Alexander Marksovich Gaifullin
Aircraft manufacturing is the most important branch of modern industry. There is a competition between aircraft manufacturing companies (including associated scientific institutes), the goal of which is to create products that are superior to competitors’ analogues: for passenger and cargo aircraft - in terms of safety, efficiency, and environmental friendliness; for military aircraft - based on combat qualities. Research in modern aviation science is characterized by the use of adequate mathematical models, the basis of which is a clear understanding of physics
phenomena under study. The development and construction of new aircraft is impossible without the use of “highly mathematical” sciences, such as aerodynamics, control theory, and strength.
Aerodynamics- a science that studies the interaction of air flow and the body flowing around it. The speed of the aircraft is so high that the flow around it becomes turbulent. Turbulent flow differs from “calm” laminar flow by a chaotic change in its characteristics over time (speed, pressure, etc.), leading to intense mixing of the gas and the emergence of vortices. The main mathematical problem of turbulence—the creation of a system of partial differential equations that would describe arbitrary turbulent flows and that could be solved on modern computers—has still not been solved. Therefore, at present, based on the equations of mathematical physics, semi-empirical turbulence models are created that are suitable for describing only a narrow class of flows.
How are the aerodynamic characteristics of an aircraft determined? Mainly by two methods: experimental and computational. To conduct experimental research in wind tunnels, airplane models are created - copies of the originals reduced several times. This is due to the fact that the size of the wind tunnels does not allow testing with real aircraft. But the data obtained from testing the model in a wind tunnel cannot be converted into aircraft characteristics by simple scaling and taking into account the similarity coefficient between the model and the real aircraft.
The fact is that the equations that govern the flow characteristics are quite complex. If we bring them to a dimensionless form, that is, express all dimensional quantities in parameters characteristic of a given flow, then the equations will include dimensionless quantities that bear the names of outstanding scientists: Mach number, Reynolds number, Strouhal number, etc. For strict similarity it is necessary so that all these values coincide during the real flight of the aircraft and when testing the model in the tube. But the specific properties of the air flow that is used in the pipe do not allow all similarity criteria to be met. In addition, both in the case of a closed and in the case of an open pipe, the fact that the flow is not unlimited affects the aerodynamic characteristics.
The problem arises of converting integral characteristics (total forces and moments) and distributed characteristics (values at specific points of pressure, temperature, etc.) from the model to a full-scale aircraft. This problem is solved by carrying out a numerical calculation of the equations of mathematical physics for two semi-empirical models: an aircraft in an unlimited flow and an aircraft model in a wind tunnel. The aerodynamic characteristics of an aircraft are obtained by adding to the data obtained from testing a small copy of the aircraft in a wind tunnel, the difference in the same type of data obtained for the two described semi-empirical models.
It would seem, why not make the calculation immediately, without resorting to experiment? The point here is precision. The accuracy of experimental data obtained in good wind tunnels is several times higher than the accuracy of calculations.
The basic formula of aerodynamics is the connection between the lift force acting on the wing and the speed of movement and circulation (intensity) of the vortex system generated by the aircraft. This formula was obtained by the “father of Russian aviation” Professor N. E. Zhukovsky and reported by him at a meeting of the Moscow Mathematical Society in 1905.
The airplane wing must be optimal. One of the most important parameters of a wing is its quality: this is the ratio of lift to drag force. To create an optimal (“high-quality”) wing, problems of the calculus of variations are solved.
Control theory. An airplane flight consists of several phases: takeoff, climb, cruising, turns, descent, landing. At each stage the plane must be controlled. A flap on the wing or an elevator on the tail are examples of controls. The control system must be designed so that simple movements of the pilot in the cockpit are transmitted and transmitted to the controls, causing appropriate reactions. On the other hand, the system must be sufficiently “smart”; its design elements must not exceed the boundaries of the safe mode.
Another task is to create an autopilot capable of controlling the movement of an aircraft without the intervention of a pilot.
The mathematical theory of automatic aircraft control, based mainly on the theory of differential equations, is responsible for all these problems. Using the same theory, a mathematical model of the spatial motion of an aircraft is created, and issues of flight stability are studied.
Strength. It is not enough to create an aircraft with good aerodynamic data; it is necessary that it does not collapse in flight, so that its resource (longevity) is sufficiently high. A science called strength is responsible for solving this problem.
Strength methods are used to study elastic and plastic deformations of aircraft structural elements, the growth of cracks in the aircraft skin (the skin material initially contains microcracks, which can grow over time), and structural failure.
The mathematical arsenal for solving strength problems includes classical and modern methods of equations of mathematical physics, differential equations, calculus of variations, complex analysis, and computational branches of linear algebra.
Anyone who has seen through a window how an airplane wing behaves in flight has noticed a fairly large amplitude of its vibrations. The fact is that in order to reduce the amplitude of the wing’s vibrations, it is necessary to increase its weight, while on an airplane they are trying to minimize the weight of the structures. Therefore, it is not possible to get rid of wing vibrations. The branch of mechanics that studies problems in the mathematical theory of vibrations and resonance is aeroelasticity.
Solution methods. Let's discuss methods for solving mathematical problems discussed above.
The governing equations in real problems are very complex and it is a priori impossible to understand what will happen when solving them.
In problems that are greatly simplified from a practical point of view, it is sometimes possible to obtain an exact solution.
Most of these problems have already been solved, although previously unknown exact solutions to the Navier-Stokes or Euler equations are still being found. But the set of such problems is limited, and they are far from practically important problems.
At the same time, the study of these problems is very important, since exact solutions create physical images - a vortex, a boundary layer, etc. - from which a physical picture of the process being studied is built, just as a house is built from elementary bricks. The obtained understanding of the physics of the process allows one to choose among many mathematical models one that sufficiently reflects the properties of the simulated process and makes it possible to technically search for a solution.
One of the solution methods is numerical. Often the numerical solution of a problem is reduced to a system of linear algebraic equations.
Another method is possible if there is a small parameter in the problem. Such a parameter can be the ratio of the chord (width) of the wing to its span, the ratio of viscous forces to inertial forces (the ratio of the friction force between layers of gas to the inertia force of these layers), the ratio of the width of the crack to its length. To date, asymptotic methods have been developed for solving problems with a small parameter, which are studied in mathematical perturbation theory.
Let us give as an example the solution to the problem of the lifting force of a high aspect ratio wing (the ratio of the square of the span to the wing area). There are two small parameters here - the ratio of viscous forces to inertial forces and the ratio of the wing chord to its span.
Thanks to the first parameter, the solution to the problem can be determined not from the Navier-Stokes equations (which model the movement of gas taking into account friction between the layers), but from the Euler equations (there is no friction between the layers of gas). Thanks to the second parameter, each wing section flows around in the same way as a wing of infinite aspect ratio with a profile corresponding to the wing profile in a given section would flow around. Thus, the problem of flow around a three-dimensional wing is transformed into a number of simpler problems about two-dimensional (flat) flow around the wing profiles.
So, thanks to these two parameters, the task has become much easier than the original one.
Requirements for aircraft are constantly becoming more stringent - environmental and economic, for flight safety and passenger comfort. Aircraft are being improved, largely thanks to mathematical advances that are translated into technical solutions.
"They sat on the golden porch:
king, prince, king, prince,
shoemaker, tailor.
Who will you be?..."
(Children's counting rhyme)
Those who have “cramped legs” sing that scuba divers are good, that they love to dive and swim. But do they like to design scuba tanks? And for those who design, whether they like to dive with their scuba gear is a big question.
What about modelers?
There is an opinion that a good aircraft modeler is a designer, a jack of all trades, and a pilot, all rolled into one. This was true under developed socialism. But not now. Today you can happily do only what you like best - fly a lot and build a little, or vice versa, build a lot and fly a little.
Those who build a little bit are becoming more and more every year. You can verify this by looking at the assortment of the nearest model store - Kits are disappearing, ARFs are arriving. Demand creates supply. I don’t want to think about the fact that models are turning into expensive toys, and aircraft modeling into a specific attraction. (I was told a case of how a certain “new Russian” concreted a special runway at his dacha and on the very first flight day he hammered a couple of thousand dollars into it up to the very tail; this was the end of his passion for aircraft modeling.) But the trend towards the transformation of aircraft modeling (as a mass phenomenon ) from TECHNICAL CREATIVITY to sports entertainment, in my opinion, is obvious. I don’t know whether this is good or bad, we’ll see. Next, I turn to those who perceive aircraft modeling specifically as creativity, and it does not matter who they are more: a pilot or an aircraft designer.
Not only my many years of observations convince me that, as a rule, those who build good airplanes fly poorly, and those who fly well are often only capable of assembling ARFs. At least, a modeler who would design and manufacture a cool airplane himself, and then show off the wonders of aerobatics with it, is a rarity today. And while a designer can become a very decent pilot, a born pilot will not become a designer. Some build, others fly. To each his own. These are different professions. There are designers, there are pilots, but there is no designer and pilot in one person.
In the field it is easy to distinguish one from another. The pilots stand with their heads in the sky, the designers “sniff” the planes.
The understanding of who you are - a designer or a pilot - does not come immediately, but it does come. Understand yourself and act accordingly. If you are a pilot, buy a plane, fly and don’t have to dive too deeply into the jungle of aerodynamics, if you are a designer, the specific subtleties of this or that radio equipment will interest you insofar as, etc.
"Warehouse manager: What is your price?
Dunce: Three hundred and thirty!
Experienced: Everyone!!"
(Scenario)
No hobby is complete without material, i.e. cash, investments. Serious pursuit of your favorite hobby requires a serious investment of money. Those who have little cash pay with their time, which ultimately has the same monetary equivalent. A modeler who says that he made a cool plane for ridiculous money is either lying, or does not value his work and his time at all. I had such a case. One modeler was bragging about his really nice airplane. He talked for a long time about what rubbish he took and what a wonderful result it turned out to be. I noticed that it must have cost him dearly. He said that it was nothing, 300...350 rubles. However, when asked to make the same candy out of the same trash for 700 rubles, he laughed in my face and twirled his finger at my temple. Was he lying about 350 rubles? No, you just need to add to these 350 rubles the cost of his labor and time by 300 dollars.
As a rule, an experienced modeller will restore someone else's model either for fun, or if it is a cool retro, exclusive, which cannot be repeated, or for good money, but not for his own use. Just like a watchmaker would not restore a watch from junk for himself. He will buy a good watch, adjust it carefully, and take care of it so that it will run long and accurately, like no one else.
Don’t chase the apparent cheapness by restoring other people’s wrecked planes for yourself. It will cost more. In general, RC aircraft modeling is not a cheap hobby. But if a penniless modeler-designer still builds airplanes from scrap materials, then the penniless modeller-pilot will very soon turn into a boring, bespectacled theorist.
"Naw, Shura, saw..."
("Golden calf")
It was decided: our own model, from scratch, according to our own design, tailored for high flight characteristics and maneuverability, i.e. just aerobatics. Approach to the project in all seriousness, according to science. The goal is to create an original aircraft with flight characteristics better than those of known models (or at least no worse than theirs).
The necessary books were opened on the necessary pages, cunning calculation programs were launched, in a word, work began to boil. Scheme, engine, layout. Preliminary main dimensions. Calculation of weights. Load on the wing, profile, polar of the wing and the entire aircraft (who doesn’t know the polar - the relationship between the drag and lift coefficients of the wing). Again the main dimensions. Longitudinal stability, roll, yaw, pitch. Again the main dimensions. Speed, rudders, ailerons. Again the main dimensions. Design, strength, technology. Again, calculation of weights, wing load, profile, polars, stability... and all around. With each cycle, the outlines of the aircraft become more and more visible and... at first vaguely, and then more and more clearly, they resemble something. Finally you realize that you have developed Extra! Well, the tail is a little different, well, the booth... but still Extra (put her in the swing)! What were they fighting for?! Having changed the outline and shape so that it is different, you recalculate and understand that it will be worse to fly than the same Extra. You can't argue with aerodynamics. All. The collapse of hopes to surprise the world. What about the effort expended? And time, which is money?
Why am I telling this? To beat off your hands? No, any model designer (no matter an airplane pilot or a yachtsman) has invented a bicycle (or a propeller) at least once in his life. This is fine. I just want to give a couple of tips to young, hot designers.
Make realistic plans for yourself. As sad as it is, we must come to terms with the fact that almost everything has already been invented before us. Of course, this “almost” warms the soul, gives, so to speak, hope, but... Optimal aerodynamic designs and layouts, for example, for the same aerobatic models with internal combustion engines, were invented a long time ago, tested and retested by more than one generation of designers. There is no revolutionary situation for a revolution. The air environment is just the air environment, the power plant based on the internal combustion engine is so polished that there is nowhere to spit, except maybe play with the muffler. Therefore, before you start developing an aircraft from scratch, look around, you will probably find a prototype (known and proven) that meets your plan.
In Soviet aircraft modeling circles, the first model for novice modellers, without fail, was some kind of schematic. When I came to the Palace of Pioneers and Schoolchildren on the Lenin Hills (it sounds like: Palace, Pioneers, Lenin...) to the aircraft modeling club in the section of cord models, I already had some experience behind me in building successfully flying models. But they still gave me a rubber-engine schematic model of the airplane. I was terribly disappointed - such garbage could have been made at home. This was in the mid-60s. Now I understand that it couldn’t have been any other way. The head of the circle could not risk scarce materials without being sure that the novice modeler’s hands were growing from the right place. Poor circle leaders were squeezed by government funding and reporting. In the circles, the emphasis was placed on 2... 3 proven guys, who “ate” the lion’s share of the circle’s budget. The rest were forced to play the role of extras. To break into the circle of the chosen ones, it was necessary to demonstrate extraordinary abilities. This was the dream of every circle member. The fiercest competition caused by a global shortage of everything forced us to achieve decent results with a minimum of resources, and there were practically no random people in modeling. For unorganized modellers, the choice of prototype was determined not so much by experience as by access to scarce materials. Money, as such, solved almost nothing. If there are materials, a good, complex plane will be built; if not, a simpler plane will be made.
Times have changed. There is practically no shortage (at least in Moscow). Build whatever you want. One thing has remained unchanged, both before and now: the choice of a prototype for building a model is made at the limit of material capabilities - previously in the sense of scarce materials, today in the sense of money. I do not share the opinion that one should definitely start with “Kartonych”. It's all nonsense. I know a modeler who made his first flight in an expensive aerobatic biplane, which was very difficult to fly. And he didn’t break anything, he learned to fly. It's all about responsibility, serious preliminary preparation on the simulator. In general, you should like the plane you fly on; it should be a pity to crash it. So count your money and invest in everything you have, to the fullest extent possible. As when choosing a car, no one will buy a used Zhiguli if they have money for a Mercedes, even with a complete lack of driving skills.
“And why all?.. And for what reason?..
And what conclusion follows from this?
(Monologue of Eeyore.)
And yet, where to start? How to choose a prototype correctly?
The prototype selection criteria are based on a solid foundation of aerodynamic theory of aircraft models. In 99 cases out of 100, a novice modeler first builds an airplane, and even more than one, and only then begins to study the theory - life forces him. It is useless to encourage people to do the opposite. Having felt a craving for the sky, the future modeler also feels a real itch of impatience - rather to the sky, no matter what! There's no time for books here. And only after getting a buzz from the first flights (who doesn’t remember the delight and jubilation in the soul from the first plane taken into the sky?), catching his breath and thinking about the next model, the modeler comes to the conclusion that it would be nice to study something.
The model must fly smoothly with the control sticks down for a long time, without going into a tailspin or falling onto the wing, not only in complete calm, but also during air disturbances. Those. it must have longitudinal, transverse and directional stability.
It is impossible to fly a longitudinally unstable aircraft, that’s a fact. But too much longitudinal stability is not always good. For example, excessive stability makes the flight of an airplane sluggish, and energetic figures turn out to be “sleepy.” The most spectacular figures - a flat corkscrew snap roll and many other 3D figures - cannot be performed at all on an airplane with excessive longitudinal stability. Subjective assessments such as “fast” or “dull” model are also mainly related to longitudinal stability. This is the most important characteristic of an aircraft. A clear understanding of its nature, as well as mastery of methods that allow one to control the parameters of longitudinal stability, is the key not only to the successful construction of new models, but also to a guarantee of competent, accident-free operation of finished aircraft.
Longitudinal stability is determined by the relative position of the center of gravity (CG) of the model and its focus, i.e. points of application of the resultant aerodynamic forces acting on ALL parts of the aircraft. For the usual, traditional model design, its focus is determined mainly by the focus of the wing (i.e., the point of application of the resultant aerodynamic forces acting on the wing, or, in other words, the center of pressure). And the position of the wing's focus, in turn, directly depends on its profile and angles of attack. Thus, on the one hand - the alignment of the aircraft, on the other - the profile of its wing and the efficiency of the tail - these, by and large, are the alpha and omega of the longitudinal stability of the model.
Now more details.
Obviously, if the CG is in front of the focus, the model is longitudinally stable (stable equilibrium is created in flight). True, too forward a centering leads to a decrease in the aerodynamic quality of the model, and in this case the effectiveness of the stabilizer may not be enough to compensate for the diving moment - the plane simply will not take off. And if it takes off, then when landing at low speeds it will definitely “bite” its nose, if not with a fatal outcome, then with great trouble for the landing gear, hood and propeller.
If the CG is behind the focus, then in principle the model is unstable. However, in a certain range of alignments - from coinciding with the focus to some rearward, the aircraft continues to be longitudinally stable due to the damping moment of the stabilizer.
The even more rearward alignment is of particular interest. Such a model is extremely unstable in flight and the pilot cannot control it without special technical means. However, the use of stabilization systems based on gyroscopes makes it possible not only to fly such aircraft, but also to obtain noticeable advantages in performing aerobatic maneuvers. It is characteristic that at the Tournament of Champions (TOC) in Las Vegas, most participants used electronic stabilization to change the stability coefficient in flight on different figures. But this is a topic for another discussion.
Do you feel where I'm going with this? Everything follows the laws of the genre: very rear alignment is no good, very forward alignment is also no good, which means...
Indeed, the optimal value of longitudinal stability is achieved if the CG lies near the focus of the model with a small margin (the CG can change its position in flight, for example, when fuel is consumed, when retracting and extending the landing gear, etc.). It remains to find out where the focus of the model is, which, as we agreed, for conventional schemes largely depends on the focus of the wing.
The focus of the wing is determined by the center of pressure of its profile, which in general does not stand still. Its position depends to one degree or another on the relative curvature and angle of attack. The easiest way is with profiles that are close to symmetrical. Their center of pressure, as a rule, is located at 25% of the MAC (average aerodynamic chord) and is practically independent of the angle of attack. For example, the NACA 2415 profile (2% relative curvature at 40% of the chord length, 15% relative thickness) has an angle of attack range from 4 to 18 degrees. the center of pressure practically does not change its position and is spaced from the toe of the profile at a distance corresponding to 25% of the MAR. For the CLARK YH profile, which has a slightly greater curvature, in the same range of angles of attack, the movement of the center of pressure is still quite acceptable. For a profile with a 6% relative curvature (and also quite thin), this movement is very noticeable.
There are profiles in which the center of pressure does not move at all. However, they are practically not used on models (except for “flying wing” type vehicles), because their aerodynamic qualities are significantly lower than those of conventional profiles.
In addition, it should be noted that the use of wing mechanization, for example, landing flaps, which create the effect of increasing the curvature of the profile, even for the NACA 2415 profile leads to a noticeable change in the position of the center of pressure.
Changing the position of the center of pressure of the profile is a very unpleasant phenomenon. The mechanism here is simple. With optimal mutual position of the CG and the focus of the model in strictly horizontal flight (CG near the focus with a small margin), the model is normally stable. When the angle of attack changes, the center of pressure of the profile begins to move (not for the better), the relative position of the CG and the focus changes, and we immediately enter the area of alignment behind the focus, i.e. into the region of instability. As mentioned, the size of the rear alignment area, where the model continues to be longitudinally stable, directly depends on the efficiency of the stabilizer, which is proportional to the product of the area of the stabilizer and the square of its arm, which can be seen in the designs of “long-tail” aerobatics.
In principle, reliable longitudinal stability of the model is ensured if the area of its horizontal tail is 25% of the wing area, and the distance between this tail and the wing corresponds to approximately 2.5 times the average chord of the wing. The given ratios take into account almost all unfavorable factors affecting stability.
A nomogram is known, with the help of which, based on the geometric characteristics of the prototype, one can determine the parameters of its longitudinal stability, characterized by the coefficient of longitudinal stability.
K - coefficient of longitudinal stability;
A = S op / S cr - the ratio of the horizontal tail area to the wing area;
L = Lpl / h - the ratio of the distance from the wing to the horizontal tail to the average chord of the wing.
In general we can say:
The stabilizing effect of the horizontal tail can be improved by using a symmetrical profile with a relative thickness of about 12%. For radio-controlled models with an active elevator, a certain increase in lift, and therefore a greater stabilizing effect, can be achieved by reducing the gap between the rudder and the tail. With a smaller gap, the pressure distribution is by definition better, especially when the steering wheel is deflected. The effect of the horizontal tail also depends on the wing extension and its position relative to the wing. However, these parameters are of subordinate importance; they cannot be used to radically improve the stability of the model. A large wing aspect ratio has the same effect as relegating the horizontal tail to an area away from the wake of the wing, such as when using a T-tail.
Let me remind you that so far we have talked about the usual aircraft layouts - straight (or trapezoid) wing, tail, fuselage. I can't imagine a modeler who would choose a canard design for his first airplane. Nevertheless, for the sake of completeness, it is probably worth mentioning other schemes.
The longitudinal stability of a model with a swept wing can be improved by twisting the wing. Here, both purely geometric (up to a maximum of 4 degrees) and aerodynamic twist are possible. In the latter case, we are talking about the transition of the load-bearing root profile to a symmetrical profile at the wing tip. A combination of both twists has become widespread, thanks to which, in addition to improving longitudinal stability, the inductive drag is effectively reduced. Wing twist was widely used on tailless gliders of the "gull" design.
Longitudinal stability on canard aircraft is also determined by the relative position of the CG and the wing focus, but there is no damping from the front stabilizer, and the centering is applied very forward.
Longitudinal stability without tails is achieved by using special profiles with the so-called. S-shaped midline. For such profiles, the center of pressure also moves when the angle of attack changes, but in the opposite direction.
Biplanes and other multi-wing aircraft stand apart. Problems of their stability are beyond the scope of this article. You cannot embrace the immensity, as Kozma Prutkov used to say.
It is known that the lateral stability of the model is interconnected with the track stability. Therefore, they need to be considered as a whole. Let’s make a reservation right away: training and free-flying aircraft need greater lateral stability. For aerobatics and advanced training models, lateral stability should be zero. The directional stability should also not be too high. Its excessive value prevents it from entering a spin, which degenerates into a spiral; in addition, with a large value of directional stability and a non-zero V of the wing, the lateral stability of the aircraft deteriorates.
To increase lateral stability, several design techniques are used. This may be to obtain stability due to the transverse V wing. Here the situation is best with high-wing aircraft, because... their center of gravity lies below the focus, i.e. a stable equilibrium is created. In addition, high-wing aircraft often use a fuselage with a large lateral surface. For most low-wing aircraft, due to the instability of the center of gravity, it is necessary to increase the transverse V angle of the model wing.
The use of swept wings also increases lateral stability. The lateral stability of tailless deltas is due precisely to the sweep of the wing.
As for directional stability, it is generally believed that the model will have sufficient directional stability if the fin area is 10% of the wing area, and the distance between them corresponds to 2.5 average chords of the wing. If the keel is located at the same distance as the horizontal tail, as is the case in most cases, then the area of the keel is taken equal to 1/3 of the area of this tail. With this ratio of areas, directional stability is quite sufficient.
Despite the huge selection, a little more than two dozen profiles are actually used in aircraft modeling. Here are some of them. Profiles from NACA 0009 to NACA 0018 are symmetrical and, since their relative thickness ranges from 6 to 12%, they are used primarily for tail surfaces. “Classic” profiles for aerobatic models have a relative thickness of 16 to 18%. Airfoils NACA 23009 - NACA 23018 are semi-symmetrical, they are widely used not only on models, but also on real aircraft. Their center of pressure changes its position slightly. The semi-symmetrical CLARK Y profile can be called truly universal. It can be used on both radio-controlled and free-flying models. Symmetrical profiles can be considered profiles with a constant position of the center of pressure, however, unfortunately, they develop little lift and at high angles of attack are prone to unexpected flow disruptions without a noticeable transition.
With the EPPLER 374 profile, the maximum thickness is located far towards the trailing edge, as a result of which the flow around it remains laminar over a wide range. It is used mainly on high-speed models, as well as on heavy gliders. The change in the position of the center of pressure is quite significant.
The wing profile should be chosen such that the change in the position of the center of pressure is minimal. It is assumed that the profile of the horizontal tail is symmetrical. If you need a well-supporting profile with a constant center of pressure position over a wide range, then you should choose NACA M6 or CLARK YH.
That's all. In the first case, this information is quite enough to, so to speak, “get into the topic”, maintain an intelligent conversation with modelers, and most importantly, wisely choose a prototype for a future model. I deliberately avoided complex calculations using tricky formulas. The modeler, who is a designer at heart, will come to them himself, and the pilot just needs to determine offhand what he is dealing with.
So, based on the above, let’s try to imagine what a model for initial piloting training might look like. Most likely it will be a high-wing aircraft with an elongated fuselage, developed horizontal tail and fin, CLARK YH wing profile and, if with ailerons, then with a small transverse V, and if without ailerons, then with a larger transverse V.
Now look at “Kartonych”...
Then it's up to you. You can, taking the geometry of the “Kartonych” as a basis, make a handsome all-balsa (if you have money and time), you can try to construct an apparatus from available materials (if you don’t have enough money), you can buy this very “Kartonych” (if you don’t have time), if you don’t have any time, no money - stop doing aircraft modeling. When I say: take the geometry of the aircraft as a basis, I mean the main dimensions, ratio of areas, weights, profiles, etc. The appearance, and even more so, the design, materials can be anything. There is room for creativity here. In addition, you can improve the flight characteristics of the model using the methods mentioned above.
"I do not believe..."
(K. Stanislavsky)
When making changes to the prototype, be careful with the aerodynamic design. If you change it, then carry out verification calculations.
A typical case. A certain modeler declares: “I’ve already made such a plane. It flies ugly. It dangles like... in an ice hole.” Strange, the plane is famous. You start to figure out what's going on. It turns out that when making changes to the prototype to suit his technology and materials, he changed the wing profile - just a little. I didn’t like that the steering gear protruded beyond the plane. Little did he know that from the provided CLARK YH profile he got a profile close to EPPLER375, in which at angles of attack in the range from 4 to 25 degrees, the center of pressure moves over a fairly wide range. In order for a model with a wing of this profile to have sufficient longitudinal stability, its horizontal tail must be much more efficient. The stabilizing effect of the horizontal tail could be improved by using a symmetrical profile with a relative thickness of about 12%. The lifting force developed by such a profile is approximately 10% greater than that of a flat profile, which is used for ease of manufacture. But the modeler was not a designer, he was a pilot.
In general, changes made to the prototype should pursue very specific, clearly formulated goals - for the sake of what to change. You can't improve the prototype at all. You can improve the appearance, but then you have to be prepared for the fact that the plane will become more labor-intensive, and therefore more expensive. Or, on the contrary, subordinate the changes to ease of manufacture and reduction in cost, but then, perhaps, it will lose its elegance, and everyone knows that ugly planes fly poorly. Replacing materials is fraught with serious structural alterations of the power circuit and, as a rule, an increase in the weight of the device. Etc. Experienced modellers refine the model over the years, improving it gradually, from sample to sample, approaching the optimum. And if you take such a model as a prototype and start messing around... Good design solutions never lie on the surface. Don't assume that you are obviously smarter than the prototype developer. If it seems to you that some knot could be made simpler and better, then try to understand why the author did it differently? If you are sure that you are right, do it your way. Then, perhaps, you will understand what the matter was, but it will be too late.
Advice for beginners. If you decide to make a model yourself (especially if this is your first model), build the plane according to a known, proven prototype, preferably from a package. Don't try to make significant changes to the prototype right away. Build the model as it is. This will give you the opportunity to feel it in the literal sense of the word, to understand the idea put into the model by the author. It is quite possible that during the construction process thoughts about modernization, improvement, etc. will come to you. My advice is to refrain from immediately putting them into practice; it is better to write them down and use them in the process of building the next model, when you take the aircraft you have already built as a prototype.
By the way, variations on the theme of this or that prototype are a common practice for modellers. As a rule, a number of models are built that have one ancestor with successively introduced changes. Often the latest model resembles the original only remotely. Sometimes an outstanding aircraft is produced in a series (not necessarily the last), and it becomes the prototype for aircraft of other modellers. One should not understand the development of a topic literally, as the construction of a number of similar aircraft in a row (although this also happens, for example among athletes). Usually a modeler has several themes in development. More than one year may pass between copies of models in a row. And yet, no matter how experienced the modeler is, when opening a new topic, he tries to make the first sample, strictly following the prototype “as it is” if possible.
"Is there one like this, but without wings?
Will seek..."
(The Diamond Arm)
Many novice modelers want to start by building, if not an exact replica, then at least a model similar to the real aircraft. What can you say about this? For God's sake! If it doesn’t work out, then you will simply lose money and time, but you will really appreciate your strength and gain experience, which is also worth a lot. For a real modeller, failure (and no one is immune from failure) will not discourage him from pursuing his favorite hobby. However, the construction of a copy model has features that should be mentioned.
One of the parameters of similarity between a model and its prototype is the equality of their Reynolds numbers. With sufficient accuracy this number is equal to Re=70vh, Where v- flight speed, m/s; h- wing chord, mm.
For example, for a sports aircraft whose wing chord is 1500 mm, the flight speed is 100 m/s (360 km/h) Re = 70x100x1500 = 10500000. For a model of this aircraft, made on a scale of 1:10, the wing chord is 150 mm , speed 10 m/s (36 km/h), we obtain the Reynolds number Re = 70x10x150 = 105000, i.e. 100 times less. This difference excludes the direct transfer of aerodynamic characteristics from the prototype to the model.
In general, the belief that an exact copy of the geometry of a prototype with high flight qualities will ensure good flight characteristics of the model is a dangerous belief. Practice shows exactly the opposite. Only in a few cases does an exact copy meet the specific requirements for the aerodynamics of the model, in particular for its stability. Therefore, with a huge variety of aircraft types and designs, choosing a prototype for a model is not an easy task. That is why aircraft modeling companies use only one and a half to two dozen prototypes for their production copy models. It’s not enough that you like the plane you want to build a model of. As a rule, upon closer examination, a simple calculation using a nomogram shows that the stability of the model will be clearly insufficient. What to do? The answer is obvious - improve the stability of the model, for example, lengthen the fuselage, change the area ratio, develop the tail, increase the transverse V of the wing, etc. True, it may turn out that after all these activities the model turns out to be little similar to its prototype.
And finally, this is my personal opinion, which plane to choose? Let them call me a cave Russophile, but I will never build a fascist Fw-190. Moreover, there are a lot of wonderful Russian planes that fly well and are beautiful. This is generally an unplowed field for a modeler. In addition, it’s nice to go out into the field with our aircraft when everyone around us is flying imported serial aircraft. It is characteristic that our aircraft, for example, from the time of the 2nd World War, are perfectly scaled with minimal distortion; their design can often be directly transferred to the model. But the final choice, of course, is yours. You build, you fly.
Our colleague, Vladimir Vasilkov, provided the author with enormous assistance in writing the chapter on the basics of aerodynamics, for which we thank him very much. In practice, this is our joint work, where the co-author’s contribution is greater than mine.
The nomogram and some other examples are taken from the book by R. Wille “Construction of flying models of spears” trans. with him. V.N. Palyanova.
Even the simplest airplane model is a miniature airplane with all its properties. Many famous aircraft designers began with a hobby of aircraft modeling. To build a good flying model, you need to work hard and study the theory of flight of heavier-than-air vehicles. But what a fascinating spectacle the model’s flight is, and what a joy it is for its creator and the audience! The entire variety of aircraft models can be divided into several classes.
The most popular among beginning aircraft modellers are paper aircraft models. In paper aircraft modeling, several areas can be distinguished.
Elementary contour models.
These are the simplest flying models of airplanes that are cut out of a sheet of paper with a few strokes of scissors. They are the simplest and most accessible for beginners. Flightless replica models. They exactly replicate the appearance of famous aircraft brands. Designing replica models requires special knowledge, great patience and labor. They are carried out by experienced modelers who collect models of aircraft.
Free-flying models.
Such models, made of thick paper or thin cardboard, can be launched using rubber from the hands, like from a slingshot, or from a special device - a catapult. To achieve the greatest flight range, the relative cross-section of their fuselage is made smaller than that of prototype aircraft. There are free-flying paper models that move due to the thrust developed by a propeller driven by a rubber motor or a miniature electric motor.
Non-motorized models launched into flight using a thread rope are called gliders.
Cord models fly “on a leash.” They are controlled by the aircraft modeler's hand using steel threads or cables called cords. The cord model cannot move more than the length of the cord away from the athlete. This is how the cord model differs from the free-flying one. On such models, internal combustion engines or electric motors are installed, powered by an external current source supplied through conductor cords. Paper cord models are usually equipped with electric motors. Today we will talk about the most accessible free-flying models that are interesting to a wide range of children - those that are launched by hand or by catapult.
Why do heavier-than-air vehicles fly - airplanes and their models? Remember how the wind blows leaves and pieces of paper along the street and lifts them up. A flying model can be compared to an object driven by a stream of air. Only the air here is still, and the model rushes, cutting through it. In this case, the air not only slows down the flight, but under certain conditions creates lift. Look at the picture here showing a cross section of an airplane wing. If the wing is positioned so that there is a certain angle a (called the angle of attack) between its lower plane and the direction of movement of the aircraft, then, as practice shows, the speed of the air flow flowing around the wing from above will be greater than its speed from below the wing. And according to the laws of physics, in the place of the flow where the speed is greater, the pressure is less, and vice versa. This is why, when the plane moves fast enough, the air pressure under the wing will be greater than above the wing. This pressure difference keeps the plane in the air and is called lift (Fig. 1)
Figure 2 shows the forces acting on an airplane or model in flight. The total effect of air on an aircraft is represented in the form of aerodynamic force K. This force is the resulting force acting on individual parts of the model: wing, fuselage, tail, etc. It is always directed at an angle to the direction of movement.
In aerodynamics, the action of this force is usually replaced by the action of its two components - the lift force and the drag force.
The lifting force Y is always directed perpendicular to the direction of movement, the drag force X is directed against the movement. The force of gravity C is always directed vertically downwards. The lift depends on the wing area, flight speed, air density, angle of attack and aerodynamic perfection of the wing profile. The drag force depends on the geometric dimensions of the fuselage cross-section, flight speed, air density and the quality of surface treatment. All other things being equal, the model whose surface is finished more carefully flies farther. The flight range is determined by the aerodynamic quality K, equal to the ratio of the lift force to the drag force V: K = -, that is, the aerodynamic quality shows how many times the lifting force of the wings is greater than the drag force of the model. In a gliding flight, the force V of the model is usually equal to the weight of the model, and the resistance force X is several times less, so the flight range will be 10-15 times greater than the altitude I from which the flight was planned, that is, K = Yu-15. Therefore, the lighter the model, the more carefully it is made, the greater the flight distance can be achieved.
For the flight to be stable, the model must have a distributed centering; the center of gravity of the CG must coincide with the center of pressure of the wing CP or be slightly ahead of it (the center of pressure of the wing is the point of application of the aerodynamic force).
For a rectangular profiled wing, the central point is located at approximately the first quarter of the wing width. For simple paper models, the wing profile is usually very thin or even flat. For such wings, the center of pressure is located at the geometric center of the area.
For rectangular wings, the center of the area is at the intersection of its diagon (see p and p. 3). Figure 3 shows how to determine the center of area of any other wing shape. You need to cut out a wing from thick cardboard, install it on the edge of a ruler and balance it. The point of intersection of the edge of the ruler with the line drawn in the middle of the wing is the center of gravity and the center of pressure of the wing. The center of gravity of the model is found when the load has already been manufactured. Why is sleep needed? The simplest free-flying models do not have an engine, and the force of the gi propels the model forward, creating its own mass. To increase the inertia of the model, a load cut from plywood or several layers of thick cardboard is glued into the fuselage. The presence of cargo in the forward part of the fuselage ensures sufficient stability of the model in flight. Knowing the center of gravity of the model and the pressure, the correct position of the wing on the model is selected.
For models flying at high speeds (launched from a catapult), the CG must be ahead of the CP, and for free-gliding models it must coincide. The straightness of flight is especially strongly affected by the “deflections” of the fuselage, that is, curvature during the gluing process. Its shape needs to be monitored; both during the adjustment process, and during launches, and when hitting obstacles, it can become deformed., In general, free-flying models, having high flight speeds, are often deformed when hitting obstacles, so they must be manufactured very carefully.
After the flight, it is not recommended to pick up the model by the wings, stabilizer and fin. Take them only by the bow, that is, by the load. When starting test flights, try to fly the models in an open place (where there are no obstacles or people). Only after studying the “habits” of the model, determining its trajectory and adjusting it well, can you launch it in the halls and corridors. But at the same time, remember that a model that has developed high speed can injure one of the spectators. Therefore, when launching, make sure that the intended trajectory of your model is not directed towards people.
How can you control the flight of a model? Unlike cord models, free-flying models cannot be controlled after takeoff. But you can adjust the model so that it flies along a given trajectory. For control in the vertical plane (pitch) on airplanes, elevators are used. On models, to do this, simply bend the rear edge of the stabilizer up or down. In this case, the model will accordingly gain altitude (and even make a loop) or dive. To control the roll, it is enough to bend the edges of the wings in opposite directions (up and down). On real airplanes, special control surfaces—ailerons—are installed on the trailing edge of the wing.
For control in the horizontal plane, rudders are used on airplanes. On the model, for this purpose, you can bend the rear edge of the vertical tail to the side. When (the model is made according to the “tailless” scheme, that is, without a stabilizer, the bend of the trailing edge of the wing provides control of both roll and pitch, in real aircraft such control surfaces, which play the role of both aileron and elevator, are called ailerons.
For our paper models, as a rule, hard types of paper are used: drawing paper - whatman paper, thin cardboard. For decoration and decorative applications, colored paper from children's art kits is used. To cut paper, we recommend making special cutters and rulers. This is especially important when younger schoolchildren begin modeling. As a rule, they still have poor control of their hands, and even ordinary cutting with scissors is a problem for them. Their hand is accustomed to holding only a pencil and a pen. Therefore, it is better to make the handle of the cutter faceted (like a pencil) and slightly curved (see Fig. 4).
Making such cutters is not difficult. They can be done by the kids themselves in technical creativity circles and clerk camps. The blade for the cutter is tool steel from a hacksaw blade for metal. You need to ask the seniors to make the blade according to our drawing (see Fig. 4). The handles of the cutters are made of sheet plexiglass. Cut blanks 120 mm long. From one end, drill two holes with a 2 mm drill to a depth of 20 mm. Then prepare a table vice - spread its jaws by about 50 mm. Heat the drilled end of the handle until the plexiglass softens and heat the tang at the same time. Take the blade with pliers and insert it into the hole of the heated handle. Once warmed up, it will go in there freely. After this, insert a cutter between two plexiglass plates and clamp the entire package in the jaws of a vice. The ends of the plates should come together and clamp the blade (see Fig. 4). Hold this for 5-10 minutes. The handle will cool down and the blade will be “tightly” pressed into it. Now process the handle - remove the sagging of softened plexiglass and make edges. Warm up the handle a little more, bend it slightly and cool. The amount of deflection should not exceed 5-6 mm. Sharpen the cutter on a whetstone - the tool is ready. To cut paper, you also need a plexiglass ruler 4-5 mm thick, 30-35 cm long and 30-35 mm wide. A strip of insulating tape 5 mm wide must be glued onto it.
Why should the ruler be made of plexiglass? And why use insulating tape?
Such a ruler is transparent, the cutter glides along it easily and does not get dull on it. The tape is glued so that the ruler does not slide on the paper when working. After all, the parts of the models must be made very accurately. Younger schoolchildren master working with these two instruments after two or three lessons. Some tips on how to work with homemade tools. The cutter should be held the same way you hold a pencil or pen. When cutting, place the ruler so that its end is directed towards the shoulder of the cutting hand, that is, you only need to cut the paper with the cutter “towards you”. When cutting, the ruler is held with spread fingers, pressing it to the paper and not removing your hand until the desired part is cut off. It is not recommended to press the cutter too hard. The sharp end of the blade can be broken. It's better to do it exactly several times. Under no circumstances should you clench the cutter into your fist or press it with force!
If the cutter does not cut, it means that it is dull and needs to be sharpened. You need to train your hand to match the force of pressure. The offered cutter will allow you to cut out parts of any, even the most intricate and complex shape. And you will have to cut out letters, aircraft numbers and other applications from colored paper. You can master such cutting only by training your hand. In order for the folds of parts made of paper and cardboard to be neat and even, they must be pre-processed. It is best to “prune” them. What does it mean to cut paper? You need to run the cutter along the fold lines along the ruler so that only the top layer of paper is cut, approximately one-third of its thickness. At first glance, it seems like a simple operation. But beginning modelers have to practice 1.5-2 hours daily to learn correctly cut the paper along the fold lines. Practice yourself. Try to make an “accordion” out of paper. Remember that the cut layer should remain outside when folded.
On our model developments, all fold lines indicated by a dotted line (— —-----) are cut along the front side of the development. Lines indicated by dash-dotted lines (—.—.—). cut from the reverse side. It is necessary to cut paper on a plywood backing, or even better on a plastic one (made of copolymer). As a last resort, if you are unable to cut the folds and have to cut through the paper, you can press these lines with the blunt side of a table knife or a special “bone”. But the quality of the folds will, of course, be worse.
Thick types of paper and cardboard can be glued with any glue. The most reliable glues are PVA (polyvinyl acetate), nitrocellulose adhesives of the AGO and Kitifix brands. Moment glue should only be used for tack work. Its adhesive seam is elastic, and it cannot reliably glue model parts. It is recommended to glue thin types of paper with BF-2 and nitrocellulose adhesives. Office glue KS (silicate) and PVA glue soften the paper and warp model parts when drying. It is recommended to glue parts made of PS grade foam plastic (polystyrene, white) only with PVA or BF-2 glue; parts made of yellow foam plastic (PVC brand) - nitro-cellulose adhesives and PVA glue. Now you can safely start making models.
Rewind Alexey
Aircraft modeling is art, sport, technology, character and a great love for the sky.
Introduction
1. At the very beginning...
2. Aircraft modeling. Basic Concepts
3. Development of sports aircraft modeling in the USSR and Russia
4. General technical characteristics of the aircraft model (sports)
5. Technical aircraft modeling
1) Experimental modeling
2) Bench modeling
3) Flying models. Copy - model
4) Radio-controlled airplane models
5) Airplane models with turbo engines
6. Assessment of aircraft modeling
Conclusion
Literature
Introduction
The sky is open to everyone: even if the plane is an order of magnitude smaller than the real one. Among anthropologists, there is a point of view that human evolution is driven by a strong desire to own all the earth without reserve. In their opinion, throughout his life, man wanted to first walk around the earth, then explore the seas and - most importantly - soar into the skies. And according to experts, a serious passion for the sky begins with aircraft modeling.
My flying model
The attitude of our society towards aircraft modeling is very ambiguous. Some people think that these are toys whose hobby is not serious. For others, idling is a kind of dream come true, for others it is an interesting applied sport, where the result of sometimes painstaking work does not just sit on a shelf, collecting dust and complementing the interior, but brings into life some incomparable sensations that arise when lifting the model into the sky.
At its core, aircraft modeling is a branch of a large tree called “big aviation,” and it develops consistently with the development of aircraft manufacturing. But even a large tree cannot grow without branches, otherwise it will be a little defective. Likewise, aviation without modeling may have had a slightly different development path.
Aircraft modeling. For me this is a whole parallel life. And I really like the fact that many people did it before me and I hope that after me they will do this smart and exciting thing.
1. At the very beginning...
In 1898, excavations of the III century were carried out in Egypt. BC. Among the various objects found there was a small figurine made of sycamore (a hard wood similar to a hornbeam), which weighed 32 grams and resembled a bird.
It was registered in the Cairo Museum of Antiquity as a "Bird Figurine" and was kept in the Bird Department under number 6347 for over seventy years. In 1969, Egyptian physicist Dr. Khalil Messiha noticed that the “bird” was too streamlined, that the wings were 18 cm long, curved differently than those of birds, and there was a vertical detail on the tail that resembled the rudder of a modern high-speed aircraft. The professor carefully studied the find and, after consulting with aviation experts, declared: “This is not a bird, but a miniature model of a glider!” 
Diagram of an ancient aircraft
In this regard, the UNESCO Bulletin wrote: “If Dr. Messiha’s hypothesis is confirmed, it will mean that the ancient Egyptians knew the laws of flight!” The professor did not limit himself to just assumptions. He built a large model of a glider from lightweight materials, where he accurately and completely recreated all the strange design features of the ancient “bird”. The scientist's glider made a successful flight!
2. Aircraft modeling. Basic Concepts
What is this anyway, aircraft modeling?
Here's how Wikipedia defines it:
Aircraft modeling is a type of technical creativity, the means of which are:
Creation of non-flying scale copies, real aircraft (bench model aircraft).
Creation and piloting of both free-flying (gliders, timer) and remotely controlled (radio-controlled, cord) aircraft.
But knowing first-hand about aircraft modeling, the following definition seems more accurate to me:
Aircraft modeling - 1) Design, creation and testing of aircraft models for technical purposes; 2) Aeromodelling sport. (New Dictionary of the Russian Language (edited by T.F. Efremova).
Hence: Aeromodelling is a technical sport where participants compete in the design and manufacture of flying models of aircraft (gliders, airplanes, helicopters, etc.) and in controlling them in flights for speed, range, flight duration and aerobatics.
Technical aircraft modeling allows us to solve important independent problems in the scientific and technical experiment of creating aircraft. This determines its great practical significance
3. Development of sports aircraft modeling in the USSR and Russia
Our country first became a member of the FAI (Fédération Aéronautique Internationale) in 1909; Russia was represented in this organization by the All-Russian Aero Club. On the initiative of Professor of the Moscow Higher Technical School N.E. Zhukovsky, on January 2, 1910, the first aircraft modeling competitions in Russia were held. This day is the date of birth of domestic aircraft modeling. Among the participants in the competition was the future outstanding aircraft designer, academician A.N. Tupolev.
NOT. Zhukovsky is a professor, the founder of aviation theory.
Chairman of the jury of the first competition
flying models in Russia (1910)
The largest aircraft designers attended the school of aircraft modeling at different times. Alexander Sergeevich Yakovlev in 1921 became the organizer of the first school aircraft modeling club in Moscow. In 1923, the Society of Friends of the Air Fleet was created in the Soviet Union, designed to manage aircraft modeling sports.
Aircraft model circle Participants of the II All-Union competition
Khamovnichesky district of Moscow - 1927, in which
winner of urban fuselage aircraft successfully flown for the first time
competition 1924 model with rubber motor
In the USSR, 70 athletes took part in the first all-Union flying model competitions in August 1926. Sports modeling in the USSR began with the “Week of the Red Air Fleet” in the summer of 1923. Aircraft modeling gained great scope after the Komsomol adopted patronage of the air fleet in 1931.
The leading role in developing the problems of aircraft modeling was played by the Central Aircraft Modeling Laboratory (CAML), created in 1931. After this, laboratories and classrooms were opened in many other cities, and aircraft modeling became the initial stage in the training of aviation personnel. The aircraft modeling movement grew and strengthened, numbering more than half a million members in its ranks. 
In 1931, with a fuselage rubber-engine model of the aircraft M. Zyurin
exceeded the world record for flight duration - 27 minutes 20 seconds.
Initially, free-flying aircraft models of various sizes and geometric shapes were created. By that time, the path for training aviation personnel had been clearly defined, perfectly formulated in the slogan: “From a model to a glider, from a glider to an airplane.”
Since 1936, the representation of the Soviet Union in the FAI was carried out by the Central Aero Club of the USSR named after V.P. Chkalova. The activities of Soviet aircraft modellers took place under the leadership of DOSAAF.
During this period, a new type of model appeared - indoor ones. To make such models, straw from various grasses was used, and the covering was made from microfilm. The weight of indoor models did not exceed 5 g; they were launched indoors. In March 1941, at the competition of Moscow aircraft modellers, M. Zyurin set an all-Union flight duration record of 2 minutes 33 seconds. His model, with a wingspan of 400 mm, had a mass of 1.69 g.
The Great Patriotic War interrupted mass aircraft modeling work: sports work stopped, there were no mass aircraft modeling competitions. Many clubs, houses and palaces of pioneers, children's technical stations and aircraft modeling laboratories were closed. But aircraft modeling continued to develop. In 1944, a model with a gasoline engine appeared; in 1946, a new step forward was taken in the development of rubber engines, where the engine was a bundle of rubber threads.
In 1950, the famous designer of aircraft model engines V. Petukhov used on his model a new engine with compression ignition of the working mixture (piston internal combustion microengines with a cylinder volume from 1 to 10 cm3). The aerodynamics of the model, wing and stabilizer profiles were selected taking into account the latest research data from aviation laboratories.
Of particular interest to aircraft modellers were new advances in aviation technology. Modelers immediately tried to transfer everything new into aircraft modeling practice. The appearance of jet aircraft was thus reflected in the works of aircraft modellers. True, even in the pre-war years, modellers built models equipped with powder rockets, and then models with liquid jet engines.
Sports aircraft modeling developed. He attracted people into his ranks who were once amateurs, but over time wanted more from their hobby and allowed the development of technical thought.
In 1952, aircraft modeling was included in the Unified Sports Classification, which affected the development of aircraft modeling as a whole. It has become one of the most popular technical sports. The sporting and technical achievements of modelers were fully assessed at the competitions. In January 1953, M. Vasilchenko’s model set a world speed record when flying on a line - 264.7 km/h. The absolute speed record of 301 km/h was set at international competitions in Brussels by I. Ivannikov. Such incredible speed was achieved by his cord model with a jet engine.
1952 was a year of success in the design of radio-controlled models. At the start of the competition near Sumy, numerous spectators witnessed amazingly beautiful flights. Models with mechanical engines, equipped with radio control devices, carried out flights along complex trajectories at the request of the judges, described figure eights, circles, and rectangular routes in the air, usually performed before landing by airplanes, and landed accurately in close proximity to the start. 
Numerous victories in the world and European championships in aircraft modeling can be explained by the massive scale and wide spread of this hobby in the USSR. The development of aircraft modeling was managed by the Central Sports and Technical Club of Aviation Modeling - TsSTKAM (formed in 1974) and the USSR Aircraft Modeling Federation (1964). By 1991, there were over 1,000 aircraft modellers holding the title of Master of Sports, and about 300 Masters of Sports of international class. Soviet athletes achieved high results in the European and World Championships. Since 1992, the Russian Aeromodelling Federation has been an independent organization. Russian aircraft modellers become members of the FAI through the Russian Aviation Sports Federation.
4. General technical characteristics of the aircraft model (sports)
Unless otherwise prescribed, aircraft models must meet the following basic technical requirements:
Maximum flight weight with fuel 25kg;
Maximum bearing surface area 500 dm2;
Maximum load 250 g/dm2;
The maximum working volume of the piston engine cylinder(s) is 250 cm3;
The maximum voltage of the motor power supply without load is 72 volts.
For all categories of model aircraft with engines, noise level restrictions apply. The noise level should not exceed 96dB(A) at a distance of 3 meters from a running engine, unless other regulations apply. Specific methods for measuring noise levels must be developed by the appropriate subcommittees for their model category.
For electric motors, noise level restrictions do not apply.
5. Technical aircraft modeling
But it’s not just sporting success that interests modellers.
1) Experimental modeling
This is the oldest direction. Models play a big role in the development of aviation. They test ideas and technical innovations and conduct scientific research. A flying model, a smaller copy of an aircraft, has brought great benefits to humanity by promoting scientific discoveries.
Back in 1754, M.V. Lomonosov designed and built one of the first aircraft models - an “aerodrome machine” for lifting meteorological instruments, the prototype of a helicopter.
Since 1876, Major General A.F. Mozhaisky conducted experiments with flying kites and spring-driven airplane models indoors (1876)
A.F. Mozhaisky is the creator of the world's first airplane.
A description of one flight is given in the newspaper “St. Petersburg News” dated June 10, 1877: “In our presence, the experiment was carried out in a large room above a small model, which ran and flew completely freely and fell very smoothly...”. Inspired by these successes, Mozhaisky decided to build a full-size model. Using models, he studied the basics of flight, studied the behavior of individual structural elements, on the basis of which the world’s first airplane was built. Using models, he tested the theory and correctness of the assumptions underlying the design of the first aircraft.
The use of aircraft models helped Nikolai Egorovich Zhukovsky, a Russian scientist, the founder of modern hydroaerodynamics, discover the laws of motion of bodies in the air. K. E. Tsiolkovsky also contributed to the spread of aircraft modeling, building and launching hot-air balloons and kites with his students.
Modern aircraft modeling is an important auxiliary tool for aircraft design. Without removing the aerodynamic, strength and other characteristics by blowing a model copy of the future aircraft in a wind tunnel, the construction of the first prototype aircraft is unthinkable.
TsAGI large wind tunnel
Flying models are one of the best means of checking the correctness of theoretical calculations. Currently, a theory has been created that makes it possible to use the results of experiments carried out with models in wind tunnels in the calculations of natural aircraft. The principles of flight, the picture of many phenomena that occur with airplanes in flight, are tested and studied on flying models.
2) Bench modeling
It would seem that inactive models are of little use, but this is not so. Non-flying models are most often copies, geometrically and sometimes structurally similar to airplanes. The most widely used are tactical models, which reproduce on a certain scale the external forms and main details of the aircraft, indicating its military or civilian purpose. Such models are used for combined filming, if there are no full-scale aircraft, when it is necessary to reproduce emergency moments, disasters, air battles, etc.
Museum models are the most complex of the flightless models. These models serve as visual aids in studying the history of aviation development.
3) Flying models. Copy - model
Copy aircraft models are aircraft that completely replicate the characteristics of their real prototype. The power plant, maneuverability, speed and, of course, appearance are taken, whenever possible, from an existing aircraft or one that existed in the history of aviation, but... Aircraft modeling companies use only one and a half to two dozen prototypes for their production copy models.
Copy - model of the Yak-3 aircraft, made by me
Many novice aircraft modellers are convinced that exact copying of the geometry of a prototype with high flight qualities will ensure good flight characteristics of the model. Practice shows exactly the opposite. Only in a few cases does an exact replica meet the specific aerodynamic requirements of the model. Designing a copy model has features that you should be aware of.
One of the parameters of similarity between a model and its prototype is the equality of their Reynolds numbers. With sufficient accuracy, this number is equal to Re = 70vh, where v is the flight speed, m/s; h - wing chord, mm. For example, for a sports aircraft whose wing chord is 1500 mm, the flight speed is 100 m/s (360 km/h) Re = 70x100x1500 = 10500000. For a model of this aircraft, made on a scale of 1:10, the wing chord is 150 mm , speed 10 m/s (36 km/h), we obtain the Reynolds number Re = 70x10x150 = 105000, i.e. 100 times less. This difference excludes the direct transfer of aerodynamic characteristics from the prototype to the model. What to do? The answer is obvious - improve the stability of the model, for example, lengthen the fuselage, change the area ratio, develop the tail, increase the transverse V of the wing, etc. True, it may turn out that after all these activities the model turns out to be little similar to its prototype. This requires precise engineering calculations.
4) Radio-controlled airplane models interesting for me from a practical point of view. In our country they became available and thus entered mass aircraft modeling relatively recently, but immediately attracted attention. Although back at the USSR Championship in 1970 there were only 5-6 radio-controlled copies, half of them flew with discrete Variofon equipment, although import into the country was already proportional. In the mid-70s, radio operators began performing in the F-3A and F-3B classes, but there were still no worthy copies.
Only in the 90s of the 20th century did a mass passion for radio models begin. Radio-controlled aircraft modeling made it possible for the “pilot” to control his aircraft without having direct contact with the model.
I am building exactly these types of models. I started participating in competitions, so far only at the regional level.
For competitions in the F5D, F5D400, Q500, Q500E and RC Combat Open Rus classes - Closing of the season. Bachata On September 24-25, 2011, I was a judge at the starts and at the long fekes.
5) Airplane models with turbo engines are of greatest interest today. I really want to look at them in more detail.
The first German turbojet engine, the HeS 3, was created by Pabst von Ohain back in 1939. On August 27, 1939, the He 178 took off, the first aircraft in the world to use only the energy of a turbojet engine for flight. But not a single Heinkel engine went into production.
It is believed that the birth of model turbojet aircraft engines, as well as full-size ones, we owe to Kurt Schreckling, who created a simple, technologically advanced and cheap to manufacture engine twenty-five years ago.
Schreckling made the compressor impeller from wood (!), reinforced with carbon fiber. The homemade turbine wheel was made from 2.5 mm sheet metal. A real engineering revelation was the combustion chamber with an evaporative injection system, where fuel was supplied through a coil approximately 1 m long. With a length of only 260 mm and a diameter of 110 mm, the engine weighed 700 g and produced a thrust of 30 N! This is still the quietest turbojet engine in the world, because the gas exit velocity in the engine nozzle was only 200 m/s.
The first fully assembled production aircraft model turbines were the JPX-T240 from the French company Vibraye and the Japanese J-450 Sophia Precision.
Jetcat P-160: serial model turbojet aircraft engine with deflectable thrust vectoring and, in fact, 16 kg of thrust
The second revolution in mini-turbine construction was made by the German company JetCat. In 2001, the JetCat P-80, a turbine with automatic start, appeared in aircraft modeling. The main know-how of the German company is the electronic turbine control unit developed by Hirst Lehnertz. How does a modern aircraft turbine work?
JetCat added an electric starter, a temperature sensor, an optical speed sensor, a pump governor and the electronic brains that make it all work together to the already standard Schreckling turbo. After the start command is given, the electric starter is turned on first, which spins the turbine up to 5000 rpm. Next, through six nozzles (thin steel tubes with a diameter of 0.7 mm), a gas mixture (35% propane and 65% butane) begins to flow into the combustion chamber, which is ignited by a conventional aircraft model glow plug. After a stable combustion front appears, kerosene begins to be supplied to the nozzles simultaneously with the gas. Upon reaching 45,000–55,000 rpm, the engine switches to kerosene only. Then it drops to low (idle) speed (33,000–35,000). A green light on the remote control lights up - this means that the on-board electronics have transferred control of the turbine to the radio remote control.
The latest in microturbine fashion is the replacement of an aircraft model glow plug with a special device that sprays kerosene, which, in turn, ignites a red-hot spiral. Such a scheme allows you to completely abandon the gas at start. Such an engine has a drawback: increased electricity consumption. For comparison: a kerosene starter consumes 700–800 mAh of battery, and a gas starter consumes 300–400 mAh. And on board an aircraft, as a rule, there is a lithium-polymer battery with a capacity of 4300 mAh. If you use a gas launch, you will not need to recharge it during a day of flights. But in the “kerosene” case it will be necessary.
Turbine planes are never small - 2–2.5 m in length. Turbojet engines allow you to reach speeds from 40 to 350 km/h. It’s possible faster, but then it’s not clear how to control it. The usual piloting speed is 200–250 km/h. Takeoff is carried out at a speed of 70–80 km/h, landing – 60–70 km/h.
MiG-29 is one of the most popular jet aircraft
Such speeds dictate very special requirements for strength - most structural elements are 3-4 times stronger than in piston aircraft. After all, the load grows in proportion to the square of the speed. In jet aviation, the destruction of an incorrectly calculated model right in the air is quite a common occurrence. Huge loads also dictate specific requirements for steering gears: from a force of 12–15 kgf to 25 kgf on flaps and flaps.
In the USSR in 1948, on the basis of very scanty information about the operating principles of such engines and without sufficient information about the achievements of world aircraft modeling in this area, a design group headed by A.I. Anisimov was created at the Leningrad Palace of Pioneers. This group managed to build a successfully operating engine in 1949.
Therefore, we can safely say that the actual emergence of jet aircraft modeling and the mass construction of flying models with jet engines must be attributed to the appearance of pulsating jet engines (PRE). The credit for introducing this type of model technology into life in the USSR belongs to Leningrad aircraft modelers.
The launch of the first model turbojet engines resembled a small feat. A team of four people was strictly required for the launch. They surrounded the model of the airplane, the first was holding a diving cylinder with compressed air in his hands, the second was a cylinder of household gas, the third was a larger fire extinguisher, and the fourth, with the control panel, was the pilot himself.
First, compressed air was blown onto the compressor impeller, spinning it up to 3000 rpm. Then they supplied gas and set it on fire, trying to get a stable combustion in the combustion chambers. After that, it was necessary to manage to switch to the supply of kerosene. As a rule, in half the cases there was a fire, the fire extinguisher did not work in time, and only firebrands remained from the turbojet model. At the initial stage, they tried to combat this using simple methods - increasing the launch team by one more person with an additional fire extinguisher.
This is the past; now our aircraft modelers use the most advanced world technologies.
WITH boronaya after the 2007 championship
The RUSJET team has been created in Russia, taking part in the world championships. The JMC, a model association that has nothing to do with the piston-glider FAI, was created. There was an attempt to unite. The “Jet Committee” puts the main emphasis on the show, the “old” FAI is a follower of the classics.
Jet aircraft models are not a hobby for beginners or even advanced aircraft modelers, but for professionals who become after graduating from aviation institutes. And I think that everyone who is passionate has this opportunity, including me.
6. Assessment of aircraft modeling
Even the simplest airplane model is a miniature airplane with all its properties. Many famous aircraft designers began with a hobby of aircraft modeling. To build a good flying model, you need to work hard and study the theory of flight of heavier-than-air vehicles.
O.K. Antonov gave preference to modellers over certified aircraft engineers without modeling skills.
OK. Antonov at the USSR Aircraft Modeling Championship in Kyiv
S.P. Korolev called aircraft modeling the science with which big aviation begins. Yu.A. Gagarin wrote in his address “Build models of airplanes, rockets, spaceships. Let their rapid flight give birth to new dreams in you and expand the horizon of technical knowledge.” But for me the most significant words are the words of the wonderful aircraft designer Alexander Sergeevich Yakovlev: “... I love small aircraft aircraft designers, jacks of all trades, tenacious, persistent, able to finish what they start. ...The path to mastering flight and complex aviation technology begins with modeling. A flying model is a scaled-down version of an airplane. By creating it, you learn to think about an airplane like an aircraft designer, and look at flight like a pilot.” This thought is very significant for me, because I dream of connecting my life with big aviation, although now I am an avid modeler. And knowing the history of aircraft modeling, it is easier to understand the logic of its development.
7. Problems of aircraft modeling and their solutions
The rapid development of aviation technology, an increase in flight speeds, the emergence of new types of aircraft, rockets and engines, the use of new materials - all this, naturally, changes production technology. Similar changes have occurred in small aviation, where speeds are also increasing, new, more advanced engines are being used, and this leads to higher prices for models.
On forums you can often see pessimistic forecasts regarding aircraft modeling. After all, in order to return modeling to its former popularity, state support is needed. For example, in China, aircraft and ship modeling are taught in labor classes. The industry meets the needs of modellers. Hence the mass participation: in Shanghai, more than 400 pilots participate in the aerobatics championship alone. Therefore, China is a leader in all technical sports, which means that a technically literate generation is growing up there. It will be the same for us if we popularize this type of creativity.
For us, this experience should become an example today, although looking back at the recent past, we see the same school of Soviet aircraft modeling among teenagers in additional education.
And now every SUT and centers for the development of technical creativity in the cities of the Kemerovo region have their own model associations. It all depends on the region. I can’t say that money is pouring in on us, we do a lot at our own expense, but the joy of flying outweighs everything.
The main problem of aircraft modeling remains the lack of entertainment and the lack of spectators at sporting competitions, because shows with jet models are few. And, as a consequence, there is insufficient coverage of sporting events in the media and little sponsorship support for aircraft modeling sports. All competitions are held outside the city, away from spectators.
The American experience is also indicative. In the United States, aircraft modeling ranks second in popularity after baseball, even ahead of basketball. At the end of the 40s, the United States adopted a national program for the development of aircraft modeling, which was recognized as “an occupation that provides universal personal development.”
The National Aeromodelling Program in the USA was implemented. And then a joint resolution was adopted to “draw the attention of the American people to an activity that millions of Americans are passionate about,” namely aircraft modeling. In addition, the governors of 25 states were ordered to organize an air show at least once a year with the participation of both state and non-state organizations and institutions, both professionals and amateurs, aircraft model athletes, parachutists, glider pilots and pilots. In accordance with the same decision, the State Academy of Aircraft Modeling was created.
Thanks to these decisions, by 1987, in the United States, more than 18.5 million aircraft modelers cultivating active (flying) radio-controlled aircraft modeling were registered with the issuance of the appropriate license. In NATO, pilots did not receive the highest rank of “MASTER” without a minimum qualification in aircraft modeling; in pre-war Germany, aircraft modeling was taught in schools as a labor in our country.
There is no need to reinvent the wheel. In pedagogical universities, we need to open special faculties, or hire those who can teach boys (and girls who want to), equip schools with machines, explain to parents how cool it is! And everyone will finally get involved in aircraft modeling!
Conclusion
Whatever direction you choose, aircraft modeling can captivate everyone. And if for “weekend modellers” the main thing is the flight itself, the radio-controlled car soaring into the air, then for “hardcore” amateurs and professionals the process of creating and finishing the model is no less interesting. Aircraft modeling has many faces, which means that there is a place for everyone.
In my opinion, the most important thing is the degree of understanding of what aircraft modeling means for the prospects of scientific and technological progress and the future of the nation. Building, fine-tuning and operating a model aircraft develops design skills and engineering thinking. It is no coincidence that our great aircraft designers Tupolev, Ilyushin, Yakovlev, Antonov started with aircraft models. One of the leading designers of modern sports aircraft, Kondratyev, also studied in such circles in his youth. And the vast majority of ordinary engineers, specialists not only in the aviation industry, but also in many branches of mechanical engineering, went through the school of modeling, the role of which is becoming even more relevant over the years.
And now, judging by the number of people who want to engage in aircraft modeling, we can say that the continuity in our aircraft modeling has not been broken, despite the socio-economic upheavals. On the contrary, in recent years there has been a noticeable increase in the influx of young people into aircraft modeling, including the most promising class of radio-controlled models. This is also noticeable in competitions in which I myself took part. In many classes of seasoned aircraft modellers, young people win, and this is great. Aircraft modeling is an activity for the future! 
Literature
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2. Grek, A. Jet microaviation: turbo models [Electronic resource] / A. Grek // Popular mechanics [site]: a portal about how the world works. - Access mode: http://www.popmech.ru/article/2153-reaktivnaya-mikroaviatsiya/. - Cap. from the screen.
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At the final stage of testing the aerodynamic model of the new civil airliner MS-21 in the TsAGI wind tunnel, the model was made on a scale of 1:8. In the modern history of the domestic aircraft industry, tests on such a large model were carried out for the first time.
Wind tunnel and computer
The MS-21 was completely designed using computers based on 3D modeling of all its components. This made it possible to analyze and predict many aspects of aircraft behavior using modern software. But blowing models in wind tunnels has not lost its relevance; in practice, they confirm many computer calculations.
The first wind tunnel tests of civil airliner models to measure the loads acting on the airframe components began back in 2011. Especially for this purpose, TsAGI produced an aerodynamic model on a scale of 1:14. Even then, Irkut designers compared preliminary calculations with the results of the blowdowns and were convinced of their coincidence.
Size matters
For the final stage of testing in the T-104 wind tunnel, Irkut and TsAGI specialists decided to use a new, even more detailed 1:8 scale model of the MS-21.
T-104 is one of the largest wind tunnels in the country, its diameter is seven meters.
The chosen scale made it possible to measure loads on assemblies, for example, landing gear doors, which could not be performed on smaller models. In addition, on such a model it is possible to install a larger number of multi-component strain gauges to measure the forces acting on the aerodynamic surfaces and mechanization elements of the aircraft airframe, including landing gear struts and doors, sections of slats and flaps, ailerons, and tail surfaces. A total of 20 strain gauges were installed. This quantity made it possible to significantly reduce the number of expensive wind tunnel launches, since information from all sensors was recorded during one blowdown.
During tests in 2014, two or three series of model blowdowns took place every hour in Zhukovsky. Engineers observed how the model behaved at different stages of flight in takeoff, landing and cruising configurations at different angles of attack and glide. At the final stage of testing in 2015, TsAGI carried out up to 700 blowdowns of the large-scale model.
Tests on such large models of civil aircraft have not been carried out over the past 20 years, says Gennady Andreev, Candidate of Technical Sciences, head of the sector of the aerodynamics department of aircraft and missiles.
The creation of such a large model of the MS-21 made it possible to take into account some factors associated with the scale effect, for example, icing of the aircraft. At different stages of flight, depending on climatic conditions, an ice cover of 2 to 76 mm can form.
At TsAGI, for example, previously and now, when blowing small aircraft models, ice simulators made of wood were used. Today, for large-scale models and semi-models, ice simulators are made using a computer modeling method from special plastic.
The results of purging with increased accuracy will further reduce aircraft testing time and reduce financial costs, because test flights are significantly more expensive than bench tests.
Domestic experience suggests that the demand for blowing aircraft models in wind tunnels is only increasing. An increasing number of TsAGI departments are switching to two and sometimes three shift operating modes. In addition to traditional customers - the military, large foreign companies - more and more work is being carried out for domestic manufacturers of civilian equipment.
Based on materials from the UAC magazine "Horizons" No. 3, 2014.
