Category Aircraft Flight

Wing sections in transonic flow

The conventional aerofoil revisited

In Chapter 5 we saw how the flow characteristics over a conventional aerofoil changed with increasing free-stream Mach number from a shock-free low speed flow (Fig. 5.18(a)) through the developing shock wave system at tran­sonic speeds (Fig. 5.18(b)) until the fully developed shock system is obtained at higher Mach numbers (Fig. 5.18(c)). In transonic aircraft we are particularly concerned with the intermediate type of flow shown in Fig. 5.18(b) in which the oncoming flow is still subsonic.

First let us take another look at the pressure distribution on a conventional aerofoil section (this is shown again in Fig. 9.4) and how this relates to the flow is shown in Fig. 5.18(b). We see at once that there are two potential problems. First there is a very high suction peak which occurs locally near the leading edge of the aerofoil. This means very high velocities in this region, and con­sequently high Mach numbers. The second problem occurs because of the very high adverse pressure gradient on the downstream side of this suction peak. This is liable to coalesce into a relatively strong shock wave (the shock wave which terminates the supersonic patch in Fig. 5.18(b)) and this may also induce boundary layer separation, with all the problems that entails!

Fig. 9.4 Low speed aerofoil pressure distribution

Mach number below 1.0 over surface

Note leading edge suction peak and adverse pressure gradient on top surface

Thin sections

The increase in the surface velocity over the aerofoil section is caused by two factors – the thickness of the section and its angle of attack. Thus one way in which the local Mach number over the top can be limited is to use a thin sec­tion. This has certain aerodynamic penalties associated with it, however, as we have already seen in Chapter 2. Firstly the range of angle of attack over which the wing will operate without stalling will be reduced, and secondly it is obvi­ous that the problems of fitting in a satisfactory wing structure get more and more severe as the section thickness is reduced (Chapter 14).

Supercritical sections

So far we have attacked the problem of developing a wing section suitable for transonic flight simply by using as thin a section as we can in order to limit the velocity increase due to thickness. However, as we get near to the speed of sound, the achievable wing loading is limited unless the flow becomes locally supersonic. We therefore have to design supercritical aerofoils in which this supersonic flow is adequately catered for.

Control harmonisation

For an aircraft to be comfortable and easy to fly, all of the primary control actions should require roughly the same amount of effort to operate them. The correct harmonisation of controls is often difficult to achieve with manual controls, but with the powered systems they can normally be tuned with precision.

Engine control

The power output of an aircraft piston engine is controlled in much the same way as a road vehicle engine, by means of a throttle, which varies the amount of air/fuel mixture admitted to the engine. A mixture control lever is used to give a rich fuel/air mixture for an extra, but inefficient boost of power for take­off and to adjust for air density changes.

In addition, most propeller-driven aircraft are fitted with an rpm control lever, which is used to set the propeller, and hence, engine speed.

On turbocharged engines, a means of varying the boost pressure may be provided, although in some installations, the process is automatically controlled.

The correct setting of the various controls depends on the chosen flight plan, and a good pilot will work out the best settings for each stage before take-off.

It is important to note that on a reciprocating engine, the rate of fuel con­sumption depends mainly on the power output. The pilot’s primary control of the power is by means of the throttle lever.

In gas-turbine systems, the primary engine control operated by the pilot is the fuel flow control. This serves a similar purpose to the throttle on a piston engine, except that in the gas turbine, it controls the thrust produced. The thrust and engine speed of a gas-turbine system cannot be separately varied to any significant extent, and any movable vanes, nozzles or surfaces are primarily used to fine-tune the operation of various components.

On more complex gas-turbine systems, with adjustable nozzles and multiple spools, there are many variables to control and monitor, and some form of automatic engine management control system is necessary. The pilot’s primary input is still via a single lever (or set of levers in a multi-engined installation). Further controls are required for reversed thrust, and reheat, where fitted. A host of minor controls can also be found, depending on the particular aircraft type. In the turbo-prop, there is also a means of selecting the propeller rpm.

For the pilot, the most obvious difference between a piston engine and a turbo-jet installation is the lack of torque reaction, and the relatively slow throttle response of the turbine. Changes in thrust and speed have to be anticipated much more carefully in the latter case. The lack of propeller drag braking effect can also make jet-propelled aircraft more difficult to handle.

Artificial stability – Mach trimmers and yaw dampers

In principle the pilot can control an unstable motion, by operating the controls directly to provide suitable forces and moments to oppose the motion. For example, in the case of the Dutch roll, the rudder is extremely effective in suppressing the yaw and hence controlling the motion. If the motion is of high frequency and poorly damped, however, this makes the aircraft very tiring to fly, and at some frequencies the pilot’s reactions will be such that he will not be able to ‘follow’ the motion correctly. In this event his efforts may well make a bad situation worse.

One way of overcoming the problem is to relieve the pilot of this part of his task altogether by the use of an automatic control system. In the case of the Dutch roll, the yawing motion can be sensed, both in terms of the degree of yaw and the rate at which it is developing, by the use of gyroscopically based instruments. In this case a position gyro can be used to sense the degree of yaw and a rate gyro to sense its rate. Once the information concerning the aircraft motion is available the rudder can be moved automatically to provide the required correction. Such a device is present on all large modern jet trans­port aircraft and is known as a yaw damper.

Details concerning the design of either the gyros or the damper control system are outside the scope of this book, however it is perhaps interest­ing to mention a few features which must be considered before leaving the subject.

One obvious feature is that the control system employed in the yaw damper must be able to distinguish between a conscious control input on the part of the pilot, and the control movement generated as a result of the unwanted motion. Thus the total movement must be determined as a combination of both inputs. Another point which must be carefully considered is the integrity of the control system. Should failure occur, the safety of the aircraft must not be comprom­ised. This means that either suitable back-up must be provided, or the system must revert to full manual control on failure. In the latter event the character­istics of the aircraft must be such that manual flight is reasonably possible, even if not very pleasant.

Further damping can be provided by the use of a similar system to control the ailerons in such a way as to oppose the rolling component of the motion. This system is known as a ‘roll damper’.

As mentioned above, the longitudinal characteristics deteriorate due to the rapid centre of pressure movement which results from comparatively small changes in the aircraft operating condition in transonic flight. This again can be ‘fixed’ by the use of a suitable automatic control system. This system uses elevator movement to compensate for the change in centre of pressure and is known as a ‘Mach trimmer’.

Flight with separated flow

On older aircraft types, it is normally necessary to avoid flow separation and stalling, since it is very difficult to maintain proper control in the stalled

Flight with separated flow

Flight with separated flow

Fig. 1.19 Flow separation

At high angles of attack, as in the lower photograph, the flow no longer follows the contours of the upper surface, but ‘separates’, producing a highly turbulent recirculating region of flow (Photo courtesy of ENSAM, Paris)

condition. However, from Fig. 1.17, you will see that after an initial drop at stall, the lift starts to rise again at high angles of attack. For thin wings, the highest value of CL may indeed be obtained in the stalled condition. The over­all aircraft lift is further increased by the fact that at these high angles of attack, the engine thrust begins to add a significant component to the lift. Such high lift can be a considerable advantage to combat aircraft performing violent manoeuvres, since it can be used to produce a large (centripetal) force for rapid pull-out from a dive. Alternatively, by rolling the aircraft on its side, the lift can be used to produce the cornering (centripetal) force for a rapid turn.

On missiles, where there is no loading on the pilot to consider, it is normal to make full use of this extended capability; indeed, missiles may spend short periods actually flying backwards after a sharp turn. In rapid manoeuvres, and with large amounts of available thrust, the high drag produced is unimportant.

The main difficulty of flight in separated flow is one of stability and control. The lift, drag, and most importantly, the position of the centre of lift, all vary rapidly. To overcome this problem, the aircraft may need artificial stability in the form of a quick-acting automatic control system. The development of reliable microelectronic systems has meant that it is now possible to fly in what would have previously been considered to be a highly unstable and dangerous condition. Recent combat aircraft have demonstrated controlled flight at angles of attack of more than 70°.

For military aircraft particularly, flight with separated flow provides con­siderable rewards in terms of improvements in both performance and manoeuvr­ability. However, even though it may be possible to control the aircraft in the stalled condition, the instability of the separated flow may still cause structural problems due to excessive buffeting. One solution is to control or stabilise the separated flow as described below.

Boundary layer and stalling problems on swept wings

On a swept wing, the pressure gradients are such that they cause the boundary layer to thicken towards the wing tips. Thus, unless corrective measures are taken, the flow is likely to separate near the tips before any other part of the wing. This is in addition to the inherent tip-stall tendency of swept wings due to upwash, described in Chapter 2. For moderately swept wings at high angles of attack, the outboard stalling is exacerbated by the formation of leading-edge conical vortices which curve inwards, away from the tips, as shown in Fig. 2.20.

One way to alleviate the problem, is to fit chordwise fences on the wing, as shown in Fig. 3.8(a) and Fig. 3.9. Wing fences effectively split the wing into separate sections and help to prevent spanwise thickening of the boundary layer. At the fence, a trailing vortex is shed, rotating in the opposite sense to the usual wing-tip trailing vortex. The vortex produced by the fence scours away the boundary layer locally.

Boundary layer and stalling problems on swept wings

Boundary layer and stalling problems on swept wings

Fig. 3.8 Devices for inhibiting flow separation on swept wings

(a) Wing fence (b) Vortilon (c) Saw-tooth leading edge

Boundary layer and stalling problems on swept wings

Fig. 3.9 A wing fence on an early jet transport

The fence helps to prevent the spanwise thickening of the boundary layer on a swept wing partly by inhibiting the spanwise flow, and partly by generating a vortex which draws in the slow-moving air of the boundary layer

It was found that this trailing vortex also had the useful effect of stabilising the position of the leading-edge conical vortices which form at high angles of attack, thereby tending to improve the stability and control near the onset of stall.

The fence need not extend over the whole chord, and the short leading-edge fence shown in Fig. 3.9 and Fig. 3.8(a) was a device used on many early swept wing aircraft.

The vortilon shown in Figs 3.8(b) and 3.10 is a small fence-like surface extending in front of the wing and attached to the under-surface close to the stagnation line. It is intended to generate a vortex over the upper surface, but only at high angles of attack, when it is most needed. Engine mounting pylons can conveniently be used for the same purpose.

In the saw-tooth leading-edge design shown in Fig. 3.11, the abrupt change of chord causes a strong trailing vortex to form at this point. A trailing vortex is formed wherever there is an abrupt change of wing geometry.

On forward-swept wings, the boundary layer tends to thicken towards the inboard end, encouraging the centre section to stall first. Although this is a safer characteristic than tip-stall, it still produces a diverging nose-up pitching

Boundary layer and stalling problems on swept wings

Fig. 3.10 The vortilon is intended to generate a vortex at high angles of attack. The vortex inhibits the spanwise thickening of the boundary layer, and helps to stabilise the position of the separated leading-edge vortex

Boundary layer and stalling problems on swept wings

Fig. 3.11 The saw-tooth leading edge also produces a vortex

Boundary layer and stalling problems on swept wings

Fig. 3.12 Inboard strakes on this model of a forward-swept-wing aircraft help prevent flow separation at the wing root

moment, and preventative measures are necessary. In the forward-swept model shown in Fig. 3.12, inboard strakes have been added so that the inboard sec­tion behaves like a slender delta, and does not stall in the conventional sense. The strong separated vortex also helps remove the thick boundary layer. On the forward-swept X-29 (Fig. 9.20) the downwash and trailing vortices pro­duced by ‘canard’ foreplanes are used to inhibit inboard separation.

More about shock waves – normal and oblique shocks

Let us look once more at the nose of our supersonic aircraft. We saw how the shock waves formed in front of it, slowing the air down almost instantaneously and providing a subsonic patch through which the pressure information could propagate a limited distance upstream at the speed of sound (Fig. 5.2). It should be noted that the shock wave itself is able to make headway against the oncoming stream above the speed of sound. Only weak pressure disturbances travel at the speed of sound. The stronger the shock wave is, the faster it can travel through the air.

Considering the problem from the point of view of a stream of air approach­ing a stationary aircraft, this means that the faster the oncoming stream, the stronger the shock wave at the nose becomes. Thus the changes in pressure, density, temperature and velocity which occur through the shock wave all increase with increasing air speed upstream of the shock wave. A mathematical analysis of the problem shows that the strength of the shock wave, expressed as the ratio of the pressure in front of the wave to that behind, depends solely on the Mach number of the approaching air stream.

If we now stand further back from the aircraft we see that the bow shock wave which forms over the nose is, in fact, curved (Fig. 5.3(a)). As we get fur­ther from the nose tip so the shock wave becomes inclined to the direction of the oncoming flow. In this region the shock wave is said to be oblique. At the nose, where it is at right angles to the oncoming flow, it is said to be a normal shock wave.

The oblique shock wave acts in the same way as the normal wave except that it only affects the component of velocity at right angles to itself. The com­ponent of velocity parallel to the wave is completely unaffected. This means that the direction of the flow is changed by an oblique shock (Fig. 5.6) whereas

More about shock waves - normal and oblique shocks

Fig. 5.6 Flow deflection by oblique shock wave

Tangential component Vt remains unchanged but V„2 < Vn

More about shock waves - normal and oblique shocks

Fig. 5.7 Flow deflection through bow shock wave

Deflection reaches a maximum and then reduces again

it is unaffected by a normal shock. In both cases, however, the magnitude of the velocity is reduced as the flow passes through the shock wave.

Looking more carefully at the effect of the bow shock wave (Fig. 5.7) we see that, in general, the same flow deflection can be obtained by two possible angles of oblique wave. The reason for this is given in Fig. 5.8. The wave of greater angle at A is stronger because the velocity component normal to the wave front is greater. It therefore changes the oncoming velocity component more than the weaker wave at point B.

Adding the resulting velocity components immediately downstream of the shock waves at two points (Fig. 5.8) shows how a particular point B (where the shock wave is weak) can be chosen with exactly the same flow deflection as at A (with a strong shock wave).

It should also be noted that for a normal shock wave the downstream flow is always subsonic, as it is for most strong oblique waves. The fact that the

More about shock waves - normal and oblique shocks

Fig. 5.8 Weak and strong shock waves

Strong shock at A gives same deflection as weak shock at B, but greater pressure jump since V2 < V2

velocity component parallel to the wave is not changed means, however, that the flow downstream of the weak oblique wave is supersonic.

Thermodynamic efficiency

In the gas turbine, the burning process causes the air to be heated at virtually constant pressure, in constrast to the piston engine, where the air is heated in an almost constant volume with rapidly rising pressure. The (thermodynamic) efficiency of both types of engine can be shown to depend on the pressure ratio during the initial compression process. Increasing the pressure ratio increases the maximum temperature, and the efficiency is, therefore, limited by the maximum temperature that the materials of the hottest part of the engine can withstand.

The temperature limitation is rather more severe in the gas turbine, since the maximum temperature is sustained continuously, whereas in the piston engine, it is only reached for a fraction of a second during each cycle. For a long time, this factor led to a belief that the gas turbine was so inherently inefficient in comparison with a reciprocating engine, that it was not worth bothering with.

At high altitude, the atmospheric air temperature is reduced, so for a given compressor outlet temperature, a greater temperature and pressure ratio between inlet and outlet can be allowed. Thus, the thermodynamic efficiency tends to rise with increasing altitude. This factor, coupled with the advantages of high altitude flight, described in Chapter 7, makes the high speed turbo-jet – propelled aircraft a surprisingly efficient form of transport. In fact, as we show in Chapter 7, for long-range subsonic jet-propelled transport, there is no eco­nomic advantage in using an aircraft designed to fly slowly.

The thermodynamic efficiency of gas turbines improved dramatically during the first three decades of development mainly because of progress in producing materials capable of sustaining high temperatures, improvements in the cool­ing of critical components, and better aerodynamic design of compressors and turbines.

Maximum angle of climb

Figure 7.11 shows the forces acting on an aircraft in a steady climb. If the climb is steady then there can be no net force acting on the aircraft either along the flightpath, or at right angles to it. If we consider the forces acting along the flightpath we can see (Fig. 7.11) that the sine of the climb angle is given by the difference between thrust and drag divided by the aircraft weight. Thus to operate at the maximum angle of climb possible we need the biggest possible value of thrust minus drag.

If the thrust minus the drag is equal to the weight we have a vertical climb, e. g. the Harrier (Fig. 7.12). If thrust minus drag is greater than the weight then the aircraft will be in an accelerating, rather than a steady climb.

If, however the difference between thrust and drag is less than the aircraft weight, some lift must still be provided by the wings. To be able to climb at all the aircraft must be operating at a height at which the engine is capable of producing more thrust than the drag of the aircraft.

If, for instance, the aircraft is flying straight and level initially we can plot the now familiar variation of drag with flying speed. Let us suppose that the

Fig. 7.13 Climbing flight

Increased throttle setting gives excess of thrust over drag for climb Best climb angle is obtained when thrust minus drag is maximum

aircraft is operating at point A on this curve. An increase in throttle setting will give an available thrust-minus-drag difference for climb as shown (Fig. 7.13). If we know the engine characteristics at the new throttle setting we can optim­ise the airspeed to give the best possible thrust/drag difference.

Here we must turn our attention to the type of powerplant being used once again. If we are dealing with a turbo-jet and thrust will not vary very much with speed in the operating range we are considering. All we need to do therefore is to gratefully accept the maximum thrust that the engine will give and fly at the speed which produces the least amount of drag (point A in Fig. 7.14).

If we are using a piston engine/propeller combination, we have already seen that the thrust falls with increasing speed and so we must reach a compromise between the requirements of airframe and powerplant and operate at a speed somewhat lower than the minimum drag speed in order to achieve the max­imum angle of climb (Fig. 7.15).

At this point a word of caution is necessary. We have estimated the best climbing angle using the drag curves derived for straight and level flight. When the aircraft is climbing examination of the forces normal to the flightpath (Fig. 7.11) shows that the lift developed by the wing will be reduced by a factor equal to the cosine of the climb angle and is thus no longer equal to the aircraft weight. Our drag curve will therefore need to be modified and this, in turn, may change the best speed for climb.

A large number of aircraft, such as civil airliners and military transport air­craft, are not required to indulge in particularly violent manouevres. Although the rate of climb might be quite high, because the forward speed is also high, the angle of climb is frequently not very great. In such cases our original approximation will not be too far from the truth.

Flying wings and blended wing-fuselage concepts

It has long been the dream of aircraft designers to produce civil airliners with no separate tail or fuselage, as with the B2 Spirit bomber (Fig. 4.19). The advantages would include much lower aerodynamic drag, and reduced weight. There are, however, several problems. Much of the structural load on a civil aircraft derives from the stresses due to pressurisation of the cabin, and by far the most efficient cross-sectional shape is a circle. Horizontally-arranged double or multiple bubble arrangements may be used, but passenger access between the bubbles then becomes an issue. Longitudinal stability considera­tions mean that the range of centre of gravity positions is relatively restricted, so passenger movements might need to be controlled. There are also difficulties involved in access and in the placing of passenger external view windows. None of these problems is insuperable, but the real constraint would be the very high costs of such a radical development.

Stability of canard aircraft

The stability criteria for a canard or tail-first configuration aircraft (Fig. 11.8) are essentially the same as for a conventional one. When the aircraft is trimmed, the forward wing (foreplane) should be arranged to generate a higher lift coefficient than the rearward wing (main-plane). The foreplane is therefore usually set at a higher geometric incidence than the main-plane, thus giving lon­gitudinal dihedral. On a canard it is the larger rear wing surface that generates

Fig. 11.8 A stable canard arrangement

The aircraft has to be trimmed with the foreplane generating a higher lift coefficient than the main-plane. The foreplane is therefore normally set at a higher incidence.

most of the lift, so it follows that on a stable canard, both surfaces must be producing lift.

Since both surfaces on a canard produce positive lift, the overall wing area, total weight, and drag can all be lower than for the conventional arrangement. Also, as we have already mentioned, pitch control is achieved by lifting the nose by increasing the foreplane lift, rather than by pushing the tail down. This shortens the take-off run, and generally improves the pitch control character­istics. The manoeuvrability of the canard configuration is one of the features that makes it attractive for interceptor aircraft (see Figs 10.1 and 10.8).

Another claimed advantage of the canard is, that since the foreplane is at a higher angle of attack than the main-plane, the foreplane will stall before the main-plane, thus making such aircraft virtually unstallable. Unfortunately in violent manoeuvres, or highly turbulent conditions this may not be true, and once both planes stall, recovery may be impossible, because neither surface can be used to produce any control effect.

The main problems with the canard configuration stem from interference effects between the foreplane wake and the main wing. In particular, the down – wash from the foreplane tilts the main wing resultant force vector backwards, thus increasing the drag. By careful design, however, the advantages can be made to outweigh the disadvantages, and highly successful canard designs by Burt Rutan such as the Vari-Eze shown in Fig. 4.20 provoked renewed interest in the concept.

For forward-swept wings, as on the X-29 shown in Fig. 9.20, the foreplane interference can be a positive benefit, as the downwash suppresses the tendency of the inboard wing section to stall at high angles of attack.

For pressurised passenger aircraft, the canard arrangement has the added advantage that the main wing spar can pass behind the pressure cabin, as in the Beech Starship shown in Fig. 4.10. A problem remains in that, unless there is a rearward extension of the fuselage, the fin (vertical stabiliser) may have to be large to compensate for the fact that it is not very far aft of the centre of gravity.