method, it is possible to produce the smooth surface and precise contours required for low – drag aerofoil shapes.

When thin sections with thick skins are employed, it is normal to use the skin to form the top and bottom of a number of closed cells, as shown in Fig. 14.5(c). No separate specific torsion box is then required.

Although wings consisting of thin flat or curved plates can produce adequate lift, it is difficult to give them the necessary strength and stiffness to resist bend­ing. Early aircraft that used plate-like wings with a thin cross-section, employed a complex arrangement of external wires and struts to support them, as seen in Figs 1.7(a) and 1.7(b). Later, to reduce the drag, the external wires were

removed, and the wings were supported by internal spars or box-like struc­tures which required a much thicker wing section. By this time, it had in any case been found that thick ‘aerofoil section’ shapes, similar to that shown in Fig. 1.5(a), had a number of aerodynamic advantages, as will be described later.

The angle at which the wing is inclined relative to the air flow is known as the angle of attack. The term incidence is commonly used in Britain instead, but in American usage (and in earlier British texts), incidence means the angle at which the wing is set relative to the fuselage (the main body). We shall use the term angle of attack for the angle of inclination to the air flow, since it is unambiguous.

The camber line or mean line is an imaginary line drawn between the lead­ing and trailing edges, being at all points mid-way between the upper and lower surfaces, as illustrated in Fig. 1.8. The maximum deviation of this line from a straight line joining the leading and trailing edges, called the chord line, gives a measure of the amount of camber. The camber is normally expressed as a per­centage of the wing chord. Figure 1.5 shows examples of cambered sections. When the aerofoil is thick and only a modest amount of camber is used, both upper and lower surfaces may be convex, as in Fig. 1.8.

A typical thick cambered section may be seen on the propeller-driven transport aircraft of the early postwar period, in Fig. 1.9. Nowadays, various forms of wing section shape are used to suit particular purposes. Interestingly, interceptor aircraft use very thin plate-like wings, with sections that are con­siderably thinner than those of the early biplanes.

Before we can continue with a more detailed description of the principles of lifting surfaces, we need to outline briefly some important features of air and air flow.

The amount of sweep required to maintain low speed flow patterns on a wing depends on the maximum flight Mach number required (the ratio of the max­imum speed of the aircraft to the speed of sound). Subsonic airliners which are designed to cruise at Mach numbers less than 0.9 (90 per cent of the speed of sound) require a sweep angle of around 25 to 30 degrees measured along the – chord line (a line drawn along the span – of a chord back from the leading edge). An aircraft designed to travel at twice the speed of sound would require a sweep angle in excess of 60 degrees. The BAe Lightning shown in Fig. 8.1 is an early example of a swept-wing aircraft designed to fly at twice the speed of sound (Mach 2).

With such large angles of sweep, it becomes difficult to build a wing with sufficient bending stiffness or strength. The wing is long in relation to the over­all span, and for reasons given in Chapter 9, it may also need to be very thin.

On the Lightning, the thickness to chord ratio was only around 6 per cent, and even this is quite thick by modern standards!

The delta planform allows the spars to run straight across, as illustrated in Fig. 2.21(b), instead of along the wing, as in 2.21(a). The delta wing was yet another feature developed by German engineers during the Second World War.

It should be noted that there are two types of delta wing. They are charac­terised by the type of flow regime employed rather than their shape, but for convenience we may classify them as broad and slender deltas. The older broad type was introduced first, and is typified by the Avro (BAe) Vulcan bomber seen in Fig. 2.22. This type of delta wing is essentially a form of swept wing with a large degree of taper. Wings of this form are designed to operate with attached flow for most flight conditions, but separated conical-vortex flow will occur at high angles of attack.

For low speed flight, the low aspect ratio, high taper, and sweepback of the delta planform result in a poor lift-to-drag ratio. This is offset by the structural advantages, and by the large wing volume that results; useful if a high fuel load is required. However, it is in high speed flight, where large amounts of sweep – back are required, that the delta shows its main advantages.

The choice of section shape depends partly on the range of CL values for which efficient low-drag cruising is required. A wide low-drag bucket will be required, if the aircraft is designed to fly efficiently for a large range of speed, weight and altitudes. For steady level flight, CL is equal to weight/(dynamic pressure x wing area), so it is the range of values of weight/dynamic pressure that matters. Note that the weight changes considerably during flight as the fuel is consumed.

The choice of section is also dependent on the maximum value of CL needed. This in turn depends on the weight, the wing area and the stalling speed that can be tolerated without flaps deployed.

The choice of section may be a lengthy iterative process, and at the end, the aerodynamic designer may well be told to go away and think again by the structural designer, who needs a thicker section, with plenty of depth at the rear to accommodate the flap mechanism. The characteristics of typical aerofoil sections are given in the Appendix, p. 361.

In addition to its use as a kind of gearing, the variable pitch mechanism can be used to reduce drag if one engine has stopped. This is done by feathering the propeller blades; turning them edge-on to the wind so that they stop rotating, as seen in Fig. 6.6.

Feathering may be automatic on some multi-engined aircraft to prevent adverse handling problems if one engine fails.

After touch-down, the variable pitch mechanism can be used to set the pitch to a negative angle, so that negative thrust or drag is produced. This reversed thrust feature can shorten the landing run considerably, and is almost invari­ably used on propeller-driven transport aircraft. It also conveniently enables the aircraft to be backed in or out of parking spaces.