Category Aircraft Flight

Trailing vortex formation

The physical mechanism by which the trailing vortices are formed may be understood by reference to Fig. 2.6. On the underside of a wing, the pressure

Trailing vortex formation

Fig. 2.5 Trailing vortex formation

Flow visualisation using helium-filled microscopic soap bubbles. The flow spirals around a stable core originating from just inboard of the wing tip (Photo courtesy of ENSAM, Paris)

Trailing vortex formation

Fig. 2.6 Spanwise flow on a wing

(a) The air flows inwards on the upper surface and outwards on the lower. This is the source of the trailing vortices

(b) View from just downstream of the trailing edge

is higher than the surrounding atmosphere, so the air flows outwards towards the tips. On the upper surface, the pressure is low, and the air flows inwards. This results in a twisting motion in the air as it leaves the trailing edge. Thus, if we look at the air flow leaving the trailing edge from a viewpoint just downstream, as in Fig. 2.6(b), it will appear to rotate. Near each wing tip, the air forms into a well defined concentrated vortex, but a rotational tendency or vorticity occurs all along the trailing edge. Further downstream, all of the vorticity collects into the pair of concentrated trailing vortices (as shown in Fig. 2.10).

If the wing is completely constrained between the walls of a wind-tunnel, the outflow will not occur, and trailing vortices will not form. This ties up with the theory of vortex behaviour mentioned above: the vortices must either form a closed loop, or terminate in a wall. It also points to one of the problems of wind-tunnel testing; the fact that the presence of the tunnel walls influences the flow behaviour.

Effect on wind-tunnel testing

A major problem in wind-tunnel model testing arises if we rely solely on increasing the speed to correct the Reynolds number. Since the chord c of the model is smaller, we must make (pV )/u larger. This in turn means that, unless we do something about the density and viscosity, a 1/10 scale model would need to be run at 10 times the full-scale speed.

Unfortunately aircraft are large objects, and we often wish to make models of 1/10 scale or less. To simulate 100 m/s at 1/10 scale, we would need to

run the tunnel at 1000 m/s which is nearly three times the speed of sound at sea level! Clearly, the resulting supersonic conditions would ensure that the flow around the model was nothing like that for the full-size aircraft.

One way to avoid this difficulty, is to use a pressurised wind-tunnel. By increasing the pressure in the tunnel, the density and hence the Reynolds num­ber may be increased at any given air speed. A similar effect can be obtained by using a so-called cryogenic tunnel where the air is cooled (usually with liquid nitrogen) to decrease the viscosity coefficient p. Gases, unlike liquids, become less viscous as they are cooled. The density is also increased.

In order to obtain similar flow characteristics between model and full scale (a condition known as dynamic similarity), it turns out that there are other quantities that need to be matched in addition to the Reynolds number. For aeronautical work, the other really important one is the Mach number, the ratio of the relative flow speed (or aircraft speed) to the speed of sound. As we shall see, the speed of sound depends on the temperature, and thus quite a bit of juggling with speed, pressure and temperature is required, in order to get both the Reynolds and the Mach numbers in a test simultaneously matched to the full-scale values.

Although less important, we should really try to match the levels of tur­bulence in the oncoming air stream, which can be difficult, because in full scale, the aircraft can sometimes be flying through still, and hence non-turbulent air.

For fundamental investigations, and exploratory test programmes, it is still customary to use simple unpressurised tunnels. When the low speed character­istics of the aircraft are being investigated, the Mach number mismatch is un­important. The Reynolds number error can sometimes be reduced by sticking strips of sandpaper on the surface to provoke transition at the correct position, which can either be estimated, or determined from flight tests.

For tests at supersonic speeds the Mach number must be matched, which is quite easy, and the Reynolds number effect is often less important. Unfortunately, most airliners, and quite a few military aircraft spend most of their time flying faster than 70 per cent of the speed of sound, where both the Mach and Reynolds numbers are important. Wind-tunnels in which the pressure, temperature and Mach number can be controlled accurately to suit the size of model are expensive to build and run, especially for speeds close to the speed of sound, but they are essential for accurate development work.

Thrust and propulsion

Propulsion systems

It is tempting to try to divide the conventional aircraft propulsion systems into two neat categories; propeller and jet. Real propulsion devices, however, do not always fall into such simple compartments. In particular, gas-turbine propulsion covers a wide range from turbo-props to turbo-jets. To simplify matters, we shall look first at the two ends of this spectrum; by considering propeller propulsion at one end, and simple turbo-jet propulsion at the other. Later on, we shall look at the intermediate types such as turbo-fans and prop – fans, and also some unconventional systems.

Propeller propulsion

At one time, it looked as though the propeller was in danger of becoming obso­lete. Since the early 1960s, however, the trend has been reversed, and nowa­days nearly all subsonic aircraft use either a propeller or a ducted fan. Even the fan has lost some ground to advanced propellers, and we shall therefore pay more attention to propeller design than might have seemed appropriate a few years ago. It is worth noting, that in 1986, half a century after the first successful running of a jet engine, 70 per cent of the aircraft types on display at the Farnborough Air Display were propeller driven.

The blades of a propeller like those of the helicopter rotor can be thought of as being rotating wings. Since the axis of rotation of the propeller is hori­zontal, the aerodynamic force produced is directed forwards to provide thrust rather than upwards to generate lift. The thrust force is therefore related to the differences in pressure between the forward – and the rearward-facing surfaces of the blades.

Thrust and propulsionRelative flow


Подпись: stream-tube Thrust and propulsion Подпись: Surrounding

Fig. 6.1 The flow past a propeller in flight

In the process of producing this pressure difference, the propeller creates a slipstream of faster-moving air. In Fig. 6.1, the dashed lines represent the streamlines that pass through the tips of the propeller. In three dimensions we have to imagine a stream-tube that encloses or surrounds the propeller disc. Downstream of the propeller, this surrounding stream-tube roughly defines the boundary of the slipstream. The rate of change of momentum of the air within this stream-tube gives a good indication of the overall thrust.

Propulsion for supersonic flight

Intake design

Existing turbo-jet and turbo-fan designs will not accept supersonic flow at inlet, but by placing the engine in a suitably-shaped duct, it is possible to slow the air down to subsonic speeds before entry.

Propulsion for supersonic flight

Fig. 6.32 The variable-geometry outlet nozzles and the louvres of the thrust reversers are seen in this view of the hot end of the Concorde engine installation

At supersonic speeds, with the simple tubular ‘pitot’ type air intake, the flow has to decelerate through a detached normal shock. This results in considerable losses. Much higher efficiency is obtained if the flow is compressed through a series of oblique shocks. Figure 6.33 shows the intake system used on Concorde. The flow is compressed, and the speed reduced through a series of oblique shock waves, a region of shockless compression, and a weak normal shock. The intake geometry has to be varied in flight to match the Mach number of the approaching flow, and to capture the shock. Movable ramps are used for this purpose. Extra intake area is provided for flight at low sub­sonic speeds. Intakes of this type are classified as two-dimensional, and are used on a number of combat aircraft.

Note that part of the compression is provided by the shock wave produced by the wing. This shows the importance of integrating the design of the engine intake with that of the wing.

An alternative axi-symmetric arrangement is to use an axially movable or variable-geometry central bullet, as shown in Fig. 6.39. In the design depicted in this drawing, a combination of external and internal shock waves is shown. Axi-symmetric bullet-type intakes are used on the SR-71 Blackbird shown in

Подпись: Thrust

Propulsion for supersonic flight Propulsion for supersonic flight

Propulsion for supersonic flightBoundary layer Movable ramp

Подпись: SubsonicOblique

shock waves shock system flow

Fig. 6.33 A two-dimensional type variable geometry intake for supersonic flight

This form of intake is used on Concorde. In supersonic cruise, the air is slowed down to subsonic speed and compressed through a series of oblique shocks and a region of shockless compression produced by the curved movable ramp (a) Subsonic configuration (b) Supersonic configuration

Fig. 6.40. Aircraft with side intakes may use two half axi-symmetric intakes, as on the F-104 (Fig. 8.8), or quarter versions, as on the F-111 (Fig. 6.35).

The design of supersonic intakes is an extremely complex subject, and further information will be found in Seddon and Goldsmith (1985) and Kuchemann (1978).

Although the variable geometry intake reduces losses due to shocks, it results in an increase in weight and complexity. A variety of fixed and variable intakes may be seen on modern combat aircraft. The Tornado (Fig. 3.15), and F-14 (Fig. 8.2) use two-dimensional variable geometry intakes, whereas a simpler fixed pitot type is used on the F-16.

The choice depends largely on the main combat role intended. The Tornado is designed for multi-role use which includes sustained supersonic flight, so that efficient supersonic cruising is necessary.

In the interests of avoiding strong radar reflections, ‘stealthy’ aircraft may have unusual inlet and exhaust arrangements, as shown in Fig. 6.34. These are not necessarily aerodynamically optimised.

Fig. 6.34 Design for stealth

On the F-117A stealth fighter/bomber the intakes are concealed behind a radar absorbent grid. Thin two-dimensional exhaust nozzles are used, with the lower lip protruding so as to conceal the exhaust aperture. The use of flat-faceted surfaces helps to reduce the radar signature. The resulting shape, which has the appearance of being folded from a sheet of cardboard, must have presented a considerable challenge to the Lockheed aerodynamicists

Subsonic and supersonic trailing edges

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

Fig. 8.12 Backward and forward sweep

Unless wing is swept forward, trailing-edge sweep is less than leading-edge sweep for conventional taper

Fig. 8.15 Loading on section of swept wing

(a) Supersonic leading and trailing edges (b) Subsonic leading and trailing edges (c) Subsonic leading edge and supersonic trailing edge

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

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.

Lateral stability

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.

Fig. 11.13 Yawing or ‘weathercock’ stability provided by the fin

The same principle has been used on weathercocks for centuries


Fig. 11.14 Lateral dihedral

The dihedral angle is the angle made between one wing and the horizontal

Fig. 11.15 The effect of dihedral

The aircraft is shown sideslipping towards the observer. The near wing presents a higher effective angle of attack. The aircraft will, therefore, tend to roll back, away from the sideslip

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.

Some Aerofoil Characteristics

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

Pressure and speed

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.

Other wing planforms

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,

Other wing planforms

Fig. 2.25 Leading-edge strakes on the F-18 help provide lift at high angles of attack and stabilise the main wing flow

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