Category Aircraft Flight

We have already explained how surface friction arises from the shearing action in the boundary layer. Because a laminar layer produces less drag on a given area than a turbulent one of the same thickness, there is an advantage in main­taining a laminar boundary layer over as much of the surface of the aircraft as possible.

Early wing sections similar to that shown in Fig. 4.5(a) were derived by adding camber to the streamlined fairing shape, and were intended to minimise the boundary layer normal pressure (form) drag. The position of minimum pressure on the upper surface is usually near to the point of maximum thick­ness, which on these early shapes is about 1/4 to 1/3 of a chord back from the

6 – six series aerofoil

5 – favourable pressure gradient to 5/10 chord

1 – low drag for a CL range of +/- 1/10

2 – designed for low-drag operation at CL = 2/10 12 – thickness-to-chord ratio 12 per cent

leading edge. A laminar boundary layer would normally extend up to this point, but beyond it, the adverse pressure gradient (air flowing from a low pressure to a higher one) would provoke transition to turbulence. It was later realised that by moving the position of maximum thickness aft, it would be possible to maintain a favourable pressure gradient, and hence a low-drag laminar boundary layer, over a much larger proportion of the wing surface.

By the 1930s, advances in theoretical methods, using a technique known as conformal transformation, made it possible to design aerofoil sections for which the form of the velocity or pressure distribution could be specified. Several low-drag so-called ‘laminar’ sections were designed, the most well known being the NACA 6-series; an example of which is shown in Fig. 4.5(b). Sections from this family of shapes came into use during the Second World War, and the adoption of a 6-series aerofoil on the P-51 Mustang is probably one reason why that aircraft had such an excellent performance.

As we have shown in the previous chapter, however, transition from lam­inar to turbulent boundary layer flow also depends on the Reynolds number and the roughness. A favourable pressure gradient alone is not sufficient to ensure a laminar boundary layer. To help maintain laminar flow over the front portion of the aerofoil, the wing needs to be manufactured to a precise profile, with a high standard of surface finish. This led to a move away from the tradi­tional riveted form of construction, to the adoption of different methods, as outlined in Chapter 14.

Despite the care taken in manufacture, it is often difficult to maintain a good surface finish in normal operational conditions. A swarm of insects squashed on to the wing can significantly affect the range and cruising efficiency of an aircraft. Small dents must also be detected and filled.

The geometric pitch angle is the angle that the blade is set relative to the direc­tion of rotation, as shown in Fig. 6.4. If we run the engine at a high rotational speed, and set the geometric pitch angle to around 45 degrees near the tips, for

Separated flow

Large pitch angle

Relative velocity due to forward motion

Effective angle of attack of blade

Relative velocity due to rotation

___

Fig. 6.7 Propeller blade section at large (coarse) pitch angle and low forward speed

The effective angle of attack is so large that the blade section has stalled

efficient cruising, then at low flight speeds, the blade angle of attack will be high, as shown in Fig. 6.7. The blade lift to drag ratio will be poor, and if the angle of attack is too large, the blade may even stall. It is advantageous, there­fore, to fit a mechanism which allows the pitch angle of the blade to be altered. Fine pitch is necessary for climbing and accelerating at low speed. Coarse pitch is required for high speed fight. The pitch-change mechanism serves a similar function to the gearbox on a car, but has the advantage of allowing continuous rather than step-variation.

To maintain the best pitch at all positions along the blade, it would really be necessary to be able to alter the twist as well, but as most of the thrust comes from the outer portion of a blade, the loss of efficiency due to non-optimum twist is small in practice.

Early variable pitch propellers were operated directly by the pilot, but the number of pitch settings was limited to two or three to avoid giving him an excessive workload. An alternative, and currently preferred method, is to use the automatic so-called constant-speed propeller mechanism described below.

The conditions of the atmosphere will obviously depend on such factors as the local weather conditions, which will vary from day to day, and also on whereabouts in the world the aircraft is operated. Because of these variations a number of ‘standard atmospheres’ have been defined which represent average conditions in different parts of the world. Aircraft performance is usually related to these standard conditions and suitable corrections are made for operation in the real atmosphere, which never quite coincides with the stand­ard assumptions.

The most important factors as far as the operation of the aircraft is con­cerned are the density and temperature. The density is important because of its major influence on the aerodynamic forces, and the temperature because this governs the speed of sound, a very important parameter for high speed aircraft (Chapter 5).

We will not delve into the physics of the atmosphere but will content ourselves with a simple statement as to how these properties vary with height. These variations are summarised in Fig. 7.1 which shows the conditions for

Temperature ( C)

Fig. 7.1 The Standard atmosphere

Temperature falls with increasing altitude in the troposphere and is constant (-56.5° C) in the stratosphere. Pressure and density fall with increasing altitude in both the troposphere and the stratosphere an atmosphere appropriate to temperate latitudes. This is known as the International Standard Atmosphere (ISA).

In supersonic flight the lift-to-drag ratio can be further refined by paying care­ful attention to the favourable interference which can be obtained between components such as wings and fuselage, and we will examine some particularly important applications of this principle when we look at hypersonic aircraft shortly.

Engine installation is another area in which careful attention to such inter­ference effects can bring great returns. An example of this is the positioning of the engines and intake system on the Concorde. The influence of the local flow field generated by the under-surface of the wing in the region of the intakes plays a very important role in this design (Chapter 6).

Hypersonic aircraft

In Chapter 5 we saw that the transition from supersonic to hypersonic flight is not sudden and dramatic as is the transition from subsonic to supersonic conditions. Hypersonic flight exhibits the same basic flow phenomena that are found in the supersonic regime but the problems of flow analysis become more difficult because of the breakdown of some of the assumptions we made at lower Mach numbers, and because of the increased importance of kinetic heating.

At the time of writing hypersonic flight has been the province mainly of missiles and re-entry capsules, together with what is really a hypersonic glider; the American space shuttle (Fig. 8.19).

In the following section we will consider the problems associated with atmospheric re-entry. We will also briefly examine the prospects for aircraft which may be able to operate in a more conventional way to provide regular passenger and freight services over long ranges.

Early aircraft and small modern types use a direct mechanical linkage between the control surface and the pilot’s control stick. The linkage normally consists of an arrangement of multi-stranded wires and pulleys. Figure 10.22 shows the complex system used on an executive jet. The rudder actuating wire may just be seen under the tailplane on the Auster shown in Fig. 10.5. Alternatively, push-pull rods and twisting torque-tubes may be used, and are in some ways preferred, since they produce a stiffer system, less prone to vibration problems.

As the speed and size of aircraft increased, so did the control forces required, and some considerable ingenuity went into devising means of reducing these loads. The position of the hinge line can be arranged so that the resultant force acts just behind it, thus producing only a small moment. A typical arrange­ment, used on many aircraft up to the 1950s, is seen in Fig. 10.5. The top of the rudder projects forward, in front of the hinge line, thereby moving the centre of pressure of the rudder forwards, towards the hinge line.

Unfortunately, the position of the resultant force changes with angle of attack, speed, and deflection angle, so that it is difficult to devise an arrange­ment that produces small forces under all conditions. It is particularly import­ant that the resultant force should not be in front of the hinge line, as this would cause the control surface to be unstable, and run away in the direction of the ever-increasing force.

In addition to such aerodynamic balancing, the control surface mass should also be balanced so that gravity forces do not pull it down in level flight, and inertia does not cause it to move relative to the aircraft during manoeuvres. A rather crude external form of mass balancing may be seen in Fig. 10.17. As described later, masses may also be added to the control surfaces to alter the natural frequency of oscillation.

So far we have looked at the short period pitching motion of an aircraft. This, however, is not the only type of longitudinal motion we shall encounter. There are, in fact, two types of oscillation which can take place. Fortunately the second motion is of a much lower frequency than the SPPO and, although the two motions will in reality take place simultaneously, we can consider them separately for a conventional aircraft without too much error.

When the aircraft’s flight path is disturbed so that its downward slope is increased, a weight component will act in the direction of flight (Fig. 12.6). This will cause the speed to increase. The fact that the aircraft is statically stable and the motion relatively slow means that it keeps in trim and the angle of attack remains nearly constant. Thus the increase of speed leads to an increase in the lift. The downward slope of the flight path is therefore reduced, as shown in Fig. 12.6.

Eventually the increase in lift causes the aircraft to rise again and another oscillating motion takes place. In this case both the aircraft speed and height change; the maximum speed corresponding to the minimum height, and vice versa. Another way of viewing this motion is to consider it as an oscillatory interchange between the kinetic and potential energies of the aircraft.

Once more, if this were all that happened the motion would persist at con­stant amplitude in an undamped state. However, as the speed increases the drag of the aircraft also increases. Conversely, when the speed is lowest at the highest point of the flight path (Fig. 12.7) the drag will be reduced. The drag variation thus works to oppose the speed variation and serves to damp out the

oscillations. The overall effect is also to damp out the variation in height which accompanies the speed change.

For most aircraft, this drag change has a very weak effect. The motion will be effectively undamped and the oscillations will persist at an almost constant amplitude. The motion has a low frequency, typically taking about a minute to complete a cycle. Because of the very long period of the oscillation, this motion usually presents no problems either to a pilot or an automatic pilot since there is ample opportunity to damp the motion by use of the controls.

This motion is called a ‘phugoid’; a term invented by F. W. Lanchester, one of the great pioneers of flying. He was, unfortunately, given to inventing impressive sounding names for such phenomena!

Although the phugoid is relatively easy to control it can cause complications if allowed to develop too far. A height change between the top and bottom of 300 m or so is quite possible, and it does not need much imagination to see the difficulties that this could cause on landing!

A further interesting thing to note is that the motion we have described depends on the aircraft remaining in longitudinal trim. Thus a rearward move­ment in the centre of gravity can not only disturb the static stability, but can also have gravely detrimental effects on the phugoid behaviour.

Lateral stability

The asymmetrical lateral motion is made up of three basic motions which can be combined together. These are sideslip, roll and yaw (Chapter 11). As in the case of the symmetrical longitudinal motions studied above, a complicated series of movements takes place simultaneously. These movements are, for most conventional aircraft, sufficiently separated in characteristic frequency and damping for us to consider them in isolation, as we did for the phugoid and SPPO. In doing this, however, we must remember that they will in reality take place simultaneously.

Figure 1.15 shows how the pressure varies around an aerofoil section. The shaded area represents pressures greater than the general surrounding or ‘ambient’ air pressure, and the unshaded region represents low pressures. It will be seen that the difference in pressures between upper and lower surfaces is greatest over the front portion of the aerofoil, and therefore most of the lift force must come from that region. This effect was quite pronounced on older wing sections, but nowadays the trend is to design aerofoil sections to give a

fairly constant low pressure over a large proportion of the top surface. This produces a more uniform distribution of lift along the section, giving both structural and aerodynamic advantages, as we shall describe at various points later.

Since the relative flow speed reduces to zero at the stagnation position, it follows that the pressure there must have its highest possible value. This maximum value is therefore called the stagnation pressure. Stagnation pressure should not be confused with static pressure defined earlier. Unfortunately, and for obvious reasons, it often is! Static pressure is just the air pressure. Stagnation pressure is the pressure at a stagnation position; a position where there is no relative motion between the air and the surface.

From Fig. 1.15 we see that the pressure falls rapidly as the air accelerates and flows away from the stagnation position, becoming extremely low around the leading edge. This low leading edge pressure is again contrary to expecta­tion, but is linked to the fact that the stagnation position is behind the leading edge on the underside. Thus, the air taking the upper-surface route has to flow forward, and then negotiate a fairly sharp curve. In order for the air to do this, rather than carry on in a straight line, there must be a low pressure on the leading edge, to pull the flow into a curved path: i. e. to provide the necessary centripetal acceleration.

As described above, separation tends to occur when air flows from a low pres­sure to a high one. This is therefore known as an adverse pressure gradient. Conversely, flow from a high pressure to a low one is called a favourable pres­sure gradient.

A favourable pressure gradient not only inhibits separation, but slows down the rate of boundary layer growth, and delays transition. In the next chapter, we will show how we can exploit this factor to produce low-drag aerofoil sec­tion shapes.

Leading-edge separation

Flow separation is particularly likely to occur when the air tries to go round a very sharp bend, as on the nose of the thin aerofoil. For air to travel around a curve, the pressure on the outside of the curve must be greater than on the inside, in order to provide the necessary ‘cornering’ (centripetal) force. Thus, the pressure on the leading edge of an aerofoil is often locally very low. On the upper surface, the pressure initially rises again rapidly with distance from the leading edge. A strong adverse pressure gradient (flow from a low pressure to a high one) is therefore produced, and the flow tends to separate at, or very near the leading edge.

When such leading-edge separation occurs, the stall or loss of lift may be both sudden and severe. Aerofoils with a large radius leading edge are less prone to producing leading-edge separation, and therefore tend to have a more progressive and safer stall characteristic. As we shall see later, however, there are various reasons why it is sometimes advantageous to use an aerofoil with a sharp leading edge.

It is a common mistake to confuse separation and transition. Transition is where the boundary layer changes from laminar to turbulent. Separation is where the flow ceases to follow the contours of the surface. The fact that separation is normally accompanied by large-scale turbulence is probably the source of the confusion.

The lift produced by a wing is dependent on the flow speed and the circulation, which is related to the strength of the vortex system. In level flight, the lift is equal to the weight. Thus, at constant altitude and aircraft weight, the required vortex strength is reduced as the speed increases. Since the trailing vortex drag also depends on the strength of the vortex system, the trailing vortex drag also reduces with increasing speed. In fact, the drag coefficient for trailing vortex drag is proportional to CL2, and it may be remembered that for level flight the CL value required reduces with increasing speed.

In contrast, the boundary layer normal pressure and surface friction drag rise roughly as the square of the speed. From Fig. 4.21 we see that as a result, there is a minimum value for the overall drag, and this minimum occurs when the trailing vortex drag is equal to the boundary layer drag. There is, therefore, a disadvantage in trying to fly any aircraft too slowly. The implications of this, in terms of performance and stability, are discussed in later chapters.

It is important to note that trailing vortex drag is not the only drag con­tribution that is lift-dependent. If a symmetrical wing section is set at zero angle of attack to a stream of air, the boundary layers on both upper and lower surfaces will be identical, but once the angle of attack is increased, and lift is generated, the boundary layers will alter, together with the amount of drag produced. Thus, it will be seen that some of the boundary layer (profile) drag is also lift-dependent.

For further information on drag, the reader is referred to Hoerner (1965), who gives an excellent detailed treatise on the subject.

Recommended further reading

Lachmann, G. V., (editor), Boundary layer and flow control, Vols I & II, Pergamon Press, 1961.

Hoerner, S. F., Fluid dynamic drag, Hoerner, New Jersey, 1965.

Although the jet engine has now been around for more than half a century, vir­tually all small private aircraft are still powered by reciprocating petrol (gasoline) engines driving propellers. Large commercial transport and military aircraft are predominantly propelled by turbo-jet or turbo-fan engines, while for the intermediate size of civil aircraft, ranging from small executive transports to short-haul feeder airliners, a gas-turbine driving a propeller is frequently chosen. The reason for these divisions will be seen from the descriptions that follow.

Reciprocating engines

Small reciprocating engines can produce a surprisingly large amount of power in relationship to their size. A large model aircraft engine can produce about 373 W (0.5 bhp), which is rather more than the power that a good human athlete can sustain for periods exceeding one minute. A problem arises, how­ever, when an engine is required for a very large or fast aircraft, where a con­siderable amount of power is required.

If we simply tried to scale up a typical light aircraft engine, the stresses due to the inertia of the reciprocating parts would also increase with scale, and we would very soon find that there was no material capable of withstanding such stresses. This is because the volume, and hence, the mass and inertia of the rotating parts, increases as the cube of the size, whereas, the cross-sectional area only increases as the square.

The way to overcome this problem is to keep the cylinder size small, but to increase the number of cylinders. Thus, whereas a light aircraft will normally have four or six cylinders, the larger piston-engined airliners of the 1940s and 1950s frequently used four engines with as many as 28 cylinders each. The complexity of such arrangements leads to high costs, both in initial outlay, and in servicing. To get some idea, try working out how long it would take you to change the sparking plugs in an aircraft with four engines of 28 cylinders each, and two plugs per cylinder. Do not forget to allow some time for moving the ladders.

Many arrangements of cylinders were tried, in order to devise a convenient, compact and well balanced configuration. By the end of the era of the large piston engines, in the early 1950s, two types predominated; the air-cooled radial, and the in-line water-cooled V-12. The latter is typified by the Rolls – Royce Merlin (Fig. 6.15), which was used on many famous allied aircraft of the Second World War, including the Spitfire and Mustang. Water-cooling was used on the in-line V-12 engines, because of the difficulties of producing even cooling of all cylinders with air. Modern light aircraft engines are normally air­cooled, with four or six cylinders arranged in a flat configuration.