Category Aircraft Flight

Reducing frontal area

Strongly unfavourable pressure gradients can be avoided by making all parts of the aircraft as thin as possible: in other words, by reducing the frontal area. In the case of the fuselage of an airliner, any reduction in cross-sectional area must be offset by an increase in length, if the same number of passengers is to be accommodated to an equal standard of comfort. The increase in length is accompanied by an increase in the surface area, and this in turn means that the surface friction drag will increase. There is always an optimum comprom­ise between decreased boundary layer normal pressure (form) drag resulting from reduced frontal area, and increased surface friction drag caused by the increased surface area.

In the case of wing sections, reducing the thickness will result in a reduction in the depth of the structural spars. The bending strength of a spar depends on its breadth, and on the cube of its depth. Any small reduction in depth must be offset by a large increase in breadth, and hence weight. Thin wing sections also have the disadvantage that they stall at relatively low angles of attack. The reasons for the use of thin sections on transonic and supersonic aircraft will be described later.


When the aircraft is in flight, the relative velocity between the air and a section of a propeller blade has two components, as illustrated in Fig. 6.4. The flight – direction or axial component comes from the forward flight velocity. The other (tangential) component comes from the blade velocity due to rotation.

If the propeller blade is set at a positive angle of attack relative to the resultant relative velocity, it will generate a force, in the same way as a wing generates lift. However, instead of resolving this force into lift and drag components, we may resolve it more conveniently into forward thrust, and tangential resistance. The resistance force produces a turning moment about the propeller shaft axis, and this is the resistance torque which the engine has to overcome.

Any point on a blade describes a helix as it moves through the air, as shown in Fig. 6.5. The angle between the resultant velocity and the blade rotation direction is called the helix angle (see Figs 6.4 and 6.5). It will be seen that the

Подпись: Relative axial velocity
Подпись: Direction
Подпись: Thrust
Подпись: Helix angle

PropellersResultant relative


Fig. 6.4 Propeller geometry

Подпись: Blade tip Fig. 6.5 Propeller helix The inner part of the blade describes a coarser helix than the tip Vortices trailing from the blade tips will leave a helical trail similar to the tip helix shown above

The resultant aerodynamic force on the blade section can be resolved into thrust and resistance

inner part of the blade is describing a coarser helix than the tip. If all sections of the blade are to meet the resultant velocity at the same effective angle of attack, the blade will need to be twisted, so that the geometric pitch angle (defined in Fig. 6.4) is greater near the hub than at the tip. The blade twist can be seen in Fig. 6.6.


Fig. 6.6 Advanced six-bladed high-aspect-ratio propellers on the Lockheed Super Hercules

The inner part of a propeller blade describes a coarser helix than the outer, so the blades are twisted along their length. The spinner covers the ineffective drag – producing centre, and also houses the pitch-varying mechanism. In this picture, the blades are feathered (turned edge-on to the wind) to prevent them from windmilling when the aircraft is parked. The turbo-prop engine, unlike the piston engine, has little resistance to turning when not in operation

The production of thrust by a propeller blade is similar to the generation of lift by a wing. It therefore follows that the blades will produce trailing vortices. Since the blades are rotating, however, the trailing vortices take the form of helical trails.

Engine installation

In many early multi-engined jet aircraft, the engines were buried in the wing roots, as in the British Comet airliner (Fig. 9.3), and Vulcan and Victor bombers. The pylon-mounted under-wing arrangement of the American Boeing 707 air­liner, and the B-47 bomber set a trend that has been followed to this day for large subsonic aircraft. The main advantage of the podded under-wing arrange­ment is that it reduces the wing bending moment, since the engine weight partly offsets the upward force due to wing lift. In addition, intake aerodynamic losses are lower in the shorter axi-symmetric pod arrangement, and access is better.

Tail or rear-fuselage mounting was once popular for all types of transport aircraft. This arrangement produces an aerodynamically cleaner wing, but the advantage is offset by the lack of wing bending-moment alleviation, and by problems arising from the engine intake being in the wake of the wing. For large aircraft, the under-wing arrangement is now preferred, but tail mounting is still popular for smaller transports such as the Hawker 800 businessjet illustrated in Fig. 10.22.

The complete aircraft

We have so far concentrated on the factors which make supersonic wings different from their transonic and subsonic counterparts and have seen some of the reasons which underlie the selection of a particular planform for a particular aircraft. Although a few aircraft, such as the Blackbird shown in Fig. 8.18, have been designed with integrated fuselage and wing geometry, by far the largest number of supersonic aircraft retain the traditional arrangement of a discrete fuselage joined to a wing.

When we were looking at the supersonic wing we were concerned mainly with the shock waves, and resulting wave drag, produced by the lifting surface. It was mentioned, albeit very briefly, that both the thickness and angle of attack

Fig. 8.17 Effect of planform on drag

Fig. 8.18 Configuration for Mach 3

The SR-71 used lifting fuselage chines as well as a highly swept delta wing (Photo courtesy of Lockheed California Co.)

of the wing would contribute to the wave drag. The ‘thickness’ contribution also applies to other components of the aircraft, particularly the fuselage. Since the primary object of the aircraft is to carry things, we are normally concerned to reduce wave drag as far as possible with respect to the volume of the aircraft; so wave drag is usually considered in two parts – the wave drag due to the volume and the wave drag due to lift. The volume wave drag is primarily affected by the cross-sectional area distribution.

Unconventional control surfaces

The use of multiple roll-control surfaces is advantageous, partly for reasons of safety, but also because conventional outboard ailerons may become just too effective at high speed, and can induce unacceptable wing bending and twisting moments. On many aircraft, including large airliners, a set of high speed ailerons may be fitted inboard of the usual low speed ones, as seen in Fig. 10.10. This reduces the amount of span available for installing flaps, how­ever, and one method of overcoming this problem, is to arrange at least one of these sets of control surfaces as so-called flaperons, where differential move­ment has the same effect as ailerons, and collective movement produces the effect of flaps. Flaperons are used on the F-16.

Fig. 10.15 Trailing-edge elevons on the delta-winged Concorde, shown drooped with power off

On delta-winged aircraft, trailing-edge elevons are fitted, as on Concorde (Fig. 10.15). Elevons are trailing-edge control surfaces which act as ailerons when operated differentially, and as elevators when operated collectively (i. e. both moving in the same direction).

One problem with delta-winged aircraft is that trailing-edge control surfaces cannot be used as flaps, without simultaneously behaving like elevators; pro­ducing a nose-down pitching moment, which has to be counteracted in some way. This is another reason why a canard foreplane is desirable on delta-winged aircraft. A combination of leading-edge flaps and elevons may also be used.

A final variant is the taileron used on the Tornado aircraft shown in Fig. 3.14. The slab tail surfaces can be operated differentially as ailerons, or collectively as elevators. Tailerons have a number of potential advantages. Like inboard high speed ailerons, they produce a smaller rolling moment than outboard wing mounted ailerons. They reduce the bending stresses on the wing, and allow more room on the wing for flaps. Notice the full-span flaps on the Tornado in Fig. 3.14.

When several sets of roll control surfaces are installed on one aircraft, the task of sorting out which surface to use in any particular condition is generally too much for the pilot to cope with, and the selection is normally made automatic­ally. In most cases, the pilot has some selection override capability. Davies (1971) gives a good account of roll control surface operation on typical airliners.

Longitudinal dynamic stability – pitching oscillations

Let us look first in greater detail at the motion we considered above in which we disturb the aircraft in pitch and then release it (Fig. 12.2). If the aircraft is

statically stable then the resulting pitching moment will be nose down, tending to return the aircraft to its original attitude. This restoring moment is very nearly directly proportional to the disturbance for a conventional aircraft operating at moderate Mach number. The way in which it is produced by the tailplane was described in Chapter 11. The resulting motion for a typical air­craft is shown in Fig. 12.2 and consists of a heavily damped oscillation in pitch, accompanied by very little change in height or speed. This motion has come to be called the ‘Short Period Pitching Oscillation’, or SPPO.

If the motion was solely caused by the restoring moment due to increased tail angle of attack, then the oscillation would continue with the same ampli­tude. It would then be said to be neutrally stable dynamically or ‘undamped’. During the motion, however, another effect is caused by the tailplane which is not apparent when we simply consider the ‘static’ forces due to the change in attitude.

Consider the instant in the motion when the aircraft is pitching, nose up, through its original attitude (Fig. 12.3). This pitching motion increases the angle of attack on the tail and hence produces a moment which opposes the nose-up pitching. Note that this effect depends on the rate of change of the attitude of the aircraft, or its angular speed. This speed is greatest at the time when the aircraft passes through the equilibrium position. It opposes the over­shoot (Fig. 12.3), thus tending to damp out the oscillatory motion. Because the oscillations eventually disappear the motion is dynamically as well as statically stable.

A further damping effect is provided because the angle of attack of the air­craft is increasing with time. The increase in the strength of the wing trailing vortex system, caused by the angle of attack increase, takes some time before it

Fig. 12.3 Damping of pitching oscillation

Angular velocity causes a lift force on tail which opposes the rotation in pitch and damps oscillation

makes itself felt at the tail. The tail lift is, therefore, a little greater than it would be if the angle of attack were held steady, and this again contributes to the damping effect.

The combined effect of these damping terms is usually very pronounced, and the motion is heavily damped, usually not lasting more than one or two cycles in a typical conventional aircraft configuration.

In the above paragraphs a very simplified view has been taken of the SPPO, since the emphasis has been on the major factors influencing the motion. In reality, as the angle of attack changes during the pitching motion of the aircraft, the lift will change, also in an oscillatory fashion. Thus the pitching motion will be combined with a vertical motion. A more detailed analysis of the motion shows that this has a slight influence on frequency but significantly increases damping.

Another, even more subtle, factor which we have ignored is the effect that the pitching motion has on the wing itself. This is explained by Fig. 12.4. As the wing rotates, the relative motion through the air produces a downwash over the front of the section and an upwash over the rear. This has the effect of changing the moment produced by the wing section, and this again will add slightly to the damping of the motion. If the wing is swept, this effect will be more pronounced because the distance between the root and tip sections will mean that an upwash will be produced at the tip and a downwash at the root.









The air flow around an aerofoil section

In Fig. 1.13 we show the streamline patterns around an aerofoil section at a small angle of attack. Streamlines indicate the instantaneous direction of flow, and if the flow is steady, they also show the path that a particle would follow. Streamlines are defined as imaginary lines across which there is no flow. Therefore, the closeness of the lines gives an indication of flow speed. If the streamlines converge, the air is funnelled through at an increased speed, just as it does in the narrowing part of a duct, as described earlier (Fig. 1.10). Notice how the streamlines converge over the front of the upper surface of the aero­foil in Fig. 1.13, indicating an increase in speed, and diverge underneath, show­ing a decrease. A similar effect may be seen in the flow around the rotating cylinder in Fig. 1.12.

Some important features of the flow around the aerofoil may be seen by looking at the dividing streamline; the streamline which effectively marks the

The air flow around an aerofoil section

Fig. 1.13 Streamlines around an aerofoil

The dividing streamline meets the section just under the leading edge, at the stagnation position where the flow speed is momentarily zero, and the pressure reaches its maximum value

division between the air that goes over the wing, and that which flows under it. We have already mentioned that the flow divides not on the nose, but at a point under it, even on a flat plate. Notice also, how the air is drawn up towards the aerofoil at the front, as well as being deflected downwards from the trailing edge. This is also true for the spinning cylinder. Behind the wing of an aircraft, there is an overall downward flow of air, or downwash, but it should be noted, that this is predominantly a three-dimensional effect, as described in Chapter 2. The downwash seen in Fig. 1.12 would not be nearly so pronounced if the cylinder completely spanned the tunnel from wall to wall.

How the boundary layers form

In a laminar boundary layer, molecules from the slow-moving air near the surface mix and collide with those further out, tending to slow more of the flow. The slowing effect produced by the surface thus spreads outwards, and the region affected, the boundary layer, becomes progressively thicker along the direction of the flow. The way in which the boundary layers grow is illustrated in Fig. 3.2.

At the position called transition, an instability develops, and the flow in the layer becomes turbulent. In the turbulent boundary layer, eddies form that are relatively large compared to molecules, and the slowing down process involves a rapid mixing of fast and slow-moving masses of air. The turbulent eddies extend the influence outwards from the surface, so the boundary layer effectively be­comes thicker. Very close to the surface, there is a thin sub-layer of laminar flow.

Surface friction drag

Just as the surface slows the relative motion of the air, the air will try to drag the surface along with the flow. The whole process appears rather similar to the
friction between solid surfaces and is known as viscous friction. It is the pro­cess by which surface friction drag is produced.

The surface friction drag force depends on the rate at which the air adjacent to the surface is trying to slide relative to it. In the case of the laminar bound­ary layer, the relative air speed decreases steadily through the layer. In the tur­bulent layer, however, air from the outer edge of the layer is continually being mixed in with the slower-moving air, so that the average air speed close to the surface is relatively high. Thus, the turbulent layer produces the greater amount of drag for a given thickness of layer.

Drag due to interference effects

Any intersection between two surfaces such as at the wing-fuselage junction has a disruptive effect on the flow, and extra drag is incurred. Acute angles such as that formed between the wing and fuselage on either high – or low-wing air­craft are worse than oblique angles. A mid-wing position would be better from this aspect, but mid-wing designs introduce structural problems. The cabin crew in a mid-wing airliner might not take kindly to the main spar getting in the way of the drinks trolly.

On a low-wing aircraft, the fuselage can interfere with the pressure distribu­tion on the upper surface of the wing, possibly inducing flow separation. A high-wing configuration is better in this respect, as in this case, the flow on the under-surface is the most affected. The under-surface flow is normally in a favourable pressure gradient, and is thus less likely to separate. The high wing arrangement has a number of disadvantages, however, including problems involved in trying to avoid long undercarriage legs, and adverse interference effects between the wing wake and the tailplane. Notice the very high mount­ing position of the horizontal tail surface on the C-17 (Fig. 10.20), and the BAe 146 (Fig. 6.26). This is necessary, in order to keep the tailplane out of the wake of the wing at high angles of attack.

The wing-fuselage interference effect is largely a manifestation of the gap in the spanwise lift distributing mentioned above (Fig. 4.11), and can be reduced by use of a lifting fuselage as on the MiG-29 (Fig. 4.12), where the interference effect is also reduced by use of a blended wing-fuselage. A blended wing-fuselage was also used on the SR-71 Blackbird spy-plane (Fig. 6.40). In this case, the arrangement has the important advantage that the elimination of sharp junctions reduces the aircraft’s radar signature. Interference effects can also be reduced by means of wing fillets, but this feature is rarely found on modern aircraft.

A more radical solution to the interference problem is to remove most of the junctions by adopting an all-wing configuration as in the B2 ‘Spirit’ (Fig. 4.19). Large slender-delta-winged aircraft lend themselves to a nearly all-wing con­figuration, and such an arrangement was considered at the early stages of the Concorde project. The idea was eliminated because it would have required a very large aircraft, in order to provide sufficient cabin depth, and would have introduced another set of novel features in an already revolutionary design. It was also realised, that passengers would react unfavourably to the idea of having traditional port-holes replaced by overhead fanlights.

The last item in the drag budget is the undercarriage. Despite the consider­able added cost and weight of a retracting undercarriage, the benefits are so great, that fixed undercarriages are rarely used on anything other than small light aircraft. An interesting solution to the problem of undercarriages is that used on the Quickie shown in Fig. 11.9. The canard foreplane has pronounced anhedral, and also serves as the undercarriage legs. The Rutan Vari-Eze shown in Fig. 4.20 uses a retractable nose wheel which is also lifted for parking, as shown. Retracting the nose wheel saves a considerable amount of drag, and the pilot would probably get away with forgetting to lower it on landing; a com­mon error with amateur pilots.

Drag due to interference effects

Fig. 4.19 All Wing, the Northrop Grumman B2 ‘Spirit’ bomber

The all-wing configuration eliminates drag-producing junctions. It represents a radical departure from the classical aeroplane, as here, the wing provides lift, volume and stability. Northrop’s all-wing technology developed in the 1940s and 1950s was revived and put to good use on the B2 ‘stealth’ bomber, as the lack of junctions helps to produce a low radar signature. Note the absence of any fin or rudder. Directional (yaw) control is produced by differentially varying the wing-tip drag, by means of ailerons that can be opened like split flaps (Photo courtesy of Northrop Grumman)

The ducted fan

By placing a fan or propeller in a duct or shroud, as in Fig. 6.10, flow patterns can be obtained, that are significantly different from those produced by an unducted propeller or fan. The flow patterns depend on the relationship between the flight speed and the engine thrust. Figure 6.10 shows two sets of patterns, one corresponding to the low speed high-power take-off condition, and the other to the high speed cruise case. In this figure, the broken lines represent streamlines which divide the flow that goes round the outside of the duct, from that which flows through it. Again, in three dimensions, these would correspond to stream-tubes, which may be termed dividing stream-tubes.

To explain how the duct or shroud works, we shall look first, at a subsonic flow of air through a converging streamlined duct with no fan to assist it, as illustrated in Figure 6.11. Since no energy is being added, the device cannot produce a thrust, so the jet of air at C (where the pressure is at the free-stream value) cannot be moving faster than the free stream at A.

Подпись: Low speed flow Fig. 6.10 Alternative flow patterns for a ducted fan At take-off, the flow accelerates towards the fan, and the pressure falls in the duct intake In the high speed cruise case, the approaching flow decelerates, and the pressure rises in the intake

The dividing stream-tube diameter at A must, therefore, be no larger than at C, since the same amount of air is passing at about the same speed at both A

The ducted fan

Fig. 6.11 Flow through a streamlined duct

If no energy is added, then the flow speed at C cannot be greater than at A, since the pressure is atmospheric at both positions. In the duct at B, the flow speed is lower, and the pressure is higher than the surrounding atmosphere

and C. As the flow enters the duct at B, however, the area is larger, so the speed must be lower there. If the speed falls, then the Bernoulli relationship tells us that the pressure will be higher.

A duct can, therefore, provide a means of reducing the air speed and increas­ing its pressure locally. If we place a fan in the duct, then the addition of energy to the flow can create a jet, and the streamline pattern can be as shown in Fig. 6.12. This is similar to the cruise case shown in Fig. 6.10.

As shown, there is still a reduction in speed, and an accompanying increase in pressure as the flow enters the duct. This is a very useful feature if the aircraft is flying at a high subsonic Mach number, because the air now enters the fan at a lower Mach number. The Mach number is lowered further, by the fact that the rise in pressure is accompanied by a rise in temperature, so that the local speed of sound is also increased.

In Fig. 6.12 we have shown the surrounding stream-tube for an unducted propeller, having the same diameter as the ducted fan, and producing the same amount of thrust. A fan operated in this way is less efficient than a free pro­peller of the same diameter, since the fan draws its air from a smaller area of the free stream, as shown in Fig. 6.12. The mass of air used per second, and the resulting (Froude) efficiency are, therefore, both smaller for the fan. The price is, however, worth paying, as the fan may be used at flight Mach numbers where conventional propellers suffer excessive losses due to compressibility effects.

It should be noted, that for high speed turbo-fan (fan-jet) propulsion, it is normal for the outer part of the blade to run with supersonic relative flow between the blade and the air, but with subsonic relative flow for the inner

The ducted fanPressure greater than surrounding atmospheric

Подпись: Dividing stream-tubeПодпись: for ducted fanSurrounding stream-tube

for an unducted propeller producing

the same amount of thrust

Fig. 6.12 Ducted fan at high speed

As with the simple unassisted flow through a duct, the flow slows down as it enters the duct, and the pressure rises. The surrounding stream-tube for a propeller of the same diameter producing the same amount of thrust, is shown by dashed lines part. We shall deal with the linking of such ducted fans to gas-turbine engines to provide turbo-fan propulsion later.