Category Aircraft Flight

For an untapered wing the trailing edge is parallel to the leading edge. Thus if the leading edge is subsonic then the trailing edge is likely to be so as well. In this context the terms ‘subsonic’ and ‘supersonic’ mean exactly the same as they did for leading edge; if the trailing edge has a higher angle of sweep than the local Mach angle then it is subsonic – if the sweep angle is lower than the Mach angle then it is supersonic.

It is perhaps worth pointing out here that, unless the wing is swept forward rather than back, the trailing-edge sweep must be less than the leading-edge value if an inverse taper is to be avoided (Fig. 8.12). The trailing edge of a con­ventionally swept wing is therefore likely to be less swept than the leading edge.

We already know what happens if we make both the leading and trailing edges either subsonic or supersonic. What happens, though, if we make the leading edge subsonic and the trailing edge supersonic? Once again it is a mat­ter of working out the zones of influence. First let us look again at the wing with both leading and trailing edges subsonic, this time concentrating on what happens to the Mach lines in relation to the trailing edge. Considering the point A on the trailing edge (Fig. 8.13), this will be able to influence the shaded area. Note, once more, that if the wing had no centre section, but went on to infinity, any point on the wing would be influenced by some point on the trailing edge and we would be back to the equivalent subsonic flow.

If we now reduce the sweep at the trailing edge it will not be able to make its presence felt anywhere on the wing surface (Fig. 8.14). The flow in this region will then look like that of the unswept supersonic aerofoil where the flow is turned through a pair of trailing-edge shock waves and a pressure

difference between upper and lower surfaces is sustained right to the trailing edge.

With the subsonic trailing edge there can be no such loading because no shock waves will be present. Consequently there can be no pressure discon­tinuity at the trailing edge between the upper and lower surfaces.

Figure 8.15 shows a comparison of the load distribution (the pressure dif­ference between bottom and top surfaces) for all the cases we have considered so far:

(a) supersonic leading and trailing edges

(b) subsonic leading and trailing edges

(c) subsonic leading edge and supersonic trailing edge.

Above we saw that one of the main advantages of the subsonic leading edge was that its performance would not appear too violently different as the air­craft accelerated from subsonic to supersonic speed, while remaining reason­ably economical in terms of drag production under supersonic conditions. The main trouble with the unswept wing is that the thin sections and sharp leading edges required for good supersonic operation lead to poor low speed perform­ance because of boundary layer separation. No such difficulty exists with the supersonic trailing edge and the main problem here is the rearward movement of the centre of lift caused by the change in load distribution (Fig. 8.15(c)).

It is worth noting that option (c) is one of the most frequently encountered solutions to the problems of supersonic flight. This is because advantages, such as improved structural properties, offered by a small trailing-edge sweep angle can more than outweigh the aerodynamic penalty mentioned above.

Roll control has traditionally been provided by means of ailerons on the outboard section of the wings, as illustrated in Fig. 10.10. The ailerons are operated differentially; that is one goes up as the other goes down. The differ­ence in effective camber on the two wings causes a difference in lift, and hence, a rolling moment.

On the Wright Flyer and other early aircraft, ailerons were not used. Instead, the whole wing was warped differentially, by using an ingenious arrangement of wires. Wing warping is an efficient method of control, as there is no dis­continuity in the wing geometry. Its use was discontinued when the speed of aircraft increased, and they began to encounter problems due to unwanted distortion of surfaces, as described later. Recently, there has been a renewed interest in the use of wing warping, because composite materials enable the stiffness to be controlled accurately.

Yawing stability

The main purpose of the vertical fin is to provide yawing stability. As shown in Fig. 11.13, by placing the fin well aft of the centre of gravity, it tends to turn the aircraft towards the relative air flow direction. This is known as weather­cock stability, for obvious reasons. The fin does not, as is often believed, tend to point the aircraft into the actual wind direction relative to the ground. The fin force merely tries to point the aircraft towards the relative wind direction. This means that it will try to turn the aircraft towards the direction of a gust, so excessive yawing stability can make the aircraft rather twitchy. Note, that since the aircraft tends to turn towards the direction of gusts, it will not main­tain a constant heading.

LATERAL STABILITY 313

The main difficulties with the yawing stability arise from the cross-coupling between yaw and roll that we mentioned in the previous chapter, and shall fur­ther describe under the heading of dynamic stability in the next chapter.

The NACA series of aerofoils was introduced in Chapter 4. In this appendix, we examine three of these aerofoils in more detail and look at the ways in which changes in cross-sectional shape, particularly camber and thickness distribution, influence their performance. In each case, the aerofoil section is shown, together with a typical distribution of pressure around the lifting sec­tion, the variation of lift with angle of attack and the variation of section drag with lift. The lift and drag are plotted in coefficient form (Chapters 1 and 3). For the pressure distribution, a coefficient form is also used. The pressure coefficient is defined as the local pressure on the aerofoil surface minus the ambient pressure divided by the dynamic pressure (p. 12). Negative pressure coefficients are plotted upwards, so that the upper surface of the aerofoil appears as the upper line on the graph.

The first aerofoil, the NACA 0012 (Fig. A.1), is a 12 per cent thick symmet­rical ‘4 digit’ series aerofoil. It is commonly used for tail surfaces and for wind – tunnel test models. It is also used as the wing section on a number of aircraft including the Cessna 152. This is a popular light general aviation aircraft and the NACA 0012 is used for the outboard wing section. From the graph of lift coefficient against angle of attack for this aerofoil, it can be seen that there is a sharp stall at about 15° angle of attack. The pressure distribution also shows quite a sharp suction peak on the upper surface.

The second aerofoil, the NACA 2214 (Fig. A.2), is used on the centre wing section of the Cessna 152. With a 14 per cent thickness/chord ratio, it is slightly thicker than the NACA 0012 and has some camber. The effect of the camber is evident in the positive lift coefficient that is seen at zero angle of attack. Minimum drag is obtained at a lift coefficient of approximately 0.2, rather than 0.0 for the NACA 0012. The drag is, however, higher for this thicker cambered section and the stall is somewhat more gentle.

The final aerofoil, the NACA 6618 (Fig. A.3), is one of the ‘low drag’ 6 series and is used on the Phantom supersonic fighter. Only the low speed char­acteristics are given here. This aerofoil was designed using a so-called ‘inverse method’. The pressure distribution on the upper surface was chosen to be as flat as possible at a particular ‘design’ lift coefficient and the resulting cross­section was then determined. The flat top surface pressure distribution allows a laminar boundary layer to be maintained over much of the surface, leading to a reduced drag. The laminar layer can be maintained over a small range of angle of attack, either side of the angle of attack at the design lift coefficient, resulting in the typical ‘laminar bucket’ drag variation which is seen in the graph of drag coefficient plotted against lift coefficient. The position of max­imum thickness on this aerofoil is further aft than on either the NACA 0012 or the NACA 2214. This leads to a much gentler acceleration of the air near the front of the aerofoil and the absence of the associated suction peak that pro­motes the transition to a turbulent boundary layer. The data are for a Reynolds Number of 6 x 106.

Angle of attack (degrees)

c) Variation of lift with angle of d) Variation of drag with lift attack

Fig. A.1 NACA 0012

c) Variation of lift with angle of attack

Fig. A.2 NACA 2214

a) Aerofoil section

Angle of attack (degrees)

c) Variation of lift with angle of attack

Fig. A.3 NACA 6618

The pressure and the relative speed of the air flow vary considerably from one point to another around an aircraft. When the air flows from a region of high pressure to one at a lower pressure, it is accelerated. Conversely, flow from a low pressure to a higher one results in a decrease of speed. Regions of high pressure are therefore associated with low flow speeds, and regions of low pres­sure are associated with high speeds, as illustrated in Fig. 1.10.

When the air pressure is increased quickly, the temperature and density also rise. Similarly, a rapid reduction in pressure results in a drop in temperature. The rapid pressure changes that occur as the air flows around an aerofoil are, therefore, accompanied by changes in temperature and density. At low flow speeds of less than about one half of the speed of sound, however, the changes in temperature and density are small enough to be neglected for practical purposes. The speed of sound is about 340 m/s (760 mph) at sea level, and its significance will be explained in Chapter 5.

Although we have generally avoided the use of mathematics or formulae, we will include one or two relationships which are fundamental to the study of aerodynamics, and which also enable us to define some important terms and quantities. The first of these expressions is the approximate relationship between pressure and speed for low flow speeds.

pressure + HI density x (speed)1 is constant or in mathematical symbols,

P + 1pV1 is constant

Where p is the pressure, p is the density and V is the speed.

You will see that this fits the behaviour of the air, as described above, in that an increase in pressure must be accompanied by a decrease in speed, and vice versa. Readers who are familiar with Bernoulli’s equation, may recognise that the above expression is just a version in which the height term has been ignored, because changes in this term are negligible in comparison with changes in the other two.

This simple Bernoulli relationship between speed and pressure, given above, applies without significant error, as long as the aircraft speed is less than about half the speed of sound. At higher speeds, some form of correction becomes necessary, and once the aircraft approaches the speed of sound, a much more complicated expression has to be used.

The straight, swept and delta planforms represent the three basic types of wing shape. There are numerous possible variations on these themes, such as forward sweep, and even variable sweep. The reasons for the use of such plan – forms will be explained at appropriate points in later chapters. In particular,

the design of wings for high speed flight will be discussed in more detail in Chapters 8 and 9.

We have already seen that trailing vortex drag is dependent on the aspect ratio. In fact, the drag coefficient due to trailing vortex drag is proportional to 1/(aspect ratio). The use of high aspect ratios, however, incurs penalties in terms of structural weight. Furthermore, high aspect ratio wings are unsuitable for aircraft that have to perform rapid manoeuvres, and for supersonic aircraft. Therefore, various attempts have been made to find other means of reducing trailing vortex drag.

Improving spanwise lift distribution

Most airliners use a fuselage with a circular cross-section, and this shape pro­duces virtually no lift. It is therefore impossible to produce a true elliptical lift distribution across the whole span. There is always a dip in the distribution at the fuselage, as shown in Fig. 4.11(a). Many modern combat aircraft such as the MiG-29 (Fig. 4.12) overcome this problem by using a cambered fuselage of non-circular cross-section, which generates lift, as in Fig. 4.11(b).

In a simple propeller, a considerable amount of energy is lost in the swirling motion of the air in the slipstream. Some of this energy can be recovered if a second propeller rotating in the opposite direction is placed just downstream, as shown in Fig. 6.8. The second propeller tries to swirl the air in the opposite direction, thereby tending to cancel the initial swirl.

Contra-rotation also provides a convenient method of increasing the power throughout for a given propeller diameter.

High-powered piston engines produce a considerable torque reaction which tries to roll the aircraft in the opposite direction to the propeller rotational direction. On the ground, the roll is resisted by the runway, but immediately after take-off the resistance is suddenly lost, and the aircraft is liable to start heading rapidly for the hangar. Contra-rotating propellers overcome this prob­lem, as they produce no net torque reaction. Gyroscopic precession effects are also cancelled, and the lack of swirl in the slipstream makes the flow around the aircraft less asymmetric, which further improves the handling qualities. For small aircraft, however, the extra cost and complication of contra-rotating propellers outweigh the advantages. On twin-engined aircraft a similar effect could be obtained by having the two propellers (and hence engines) rotating in opposite directions. For practical reasons this has rarely been adopted. The De Havilland Hornet was one example.

On multi-engined aircraft, the lack of torque reaction reduces structural loads. The experimental engine installation on the Ilushyin shown in Fig. 6.8 used a large diameter multi-bladed contra-rotating propeller unit. The efficiency of the propeller is an advantage for this aircraft which was designed for long range.

The disadvantages of contra-rotation are the extra complexity, the weight of the necessary gearing, and the noise caused by the highly alternating flow as the second propeller chops through the vortex system of the first.

If we change the wing area of the aircraft while keeping the weight constant we change its wing loading (aircraft weight/wing area). The effect of this is shown in Fig. 7.5 where it can be seen that the result of an increase in wing loading is to move the drag curve to the right of the picture without altering the drag values.

The explanation of this is quite simple. At any point, A, in Fig. 7.5 the lift (equal to the weight of the aircraft) is given (Chapter 1) by the lift coefficient multiplied by the wing area and the dynamic pressure (-pV2). Assume that we reduce the wing area. If only the size of the wing is changed but its geometrical shape and angle of attack remain the same, the lift coefficient will be unaltered. We can then obtain the same lift force by increasing the speed to raise the dynamic pressure, so compensating for the area reduction.

The drag coefficient will also be unchanged for our smaller wing. Therefore, since the product of dynamic pressure and wing area is unaltered, the drag force will also be unchanged. Point A is therefore simply moved horizontally to A’ (Fig. 7.5) and the entire curve is shifted as shown and somewhat spread out, the minimum drag retaining the same value as before.

At this point it is worth pointing out that our argument is somewhat approximate. Unless the fuselage and tail assembly are scaled in the same way as the wing, the drag coefficient will be changed as we go from point A to point A’ (Fig. 7.5). Thus some change in the minimum drag value will be obtained.

A further factor we have ignored is that a change in the size of the wing will also require a change in the weight of the structure, so our assumption of constant weight is questionable, particularly if we consider large changes in wing area.

However, it remains generally true that increasing the wing loading means that the aircraft can fly faster with little penalty in terms of increased drag. This has led to an increase in wing loadings for many aircraft types, and this is further described in Chapter 9. It must be remembered that any such increase in wing loading will mean a higher minimum flying speed, and so a com­promise must be reached between requirements for cruise and landing and take-off performance.

Hypersonic flight using a scramjet engine has been something of an aero­nautical engineer’s dream ever since the late 1960s. The American National Aerospace Plane (NASP) programme involved building a prototype, the X-30 research aircraft. However after some 2.4 bn dollars was spent of the project,

it was abandoned in 1994. This project was then followed by a lower cost approach involving the use of an unmanned 12 ft long vehicle, the X-43, shown in Fig. 8.24. This was mounted on the nose of a Pegasus booster rocket, and the combination was launched from under the wing of a B52 bomber. After a major failure in the first flight, two later successful flights were made, with the X-43A finally reaching a maximum speed of Mach 9.68 in 2004, after a fuel burn of some 11 seconds. The viability, though perhaps not yet the financial practicability, of scramjet-power hypersonic flight was thus established.

Recommended further reading

Kdchemann, D., The aerodynamic design of aircraft, Pergamon Press, 1978, ISBN 0080205143. A masterpiece from the ‘Father of Concorde’ which stands the test of time. Peebles, C., Road to Mach 10: Lessons learned from the X-43A flight research program, AIAA, Reston VA, USA, 2008, ISBN 9781563479282. A fascinating and detailed description of the X-43 project.

Flight in the range between the onset of important compressibility effects (M = 0.7) and the establishment of fully supersonic flight conditions on the other side of the drag coefficient rise (M = 1.4) is said to be transonic. The tran­sonic range poses some of the most difficult problems for the aerodynamicist but it is of great practical importance. Not only do supersonic aircraft need to have satisfactory characteristics to accelerate and decelerate safely through the transonic range but currently many aircraft are designed to cruise close to the speed of sound.

The reason for this has been given in previous chapters. Because the efficiency of a gas turbine engine increases with design speed, we wish to fly fast. How­ever, as the speed of the aircraft approaches the speed of sound a sudden rise in drag occurs, together with other problems such as the production of sonic bangs on the ground. For most transport aircraft, and a number of military air­craft designed for such roles as ground attack, a suitable solution is obtained by restricting the cruising speed to just below the drag-rise Mach number.

In Chapter 5 we saw how compressibility effects and shock waves put up the drag as the speed of sound is approached. For a given aircraft the typical vari­ation of drag with Mach number is shown in Fig. 5.19. The very rapid increase in drag coefficient near the speed of sound is clearly shown. Some wing sections also produce a slight dip in drag immediately before the rise. Figure 9.1 shows this effect. It is caused by the rise in lift coefficient in Fig. 5.19 which offsets the smaller rise in drag coefficient initially for a wing operating at constant lift rather than constant angle of attack.

At first sight it might seem to be best from the point of view of obtaining economical cruise conditions to keep well below the drag rise Mach number. However as we saw in Chapter 3, the efficiency of the gas turbine rises with Mach number and it is therefore worth pushing the cruising speed as close to the speed of sound as possible to obtain the best compromise between airframe and engine performance. It may also be worth exploiting the drag coefficient ‘dip’, mentioned above, at the same time.

These factors have resulted in the development of a whole series of airliners cruising at a speed just below that at which the transonic drag rise occurs. This has had the added advantage of providing the travelling public with high speed transportation over a wide variety of distances – and one of the most appeal­ing features of air transport has always been speed.

In this chapter we will consider the aerodynamic development of aircraft designed for flight at transonic speeds, with particular emphasis on the prob­lems associated with transport aircraft. However it must not be forgotten that many military aircraft, such as ground attack aircraft (Fig. 9.2) are also designed primarily for transonic operation and some reference will also be made to these where appropriate.

The development of civilian transport aircraft over a period of some 30 years is illustrated in Fig. 9.3 in which two aircraft are shown spanning the period from the earliest jet transport, the de Havilland Comet, to a much later design, the Airbus A340. An intermediate development, the Trident is shown in Fig. 3.9. In some ways the three configurations look remarkably similar, the main obvious development being the introduction of pylon mounted engines rather than the buried installation of the Comet. Closer examination, however, reveals other changes. Firstly there has been a reduction in the plan – form area of the wing for a given aircraft weight; in other words an increase in the wing loading. Next there has been a tendency for the sweep angle firstly to increase but, surprisingly to be reduced in the more modern designs. Close examination of the aircraft themselves would also reveal considerable differ­ences in the wing sections used.

The choice of sweep angle is a question of a compromise between using enough sweep to reduce the effects of compressibility, as will be explained below, and avoiding the unpleasant low speed handling effects (Chapter 2).

The reason for wishing to use high wing loading simply comes from the need to reduce area for a given weight, and the need for this was discussed in Chapter 8.

As we have seen previously, all aircraft design is a compromise, and the actual minimum area may well be dictated by landing requirements rather than cruise requirements. The increase in wing loading thus owes a great deal to the work of the low speed specialist in producing ever more sophisticated and effective high lift devices for use during take-off and landing. Some of these have been described in Chapter 3, and this is likely to be a major field of aero­dynamic research and development for some considerable time.

Even the term ‘low speed specialist’ used in the above paragraph must be treated with some caution. The aircraft may itself be flying at low speed in the sense that the speed of flight is well below the speed of sound. However, extremely low pressures may well be developed over the upper surface of such devices as leading edge slats, and what at first sight may appear to be a low speed flow, may well contain localised regions in which the flow is near to, or even exceeds the speed of sound.

After this slight digression into the necessary problem of ‘off design’ perform­ance, we now return to the problem of designing a wing with good performance at the cruise condition. At this stage it is worth emphasising that, for the type of aircraft we are considering, the cruising speed will be just below the speed of

sound, in order to avoid the full effects of the transonic drag already described. The basic problem is therefore to try to push the wing loading as high as possible, while at the same time delaying the onset of this drag rise to as high a Mach number as possible. The requirement for high-wing loading implies low local pressures on the upper surface of the wing, and consequently high local speeds. These high speeds, however, are the very thing that is likely to lead to the formation of shock waves which cause the transonic drag rise. It is to the problem of resolving this dilemma that we now turn our attention.