Shape-Adaptive Wings—The Unfulfilled Dream of Flight

Shape-adaptive wings—the unfulﬁlled dream of ﬂight

L.F. Campanile Institute of Composite Structures and Adaptive Systems, German Aerospace Centre (DLR), Germany.

Abstract

There is no achievement of man for which biological models play such an important role as in aeronautics.And in no technical development is the relationship between technology and nature so difficult. Man became able to fly; he became able to fly at supersonic speeds; and he became able to explore space with his flying machines. Still, even after 100 years of aeronautics, the yearning for the silent, efficient, reliable flight of birds remains strong. The question whether the ‘natural’ way of flying is technically reproducible or is going to remain a dream for the engineer is still an open one. This question is strongly related to the question of geometrical adaptability of airfoils; in other words, with the technical possibility of realising airfoils which can be properly deformed, statically as well as dynamically. In the most advanced conception of bio-inspired flight, wings work additionally as rudders, flaps and propulsion systems; but even small steps towards this vision, such as quasi-static adaptation of airfoil geometry for a conventionally propelled aircraft, promise a dramatic improvement in efficiency and manoeuvrability. The above-mentioned crucial question concerning geometrical adaptability of airfoils constitutes a multidisciplinary question of applied mechanics, primarily covering the areas of structural mechanics, material science and actuator technology but also strongly related to other disciplines, among them fluid mechanics and aeroelasticity. This contribution gives a broad insight into the conceptual and historical back- ground of the adaptive airfoil issue and provides an overview on the actual stand of research on this topic. Some crucial aspects like the conflict between the main requirements of deformability, load-carrying capability and low weight as well as the role of a coupled mechanical design are addressed in more detail. The final part of the paper focuses on the author’s own work on airfoils with variable camber and optimisation of compliant systems for shape control. In particular, the so-called ‘belt-rib’ structural concept for shape-adaptable airfoil structures is presented and discussed. This concept implements a revolutionary design philosophy which completely relies on structural flexibility in order to produce large geometry changes. Former approaches to shape- adaptable airfoils, which are documented in hundreds of patents or patent applications worldwide, were substantially based on conventional articulated systems with moveable parts, involving strong weight penalties which made them unfeasible for practical applications. Due to their

WIT Transactions on State of the Art in Science and Engineering, Vol 4, © 2006 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) doi:10.2495/1-84564-095-0/5c Shape-Adaptive Wings—The Unfulfilled Dream of Flight 401 optimised design, belt-rib airfoils keep a light construction while offering large shape adaptability as well as the capability of withstanding high loads, and therefore constitute a major step towards the realisation of nature-inspired airfoils with full geometry control.

1 Introduction

In one of his books about bird flight, Nachtigall [1] raises the interesting question why a relatively simple flight device like a hang glider was not already invented by the ancient Egyptians. Looking for an answer, it is natural to start comparing man-made flight with the other great achievements of engineering and look for substantial differences. If an ancient Egyptian was given the opportunity of living in our times, he would perhaps be more fascinated by a cellular phone or a laptop computer than by an aircraft. And this not because the first two would be, in his eyes, more complex or powerful or important inventions than the last one; they would just surprise him more. He would probably expect to find some kind of flying machine after more than 4000 years of technical progress. Unlike a cellular phone or a laptop computer, an aircraft belongs to the technical visions of mankind since the earliest times, and in a very concrete form. Man knew since the beginning that a heavier-than-air mechanical system could be realised which could move through air in a controlled way. Nature supplied the evidence that physics allows flight and at the same time set a clear framework for the development of a man-made flying machine. Due to this reason, the development of man-made flight was given the character of a formidable design project whose target was the emulation of bird flight, while other inventions—among them cellular phones and laptop computers—virtually evolved together with analytical and technical skills without a pre- defined point of arrival. The reader will agree with the assertion that the first way to proceed, for a complex system to be developed, is definitely more difficult than the second one. As a matter of fact, aeronautics experienced a decisive turn when engineers abandoned, at least in part, the idea of flying in the same way a bird does. Back to the ancient Egyptians: paradoxically, it is likely that the availability of models from nature for flight systems retarded the realisation of a man-made flying machine rather than speeding it up. After more than one century of aviation, the discussion about the technical emulation of nature flight is far from being closed. During these years, biologists and engineers created an increasingly synergetic research community around flight. While biology can gain a deeper understanding of flight phenomena in nature by means of the analysis tools which were developed for aeronautics [2–4], engineers look at biology as a rich source of ideas for innovative aircraft concepts [5–7]. The advantages and disadvantages of the biological and of the engineering approach represent a quite popular discussion topic within this scientific community [3–5]. ‘The flying machine which will really fly might be evolved by the combined and continuous efforts of mathematicians and mechanicians in from one to ten million years’. This popular excerpt from the New York Times of 9 October 1903 [8] (a few weeks before the first successful flight of the Wright Brothers’Flyer) surely includes an overestimation error. By how much, it depends on what exactly ‘really fly’ means. If the ancient dream of flight is meant, with the unique combination of efficiency, noise level, manoeuvrability and reliability that we know from nature, the project is still in progress.

2 The bio-mimetic way and its potential

Biologically based, innovative approaches to man-made flight can be firstly divided into two groups. The first one includes measures for extended variability of airfoil geometry, with the long-term target of full aerodynamic control by means of proper surface adaptation. The second group contains bio-inspired thrust production concepts (like the flapping wing). The corresponding WIT Transactions on State of the Art in Science and Engineering, Vol 4, © 2006 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) 402 Flow Phenomena in Nature vision here is the ornithopter [9], equipped with bio-mimetic thrust production devices that replace conventional propellers, rotors and fans. Since no clear distinction is present in nature between devices for thrust, lift, control and stability, an increasing coalescence of these two research areas can be expected in the long run, not least because they share the sort of technological and analytical challenges to be faced. Still, starting from the present aerospace technology, a quite sharp distinction can be made on the basis of energetic considerations: dynamic, cyclic, geometric changes of the aircraft’s surface intended to continuously transfer mechanical power from an internal energy reserve to the flow fall in the second category; quasi-static as well as dynamic, but mostly non-cyclic, geometry changes aiming at adapting to different conditions or at producing forces for flight control belong to the first one. In the first group, a further distinction can be made on the basis of the desired performance improvement: quasi-static geometry adaptation mostly aims at reducing off-design drawbacks, which are typical for fixed-geometry airfoils, and at increasing in this way the aircraft’s efficiency and operational flexibility, while load control by means of fast airfoil shape modifications usually aspires to increase manoeuvrability. The perhaps simplest abstraction level on which the potential of bio-inspired approaches to flight can be evaluated regards the flying machine (aircraft or flying animal) as a mechanism, with a certain spectrum of realisable body geometries. Otto Lilienthal’s explanation of the flight phenomenon (‘Birds fly because they process the air surrounding them with properly shaped wings in a proper way’ [10]) suggests this kind of abstraction: a bird has ‘just’ to change properly the geometry of his body’s surface in order to fly. This applies to a man-made aircraft too, not only as far as lift, control and stability are concerned, but even to thrust production by propellers, rotors and turbofan engines, as long as the hot exhaust flow of the latter is neglected. On this abstraction level, differences between an aircraft and a flying animal reduce to corresponding differences in geometry management. Typical differences are in the number of controllable degrees of freedom, in the sort of realisable deformations (smooth geometry changes versus rigid-body motions) as well as in the deformations’ extent and speed. The strong relationship between geometry management skills and flight performance is a widely accepted fact in the bionic scientific community; most discussions on bio-mimetic approaches to man-made flight include a, at least qualitative, hint on this [3, 11]. Some quantitative insight was achieved in the framework of several projects dealing with extended geometry control of airfoils. Szodruch [12] analysed the advantages of variable camber for transport aircraft. According to his results, camber modifications in the rear 10% of the wing chord, ranging between −3◦ and 6◦ (trailing edge slope) and properly distributed along the span, improve the wing lift-to-drag ratio by up to 9% and the buffet boundary by up to 12%. A study of Bolonkin and Gilyard [13] on camber changes obtained by deflecting a conventional flap device in the range between −2◦ and 16◦ shows an improved lift-to-drag ratio by up to 14%. Effects on section lift and drag due to changes in camber extent and chordwise distribution were analysed by Wickenheiser et al. [14], who determined a 20% increase in lift (accompanied by 6% increase in drag) due to a 10% camber increase as well as a 13% drag increase (with a lift increase of 3%) as a result of a 10% forward shift of the camber maximum. Both measures can be advantageously used for yaw and roll control. Experimental evidence of the large advantages of an even simple extension of airfoil geometry management was achieved in the framework of the Mission Adaptive Wing program. Four geometrical degrees of freedom (a single variable camber device for the leading edge region and a trailing edge device with three independent segments along the span, [15]) were added to the wing of a fighter aircraft and delivered clear improvements in range and manoeuvrability [16, 17]. A more complex kind of geometry management (HECS—hyperelliptic cambered span—wing), which involves changes in camber, dihedral and sweep angles combined in a single degree of freedom, was investigated by Manzo et al. [18]. The authors report advantages of up to 15% in terms of lift-to-drag ratio with respect to a conventional wing of comparable size. Bowman et al. WIT Transactions on State of the Art in Science and Engineering, Vol 4, © 2006 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) Shape-Adaptive Wings—The Unfulfilled Dream of Flight 403

[6] analysed prospective advantages of morphing — defined as the capability of realising radical changes in aircraft’s shape — in terms of reduced off-design drawbacks and improved operational flexibility. An aerodynamic analysis methodology for morphing wings, based on numerical fluid computations as well as on statistical data, is presented by Wickenheiser and Garcia in [14], and its application to an HECS wing is discussed. Effects on performance as well as on stability of the aircraft are analysed by the authors. In the already referenced contribution of the same authors [7], the problem of the aerodynamic and control analysis of a perching aircraft is systematically addressed by means of an analytical approach (lifting-line theory). The validity of such a model is, however, restricted to the moderate angle-of-attack regime and is therefore intended to be used only to predict the aircraft’s dynamics in the transition phase from cruise flight to perching landing. Analysis of the perching manoeuvre itself is to be performed on the basis of thorough wind-tunnel measurements. This is a typical case in which the intuitive insight into the advantages of a bio-mimetic approach, which is provided by direct observation of nature (see Fig. 1), plays an important role in motivating extensive research efforts.

Figure 1: A perching goose suggesting nature’s superiority in managing high levels of air trafﬁc (Photo by John Conrad, licensed).

All mentioned performance analyses rely on the above-introduced abstraction of the ‘flying mechanism’, completed, when necessary, by a mass distribution modelling. On this basis, also a rough estimate of the cost—in terms of actuation energy—of advanced geometry management (or, according to modern terminology, of morphing) is possible. For this purpose, Pettit et al. [19] developed a model with four components dealing with shape generation, aerodynamics, flight dynamics and control, respectively. The model computes appropriate geometry changes for a given course of the aircraft and determines the power required to deform the system against the aerodynamic forces. Since the model does not include the structural behaviour, it cannot compute the strain-related term in the actuator energy balance. A possible energy transfer from the flow to the mechanical system is globally addressed by analysing the reversible work (i.e. by taking into account phases of negative power while building the time integral of the required power).Actuator power analysis of morphing airfoils with inclusion of the strain contribution was performed by Gern et al. [20]. The authors computed, for a selected case, an increment of almost 400% in the required actuator power with respect to an airfoil with conventional flaps and for the same increase in lift coefficient. This estimate, however, is expected to be largely in excess since it relies on a structural model conceived for a fixed-geometry wing and does not include the effects of a possible flexibility tailoring.

3 The unfulﬁlled dream of ﬂight

In his autobiographic book [21], while describing the development in aeronautics between 1909 and 1929, Anthony Fokker enthusiastically emphasises: ‘Although I partially predicted it, some- times I rub my eyes and wonder if I am just dreaming. In these years ranges increased from 80 to 10000 kilometres, flight times from one to 647 hours and speeds from 48 to 655 kilometres per hour. (…) I have absolutely no idea in what we will fly in ten years’. Even though such gradients could not be kept up until our times, an extension of this review to the first century of aeronautics still remains impressive. Anyway, if we follow the path from the 1903 Flyer to modern commer- cial aviation and look for a possible biologically inspired component in this development, we would have some difficulties in finding bio-mimetic influences at all—in evident contrast to the aeronautic development before 1903—and, if any, they would, quite surprisingly, show a slight divergence from the bio-inspired way rather than a convergence. As compared with other features like structures, materials, control and propulsion, we find an impressively poor development of airfoil-geometry management: today’s aircraft fly, for the main part of the flight, with virtually the same number of controllable geometrical degrees of freedom as their ancestors of the pioneer years, i.e. with as many degrees of freedom as is absolutely necessary to perform controlled flight at all. Geometry adaptation approaches based on flexible structures, like the Wrights’ wing-warping device for roll control, were replaced in the first years of aviation history by machine-inspired solutions which strongly restrict the realisation of smooth shape changes, and turbofan engines rely only partially on ‘air processing’(see Lilienthal’s citation in the previous section) to produce thrust. The fact that aerospace engineering followed—with undisputable success—a flight approach that in some important aspects is definitely different from flight in nature can easily induce to consider the technical approach as the ‘right way’ to man-made flight, discovered by early flight pioneers like the Wright brothers and further developed in the following years. Such an inter- pretation tends to disregard bio-mimetic approaches as not feasible or at least not appropriate. Things look quite different if one happens to study the patent literature of the last century on airfoil geometry management. Instead of celebrating the ‘discovery’ of man-made flight, an astonish- ingly large number of engineers kept working hard on concepts which would allow extended

WIT Transactions on State of the Art in Science and Engineering, Vol 4, © 2006 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) Shape-Adaptive Wings—The Unfulfilled Dream of Flight 405 geometry control, both in the sense of producing smoother contour changes and in the sense of increasing the number of controllable geometrical degrees of freedom. The number of patents and patent applications is countless; the reader can convince himself by starting a simple search on an intellectual property right database. A selection of patents can be found in [22]; a representative example is reported later in this paper. In 1924, more than twenty years after the Wright brothers’ first flight, Birnbaum published a historical paper [23] on flapping flight which, by the way, was destined to provide a substantial contribution to research on flutter phenomena in the following years, after a series of accidents dramatically draw the attention on dynamic aeroelastic instabilities. The commitment towards bio-mimetic issues, which evidently survived—with unchanged strength—the electrifying atmosphere of the pioneer years as well as the impressive development of aeronautics in the following decades, testifies the strong belief in the potential of bio-mimetic approaches also in the engineering community. The intensive research efforts of the last 20 years, performed in the framework of large programs like Mission Adaptive Wing (MAW) [17], Adap- tive Wing (ADIF) [24], Smart Wing [25], Active Flexible Wing (AFW) [26], Active Aeroelastic Wing (AAW) [27], the NASA Morphing Project [28] and, finally, DARPA’s Morphing Aircraft Structures (MAS) [29], which share targets and approaches with an unmistakably bio-inspired content, just confirm this view.

4 On the signiﬁcance and limits of scale-analysis for feasibility predictions

If the focus of discussion moves from the mere advantages of bio-inspired approaches in terms of flight performance to the feasibility of an ‘artificial bird’, the kinematic abstraction level introduced above is no longer appropriate, since structural and energetic issues—just to cite two—play a major role in this context. To consider most relevant aspects, we can now think to the general flying-machine as a body with a proper distribution of passive (load-carrying) and active material, a—somewhere located—reserve of chemical energy, a suitable sensor system, a signal as well as an energy transfer network, an appropriate controller and, last but not least, a payload. All components, which involve a virtually infinite number of design variables, are optimised in a sense discussed later in the paper. As pointed out by Ifju et al. [30], the design of a proper controller for a hypothetical artificial bird with an airfoil geometry management comparable with the one implemented in a bird is a formidable synthesis task. Nevertheless, the performance of a control system has a definitely weaker impact on the system’s overall weight than, say, the structure. The same holds true for the sensor and the network components. Due to these reasons, and since gravity is expectedly the dominant constraint of such an optimisation, the structure and actuator component together with the energy reserves and the payload, determine most of the challenges which are relevant to a fun- damental feasibility discussion, i.e. on whether and by which extent physics (and not for instance the designer’s optimisation skills) can limit or even prevent the realisation of an artificial bird. Even when restricted to these components, the analysis of such a model—and the related optimisation task—can be extremely complex. For such level of complexity, dimensional analysis is a powerful tool, and it is therefore no wonder that a large part of the discussion on feasibility of man-made flight which is documented in the literature relies on it (see for instance [4, 5, 31]). Searching for physical limits to bio-mimetic solutions to flight, and since aeronautics covers a definitely different size range than nature, scale effects understandingly represent a highly relevant issue in this context.

As in every other sort of powerful tool, however, dimensional analysis must be employed carefully in order to avoid producing wrong conclusions. In the early years of aviation, a ‘well- known authority’ [32] prognosticated a physical limit of five tons for an aircraft on the basis of the so-called square-cube rule. In 2005, the Airbus A380 will exceed this prediction by more than 110 times. The square-cube rule [33] expresses the fact that, for a structural system which is loaded by its own weight, forces tend to increase proportionally to the cube of the size and areas just to the square of the size itself. Consequently, stresses increase linearly with the size, which leads to a size limit due to the limited material strength. In order to understand how a seemingly correct reasoning can lead to an obviously wrong result, it must be made clear what can be asserted on the basis of this kind of scale analysis and what not. If our abstract artificial bird, feasible at a given size, was to be similarly scaled by a given factor, the square-cube rule allows the assertion that mechanical stresses would linearly increase with the scale factor and a limit size would be reached, whose actual value can be easily computed if the maximum stress in the original model, its size and the allowable stress of the structural material are known. ‘Similarly scaled’ means here that not only the external shape but also the internal layout (in particular, the distribution of passive and active material, fuel and payload) remains the same. In this form, such kind of analysis would be of little use for a feasibility statement of general validity since it would require a separate analysis for each design. In order to overcome this problem, one usually refers to a—somehow—optimal system, which, for a given optimisation problem, is supposed to be a uniquely defined function of the size itself. This approach allows a surely more general result but it is definitely more complicated since all scaling effects (not only structural scaling but also scaling in the aerodynamic forces, fuel efficiency, work performance of the active material, and so on) must be simultaneously considered, because they determine how the optimal design changes as a function of size. While studying birds as optimised flight systems, some changes in design are evident by statistical significance, like the increase in aspect ratio with size [31]; but the underlying optimisation targets followed by nature are not exactly known, which makes extrapolation of such design trends quite difficult. Apossible source of error in the application of these abstract considerations to a practical case is that every real system is suboptimal to some extent and its degree of optimality (defined as the ratio between the value of the objective function computed for the realised design and the absolute optimum) is usually unknown. Back to the anonymous authority of the pioneer years, his prediction may have been wrong due to a large difference between the degree of optimality of the reference system used by him and the actual A380 design. Another substantial problem in this sort of esti- mates (which may have affected the above-mentioned prediction as well) is represented by the inherent difficulty of foreseeing future developments in material science and manufacturing technology, which can dramatically affect the active restrictions of the optimisation problem.The introduction of carbon-fibre reinforced composite material, for instance, virtually increased the limit size of a structure—as it can be computed by means of the square-cube rule—by a factor of 6.61 with respect to aluminium alloys (computed for unidirectional high-strength laminate with 60% fibre content and an Al Mg 10 alloy, material data from [34, 35]), and the limit weight by almost 290 times. The relevant material parameter here is σ/ρ1/3 (specific strength for structures loaded by their own weight), with σ as the allowable stress of the material and ρ as the material density. But the perhaps most obvious—and, still, too often overlooked—source of incorrect predictions is related to the fact that it does make little sense to compare, in this context, systems that were optimised for a substantially different target (different cost function and/or different performance restrictions). This may play a minor role in the above-mentioned example, if both the reference and the A380 airplane are supposed to be lightweight-optimised, but is a central issue in bionics, as it will be addressed in the next section.

5 The ‘great optimiser’ and the bio-mimetic challenge

Nature is often referred to as the ‘great optimiser’[30], which is surely an appropriate expression as far as the superiority of its optimisation skills is concerned. In the kind of scale analysis described in the last section, it would be surely not daring to assume a degree of optimality of nearly one for a biological system. While comparing nature’s solutions with engineering products, however, overlooking differences in the optimisation target can lead to quite distorted results. It is a fact, for instance, that the expected limit size for a passenger airplane is definitely larger than the expected limit size of birds. With respect to the cubic root of weight, and by relating the A380 (maximum take-off weight 560 tons [36]) to a mute swan or black vulture of 15 kg, we compute a factor of more than 33. Taking span as reference length and the wandering albatross as the limit example (3.20 m) the factor amounts to almost 25 (wing span for the A380: 79.8 m). This difference can be hardly ascribed to disparities in the optimisation skills of nature and engineering, since we reasonably expect nature to realise a degree of optimality near to unity, or, if lower, anyway larger than for a technical product. Material properties may surely play a significant role: for instance, the specific strength of bones (see e.g. Fung [37]) amounts to just 9.4% of that of carbon-fibre composites (see section 4 for material specifications and data source); but the most relevant effect is likely to come from the different optimisation target. To make the point, if the aircraft design engineers was given the task of developing a flying machine which has to be not only able to carry a given payload, but also a complete production line for all mechanical parts of the aircraft itself, a maintenance and repair equipment as well as an oil drilling plant and a refinery for the fuel, this could represent a fairer basis of comparison. This means two things: first, the feasibility of an artificial bird, no matter how sophisticated it is, cannot be excluded on the basis of a simple extrapolation of scaling considerations which are valid for nature systems; second, if a passenger ornithopter or a perching vertical-landing aircraft should be built, it will not look and work exactly like the corresponding biological model. Reynolds-number effects, for example, induced De Laurier to depart from bird emulation in the conception of his large-scale ornithopter [38]. The task of realising such an aircraft which implements a deeply bio-inspired approach to flight represents, however, a huge challenge which covers a broad range of engineering disciplines. In the following, we will focus on some essential aspects, mainly in the area of applied mechanics, which arise from the interaction of the weight-sensitive components mentioned in Section 4. The first substantial issue is materials. As it was exemplarily shown in the previous section for fibre-reinforced composites, progress in material science can radically change feasibility predictions. Even though thousands of pages on optimal mechanical design can be written without mentioning one single value of a material parameter, no quantitative assertion about the performance of a mechanical system can be made without knowing the material data. Materials shape technical development and it is surely not a coincidence that they even label the eras of mankind’s history. Gordon [39] even ascribes the evolution of a wheel-based technology (or, more generally, of machine concepts relying substantially on rotating or sliding parts) to the availability of metals as a construction material. A second possible reason for this evolution, and for the obvious differences to nature’s approach to motion, will be discussed in the next section. Decisive impulses to the intensive research effort of the last two decades in the field of active structural systems, which is highly relevant to the issue of bio-inspired flight, came, after all, from the availability of activable materials like piezoceramics or shape memory alloys. Beyond the above-introduced specific strength, allowable strain and specific stiffness (E/ρ, with E as the Young modulus) belong to the relevant parameters of the structural material. As far as the active material is concerned, the key parameter is represented by the specific energy

WIT Transactions on State of the Art in Science and Engineering, Vol 4, © 2006 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) 408 Flow Phenomena in Nature density factor (σaεa/ρ, with σa as the maximum active stress and εa as the maximum active strain of the material). This determines the quantity of mechanical work which can be performed by the actuators in an activation cycle and per unit mass (see for instance Huber et al. [40]). Finally, and especially for bio-inspired thrust production, the quantity of storable energy per unit fuel mass constitutes a further substantial material-related quantity. In the last few years, remarkable research efforts were put in investigating and developing several classes of materials with promising properties, like carbon nanotubes [41], electro active polymers [42] and the so-called nastic materials [43]. The second area in which the future of bio-inspired flight approaches will be decided is the one of manufacturing technology. Manufacturing constraints have a strong influence on the design space of a system to be optimised and, consequently, on the performance of the optimal layout. For an active mechanical system, in particular, the predominant manufacturing issue is the high integration level of components. The primary requisite is the distribution of active and compliant elements over the structure in order to avoid load concentrations and the resulting weight penalties. This, in turn, involves small-scale integration of data and power busses, sensors and even of the fuel material as an additional relevant concern. The third and, from the point of view of analytical complexity, probably the most challenging subject is optimisation. The coupling of several strongly interacting effects, together with the above-mentioned need of distributing the single components over the system leads to a huge number of design variables. For this reason and due to the complexity of the functions involved, the determination of a global optimum is virtually impossible, and to find a design with an appropriate degree of optimality still causes large difficulties. Similarly to what happens in the case of lightweight structures, the optimal design of a bio-inspired aircraft cannot be achieved directly by means of a global optimisation algorithm but is to be completed by a joint effort of mathematical optimisation and analysis. The analytical work, performed on a theoretical, numerical and experimental basis, helps decomposing the global optimisation problem into smaller subproblems with weak mutual interactions as well as identifying proper design space reductions. Mostly, this kind of design analysis is performed on representative elements or subsystems and results in design criteria of general validity. While a large number of criteria and procedures is available for the design of lightweight structures with fixed geometry, proper criteria and representative results for the sort of highly integrated, light, active mechanical systems discussed above are widely missing and will be the topic of large research efforts in the next few years. The rest of the paper will focus on some selected issues which will play a central role in this context.

6 Sir George Cayley and the de-coupled mechanical design

In Section 3 the reader may have missed an explanation why the huge amount of engineering work which is documented in the patent literature on extended geometry control of airfoils never lead to significant changes in the way modern airplanes manage airfoil geometry. More generally, the reader might be wondering why the development of aeronautics after 1903 was not appreciably influenced by bio-mimetic ideas. The inquiring reader will find a possible answer in this section. As mentioned in Section 1, the development of aeronautics was decisively accelerated when man freed himself from the plan of reproducing the mechanism of bird flight in all its aspects. The undisputed protagonist of this paradigm change was Sir George Cayley, a British engineer and scientist. Cayley is regarded as the first one who recognised the advantages of separating the tasks of lift and thrust production and assigning them to different subsystems of an aircraft [44].

Figure 2: Cayley’s silver disc (Science Museum, London). The first face shows Cayley’s airplane concept with a fixed wing, a cruciform tail and a separate propeller (of the flapping sort, though). The second one illustrates how the aerodynamic forces acting on an airfoil are decomposed into lift and drag.

Figure 2 reproduces the silver disc on which this idea is engraved. Today, more than 200 years later, such a separation of functions is still considered one of the key principles of airplane design. Quite suggestively, Staufenbiel [45] asserts in this respect: ‘Lilienthal would surely have achieved a better success, had he followed Cayley’s principle. Birds did not either; however, they took millions of years to be able to fly’. This also makes the point on what kind of advantages result by Cayley’s task separation principle: an easier, faster design procedure, but not necessarily a better performance. On the contrary: an arbitrary reduction of the design space which just aims at simplifying the optimisation procedure itself leads, in all probability, to a poor optimality level. For instance, if vertical take-off and landing is an issue, separation of lift and thrust production devices is no longer practicable [45]. In this context it is worthwhile to mention the discussion reported by Norberg [3] on the suitability of flapping wings for micro air vehicles. While commenting a statement of Spedding and Lissaman [46], who asserted the superiority of a rotating wing system (ThrustWing) as compared to flapping wings and asked why such a system is not present in nature, Norberg answers: ‘because animals do not have wheels’. Indeed, while studying the evident differences between biological and technical transportation systems, a stronger common basis can be detected, extending through ground, water and air locomotion, than would be seen at first glance. One of the most entertaining discussions on locomotion in nature and engineering deals with the question whether nature ‘invented’ the wheel or not. Since the wheel represents a sort of epitome of technical progress [47], the underlying issue of this discussion was to find out whether man can be considered—to some extent—a better designer than nature. The reader who shares the arguments of Section 4 will surely agree that this kind of concern makes little sense; however, the scientific literature which arose around this point is highly interesting and of substantial relevance to bio-mimetics. To guard the supremacy of the ‘great optimiser’, biologists actually came out with two alter- native approaches: admitting that the wheel represents a ‘superior’ concept for locomotion and showing that organisms with some kind of wheels are, indeed, present in nature [47] or recognis- ing the absence of biological wheels—with some singular exceptions—and arguing, on the other

WIT Transactions on State of the Art in Science and Engineering, Vol 4, © 2006 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) 410 Flow Phenomena in Nature hand, that wheels are highly suboptimal devices for transportation [48]. Both are probably true: a wheel is just optimal or suboptimal, depending on the optimisation target. While analysing the essence of the wheel as an invention for locomotion, we recognise a task separation idea which recalls Cayley’s principle: the tasks which are de-coupled here are carrying load in one direction (the radial one) and allowing motion in an other direction (the circumferential one). Referring to a wheeled vehicle on a flat ground, this is not quite far from the issue of separating lift and thrust. And, in this case too, the de-coupled design approach limits the optimality degree. Or, put in a different way, if a de-coupled design is a given restriction of the problem, a wheel is an optimal system in its way; but, in this case, the optimisation target is defined with the dominant aim of simplifying the design itself as well as the manufacturing process and a comparably very small consideration is given to the system performance. In this connection, La Barbera [48] points out that wheels are efficient only on prepared terrain (unrestricted and flat) and rotating systems for aerial and aquatic propulsion are aerodynamically less efficient than oscillatory ones, at larger sizes (higher Reynolds numbers) even more than at small sizes [48, 49]. In conclusion, the fact that aircraft and ships use propellers instead of flapping or swimming and trains do not walk or run has a great deal to do with the need of simplifying the design process and making it affordable. Back to the development of aviation, de-coupled mechanical design not only determines, in the sense supported by Cayley, the configuration of a modern airplane with separate devices for lift and thrust, but also exerts a strong influence on the way how airfoil geometry management is realised in an aircraft. A revolute hinge in a rudder is not substantially different from a wheel, as far as the design principle is concerned. In designing an airfoil with selectable geometry, the main design problem is conciliating the needs of producing deformations and carrying loads; by implementing the wheel principle into the airfoil, this requirement conflict is strongly weakened by restricting it to a single degree of freedom. The remaining motion component is then controlled actively or passively by coupling with a proper actuator device [50]. If helicopters are considered instead of airplanes to represent man-made flight, the separation between lift and thrust production disappears; however, a strong influence of de-coupled mechanical design can be still detected in the evident differences between flapping wings and rotor. Similarly to what concerns thrust production, also with respect to airfoil geometry management the original conception was definitely more bio-inspired than the one adopted in modern airplane design. This is not only reflected in early concepts for control surfaces (see Fig. 3), but also in

Figure 3: An early concept for a control surface [52].

WIT Transactions on State of the Art in Science and Engineering, Vol 4, © 2006 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) Shape-Adaptive Wings—The Unfulfilled Dream of Flight 411 the design of the first successful airplanes [51], in which roll and pitch control were realised by means of flexible devices. The process that finally led to a hinge-based technique, driven by the continuous increase of the loads acting on the airfoils, was virtually completed by the First World War [22]. The performance drawbacks of a hinge-based geometry management device are manifold: wear, backlash as well as costs for assembly and maintenance are just some examples [50]. From the specific point of view of aerodynamics, inherent discontinuities in the deformation pattern and the related peaks in the pressure distribution [53] are worth mentioning. But the major role is surely played by the serious weight penalties implied by such a design option. A measure for this kind of weight penalties was introduced in [54] by referring the volume V of the additional material required by the hinge to a reference volume, obtained as a function of the cross section A of a fixed-geometry structure which is dimensioned for the same load: V α = . (1) A3/2 Values for this weight penalty factor range between 6.27 for a bolted joint with tight clearance [22] to over 200 for ball bearing hinges [54]. Figure 4 illustrates the physical meaning of these results: introducing, for instance, a ball bearing joint in a cylindrical rod subject to an axial load leads to a weight penalty effect which is equivalent to providing the rod with√ a disc plate (made of the same material) whose thickness is nearly the√ same of the rod (exactly π/2 = 0.89 times the rod thickness) and whose diameter is equal to α = 14.4 times the rod diameter. Considering now the invention exemplarily shown in Fig. 5, it should be evident why such kind of devices for airfoils with extended geometry adaptability were not practicable and why geometry adaptability of airplane airfoils was always kept at a minimum. The only available technology for high-load, high-deformation systems was not able of keeping weight low. By the way, the concept represented in the figure is the one which was implemented in the MAW aircraft (see Sections 2 and 3) and resulted in substantial weight penalties [6]. A design discipline for mechanical systems that are light, highly deformable and able to carry high loads is still not available [22]. A large potential for the development of such a design methodology is shown by the so-called compliant systems, which achieve deformability by means of mechanical strain instead of relying on moveable parts.Available design methods for compliant systems [56–59], mostly developed with the target of mechanism miniaturisation, usually focus on

Figure 4: Weight penalty effects for conventional hinges.

Figure 5: Shape-adaptable airfoil design by Statkus [55].

precision and mechanical efficiency and give the load-carrying aspect a lower priority. Flexures of the notch hinge type (see, for instance, [60]) are conceived as light, highly deformable components for small loads. A design methodology for high-load, low-weight compliant systems is still not available. Expectedly, the missing design de-coupling leads—as compared to mechanism based on conventional hinges—to a better performance at the price of a definitely more complex optimisation procedure: for instance, a solid-state hinge can be tailored for a certain limited swing angle, with the effect of limiting stress concentrations and, consequently, reducing weight [22]; on the other hand, such an optimisation involves geometric non-linearities and requires, as a rule, a three-dimensional stress analysis. Afurther source of complexity—and, correspondingly, of potential performance enhancement— arises from possible coupling with other mechanical subsystems like actuator, flow, and inertia forces. In an active mechanical system whose deformability relies on a compliant structure, the restriction of the system’s kinematics to virtually one degree of freedom (or, in general, to a small number of degrees of freedom) is no longer possible. A first consequence of this fact concerns the actuator design: since the conventional actuator technology based on discrete actuator forces does not suit such a passive system with distributed flexibility, distributed actuation is definitely more appropriate, if not even necessary. In this case, since the structure–actuator interaction concerns a large number of degrees of freedom, structure and actuator design are strongly coupled to another. The optimality bonus of the actuator–structure coupling is given by the possibility of exploiting advantageous synergies while carrying external loads. Additionally, distributed actuator forces reduce load concentrations (and therefore weight) and increase reliability owing to a higher redundancy level [20]. A second substantial fact is related to aerodynamic forces: owing to the presence of flexible components, structure-flow coupling is to be considered in most cases at an early design stage; on the other hand, this offers the possibility of exploiting beneficial aeroelastic effects. Exploitation of aeroelastic effects is a well-known phenomenon in biological flight: the asymmetrical layout of feathers in birds, for instance, generates a continuous adaptation of the angle of attack to the varying flow conditions during the cycle [3]. Engineering solutions which take advantage from such a principle can be found in the wing design of micro air vehicles [30]. At a larger scale, concepts relying on active aeroelasticity were addressed by Loewy and Tseng [61] on a theoretical basis. They analysed the case of a wing with a conventional two-segment control surface which is purposely made aeroelastically unstable in order to extract energy from

WIT Transactions on State of the Art in Science and Engineering, Vol 4, © 2006 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) Shape-Adaptive Wings—The Unfulfilled Dream of Flight 413 the air stream to actively deform the wing. A similar approach was successfully followed in the framework of the already mentioned (see Section 3) AAW program. The third effect, concerning inertial forces, is similar: due to distributed ﬂexibility, possible vibration phenomena deserve greater consideration in the design process, which, on the other hand, allows exploiting them for better performance. Also this effect is advantageously used by nature: structural resonances not only improve the energy management of insects and birds [3, 4], but also play an important role in terrestrial and aquatic locomotion [62].

7 Coupled mechanical design for ﬂight: the belt-rib structure

The idea of shape-adaptable airfoils by means of compliant structures inspired the belt-rib structural concept, developed at DLR in the framework of the Adaptive Wing (ADIF) program [63]. In recent years, several contributions on compliance-based approaches to airfoil geometry adaptation appeared in the literature [64–66]. This, together with the increasing research activity on the exploitation of beneficial aeroelastic effects [29, 67] attests that the potential of a coupled mechanical design is widely recognised in the aerospace community. The development of the belt-rib structure focused on a quite specific task (as compared to the wide spectrum of bio-inspired approaches to flight), namely reducing off-design effects on the wing aerodynamic performance of a passenger airplane, in cruise flight, by actively changing the wing camber. Nevertheless, a belt-rib structure is a quite representative example and offers a good insight into the kind of mechanical problems which can be encountered, in general, while designing an aerospace structure with extended geometry adaptability. The basic principles of its design philosophy are neither strictly related to the particular kind of measure to be realised (camber change) nor to the specific performance target (quasi-static adaptation to different flow conditions) and are therefore relevant to a broad range of bio-inspired approaches. The requisite scenario which generated the belt-rib structural concept was chosen with the purpose of addressing one of the main challenges of airfoil geometry adaptation: conciliating load-carrying capabilities and deformability without creating appreciable weight penalties. The requirements concerning the load-carrying capabilities (stiffness and strength) virtually repro- duced the ones which are valid for the design of a given conventional wing; the deformability requirement was assigned by defining the maximum positive and negative camber variation, with respect to the conventional wing, which the system must be able to realise; finally, the lightweight requirement was indirectly imposed by choosing the option of a compliance-based deformability and by substantially keeping the structural layout unchanged with respect to a conventional airfoil. The conventional airfoil which served as a reference was the Airbus 330/340 main wing. Figure 6 shows a detail of the corresponding cross section at the spanwise location chosen as a standard. The required camber changes involved deformations only in the trailing edge region, which limited structural changes to the fowler flap and avoided modifications of the wing box. The amount of camber was associated to the trailing edge displacement; in order to express it in a non-dimensional way and make it independent of scaling, the rotation angle with respect to a given reference point was chosen as a measure of camber, as shown in the figure. In Fig. 7 the structural layout of the belt-rib airfoil is shown. The core of the compliant mechanism is the belt rib, which mainly consists of a closed shell (belt) and an optimised arrangement of stiffeners (spokes). The spokes are connected to the belt by means of flexure hinges. The belt rib is bonded to the outer skin of the airfoil like the plate-shaped rib of a conventional airfoil construction.

Figure 6: Cross section geometry of the ADIF reference wing (Airbus A330/A340) with the corresponding deformability requirements.

Figure 7: Structural layout of the belt-rib airfoil.

Figure 8: Belt-rib prototype.

The belt-rib structural concept was verified on a numerical basis as well as experimentally. Several prototypes were built and tested. Figure 8 shows an integrally manufactured composite belt-rib prototype. A hybrid carbon/glass fibre system was selected as reinforcing material, with the glass fibre component mainly used in the bending region of the flexures. The design of the solid-state hinges deserved particular care, due to the complex requisite scenario resulting by conflicting requirements concerning compliance, stiffness and strength, geometric restrictions as well as manufacturing constraints. A detail photo showing a spoke with the corresponding hinges is shown in Fig. 9 together with a schematic description of the related manufacturing concept.

Figure 9: Abelt-rib section segment with manufacturing details.Aglass-ﬁbre roving, which builds the core of the spoke, is winded around an inner carbon-ﬁbre bundle to assure tension strength of the hinge. An outer layer protects the hinge connection and provides additional compression strength.

The required minimum camber adaptability of ±5◦ is matched by the belt-rib prototypes while fulfilling the standard stiffness and strength requirements. The belt-rib structural mass—measured for a 1:2 scale prototype—amounts to 0.242 kg, which corresponds to 1.94 kg at full scale. Activation at maximum camber requires ca. 20 J/m actuator work per unit span length (only strain energy [68]). The internal structural layout of the belt rib was optimised by a modal procedure [50]. The procedure enables to exert a broad influence on the deformation behaviour of the belt-rib structure and to substantially affect, in this way, interaction effects with inertia as well as aerodynamic forces. Coupling phenomena between compliant structure and fluid play a determinant role in the energy balance [68]; the exploitation of aerodynamic as well as aeroelastic amplification effects leads to large savings in the required actuator work and involves, as a result, a sensible reduction in the needed actuator size and weight.

8 Concluding remarks

Bio-inspired approaches to flight offer a huge improvement potential with respect to conventional aircraft as far as performance and efficiency is concerned. On the other hand, they represent a highly challenging design task which involves a broad spectrum of disciplines: material science, actuator and sensor technologies, control, structural mechanics, fluid mechanics, aeroelasticity and optimisation. One of the central issues is the inherent coupling of mechanical subsystems like structure, mechanism, fluid and actuator, which requires approaches of high complexity at the analysis as well as at the design level. The study of published scientific work on this subject not only shows the strong interest of the aerospace engineering community towards the bio-mimetic vision but also provides a large quantity of valuable results on which the development of a suitable design methodology can be based. Whether, and to what extent, the bio-mimetic dream can be fulfilled will actually depend on what factors will motivate engineers and scientists to face the above-mentioned challenge so in Section 5 it was stressed that engineering and nature do not necessarily choose the same design options since they do not pursue the same optimisation target. The obvious question which arises

WIT Transactions on State of the Art in Science and Engineering, Vol 4, © 2006 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) 416 Flow Phenomena in Nature from this fact is why should a successful concept like the conventional approach to flight be subject to profound changes just to emulate nature (‘never change a winning team’). The ‘great optimiser’ nature actually never optimises a single isolated organism or species, but rather develops a global system while fulfilling reciprocal constraints between the single life forms. If the optimisation target of aeronautics is to become more global, engineering solutions will probably have to get closer to biological flight. The development of energy resources as well as future environmental constraints will provide the answer.

Acknowledgements

Thanks to Ms. Monika Junge for the fruitful discussions on bionics and for having established contact with the editor.

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