Some problems of complete aircraft

We conclude this chapter with some very brief remarks on how the requirement on the motions which the aircraft as a whole should be able to perform may affect the design. It must seem rather strange that these remarks come at such a late stage and that they are so short. One would have thought, that the need for the aircraft to move about readily and safely at the pilot’s will would have furnished the overriding design criteria. Indeed, these were vital considerations and matters of life or death for the early pioneers of flight, such as Lilienthal and the Wright Brothers. A very large amount of work on these problems has been done since then and certain broad notions exist of what is acceptable to the pilot but, as we shall see, we are still not in a position to specify precisely the flight and handling qualities that are wanted and then to design the aircraft to have exactly these characteristics. Thus much of this work lies before us and many problems remain to be resolved. What may have made conditions

* For a discussion of how some design aspects of engine and airframe may affect noise see e. g. D R Hinton and T A Cook (1973) and F W Armstrong & J Williams (1975).

tolerable in the meantime and allowed safe aircraft to be designed, in spite of our incomplete knowledge and understanding, may be the fact that, within limits, the skilled and adaptable human pilot appears to be able to cope remarkably well with difficult and even unforeseen problems and that a broad spectrum of flying and handling qualities is acceptable to him.

In general terms, we are now concerned with time-dependent motions, involving unsteady aerodynamics, and it is convenient to define four categories of such motions, bearing in mind that these are all interdependent and not mutually exclusive:

(1) The motion of the vehicle varies with time. This category includes the problems associated with the flight mission, with control applications and manoeuvres, and with stability.

(2) The shape of the vehicle changes with time. This category includes the problems of elastic deformations of the flexible structure caused by different loading actions. The structure may deform either periodically or aperiodically. It is convenient to distinguish between situations where the motion of the whole vehicle is affected by the deformation and where it is not.

(3) The flowfield relative to the aircraft is time-dependent. This category includes the problems associated with unsteadiness in boundary layers, in separated flows, and in flows with shockwaves. Such unsteadiness includes acoustic disturbances and they may occur not only in the flows over the lift­ing and volume-providing parts of the aircraft but also in the propulsive part of the airstream, as in intakes and jets. These phenomena have already been discussed many times in this book.

(4) The atmosphere changes with time. This category includes the problems associated with small-scale turbulence in the air, with gusts, and with large – scale wave motions and vortex motions. These problems have already been dis­cussed in section 5.8.

We are left here then with the first two categories in which, strictly, the aerodynamics of the flows is almost invariably coupled with some structural response. What is wanted, therefore, is an integrated aerodynamic and struc­tural analysis of the dynamics of the flying vehicle as one deformable body with a built-in control system. Such a combined treatment has not yet been developed. Traditionally, the various aspects have largely been treated in isolation and conventions have been established whereby subjects such as flight dynamics, loading actions, aeroelasticity, flutter, noise, control systems tend to be regarded as separate fields of work. These conventions are now slowly broken down, because the need arises in some cases, and may do so more frequently in the future, to treat the many aspects of the problem in an integrated manner.

It is clear that this unsteady aerodynamics covers a very wide field and, in view of the complexity of the physics involved, it is not surprising that there are the strongest incentives to ignore the time-dependence and to assume the aircraft to be rigid, and thus to simplify matters wherever possible in solving practical problems. Some motions to be considered should be steady, anyway; others may be slow enough to be regarded as quasi-steady; and some may be so fast that time-average quantities may be used. This may explain the specially strong trend in this field to break up the overall problem into partial problems and to solve them. sequentially.

Consider now the special problems of stability and control of aircraft. Following the pioneering theoretical work of F W Lanchester (1908) and G H Bryan (1911), these problems have been treated in many textbooks, and we refer here to those by В M Jones (1935), C D Perkins & R E Hage (1949),

W J Duncan (1952), В Etkin (1959) and (1972), and to papers by R D Milne

(1964) , X Hafer (1972) and in AGARD Conference Proceedings CP 119 (1972). We follow here mainly the presentations by E G Broadbent (1966), H R Hopkin &

H H В M Thomas (1967), H R Hopkin (1970), В Etkin (1972) and H H В tl Thomas

(1975) , but we can do no more than to give the scantiest outline with some references to further reading.

For the present purpose, we may regard the aircraft as a system, that is, an interconnected set of elements, which is clearly identifiable and which has a state that is defined by the values of a set of variables which characterise its instantaneous conditions. We usually deal with a mathematical model of a physical system. Quite often this is not a sufficiently faithful representa­tion of the actual physical system and, in some cases, the governing equations may not be known. Hence the great importance of obtaining reliable informa­tion about the dynamics of the system from tests in windtunnels or in flight.

In general terms, three sets of equations govern a system which represents the flight of an elastic vehicle subject to aerodynamic and gravitational forces through the atmosphere:

The force equations, which relate the motion of the centre of gravity to the external forces;

the moment equations, which relate the rotation about the centre of gravity to the external moments;

the elastic equations, which relate the deformations to the loadings on the vehicle.

Considering that aircraft fly in a layer of air wrapped around the near­spherical rotating Earth, we note that there are cases where account must be taken of the unsteadiness in the atmosphere (see section 5.8), or of the variation of density with height (see e. g. S Neumark (1948)), or of centri­fugal acceleration and Coriolis forces (see e. g. A M Drummond (1972)). What simplifies matters, on the other hand, is the fact that most aircraft have a plane of symmetry. Then the equations of motion can conveniently be split into two sets: one of these governs the longitudinal or symmetric motions, where the wings remain level and the centre of gravity moves in a vertical plane. The other governs the lateral or asymmetric motions, where the air­craft may roll, or yaw, or sideslip, while the angle of attack and the speed in magnitude and direction remain essentially constant. The lateral – directional equations separate out only for small perturbations, whereas a purely longitudinal motion of a symmetrical aircraft can exist even for large displacements. Even so, the two sets of equations may still be very complex, depending on the shape of the aircraft and on the degrees of freedom to be considered, i. e. on the number and nature of the elements in the system as well as on internal (controls, interconnections, or feedbacks) and external (aerodynamic, gravitational) inputs or motivators (devices which produce changes in the forces and/or moments).

In view of this obvious complexity of the system, it is not surprising that linearisation of the equations, introduced by G H Bryan (1911), brings about especially desirable simplications. The linearised model is based on the assumption of small disturbances about a reference condition of steady recti­linear flight over a flat Earth. The aerodynamic forces and moments are assumed to he functions of the instantaneous values of the perturbation velo­cities, control angles, and of their derivatives; they are obtained in the form of a Taylor series in these variables, and the expressions are linearised by ignoring all the higher-order terms. It is surprising that this linearised model gives adequate results for engineering purposes over a wide range of applications; probably because, in many cases, the major aerodynamic effects are nearly linear functions of the state variables, and because quite large disturbances in flight may correspond to relatively small disturbances in the linear and angular velocities.

The motion of the aircraft is now described by a system of linear differential equations, the Eulder equations, with coefficients – the so-called stability derivatives – obtained from the Taylor expansions. If only the more important possible motions of a rigid aircraft are considered, there is still a large number of equations to be solved, and В Etkin (1972) lists 18 major longitudi­nal and 18 major lateral derivatives, or groups of derivatives (in his Tables

7.1 and 8.1), pointing out that, in some cases, convenient formulae to define them are not yet available. Thus much of the work in flight dynamics is con­cerned with determining the values of these derivatives, theoretically or experimentally (see e. g. the textbooks mentioned above; also H H В M Thomas

(1961) , C G В Mitchell (1973), J A Darling (1973), M L Goldhammer et al (1973), E Schmidt (1974), and R Fail (1975)). Many of the methods discussed so far can be used for this purpose. The measurement of dynamic derivatives poses especially difficult problems, and techniques for doing this in ground test facilities have been reviewed by C J Schueler et al (1967). One successful technique, by J S Thompson and R A Fail (1966), is to excite and to measure model oscillations in yaw, sideslip, and roll at the same time. Our present testing capability and what will be needed in future have been set out very clearly by К J Orlik-RUckemann (1973).

A peculiar difficulty in this work is that state variables which are conveni­ent in mathematical models need not necessarily be the same as those that can readily be calculated or measured on models in windtunnels or in flight (see e. g. F E Douwes Dekker & D Lean (1962); E J Durbin & C D Perkins (1962)).

Thus methods are needed not only for solving the equations of motion but also for analysing dynamic response data in flight and for extracting those deriva­tives, or groups of derivatives, which are required from the experimental results. Graphical methods for doing this have been developed by К H Doetsch (1953), and computer techniques are now also available (see e. g. A P Waterfall (1970) and С H Wolowicz et al (1972). This should also make it clear why we are still such a long way from solving the general design problem: it would be necessary to specify, and then to achieve, values of the derivatives which lead to solutions of the equations of motion that satisfy the required flying characteristics. So far, only a few rather general design criteria for derivatives are known.

Apart from the aerodynamic derivatives, the equations of motion contain also stiffness, damping and inertia terms, describing the structural properties, as in any mechanical system. If the complete equations are known, the stability of the system can be investigated. Static stability is essentially a concept related to a steady, or equilibrium, state of a system. Equilibrium denotes a steady state of the system in which all the state variables are constant in time. The motion corresponding to equilibrium is represented by a point in

the state space. A disturbed system is sometimes explained in terms of a ‘giant hand’ which changes the system, holds it at a constant deviated posi­tion, and then releases it. If the forces acting at the instant of release are in a sense to restore the system to its original steady state, then the system is said to be statically stable.

More generally, three possible motions may happen:

(1) the state point moves back to the origin;

(2) it remains within a finite distance from the origin within the state space at all subsequent times;

(3) it departs from the origin and moves to infinity.

Only the first of these indicates stability. For a given system, the actual motion or trajectory, depends on the way in which the hypothetical giant hand disturbed the system, and an equilibrium point may be deemed stable only if the system is restored to its steady state regardless of the nature of the disturbance. For stricter and more detailed definitions and discussions of stability problems see e. g. В Etkin (1972) and J LaSalle & S Lefschetz (1961).

In many cases, the motions resulting from disturbances may be osei. Vta. tovy, and the three possibilities are then damped periodic oscillations, limit cycles, and divergences. But it should be noted that there are limitations to this linearised model and that some aircraft motions of practical importance require that non-lineccr and special time-dependent effects are taken into account. Thus small-disturbance theory is not suitable, for example, for post-stall gyrations and for spinning motions. Special problems have to be solved when considering aircraft motions at high angles of attack (see e. g.

H H В M Thomas & J Collingbourne (1973)), when cross-coupling terms between inertia and aerodynamic forces and moments may lead to critical flight condi­tions (see e. g. W J G Pinsker (1957)), or when gyroscopic effects of the engine are coupled into the motion of the aircraft (see e. g. W J G Pinsker (1970)). The theory of aircraft response in rolling manoeuvres under the influence of inertia cross-coupling effects has been developed by W H Phillips (1948), H H В M Thomas & P Price (1964), and T Hacker & C Oprisiu (1974) (see also Data Sheets of the Royal Aeronautical Society, Anon (1966)). Non-linear mechanics (see e. g. N Kryloff & N Bogoliuboff (1947)) introduce considerable complications into the dynamics of flight, and practical methods and tech­niques for the analysis of non-linear dynamic characteristics are only now being developed (see e. g. A J Ross & P A T Christopher (1972); I M Titchener 0973)).

Static stability criteria are clearly related to trim criteria. An aircraft is said to be trimmed when control surfaces, or motivators, are set to such values that the system maintains the steady state which is desired at that time. A convenient way of devising trim criteria is to consider two neighbour­ing steady states, one being taken as a perturbation of the other. This will require an increment in motivator application which, in turn, will result in corresponding increments in the variables of the system. The relationships between all these will reveal any trim criteria that may be useful.

For a simple illustration of these concepts, consider the case of the longitu­dinal motion of a rigid aircraft at low speeds, where we have to deal with an overall lift coefficient Cl, an overall pitching moment coefficient Cm (always including contributions from control surfaces, tail, propulsive system etc.), and an angle of incidence a. There must be one position (hu) of the overall centre of gravity (CG) where ЭСц/Эа is zero, which represents the boundary between positive and negative pitch stiffness. This is the neutral point or the aerodynamic centre of the vehicle. If the CG is at another position (h) , the pitching-moment slope can be written as

ЭСм/Эа – OCj/SctHh – hn) . (5.45)

As introduced by S В Gates (see S В Gates & H M Lyon (1944)), the difference hn – h between the neutral point and the actual CG position is called the static margin. The criterion for static stability is obviously ЭСц/Эа < 0 , i. e. a nose-down pitching moment or positive pitch stiffness. Thus, in a statically stable aircraft, the CG position must be forward of the aerodynamic centre: the further forward it is, the more stable is the vehicle. Alternati­vely* the concept of a trim margin may be used; it is proportional to the static margin. This, then, is a simple design criterion which the designer must and can satisfy. There are some other design criteria of a similar nature concerning lateral motions.

Consider now the actual longitudinal motion of an elastic aircraft. There may be some high-frequency structural modes which usually have a negligible influence on the overall motion. But some low-frequency elastic mode may exist and must be taken into account. Other oscillatory motions may be deter­mined from the linearised small-perturbation model of the system. First, there is a slow phugoid mode, described by F W Lanchester (1908), which has a long period (about 2min for a turbojet transport aircraft of medium size) and is lightly damped. Second, there is a short-period mode, which is quite rapid (with a period of 3 to 5s) and usually very heavily damped. Changes in air density may bring about another slow mode (see e. g. S Neumark (1948)). All these oscillations may now readily be computed numerically, but more physical insight is needed for design purposes and may be obtained from approximate analytical solutions. For example, some general knowledge of the expected modal characteristics will allow the exact system of equations of motion to be simplified to one of lower order, which can be solved analytically in closed form – a technique already applied by Lanchester. But the simple analytical solutions cannot be relied upon to give adequate answers in all circumstances and, in the final step, numerical results will be needed to check their accuracy.

In reality, the motion of an aircraft has six degrees of freedom and can take many and much more complicated forms. What is essential for the designer to know or to specify are the boundaries within which a given aircraft is stable and may be trimmed. Such trim boundaries define the limits of steady-state flight conditions. For example, the trim boundary for the longitudinal motion is, in general, a plane contour giving values of the trimmed angle of incidence as related to particular limiting values of control deflections and CG posi­tions. To obtain these trim boundaries in the conventional way is a very laborious task. In an experiment, the appropriate combinations of angles of incidence and control deflections corresponding to trim about all three axes must be found simultaneously. A considerable amount of interpolation is usually involved with a consequent loss of accuracy in the characteristics deduced for trimmed flight. Here, a windtunnel dynamic simulator, as developed by L J Beecham (1961) (see also L J Beecham et al (1962); В E Pecover (1968);

I M Titchener & В E Pecover (1971)), can expedite matters considerably and has been proved to be a successful and useful design tool, especially for the simulation of non-linear flight-dynamic problems. The simulator consists of a computer which is programmed, as are other dynamic simulators, to solve Euler’s dynamical equations, but which has the essential distinction that the incidence-dependent loads (or, in principle, any other forces and moments) are measured on-line by means of a slaved model in a windtunnel. Model and windtunnel are parts of the computer loop, with the model being commanded to move to simulate continuously the orientation of the full-scale vehicle to its flight path, according to the solutions obtained from the computer. Trim boundaries can then be determined directly and generated automatically and a large amount of irrelevant data outside the boundary excluded. The direct input of experimental data removes the need for modelling these contributions mathematically and thus makes it possible to examine motions which arise from disturbances, no matter how large they are, nor how non-linear the aerodyna­mics, nor how much aerodynamic cross-coupling is involved*. Such tests can give valuable insight by economical means and also indicate clearly the relative importance, in any particular case, of various departures from perfect stability and control characteristics.

This brings us to a brief discussion of some control ‘problems of aircraft, following the basic concepts introduced by S В Gates (1942) (see also S В Gates & H M Lyon (1944)). Controls, or motivators, are used to put the aircraft into a trimmed condition for stable flight, but their main function is to enable the aircraft to perform required manoeuvres. Consider, for example, a steady longitudinal pull-up motion where the load on the aircraft is n times the weight of the aircraft, i. e. n = L/W. At a point where the tangent to the flight path is horizontal, the net normal force is L – W = (n – 1)W and directed vertically upwards. There is thus a normal acceleration of (n – l)g, n = 1 indicating straight level flight. To per­form the pull-up manoeuvre, the elevator angle and the control force, or stick force, have to be changed from the values they have in trimmed level flight, and from these the required values of the ‘elevator angle per g’ and of the ‘control force per g’ may be determined. The flight path is curved, and the angular velocity of the aircraft is fixed by the flight speed and the normal acceleration. This curvature of the flowfield relative to the aircraft affects the aerodynamic forces and moments and should be taken into account. This is particularly so if the required acceleration is large, as it may be in some combat manoeuvres. We should recognise the severity of this problem by reminding ourselves of the complexity of the flow pattern over a supercritical sweptback wing, typical of this type of aircraft even in level flight, as sketched in Fig. 4.71. Matters are even more complicated when the angle of sweep is varied during flight (see e. g. D Schmitt (1975)). It would be quite presumptuous to suppose that our present computing or experimental capability could bring us confidently anywhere near this important design target, even in this relatively simple manoeuvre of a longitudinal pull-up: the development of adequate design methods requires a great deal of further work.

In analogy to the static margin discussed above, a manoeuvre margin may be defined, as a measure of the ‘stiffness’ term in the simplified equations of motion, if the speed is constant. In the example of the pull-up manoeuvre, there must, in general be one CG position (Ьщ) where the value of the required change of elevator angle per g is zero for a fixed stick position.

* It should be noted that the model was moved in slow time in Beecham’s simu­lator so that real time-dependent effects could not be measured and estimates for these had to be made in the computer program. But this restriction could, in principle, be removed.

The difference hjj, – h between this position and the actual CG position is called the manoeuvre margin, after Gates. The concept may be generalised to cover other manoeuvres.

In the particular example discussed here, we have tacitly assumed that only the one motivator, the elevator, which is designed for this purpose, is actu­ally sufficient to perform the manoeuvre and that no other controls are needed. This assumption brings about a considerable simplification in the equations of motion. Corresponding approximations are often used also in other cases by assuming that one specific type of control action is mainly associated with one particular motivator and, consequently, that any important basic type of manoeuvre will also be mainly effected through the operation of one particular motivator. Such simplifications are typical in theoretical work in flight dynamics and often go a long way towards practical solutions. They also help the understanding, but it must be expected that there are many situations where they are too crude and where a more complete treatment is needed.

We can now also appreciate one of the fundamental conflicts in the dichotomy of stability and control: to prevent a system from suffering large deviations following a disturbance from a steady state, it is an advantage if the system possesses a strong natural static stability of its own; to change the state of the system in an efficient manner and to perform a manoeuvre, the natural static stability may be a nuisance. Thus the basic stability and response characteristics of aircraft and control systems constitute a handling problem for the pilot who forms an essential part in the loop. An aircraft will be regarded as having ‘good handling qualities’ when its characteristics are such that they allow the pilot to maintain those conditions of flight which are necessary or desirable, and to complete those manoeuvres which are required, with little mental or physical effort; conversely, an aircraft will be regarded as having ‘bad handling characteristics’ when the pilot can achieve these ends only with great effort and concentration, if at all. If the assessment of ‘goodness’ or ‘badness’ were essentially a matter of a pilot’s judgements and opinions in any given case, this would rule out a completely rational design of the man-machine combination. But it may be possible, in time, to develop more satisfactory concepts.

The establishment of reasonable and safe handling criteria and their attain­ment may be regarded as the central and most important task in aircraft design. It must include not only the stability and control characteristics of the aircraft but also such matters as the pilot’s view, flight instruments and their presentation, cockpit position, etc. Here, we can refer only to the pioneering work on handling problems by H J van der Maas (1932) and to summary reports on these problems by P L Bisgood (1964) and (1968) and by F O’Hara (1967), and the papers in the AGARD Conference Proceedings CP 106, 1971. We refer also to work aimed at rationalising as far as possible the characteristics of man-machine combinations and at rating pilot’s judgements and workloads, using results from flight tests and from ground-based flight simulators (see e. g. К H Doetsch Jr (1971), J T Gallagher (1971), R 0 Anderson

(1971) , R К Bernotat & J C Wanner (1971), R G Thorne (1972)) as well as calculations (see e. g. W J G Pinsker (1972)). Because of the fundamental difficulties involved and the incompleteness of our knowledge, it is customary for individual government agencies responsible for licensing civil aeroplanes and for procuring military aeroplanes to specify certain handling qualities that must be complied with. It is in their nature that they usually specify minimum requirements for the various aspects of handling qualities or merely state that the aircraft’s behaviour (e. g. following a stall or a spin) should not include any dangerous characteristics, and that the controls should retain enough effectiveness to ensure a safe recovery to normal flight. The fact that the requirements differ from country to country and from agency to agency is an indication of our still relatively poor knowledge and makes us aware of the great need for further work to come nearer to a solution of this crucial problem in aircraft design.

To complete this brief review, we consider how the pilot can be helped in his task, and his workload reduced, by artificial or automatic means of control, that is to say, by an autopilot, A set task must always be accomplished during every phase of the flight of an aircraft. This implies that a desired state, steady or transient, is specified at all times, and that departures from it must be regarded as errors. These errors must be detected and measured. They can then be corrected by the actuation of motivators in such a manner as to reduce them and to return the aircraft to the specified state. In principle, the detection and feedback control in this closed-loop operation can be exercised by a human or by an automatic pilot, provided that all the necessary information can be obtained by suitable sensors and that suitable control mechanisms are available. For example, it is possible to maintain level flight at constant speed by means of an autopilot which suppresses variations in speed, height, and attitude. In particular, a simple feedback of pitch attitude is sufficient to eliminate effectively the phugoid motion. Other automatic systems for guiding and controlling less simple motions may be much more complicated, especially if guidance and stabilisation is wanted. The sensors must then provide a great deal of information to define the state, which is accurate and in a suitable form to be incorporated into a control system, such as vectors of position and velocity relative to a suitable frame of reference; aircraft attitude; rates of rotation; angles of attack, side­slip etc.; acceleration components of a reference point in the vehicle. Much work remains to be done on sensors and control elements, and there is a wide scope for the flight dynamicist and the control engineer to achieve further progress in this field of avionics.

These devices may also be used as servomechanisms to augment inherent stab­ility; or to provide powered controls when the control forces needed exceed the capability of the human pilots; or to provide increased damping of some mode of flight; or to alleviate gusts or undesirable flutter characteristics. There are stall-warning devices and associated motivator actions to prevent dangerous post-stall gyrations (see e. g. G J Hancock (1971)). Since transport aircraft spend much of their flight time under automatic control, attention is directed now mainly to making manual control easier and safer, or to providing automatic control, in the’ other phases of flight, within a set of air-traffic – control rules: take-off and climb-out, approach and landing (see e. g.

W J G Pinsker (1968) and (1969); P Robinson & D E Fry (1972)). In the present context, we must observe that these devices and systems can only be applied if the inherent aerodynamic control mechanisms function effectively throughout. This, then, remains one of the objectives of aerodynamic design.

Attempts are now also being made to design, or ‘to configure’, the aero­dynamics and the avionics of an aircraft together from the outset, with a view to achieving better performance, or manoeuvrability, or economics, or safer operation. Some objectives would be to relax natural stability requirements, to incorporate manoeuvre demand systems as well as automatic manoeuvre limita­tions, to alleviate gusts and to control flutter. For example, there would be an obvious benefit if the tailplane (which causes about 10% of the drag of an aircraft) could be sized for control only instead of for stability.

Work on such control-configured, vehicles (CCV) is only at the beginning and it remains to be seen how far the potentially large benefits can be realised in practice (see e. g. C A Scolatti & R P Johannes (1972); R В Jenny et al

(1972) ; H WUnnenberg & G SchSnzer (1974); papers by J C Wanner and by R В Holloway in AGARD Conference Proceedings CP 147 (1974); G Hirzinger et al

(1975) ; and J C Wanner (1975)). Nevertheless, this work gives a clear indica­tion of the strong and necessary trend to integrate ever more closely the aerodynamic design of aircraft with that of stability, control, and guidance systems and with the structural design. It may be said that we have only now arrived at a point in the development of aircraft where we recognise and can define what the real design problems are. We are a long way away from solving them, but aviation is at least ‘growing up’.