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by Yevgeny SOKOLOV, Dr. Sc. (Phys. & Math.), Head of Laboratory of Microaircraft, the Central Scientific Research Institute of Robotics and Technical Cybernetics (St. Petersburg)
Recently many countries have been developing flying vehicles with a mass of up to 0.5 kg and dimensions less than 0.5 m. They are mainly designed for an analysis of environmental monitoring and operational surveillance in areas of combat operations, as well as natural calamities, emergencies, and disasters. Importance of these studies is increasingly great in the context of search for effective tools to counteract terrorism. What problems are faced by the designers of super-miniature aerial vehicles?
FEEL THE DIFFERENCE
Any aircraft is characterized by dimensions, weight (empty and take-off), engine thrust, speed, height and range of flight. Aviation handbooks also indicate two relative factors defining basic performance parameters: specific wing load (gross weight of the machine-towing area ratio) and thrust-weight ratio (the same weight-engine thrust ratio). Maximum speed of an aircraft is proportional to square root of the product of these two parameters.
What happens to the listed parameters if we reduce dimensions of a flying vehicle? Let's consider a lightweight single-seat aircraft with a wing span of about 5 m weighing several hundred kilos. Its typical characteristics are as follows: speed 200 - 250 km/h, range of flight-400 - 600 km, height 4 - 5 km. Let's reduce dimensions of the plane 10 times. Now the wing span is 50 cm. Volume-and weight-is reduced 1,000 times, wing area-100 times, and specific wing load-10 times. As the engine thrust is proportional to its weight, and
Reynolds number influence on the aerodynamic force components affecting the wing profile. On the right figure, hysteresis of lifting force of the profile is shown.
the weight in its turn is proportional to the plane's weight, we may assume that the decrease of general linear dimensions does not mean the reduction in thrust-weight ratio. As a result, as compared with the model single-seat plane the microairplanc speed is decreased more than 3 times, i.e. approximately down to 60 km/h (15 m/s). Range of flight, proportional to the fuel load, is decreased much more and will make up just several kilometers. But basic problems are not limited by this "arithmetics": to get to full understanding we need to consider the nature of some flight phenomena.
Any body streamlined at speed V is affected by aerodynamic force equal to the sum of elementary forces (stresses) applied on each element of the body surface. Aerodynamics distinguishes between normal and shearing stress or, in other words, pressure p and friction τ. Pressure arises because a flying body forces apart air panicles. Friction by contrast is caused by air particles adjoining to the body which are stuck to its surface and move together with it-whereas those located at a distance are motionless.
It is well known that the nature offers two essentially different types of liquid and gas flows-laminar and turbulent. In the first one, particles (air in this case) move steadily and regularly, and in the latter they move irregularly. But it is important for us that the aerodynamic force affecting the body may vary manifold here. To give these flow types a quantitative characteristic Osborn Reynolds, English scientist (1842 - 1912), offered a parameter named today after him-Reynolds' number (hereinafter-Re). This number is obtained by multiplying of linear dimension and flight speed divided into viscosity of air, which depends on temperature, humidity, and atmospheric pressure. For any body the value, corresponding to transition from laminar to turbulent current with an increase of Re, is obtained experimentally.
Let's turn back to the analysis of microplanes. In a traditional single-seat machine Re number may be several millions with turbulent streamline mode, but for the one we are interested in, Re may vary between dozens of thousands and 100 - 200 thousands depending on speed. For a wing this range corresponds to laminar-turbulent transition. Actually, that is where major aerodynamic problems arise. To increase lifting force and to reduce drag, it is necessary to use a thick airfoil profile with a smooth rounding of the leading edge for a large aircraft, and a thin profile-approximately of the form of a curved plate-for a "micro" one. It is common knowledge that the permanent trend in aviation is to make aircraft surface as smooth as possible. However, experiments proved that at a small Re number the wing of a microplane performs best if its surface is rough.
So, the microaircraft aerodynamics is fundamentally different from that of "big" aircraft. Indeed, during a tlight of a full-sized plane, a small part of the overall drag is exerted on friction, while on reducing dimensions of the machine, it, on the contrary, is increasing. This leads to an increase in relative drag and reduction of the lifting force of a microplane as compared with a geometrically similar full-sized aircraft. Standard wing profiles and aerodynamic solutions for such devices become inefficient, and propeller efficiency is decreasing. The problem is further complicated by the fact that on increasing speed the laminar stream is abruptly
transformed into turbulent one which is different in quality and in quantity. On reducing the speed, reverse transition, as a rule, requires a different value, i.e. takes place hysteresis* of all aerodynamic parameters. It means that the major parameters of microplanes (range, ceiling, etc.) in some ranges of flight speed, air humidity and height above sea level may change several times if the above-mentioned processes are not taken into account. At the same time these devices should meet wide range requirements of potential application conditions (city, desert, mountains, etc.) and to carry out flights in various weather conditions.
How can one possibly handle all these technical challenges? First of all, we should point out methods of controlling air flows around microa ire raft by way of changing the form or properties of the surface itself. Such possibilities arc available due to microelectro-mechanical systems as the design solution of required onboard equipment impossible within standard design solutions. Besides, microequipment units are rather complicated for production, though they should be inexpensive. This can only be provided by the above-mentioned technologies in which galvanic functions are closely interacting with mechanical ones. In this case the complexity, estimated by quantity of assembly parts, does not lead to significant rise of price of the product, while the performance of some functions of the device, e.g. terrain video surveying, is decreasing in cost while retaining its quality.
Now we can review some other challenges of microaviation.
Power, i.e. the thrust of an aircraft inner combustion engine, is proportional to the volume of a cylinder, pressure inside it and engine speed. Reduction of the size of a power system 10 times results in a decrease of power a thousand times! Manifold increase of the cylinder pressure may compensate for the power loss. However, this method may lead to extreme complication of other systems of a micromotor, mainly the fuel supply system. Therefore, in order to preserve the required capacity, it is more expedient to increase the engine speed. The same approach may also be applied in turbojet micromotors where the thrust depends on the level of compression or, to be more precise, on the engine speed of the compressor per its radius.
One of the best Russian inner combustion micromotors was designed at St. Petersburg State Polytech-nical University** in 1995 by Valentin Alyoshin. Having 0.3 cm cylinder volume and 22,000 rpm, it generates power of 150 W. The fuel (methanol - 70 percent, castor oil - 30 percent) consumption is 70 g/h.
Note: losses of heat through walls of the micromotor increase proportionally to reduction of its size. The experience shows that this is the reason why released heat in certain conditions may, unfortunately, be completely spent on evaporation of fed fuel drops. In other words, fuel "extinguishes" burning in the cylinder.
Electric micromotor engines without a commutator produced in some countries for model aeroplanes may be used as an alternative to inner combustion engines. The major problem here-effective sources of direct current-is efficiently solved by modern physical chemistry. To retain power while reducing the size-as in heat units-engine speed should be increased. According to some experts, by the end of 2006, the efficiency of such electric devices will be equal to that of microengines of inner combustion, surpassing them in serviceability.
It must be pointed out that for flights with speeds of dozens of meters per second the standard propulsion device-propeller-is used. Unfortunately, increase of the shaft revolution number results in its efficiency decrease. The way out is traditional: to install a reducer between the engine and the propeller to reduce the engine speed down to optimal.
Response of a body to controlling forces depends both on its weight and on the so-called inertia moment. Reduction of the size of a body 10 times results in its weight decrease 1,000 times, while the inertia moment decreases 100,000 times! Apparently the microplane will be very "nimble", and that must be taken into consideration while designing control systems. It is easy to calculate its required quick response.
* Hysteresis: a lagging of the change of one physical value from that of another one. It is observed in cases when a body stale is determined by external factors both at the present moment and at previous moments. - Ed.
** See: Yu. Vasilyevet al., "Scientific, Educational and Cultural Center", Science in Russia, No. 3, 2003. - Ed.
Diagram of air stream around "left" semi-wing of a fly-down stroke.
At a flight speed of 10 m/s, air particles pass along the 0.1 m width wing in 0.01 seconds. Hence, the typical frequencies used in the system, which reacts to the change of flight conditions and forms controlling forces, should be at least 1 kHz. In case of a large aircraft, these forces are created by deflection of control surfaces, streamlined by the flow. Taking into account requirements to quick response, in our case other approach is advisable. Earlier we mentioned artificial wing surface roughness to ensure steady flight performance of the machine. Obviously, its uneven distribution along the wing will create force and moment, which can be used in controlling the micro-aircraft.
Fully autonomous flight of a microplane can only be realized when it is stabilized. Stabilization is a function of the autopilot, and a gyroscope is the core of it. Its "top" is capable to keep its rotation axis position in space under any movements of an aircraft and thereby to create a fixed reference system on board. Operation accuracy of the device depends on the rotation speed and inertia moment, i.e. it drops drastically with a decrease of the size. Therefore, experts are trying to find an adequate replacement for a gyroscope. In fact, there are some systems using infrared sensors to determine a horizon line and serve as a "reference level" for stabilization.
Yet another challenge of control is determination of an aircraft's "own" position in space, and it is solved due to light-weight (several grams) receivers of existing global positioning system (GPS)*.
Note two more important considerations. First, talking about the dependence of some function on other ones, we did not consider coefficients of aerodynamic forces and moments, density, net efficiency, complete combustion, and other proportionalities. They depend on the quality of materials, perfection of design and technology. In other words, they serve as tools helping microplane designers to mitigate or diminish problems associated with a change of scale. Unfortunately, their analysis is a subject of another article.
And second, the range of dimensions and speeds typical for the aircraft under consideration is successfully used by model airplane builders. Using creative approach in their designs, they have long realized the challenges considered above, and even found ways to solve them. Here we have a situation when scientists have caught up by dabblers.
LEARNING FROM NATURE
Creators of microdevices in their designs are also trying to find new approaches not concentrated only on the reduction of scale.
* GPS - a system of determination of coordinates created in the USA. Its major component is several dozens of space satellites permanently transmitting radio signals, thus creating a global information field around the Earth. GPS receiver receives and localizes them measuring distance to some of the satellites, - Ed.
Magnified wing fragment of a butterfly.
Hummingbird is the smallest bird in the world-its weight is 2 g. There is reliable evidence that a flock of hummingbirds had flown 800 km along the Gulf of Mexico coast non-stop with average speed of 40 km/h! Is it possible for a 2 g device, created by man, to fly at least 8 km? Let's add: the hummingbird is capable to hover over a flower and collect honey as a bee.
Let's recall: living creatures "conquered" air elements several times. First-350 mn years ago-insects, and then-130 mn years later-pterodactyls. Another 70 mn years passed, and the sky was conquered by birds.
The man aspiring to tear off from the ground studied flying creatures with close attention for a long time. Let's recollect sketches of Leonardo da Vinci*, and much later-research of Otto Lillenthal, German engineer, a pioneer of aviation, "Flight of Birds as an Art to Fly" (1902) and other examples. In the 1970s a seminar at the Scientific Research Institute of Mechanics of Lomonosov Moscow State University, led by Academician Georgi Petrov (1912 - 1987). more than once examined the problem of insect flight at its meetings. Finally, we should note the works of Biological Department staff members of Leningrad State University (now St. Petersburg), summarized by Professor Andrei Brodsky in his study "The Mechanics of Flight of Insects and Evolution of Their Wing Apparatus" (1988). Recently due to the progress of microaircraft aviation, it's the insects" flight that draws increasing attention of scientists.
In this connection we should note the following. While large birds are mostly just soaring during their flight without flapping their wings, the smaller birds behave quite differently. We would often admire soaring seagulls over the sea, but T am quite sure that nobody would recall a soaring sparrow-just for a minute. Therefore, flapping flight becomes more effective with reduction of the size. Hummingbirds, as well as insects, arc not able to soar at all-they share similar flight mechanics.
Experiments proved that the mechanism of lifting force generation in insects is fundamentally different from that in big birds and aircraft. In the latter case it is constant at steady speed and is generated by the difference of pressure over and under a wing. In this case the air always moves strictly in one direction-from leading to trailing edge profile. But in insects the same parameter cyclically varies in time and is generated by a sharp "stroke" downwards with all flatness. Eddies generated over the top surface and along the edges are disappearing in extreme bottom position of the wing. It is established, that eventually it is their intensity that determines lifting force of insects.
Efficiency of their flight is impressive: for 1 kg of weight an insect spends 70 W, a bird - 80 W, and an aircraft - 150 W. One can add to it surprising maneuverability of the creatures: remember a dragonfly instantly changing direction and speed of flight? This is achieved by the structure of its wing-it is not smooth, but covered with regular hairs visible when magnified a little. Moreover, the leading edge may deflect depending on the intensity of whirlwinds on the top surface, which is defined by sensitive receptors. Both of them form pairs (a butterfly may have up to 30,000 pairs), actually controlling the flow about the wing of an insect and adjust lifting force in volume and direction. Clearly, damaging even several hundreds of such pairs would not affect the flight. Here we have a fundamental principle of living nature: decentralization of func-
* See: K. Frolov. "A Genius of the Renaissance", Science in Russia, No. 6, 2003. - Ed.
tions. Technical devices are designed just the other way round. Indeed, the fifth generation fighter has the central processor permanently controlling six parameters, but if it fails to operate the plane would turn to a bunch of fragments.
Currently available entomopters (aircraft simulating flight of insects), as a rule, are of small size. In their case standard engines used as a wing drive proved extremely inefficient. "Artificial muscles" are more promising here. They represent cylinders of various sizes, deformed as required when affected by electric signals or chemical agents. So-called dielectric elastomers-among others-are proposed as a material for their manufacturing; elastomer is a kind of swelling gauze polymers, currently being intensely studied by experts. The attractive property of these materials is their ability to sensitively response to minor alterations in external conditions (temperature, solvent's composition, electric field, etc.) by repeated change of volume or form. Such "smart" polymers are currently used to create sensors, flexible manipulators and other directors in robotics.
The author was a participant of the First European Conference on Micro Aerial Vehicles in Braunschweig (Germany, 2004) and two American-European seminars held in the same country in 2003 and 2005. The competitions confined to the last of these events presented also a Russian microaircraft designed and produced jointly by the Central Scientific Research Institute of Robotics and Technical Cybernetics and Polytechnical University (St. Petersburg). Its engine-parameters are stated above-and aerodynamic solution assure its steady flight under wind conditions up to 15 m/s, the result other aircraft failed to achieve. The majority of microplanes are created according to "flying wing" solution. It is presumed that providing rigid restrictions on dimensions it assures maximum lifting force due to a large area of the wing. But such approach-as proved by experience-is not universal.
As of today microaircrafts smaller than 40 cm are capable to perform autonomous flights following a predetermined route during half an hour and transmitting from board color teleimage. Note that all the elements used in the design are of mass production and are available for the public.
This article outlined just the most important problems being solved by the creators of microaircraft. It should be stressed that all of them are closely interconnected. This feature (by the way also typical for large aircraft) is most obviously shown on sizes of several decimeters.
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