Category Aircraft Flight

The movement of the centre of lift on a cambered wing has a destabilising effect. Figure 11.4 shows a cambered-section wing that is balanced or trimmed

Constant

moment

Aerodynamic centre

Fig. 11.2 Centre of pressure and aerodynamic centre

(a) The centre of lift or centre of pressure moves forward as the wing angle of attack increases.

(b) For an aerofoil, the situation shown in (a) above can be represented by a constant moment or couple (shown here in its true directional sense) and a lift force acting through a fixed point known as the aerodynamic centre.

N. B. The sign convention is that nose-up pitching is positive. A cambered aerofoil as shown above therefore gives a mathematically negative moment about the aerodynamic centre

at one angle of attack, by arranging the line of action of the lift to pass through the centre of gravity. If the angle of attack increases due to some upset, then the lift force will move forward, ahead of the centre of gravity, as shown. This will tend to make the front of the wing pitch upwards. The more it does so, the greater will be the upsetting moment. Such a wing is, therefore, not inherently stable on its own.

The condition for longitudinal static stability is that a positive (nose-up) change of angle of attack should produce a negative (nose-down) change in pitching moment.

where M is the pitching moment, and a is the pitch angle.

The conventional method for making an aircraft longitudinally stable, is to introduce a secondary surface, which is called a tailplane in the British con­vention, or more aptly, a horizontal stabiliser in American terminology.

To give some idea of how the tailplane works, we will consider two simple cases, one very stable, and the other highly unstable. Fig. 11.5(a) shows an aircraft trimmed for steady level flight. For simplicity we consider a case where the thrust and drag forces both pass through the centre of gravity, and thus produce no moment. We also ignore the forces and moments on the fuselage. The tail is initially producing a downward force, and hence, a nose-up pitching moment about the centre of gravity, whereas the wing lift produces a nose – down moment. The couple Mo is drawn nose up in Fig. 11.5, which is the normal mathematical convention.

If the aircraft is tipped nose-up by some disturbance as in Fig. 11.5(b), then the tail downforce and its moment will decrease, and the wing lift and its moment will increase. The moments are, therefore, no longer in balance, and

there is a net nose-down moment, which will try to restore the aircraft to its original attitude. This aircraft is thus longitudinally statically stable.

Note, that in the simplified description above, we have ignored the inertia of the aircraft, and we have neglected the flexibility of the aircraft and its controls. Most importantly, we have ignored the effect of the fuselage which normally has a significant destabilising effect. It should further be noted that our simple example does not include any effects due to wing sweep. We should also have taken account of the fact that as the wing angle of attack and lift increases, so will the downwash at the tail. The increased downwash at the tail means that the tail downforce does not fall off as sharply with changing angle of attack as would otherwise have been expected. The restoring force is thus weakened.

Wing downwash on the tail generally has a destabilising effect. The influence can be reduced by mounting the tail high relative to the wing.

Figure 11.6 shows a case of an aircraft which is trimmed, yet in a longitudin­ally unstable condition. The wing is initially at 2° angle of attack, and the tail is at 4° angle of attack. If we look at what happens when the angle of attack increases by 2°, due to a disturbance, then we see that the wing angle of attack will double. Since lift is directly proportional to angle of attack, it follows that the wing lift will double. In contrast, increasing the tail angle of attack by 2° from 4° to 6° represents only a 50% increase, with a corresponding 50% increase in tail lift (which is further reduced by the effects of downwash). The resulting forces will, therefore, produce a nose-up pitching moment, and the aircraft will continue to diverge from its original attitude.

The final stages of the landing also offer the pilot a choice of techniques. Two alternatives are illustrated in Fig. 13.8. In the first the angle of attack is increased over a comparatively short period to arrest the descent, a manoeuvre known as the flare. The aircraft then flies parallel to the runway as the speed falls further and finally sinks onto the undercarriage. In the now less-common tail-wheel undercarriage, the final touch-down can either be on the main wheels only, or, with a greater amount of pilot skill, the aircraft can be brought to the angle of attack which results in all three wheels touching simultaneously, the so-called three-point landing.

An alternative method is to reduce the glide angle more progressively and to fly the aircraft along an almost circular path onto the runway. This type of approach is less demanding on the pilot, but results in slightly worse ability to clear obstacles near the threshold.

In order to understand how the planform of the wing affects lift and drag, we need to look at the three-dimensional nature of the air flow near a wing.

You may remember, that we described in Chapter 1, how the wing pro­duced a circulatory effect; behaving like a vortex. A major breakthrough in the

Fig. 2.1 Wing geometry understanding of aircraft aerodynamics came at the end of the nineteenth century, when the English engineer F. W. Lanchester reasoned that if a wing or lifting surface acts like a vortex, then it should possess all the general prop­erties of a vortex. Long before the Wright Brothers’ first flight, a theory of vortex behaviour had been developed which indicated that a vortex could only persist if it either terminated in a wall at each end, or formed a closed ring like a smoke ring. In Fig. 2.3 we show in very simplified form, how this requirement of forming a closed circuit is met. In the diagram we see that the circulatory effect of the wing, which is known as the wing-bound vortex, turns at its ends to form a pair of real vortices, trailing from near the wing tips. The ring is com­pleted by a so-called starting vortex downstream.

These vortices do exist in reality and we can easily detect the trailing vortices in a wind tunnel by using a wool tuft which will rotate rapidly if placed in the appropriate position behind a model. On a real aircraft they can sometimes be seen as fine lines of vapour streaming from near the wing tips, as seen in Fig. 2.4. This often occurs at airshows, particularly on damp days. They are most likely to be seen when an aircraft is pulling out of a dive, and is therefore

generating a large amount of lift, so that the wing circulation and trailing vortices are strong.

In the wing trailing vortex, as in a whirlwind or whirlpool, the speed of the rotating fluid decreases with distance from the central core. From the Bernoulli relationship, we can see that, since the air speed in the centre of the vortex is high, the pressure is low. The low pressure at the centre is accompanied by a low temperature, and any water vapour in the air tends to condense and become visible in the centre of the trailing vortex lines, as in Fig. 2.4. Note that the vapour trails frequently seen behind high-flying aircraft are normally formed by condensation of the water vapour from the engine exhausts, and not from the trailing vortices. Figure 2.5 is a flow-visualisation picture showing the trailing vortices forming at the wing tips.

In Fig. 3.18 we show two thin almost flat wing sections, a full-size one and a scale model, placed at zero angle of attack in a stream of air. In this situation, the position of transition from laminar to turbulent flow will be roughly the same distance from the leading edge in both cases, as illustrated.

From the diagram, you will see that the scale model will therefore have a greater proportion of laminar boundary layer, and consequently a lower drag per unit of area than for the larger one. So the drag per unit area measured on the model is not representative of full scale.

To correct for the effect of scale, the model could be placed in a stream of air moving faster than that for the larger section. This would increase the Reynolds number, and move the position of transition forward. If the speed were sufficiently high, transition could be moved to a position corresponding to that of the full-scale section.

The same principle applies to all shapes, and to obtain similar flow patterns between model and full scale, it is necessary to ensure that the Reynolds num­ber in the model test is the same as for the full-size aircraft in flight.

The Wright brothers and other early experimenters were either unaware of this fact, or did not bother about it. Their simple wind-tunnel tests conducted on very small models at low speeds indicated that thin plate-like wings gave a better ratio of lift to drag than ones with a thicker aerofoil type of section. Thus, early aircraft had thin plate-like wings. It was Prandtl who spotted the error, and found that when the Reynolds number of the tests was increased by running the tunnel faster, or using larger models, thicker wing sections pro­duced a better lift-to-drag ratio than curved or flat plates.

The reason for the poor performance of thick aerofoil sections at very low Reynolds numbers (small models at low speeds), is that the flow will be laminar over most of the surface and thus will separate very easily. A thin plate with a sharp leading edge generates turbulence at the leading edge, and the resulting turbulent boundary layer is better able to stay attached. Model aircraft often perform better when equipped with means of turbulating the boundary layer, and require quite different wing section shapes from full-size aircraft, as described by Simons (1999).

We have examined the way in which the flow changes as the speed of sound is exceeded and in Chapter 8 we will look at the way aircraft have developed to operate at speeds up to about twice the speed of sound (Mach 2). Some aircraft, however, have to operate at very much higher Mach numbers, particularly re-entering satellites and space shuttles. We find that a number of problems are associated with flight at these very high Mach numbers (up to about 27). Some of these are direct aerodynamic problems associated with the extreme speeds. Some are primarily structural and material problems caused by the high temperature induced by the flow. The SR-71 spy-plane used expansion joints in the structure, which lead to conspicuous, but not dangerous, leakage of fuel when on the ground. Other problems are due to the height at which such flight conditions are most likely to be made and are caused by the very low density encountered. For realistic flight conditions these problems begin to be felt at Mach numbers above about six, and so flight above this rather imprecise demarcation line is known as hypersonic.

What, then, are the aerodynamic problems associated with this flight regime? Initially nothing particularly dramatic occurs. All the main features of the supersonic flow are there, such as the bow shock wave and expansions. As would be expected from the increase in Mach number, the bow shock wave is more acutely swept to the free-stream direction. It is when we come to look at the details of the flow that we find the important changes that have taken place.

We have already seen that the shock wave is quite a traumatic experience for the flow passing through it. Pressure, density and temperature all increase dramatically over a very short distance. However, the basic composition of the air passing through the wave does not change in supersonic flow. It still consists of a mixture of roughly 70 per cent nitrogen, 20 per cent oxygen, 9 per cent carbon dioxide, with a few rare gases thrown in for good measure. The molecules of each of the various constituents are in their usual form with the nitrogen and oxygen molecules both being diatomic (i. e. with two atoms to each molecule). All the constituents are also electrically neutral, the electrons in each molecule exactly balancing the charge in the molecular nucleus.

As the Mach number increases and the shock wave gets stronger this situ­ation changes and the so-called real gas effects become important. The relatively simple relationships between gas properties which occur under moderate con­ditions of temperature and pressure break down. The two atoms in the gas molecules become detached from each other, a process known as dissociation and energy is released into the flow. This dissociation may also be present in the high temperature regions of the boundary layer near the surface of the vehicle.

A further problem occurs due to the fact that molecules may become elec­trically charged, or ionised. This means that electrical forces may further com­plicate the fluid motion. This may not necessarily be a bad thing, and schemes have been suggested to use this feature to control the flow or even provide a propulsion system.

Yet another complication arises when we consider flight at extreme altitude. For normal aircraft operation, the air molecules are very close together. The average distance between molecular impacts (the mean free path at sea level) is about 6.6 x 10-5 mm. At 120 km altitude, this distance increases to 7 m, a distance that is quite large when compared with the size of the vehicle travel­ling through the air. In this case we can no longer think of the air as being a continuous fluid, but must consider the action of individual molecules, and average their effect.

From the above, it will be appreciated that the theoretical prediction of such flows becomes very difficult. Experimental work under such extreme condi­tions is also an arduous and costly undertaking. For further information, the interested reader is referred to Cox and Crabtree (1965).