2017. № 92
Mechanics  
Theoretical mechanics  
Many problems of mechanics and mathematical physics associated with perturbation of normal operators with discrete spectrum, reduced to consideration in Hilbert space of a compact operator , which called for a compact as a weak perturbation or as operator of a Keldysh type. In present paper we consider operators of Keldysh type, associated with boundary value problems for differential equations of second order with fractional derivatives in lower terms. Such problems simulate various physical processes. In particular, the oscillations of a string in viscous media, changes of deformable and strength characteristics of polymer concrete during the loading and etc. Since, considered boundary value problems simulate the oscillations of physical systems, then those problems shall to have a basic oscillational properties. In case when fractional derivatives have order less than 1, such oscillational properties are wellknown. In given paper, this properties were proved for order , and there is shown, that mechanical systems, which are described by differential equations of second order with fractional derivative in lower term, are very sensitive to changes of fractional damping order. For example, if we consider a fractional damped van der Pol equation then periodic, quasiperiodic and chaotic motions existed, when the order of fractional damping is less than 1. When the order of fractional damping is , then there are chaotic motions only. This partly explains why oscillational properties (all eigenvalues are primary, and main tone has no nodes), obtained for fractional derivative order is less than 1, not available for fractional derivative order more than 1 but less than 2. In addition, in paper was shown, that operator, generated by the differential expression of second order with fractional derivatives in lower terms and boundary conditions of SturmLiouville type, is an Keldysh’s operator. From this, in particular, follows the completeness of a system of eigenfunctions and associated functions for this operator. Keywords: asphalt concrete, string oscillations in viscous media, fractional derivative, oscillational properties, operators of a Keldysh type 

The problem of space debris it is one of the most important problems of modern astronautics. According to the forecast made by Donald J. Kessler, the space debris can put an end to further space exploration. One of the solution its problem are socalled the active debris removal systems. The essence of this concept is the use of the special space tugs, which carry out the capture of the large space debris objects and their leading away from the orbit. This work focuses on the stage of pulling the space debris by the tug. The main particularity of this paper is to that the rendezvous of the tug and the space debris is done by controlling the length of the tether according to a prescribed law. A mathematical model describing the spatial motion of the tug — space debris system was developed. The tug and the space debris are considered as material points, which connected by a viscoelastic tether. Internal interaction of the tug and the space debris is determined by the viscoelastic force of the tether. The tug is under constant thrust. Motion occurs in the gravitational field of the Earth. The linearized equations of motion was derived. The tether length control law for the rendezvous of the space debris and the tug by means of the viscoelastic tether is proposed. An analytic expression for the frequency oscillations of the tether was obtained. A series of numerical simulations was performed to study the dynamics of the system at the time of the maneuver rendezvous. The simulations are run for 50 seconds with the tug thrust constantly on and without any active control system. The initial altitude is set to be 800 km and the initial velocities of the spacecraft are equal and in accordance to a circular orbit. The RungeKutta method is used to propagate the differential equations. Results show that at the end of the maneuver rendezvous in the tether, there are highfrequency oscillations and their frequency increases. That confirmed our analytical expression for the frequency of oscillations of the tether. Influence of the viscoelastic properties of the tether on the dynamics of the system was studied. It is shown that higher stiffness for the tether is better for implementation safety rendezvous of the tug and the space debris. The results of the calculations show that the practical implementation of the rendezvous of the tug and the space debris is possible, but requires additional measures to damping of the oscillations. The obtained results can be applied to study the properties and possible configurations of the active debris removal system, as well as applications for the tasks of implement rendezvous of two bodies using tether. In future research on the subject we should find ways to reduce the oscillation of the tether and verify the dynamics with regard to the consideration of the tug and the space debris as solids bodies. Keywords: spacecraft rendezvous, active space debris removal, tethered system, space tug, tethered control 

Deformable body mechanics  
A great number of aircrafts parts, modeled numerically, can be treated as a flexible rod, which exhibits large displacements and rotations, but which strains remain small. Spars wing panels, fuselage stringers, screw blades are among these parts. The paper presents derivation of tangent stiffness matrix and deformation loads vector of a geometrically nonlinear flexible rod finite element with large rotations and small increments stored separately. The tangent stiffness matrix and the deformation loads vector are both written in the closed forms and can be programmed relatively easily. The element is derived with conventional finite rotations theory, based on the Euler vector and rotation tensor. Following the Updated Lagrangian formulation, the element rotations are decomposed into to the accumulated part and the small incremental one. This approach allows avoid possible singularities and reach rotation angle magnitudes as large as 2p and even more. The proposed algorithms for the stiffness matrix and deformation loads vector computation are verified by some classical benchmarks. The thorough comparison of the obtained numerical results with existing publications, presenting alternative nonlinear beam formulations, reveals the high accuracy and numerical stability of the developed finite element. It is worth noting, that in the majority of works in this area the authors derive their nonlinear beam models departing from general expressions of the elasticity theory, which are subjected to certain assumptions regarding the dimensions and kinematics of the analyzed object. Such approach though being general (can be applied not only to beams), suffers from excessive complexity for one’s understanding and can hardly be implemented straightforwardly. In the current contribution an alternative paradigm is proposed: the finite element is constructed on the basis of a wellknown linear ancestor, which operates with simple strength of materials hypotheses. The classical beam stiffness matrix is wrapped by specific mathematics responsible for the proper description of large rotations and displacements. In this aspect, the developed finite element reminds the corotational FEA concept, described in [28]. Another important advantage of the presented nonlinear beam formulation is the symmetry of its tangent matrix, which is particularly important for numerical implementation, since it permits the more efficient linear equations solvers to be invoked and significantly improves convergence of NewtonRaphson iterations [29]. Not all the geometrically nonlinear beam models (see, for instance, [30]) possess this property. Keywords: flexible rod, finite elements, Euler vector, rotation tensor, large displacements, large rotations 

Fluid, gas and plasma mechanics  
The calculation of chemically nonequilibrium flows in the nozzles of rocket engines is normally performed using numerical implicit schemes (due to the stiffness of chemical kinetics equations). But the progress in developing of the stable explicit methods creates the possibility to use these simple methods instead of the implicit schemes. In this study, we introduce a calculating method of potential number of integration steps for explicit schemes, and their effectiveness is evaluated. The method includes: calculation of a chemically nonequilibrium flow along the nozzle length using the implicit scheme; parallel determination of the Jacobi matrix eigenvalues; calculation of the number of potential steps for the explicit integration scheme based on the stability bound. The calculation of flows was carried out within the framework of the inverse nozzle problem, using the implicitly differential scheme of Pirumov U. G. Numerical research was carried out for the combustion products:  liquid propellants (O_{2} + kerosene; N_{2}O_{4} + C_{2}H_{8}N_{2}) for Laval nozzles at: excess oxidant ratio; pressure P_{oc} = 20…100 atm; minimum radius r_{m} = 0.006…0.06 m and geometric expansion f_{a} = 53.0;  solid propellants (metalized fuel  C_{10.8760}H_{46.546}O_{25.806}AL_{9.665}CL_{1.517}N_{6.781}; nitrocellulose fuel  C_{23.498}H_{30.259}O_{34.190}N_{10.011}) for Laval nozzles at pressure P_{oc} = 20…70 atm; minimum radius r_{m} = 0.005…0.05 m and geometric expansion f_{a} = 33.9. The number of steps of the explicit scheme (K_{1}) was calculated for the RungeKutta method of the 4^{th }order. For the reactive media of liquid propellants, a huge number of potential steps (К_{1} ≈ 10^{9}) were obtained at high P_{oc} and r_{m} values. However, with a decrease of the P_{oc} and r_{m} parameters, K_{1} also decreased (to about К_{1} ≈ 10^{7}). In the subsonic part of the nozzle, the K_{1} values were approximately 10 times higher than in the supersonic part. For the reactive media of solid propellants, the results show the same trend, but at a lower level of K_{1} values, especially in the case of nitrocellulose fuel, when max (K_{1}) ≈ 10^{6}. Keywords: chemical nonequilibrium flows, engine nozzles, mathematical model, eigenvalues 

In the bginning of the paper a lowtemperature xenon plasma of Hall Thruster (HT) was investigated by spectroscopic measurements in the 250‒1100 nm range. More than 50 xenon atoms (Xe I) transitions were explored. A measure light power emitted by the plume at optical range was found to be about 0,5 W. The spontaneous emission probabilities (Einstein coefficients) for xenon atom were calculated at the Coulomb approximation (~800 transitions). The obtained results were compared with the results of other authors. By analysis the Hall thruster spectrum Xe I excited state concentrations were identified for 25 terms use getting Einstein coefficients. According to Maxwell’s electrons and Boltzmann distribution the value of excited state concentrations as a function of their energy is a line with line inclination equal to , where – ionization potential from ground state. However, the obtained excited state distribution is poorly approximated by linear dependence and more resembling «swarm» distribution. Measured spectral lines intensities have little differences for each location of collection optics. That could be conditional on heterogeneity of HT plume. However, the mode of the excited state population density persist. That gives evidence of plasma beyond the thruster exit plane common character and unfitness local thermodynamic equilibrium or Coronal model for describe HT plume plasma. In other words, one needs multilevel kinetic model allowing calculate excited state population density which agrees with experimental results for identification electron and nuclear temperature and concentrations. Keywords: xenon, phototransition probabilities (Einstein coefficient) XeI, Hall Thruster excited plasma states concentraions 

The modern phase of competitive liquidpropellant engines design is based on employing various mathematical models, including the knowledge of both fluid mechanics and thermochemistry. Mathematical models provide a number of possibilities to study both the most idealized processes and of the special phenomenons, such as the intermolecular reaction of substances, by the equation for real gas state process. Wellknown works on the studies of fluid by real gas are based on the accentuate of the amount of virial coefficients in the equation. The presented work is dedicated both to define the each mathematical model as an element of variational calculus tasks class, and to explore mathematical models to find the identical to the initial theories confirmations. The formal expression for the chemical potentials correlation for any substance of the thermodynamic system, described by the equation of the ideal gas state and by the equation of the real gas state, has the integral form. Thus, the mathematical model for any equilibrium state is the task of the variational calculus. Special mathematical technologies (the equivalent transformation, structuring, averaging of integrals) define the task or the subtask of models as the element of classes for the linear or the convex programming. Thus, there is compared to the correct technology of calculations, describing criteria of the identical with model and the acceptable precision of the solution, for the mathematical model of any equilibrium state. The results of mathematical calculations confirm the efficiency of technologies and present the variations of fundamental properties of fluid mechanics. Keywords: nozzle, the liquidpropellant rocket chamber, equilibrium state, real gas 

Dynamics, strength of machines, instruments and equipment  
Description of SNCalculator software for fatigue life calculation for aviation structures with geometric stress concentrators is given in this paper. SNCalculator is integrated in engineering analysis program Femap. This feature helps to increase automation of fatigue life calculation. Material constants, stress history mask, parameters of calculation theories and mechanical stress level are initial calculation data. Stress data are automatically loaded from Femap model for which static analysis was accomplished. Libraries allow reuse of materials and stress history mask. SNCalculator has postprocessing features such as: save results, export results to Excel spreadsheet, export results to Femap FEM, stress cyclogram viewer. Fatigue life calculations algorithm is based on three most widely spread in aviation branch methods: “quality” of construction (developed by Loim V.B.), similarity theory (developed by Kogaev V.P.) and fatigue rating theory (developed by Strigius V.E.). The first two methods are using conception of effective stress concentration coefficient. First method use “quality” as a parameter, which is identified by experimental data and exploitation of analogous structures data. Effective stress concentration coefficient in second method is calculated by Kogaev’s theory of similarity. Third method uses fatigue rating which defined as maximal normal stress of zerototension cycle for which fatigue life is equal 10^{5} cycles with 50% probability with reliability level equal 0,5. Main steps of above mentioned methods are described. Scheme of algorithm of fatigue life calculation realized by SNCalculator is given. Keywords: fatigue life, stress concentration, airframe, automation 

The principle structure component of any soft landing system with air dampers is shell with a gas inside it. Behavior of such shell component during the landing defines the safety of the landing object. Area landing relief, weather, soil elasticity etc. defines the conditions of landing. Thereby, the deformation of the landing system every damper could be unique. However, different approaches are developed by other engineers and scientists, and the most popular — numerical methods to develop in LSDYNA. The main idea is to develop a mathematical model to estimate the behavior of the dampers under loading and also take into consideration elasticity of soil and cargo. Herewith, an interaction between inside and outside gas with shell is included into consideration. The proposed mathematical model is developed using combination of finite element and finite volume methods. Besides, the developed model uses an Arbitrary Lagrangian Eulerian (ALE) approach. Such mathematical model has to be verified. Therefore we solved different problems using this model and compared them with wellknown analytical solutions. The first problem is to define a behavior of a closed cylindrical shell container. The air fills the inside volume of the container and the outside one. The inside and outside pressures differ from each other. The shell is considered as elastic and is loaded by the other body with various initial velocities. Furthermore, all bodies are in the gravity field. We obtained results by means of the developed analytical approach and ALE approach. These results show a satisfactorily difference. Then we considered the problem of air flux through the perforation in the air damper during the landing. It helps us to define the influence of the outside air volume on the flux from the damper in case of numerical approach. We also used ALE approach to simulate the deformation of the two air dampers with perforations during the landing. The influence of the considered dampers on each other is presented. Hereby, verification of the developing mathematical model to analyze the soft landing system with air dampers shown good convergence with analytical solutions. Then we will try to solve more sophisticated problems and compare the results with appropriate experimental data.Keywords: soft landing system, dropped cargo landing, air dampers 

Aeronautical and SpaceRocket Engineering  
Aerodynamics and heatexchange processes in flying vehicles  
Flow patterns obtained in water tunnel are presented for helicopter models and their components. Flow visualization was performed using the method of dyed jets. A detailed description is given for the models in which the jet blowing was realized. Visualization of Ka50 glider model has shown that with decreasing the angle of attack the rearrangement of limit streamlines occurs in nose fuselage so that at α = −10^{о} they are drawn in the underwing area. At α = −10^{о} the vortex cores are generated initiating from the nose section then following under fuselage and along it to the area of horizontal tail. During slip these vortex cores become greatly distorted that may have a significant influence on horizontal tail operation. Investigations of flow structure in the vicinity of Ka50 glider model with backswept wing has shown that trailingedge vortices running from tip to root wing sections and further along the aft fuselage to stabilizer area are clearly visualized on this model. In the presence of slip the said vortex structures of the model become visually distorted that may have a significant influence on its longitudinal static stability. Investigations on Mi26 helicopter model with main rotor simulation has shown that even in the absence of slip (β=0) the flow over the right and the left side of fuselage is essentially asymmetric due to the impact of rotating rotor. On the right side behind the pylon the area of disturbed flow generated by the main rotor disturbances is formed. This is confirmed by comparison with the flow pattern in the rightside view with inoperative rotor. Then this area drifts downstream towards horizontal tail. The flow over the left side of fuselage is much smoother. Only some of pylon disturbances reach the area of tail boom and loading ramp joining. Flow patterns obtained at negative and positive slip of this model are also presented in the paper. The paper presents the results of the investigation of the cylinder model with controlled circulation using a specially contoured slotted nozzle. Visualization was performed in the water tunnel and weight tests were carried out in the wind tunnel. The azimuthal position y of the slotted nozzle determined in reference to the direction of the incoming flow velocity vector and the jet pulse coefficient с_{μ} varied over a wide range. Tests showed that in the region of 100° ≤ Ψ ≤ 135° in lift coefficient and drag increment dependencies on ψ there appeared discontinuities and ambiguity characteristic of hysteresis effects indicating the presence of two possible flow regimes. At small values of c_{μ}_{ }separation occurs above the slotted nozzle, the lifting force increment is caused by air suction from separation zone near the cylinder and by reactive force of the jet. With increasing c_{μ} the boundary layer is attached by the shock, the lift increases drastically, the flow over the upper part of the cylinder is without separation. Investigations of Ka60 helicopter model in water tunnel with simulation of jet blowing from the slotted and jet nozzles, as well as the air intakes operation have shown the following. The air intakes take water from behind the rotor hub allowing for elimination of separation area behind it that causes the essential part of parasitic drag of helicopter body. The unseparated flow over the tail boom in the vicinity of the slotted nozzle is clearly seen that induces a side force compensating a considerable part of rotor reaction torque. Flow patterns near Yak24 tandemrotor helicopter model are also presented in the paper. Visualization of tip vortices shedding from the aft rotor is especially clear. At fixed rotation frequency of rotors the spacing between these cycloid vortices increases substantially with increasing the incoming flow velocity. It is noted that flow visualization in lowspeed water tunnel is a highly effective and lowcost technique to reveal characteristic features of the flow over aircraft models in addition to windtunnel investigations. Keywords: method of dyed jets, vortex cores, main rotor, slotted nozzles 

The paper presents the comparison of various types of aerodynamic characteristics of compact wing types using computer simulation. This problem was solved in threedimensional statement given viscosity and compressibility. the author studied three types of grid wing; four types of contour wing, such as biplane cellule, which lifting surfaces were joined by vertical wingtip pylons; and triplane cellule with vertical wingtip pylons. The purpose of this research consists in checking appropriateness of using grid wings with planar airfoil as lifting and control surfaces for smallsize subsonic unmanned aerial vehicles, compared with contour wings with convex airfoil. The sturies revealed that grid wings at subsonic speed have a great value of drag coefficient and very low value of lifttodrag ratio. These parameters can be slightly improved by plane edges revision. The advantage of grid wings with planar airfoils is the ability to operate at very high angles of attack and a smooth nature of flow separation. Reducing the number of internal surfaces significantly reduces the drag coefficient, but lift coefficient reduces either (though not so much). We got in the limit the contour wing with planar airfoils of lift surfaces. It has rather high lifttodrag ratio, but low lift coefficient. It may be increased by replacing planar airfoils by thick convex airfoils. Simulations have shown that at subsonic speed lifttodrag ratio of the contour wing is higher than that of a grid wing by several times. Maximum lift coefficients of both types are approximately equal. This allows conclude that under the condition of solving problems of strength and rigidity, the contoured wing is more promising than the grid wing for most types of compact unmanned subsonic aircraft. Keywords: aerodynamics, biplane, triplane, contour wing, grid wing, compact lift systems 

A helicopter uncontrolled left rotation mode (for the main rotor clockwise rotation) is one of the worst modes for the helicopters of classic structure. This phenomenon was repeatedly observed at the stages of a helicopter hovering, takeoff and landing, requiring increased values of engines’ apparent power at low flight speeds. The main cause of helicopter’s entering the uncontrolled rotation mode is the main rotor operation special feature, associated, in the first place, with the flow induced by the main rotor impact on the tail rotor under a certain air speed direction [1]. There are other contributing factors, which may cause helicopters’ entering uncontrolled rotation mode, such as maximum gross weight; high ambient air temperature; engine low power margin; main rotor reduced rotational speed, blustery wind, landing site blanket created by buildings and constructions capable of generating wind flow vortices, or its directivity and velocity variations. The takeoff or the sideslip landing can be considered as contributing factors as well. At the uncontrolled rotation mode itself, the conditions of tail rotor flow conditions altering. However, this alternation does not facilitate the dangerous mode quitting. Moreover, the angular velocity progressively increases. In the course of this work, the characteristics of various tail rotors have been calculated under rotation conditions with the left angular velocities of ω_{у}=0; 30; 60; 120°/s, when hovering out of aircushion effect. The computational studies have been carried out by using the helicopter mathematical model, developed in TsAGI [2]. A relationship between the tail rotors relative thrust coefficient and the angular velocities С_{t}/σ(ω_{у}) has been obtained.
The computational results of studies of the tail rotor with the solidity σ = 0,12 are shown in Figure 1. Under minor tail rotor pitch φ_{tr}, the coefficient C_{t}/σ is increasing insignificantly, and the blades rotate under prestall mode. When the φ_{tr}_{ }is increasing_{ }up to 21° and more, the coefficient C_{t}/σ is sharply decreasing. The tail rotor thrust is not increasing, but is sharply decreasing.
Figure 1. Relationships С_{t}/σ = f(ω_{у}) for σ = 0,12
The angular velocities ω_{у} influence on the tail rotor operating conditions has been analyzed. The distributions of the lift force coefficients С_{у}
and the tail rotor blade angle of attack α, on the r = 0,75R blade section, vs the blade azimuth and the angular velocity have been obtained. The changes of the tail rotor blade lift force coefficient С_{у} on the φ_{tr }= 25° are shown in Figure 2. The Graph shows, that when the ω_{у} increases, the lift force coefficient С_{у} decreases.
Figure 2. Relationships C_{y }= f (ψ) for σ = 0,12, φtr 25º Keywords: helicopter, hover, rotation, tail rotor, stall 

Drained dynamically scaled models have been designed to study aircraft unsteady aerodynamic performance in wind tunnels. Nowadays this kind of experimental research is preferred for future aircraft both flutter and buffeting safety studies, along with verification of CFD methods with allowance for the structural elasticity. While drained dynamically scaled models developing a number of requirements, including geometric, mass, stiffness and dynamic similarity, should be met. Furthermore, additional requirements for safety margins and high fidelity of measurements are implied. In the Laboratory of Dynamic Modeling of the Central Aerohydrodynamic Institute several models have been designed and manufactured: — Drained dynamically scaled model of shortrange passenger aircraft wing — Drained reference dynamically scaled model of transport category aircraft wing — Drained dynamically scaled model of shortrange passenger aircraft horizontal tail — Drained dynamically scaled model of mediumrange passenger aircraft flap The creation of drained dynamically scaled models became possible through the use of advanced polymer composite materials and FDM (Fused Deposition Modeling) additive technologies. Verification of the model geometrical characteristics is carried out on a coordinate measuring machine. The results of this work are as follow:
Keywords: aeroelasticity, model, additive technology, timedependent loads, aerodynamic experiment, composite materials 

Design, construction and manufacturing of flying vehicles  
The studies conducted in the 1980s of the 20th century by a number of the US aircraft manufacturers under project administration of U.S. Air Force Materials laboratory, has shown that practical application of polymeric composite materials (PCM) in military airplanes and helicopters design results in not only considerable decrease of their weight and cost, but also in higher survivability, maintainability, many other improvements. In the late 70s of the 20th century the U.S. Government, by request of the Air Force, invested in research work and Advanced Composite Airframe Program (ACAP) to demonstrate helicopter weight and cost reduction potential with maximum wide PСM application in its design. The ACAP program results were extremely successful. S75 and D292 demonstrators made clear the advantages of PСM application in the helicopter airframe structure achieved by maximum structure integration and use of largesize threelayered panels with honeycomb core, special shape of external panels to reduce the radar signature, as well as the implementation of the parts highly resistant to battle damages and capable of energy absorption at crash landing. At about the same time, the helicopter development projects known today as Ka50, Ka226, Ka60/62 were in progress in our country. From the very beginning wide application of PCM in the helicopter structure and, first and foremost, in the airframe was the target goal. PCM implementation in the fuselage structure purported weight reduction, labor hours and industrialization cost reduction, as well as lifetime and combat survivability increase, and operational costs reduction. This task was successfully solved. Based on worldwide successful results of PCM implementation in primary and secondary helicopter airframe structures, the 90s of the 20th century marked a consistent trend among all key helicopter manufacturers to extensive PCM application in new helicopter airframes. That is why when the development of Ka60/62 helicopter project was initiated in the late 80s, Mr. S.Mikheev, Kamov Company General Designer, set up the task of extending PCM application in the fuselage design up to 60‒70%. The manufacturing technological problems of largesize integral threelayers panels made from PCM were solved successfully. At the same time the manufacturability and costs analysis of the proposed technical solutions led to refusal of PCM application in the critical parts and assembles of Ka62 fuselage. Based on the analysis of design and manufacturing experience on helicopter airframe parts made of PCM, the paper offers substantiations and main conclusions on PCM widescale implementation in the helicopter design. Advantages and disadvantages of PCM application are demonstrated and main presentday obstacles on the way of wide PCM implementation in Russia in the helicopter design are outlined. Possible ways of their overcoming are suggested as well. Keywords: composite material, fatigue and static strength, layers laminate structure, energyadsorbing structures, wholecomposite fuselage, integral panels, manufacturability 

The subject of research is the air pressure regulation system in the aircraft pressurized cabin. The purpose of the work consists in developing a mathematical model of predicting the required air pressure in the aircraft pressurized cabin with a view to predictive actuation of control valves of conditioning and pressure regulation system to prevent accidents. The performed evaluation of air pressure regulation in modern aircraft of the fifth generation pressurized cabin capability revealed that at intensive combat maneuvering mode in vertical plane, and in case of the aircraft cabin decompression at high altitudes, the conventional facilities did not ensure pressure regulation in the cabin according to medicaltechnical safety requirements for crewmember safety under extreme conditions of highaltitude flight. These modes do not ensure reliable protection of crew members fr om unfavorable factors of highaltitude flight. The evaluation of the technical capabilities of air in the pressurized cabin of modern aircraft 5th generation pressure control systems showed that there are modes of intensive combat maneuvers in the vertical plane, as well as instances of cabin depressurization of the aircraft at high altitudes existing facilities do not provide pressure regulation in the pressurized cabin according to health technical requirements of crew safety in the extreme conditions of highaltitude flying, thus these modes do not provide reliable protection of the crew from the adverse factors of high altitude flight. The paper proposes the method for air pressure control based on the flight parameters control and computing for the preset time interval the pitch and vertical speed values, depending on the control stick position changes, according to previous calculations our mathematical model shows required pressure in the pressurized cabin and its rate of change. If the pressure in pressurized cabin deviates from the lim it value, the proactive changes in pressure in the pressurized cabin are performed in precalculated time interval by affecting air regulator and pressure regulator valves. The paper presents mathematical model of pressure control in the pressurized cabin and the valve control algorithm in the pressure control system. Keywords: сombat aircraft, pressurized control system, pressurized cabin 

Thermal engines, electric propulsion and power plants for flying vehicles  
The paper presents the developing principles of dynamic mathematical model of oil systems with electrically driven pumps for gas turbine engines (GTE). The oil system with electrically driven pumps can replace the traditional system with pumps driven by gearbox. The demonstrational oil system model with adjustable electrically driven pumps was developed in the CIAM. Experimental studies of its characteristics on the workbench with the simulator oil chamber GTE demonstrated the complexity of hydro and gasdynamic processes occurring in it, and the need to develop dynamic models of such systems. The literature generally discusses the mathematical models for the study of oil systems based on static hydraulic ratios without considering the dynamic characteristics of pipelines, gas content changes over the path of pumping the twophase mixture, and others. The dynamic mathematical model of the system based on finite element with lumped parameters is designed to sel ect its characteristics and control laws. The finite element describes the part of pneumohydraulic circuit of oil system. Gas and hydraulic network system are divided into separate sections of working medium flow (pipelines, etc.), concentrated volumes, pumps, located on sections, are described by quasistatic characteristics. The distributed pressure losses due to friction within the pipeline are focused at the border and summed with the losses on other hydraulic resistances of this section. It is assumed, that the pressure, temperature, mass gas content and thermal characteristics of the working mixture are constant along length of the concentrated section and vary only in time. The volumes of the type of oil cavity, where twophase medium is formed fr om air and oil, describe the stratified flow of oilair and airoil mixtures. The change of thermal and thermodynamic characteristics is calculated in the acoustic volumes, where the twophase flows merge. Calculation of twophase mixture movement in the pipelines is made with allowance for its inertia and compressibility. Solution of the system model is carried out in a computer program by direct numerical calculation without iterations (Euler method). Comparison of the calculated and experimental processes in the demonstration lubrication system revealed their good agreement in the area of the 1st tone oscillations of hydraulic network system 0.2 ... 5 Hz. Keywords: gasturbine engine, lubrication system, controlled electric drive, dynamic mathematical model, twophase flow 

The paper tackles with the issue of a gas turbine and steamturbine cycles’ basic parameters of a gas turbine installation under development for gas pumping units, based on aircraft jet engine. The goal of this work consists in gas pipelines pumping units’ efficiency increase by utilizing a gas turbine engine hightemperature exhaust heat energy and the realizing a lowertemperature steam cycle. With the combined power plant processes TSdiagram it was performed the selection of the main parameters of the gas turbine and steam turbine cycles according to the needs of temperature differences. Calculations show that the creation of a combined gas and steam power unit is possible. The initial temperature of the gas turbine cycle should not exceed 1500 ... 1600 K to ensure that the free power turbine will work without blade cooling. Based on a combined power plant processes’ TS diagram the authors carried out selection of the gas turbine and steamturbine cycles’ basic parameters with allowance for the temperature difference requirements. The computations demonstrated the possibility of such combined gas turbine installation development. The gas turbine initial temperature herein should not exceed 1500 ... 1600 K to ensure the free power turbine operation without blade cooling. pumping unit based on aircraft jet engine RD33. Whereby the results demonstrate that the power of such combined plant will be 20 MW (15.5 MW and 4.5 MW) with effective efficiency of 45‒50%. All the above said allows draw a conclusion that gasturbine installations are prospective for gas pipelines gaspumping units’ drives and allows reduce of fuel gas consumption for compressor station’ auxiliaries. Keywords: gassteam turbine plant, the basic parameters of the cycles of the Gas turbine plant and steam turbine plant, free power turbine, combined thermodynamics cycle of gassteam turbine plant 

Control and testing of flying vehicles and their systems  
The work is dedicated to the development of flaw control information diagnostic system, the ability to expand the possibility of nondestructive testing devices which operation is based on optical radiation speckle patterns method. Method of «chessboard» is used as speckle imaging tool. This method allows analyze the dynamics of the parameters changes in a defect by analyzing the changes in the studied surface roughness parameters, as well as to carry out work on determining the depth of defects in the internal structure of composite materials. This method is applied to control the subsurface structure. Its operation principle consists in sensing of the object with increasing laser power. Experimental studies have confirmed the effectiveness of these methods, and proved that the method of «checkerboard» can be used to monitor the cracking and residual lifespan assessment of details, employing the method for determining the internal structure of composite materials, and the depth of the defect in the internal structure of an object. Thus, the introduction of the developed informationdiagnostic system will allow for flaw detection of aircraft control units and assemblies at a new technological level. Keywords: nondestructive testing, flaw detection, speckles, composites, roughness, image processing, Java SE 

Drop tests present a necessary part of a helicopter design and certification. However, manhours necessary for carrying out these tests are rather labor consuming, and the tests themselves are not safe. Thus, helicopter chassis drop test mathematical model development is considered as a topical task. Drop tests consist in dropping the aircraft landing gear with the reduced weight attached to it from a specified height. this weight is selected according to the norms of safety. The paper considers mathematical modeling of drop testing of the main and front landing gear struts of the Mi38 helicopter with software packages LMS. Amesim. Imagine. Lab and LMS.Virtual. Lab. The authors describe the methodology and stages of front and main landing gear shock absorbers mathematical models development with the data packs, and the numerical experiment obtained results. The synthesis of shock mathematical models, as a combination of the pneumatic, hydraulic and mechanical systems operation, held in LMS.Amesim. Imagine. Lab package. Validation of models of shock absorbers made by comparing with the received data compression diagram of the manufacturer. Building a model of the landing gear mechanical and mathematical modeling of its contact with the surface of pneumatics was performed in LMS. Virtual. Lab pack. The landing gear drop tests modeling carried out by sharing calculation in packages LMS. Virtual. Lab and LMS. Amesim. Imagine. Lab. The simulation results are compared with manufacturer’s experimental data of field tests. is confirmed The reliability of the used models is confirmed by operational work diagram representing the dependence of force at the point of contact on pneumatic vertical movement of the center of gravity of the dropped cargo at various test conditions. Comparison of the calculated and experimental data demonstrated the possibility of using this method for the preliminary analysis of the permissible loads in the tests for dropping, which provides a significant reduction in the volume of drop tests. The possibilities of further development of the developed method for helicopter landing simulation in various conditions regulated by the rules of safety. Keywords: helicopter chassis, mathematical modeling, drop work test 

Control and testing of flying vehicles and their systems  
The basis of technical information, measurement and control systems support consists of electronic devices and systems for information communicating, gathering, processing, transmitting and displaying, which, belong to subjects to diagnosis at the stages of development and production. For means of control and most of other types of inertial control system tests, it is generally accepted to implement checkout equipment (CE). Hardware and software of the CE are developed individually for the requirements of inertial control system specific tests. To simplify the design and improve versatility, this paper offers to rethink CE software design methodology, allowing form CE software automatically for control and diagnostics purposes of several similar inertial control systems. This solution will significantly reduce the time and cost of the CE hardware and software parts developing. The software forming is carried out by attaching additional software modules (ASM), responsible for unique to a particular inertial control system (ICS) equipment or functionality, to basic software module (BSM). The developed software remains intact while being used for control and diagnosis of various ICS’s. BSM performs functions such as distributing software threads and their priorities, launch and control of ASM. ASM are developed in conjunction with CE, and possess unique features. Interaction between modules is carried out through the shared memory and communication protocols between modules. Considering the fact that ASM’s are designed to perform specific tasks, such as recording telemetry in the selected format, working with mezzanines boards, or record sensor readings, as well as due to the fact that they are designed as a separate project, the developers unassociated with basic module design can be involved in their creation. Small size and relative simplicity of development of each module significantly accelerates this process. Uniqueness of each CE set of hardware components, such as a set of sensors, optoboards, interfaces, makes it possible to determine most of required ASM, by selfcontrol using the ICS simulator. Trial ISU run and analysis of incoming telemetry can help to determine additional software modules. Keywords: test instrumentation, modular system, software, inertial control system, control and diagnosis 

Dynamics, ballistics, movement control of flying vehicles  
A controlled flight into terrain remains a serious problem for the commercial and military aircraft. It is difficult for a pilot to adequately estimate the degree of maneuverability and safety on a modern maneuverable aircraft. To improve the flight safety applies systems which warns the pilot of the ground proximity and performs an automatic collision avoidance maneuver in case of security threats. The article deals with the control algorithm for performance of the automatic maneuvers intended to avoid collision with the ground. The proposed algorithm is designed for the aircraft with control loops of gload and roll angle. A collision avoidance maneuver is divided into two phases. The first phase is focused on stopping the descent of the aircraft. The goal of the second phase is the safely transfer control of the aircraft to the pilot. The first phase of maneuver can be performed by using two control strategies. The first control strategy consists of a roll to wings level combined with performing a desired gload. Desired gload is negative when roll angle more than the point ahead angle and positive in other case. The point ahead angle depend on the ratio of performances of gload and roll angle control loops. The recommendation for chose the point ahead angle for a particular aircraft is given. The second control strategy is to perform aerobatic figure, called “overturn”. The control algorithms of vertical flight speed and altitude to execute the second phase of the avoidance maneuver is designed. The logic for perform avoidance maneuver and block diagram of the control algorithm is created. Keywords: control algorithm, automatic maneuver intended to avoid collision with the ground 

Instrument making, metrology, information and measuring equipment and systems  
Navigation systems  
The paper tackles the issues concerning a process of methods and techniques development, meant for increase the quality factors of the highmaneuverability dualpurpose aircraft avionics through enhancing the technical performance of the standby instrument system. The authors proposed, in particular, to employ an electronic integrated standby instrument system, in which the indigenous compact mediumaccuracy sensors are used. The distinctive features of the systems are the data communications between the elements, as well as software and hardware tools based on them. It allows measuring the significant number of an aircraft movement parameters, increasing the accuracy of measurement and enhancing the reliability and usability factors. The results of the semiscale modeling are given with the use of the realtime telemetry under real flights of the highmaneuverability aircraft, groundbased adjustment and flight tests. Keywords: integrated standby instrument system, complexation schemes, complex correction, accuracy, reliability, usability 

Metrology and metrological assurance  
The exact knowledge of an aircraft takeoff weight, including the actual fuel weight on board and center mass is a factor in flight safety and its controllability. Conventional weight measuring systems do not allow for the rapid control of these parameters in real time. The authors consider the possibility of an aircraft takeoff weight operational determination while maneuvering along the taxiway to the runway starting area. For this purpose, the taxiway must hold the traceable area equipped with sensor bars, embedded in an underlying surface according to the number of the aircraft’s support landing gears, and electronic component to ensure the operability of the sensors, information processing, and remote transmission to Central office for decision making. The paper justifies the layout of sensor bars, the geometry of the receiving surface, perceiving the pressure force of the aircraft landing gear on the underlying surface, and specifies the requirements to the primary sensors energy characteristics, which converts the pressure force into an electrical signals and their number. Particularly, the longitudinal dimension of the sensor bar must have a phase of whole position of contact patch of wheels on the perceiving surface of the sensor. This allows extracting the additional information useful to diagnose the state of the wheel elements of the landing gear. The main requirements to the primary sensors are high accuracy and versatility. The most promising seems to be the sensors, such as electromechanical transducers, based on amorphous and crystalline quartz with frequency dependent output signal. This can be unified quartz string transducers of forces and deformations. Quartz capacitive transducers can be in conjunction with the quartz crystal oscillators as well. Further, the paper presents the main available characteristics of the sensors, which determine the ultimate load, steepness and temperature error. Keywords: aircraft takeoff weight, metrological zone, sensor bar, primary sensor, capacitive transducer, strain sensitivity, electronic module 

Information and measuring and control systems  
The questions of creation of a highly stable promising means to confirm the performance of optoelectronic equipment for remote sensing at the stages of flight test and operation during the active lifetime of the spacecraft, which provide the possibility of highprecision onboard calibration with traceability to national standards. The objects of research are models of onboard black bodies based on phase transitions of highpurity substances and their eutectic compounds, which build to confirm the accuracy characteristics of remote sensing equipment in the infrared spectral range, as well as highly stable detectors that measure external influencing factors around the spacecraft area. Creation of highly stable onboard equipment is based on unique property of substances in the process of phase transitions, as well as a special design for the required characteristics. Theoretical and experimental research, including microgravity, was conducted. As a result, found that the physical principles and design features underlying the work of emitters allow to ensure the traceability of measurement results to national standards, the compensation of the temperature dependence of sensor equipment will provide the reliable data on the measurement object, namely, the state of its own outer atmosphere of the spacecraft. Development of advanced tools onboard calibration confirmation of the accuracy characteristics of remote sensing equipment will deliver the required level of output quality. The results are used to implement the requirements of international and national standards, which are needed to confirm the accuracy characteristics during operation, what is currently not provided with the required metrological characteristics. Creating a promising onboard calibration means for verification accuracy characteristics of remote sensing equipment will ensure the achievement of the required level of quality of the data and improve their competitiveness. Keywords: onboard emitter, a phase transition, model of a black body, onboard calibration, temperature dependence 

The absence of common methodological base for functioning efficiency evaluation and capabilities of Ground Automated Control Complex (GACC) makes practically impossible the procedure of scientific study and evaluation of various options for its development and introduction of advanced unified spacecraft management tools. The results of scientific and methodological groundbased activities applicability analysis from the viewpoint of an individual spacecraft GCC evaluation capabilities, revealed the difficulties in estimation GACC overall efficiency. Thus, it becomes urgent to develop alternative approaches to estimating the GACC effectiveness, allowing obtain estimates of GACC’s operating efficiency indicators based on composition, structure and parameters of the Orbital Constellation (OG) of space crafts, as well as the requirements and limitations of spacecraft control technology. Spacecraft GACC functioning efficiency estimation method was designed for this purpose. It allows obtaining rational GACC structures for controlling spacecraft OG and evaluating their implementation effectiveness. The developed method demonstrates several advantages over the existing conventional approach, such as: – The ability to plan collaborative control operations in automatic mode; – The plans obtained using the conventional approach do not always meet the required sequence order of control operations, unlike the plans prepared using the developed method; – Сomputation speed with the proposed method is 1.5 times higher than with the existing approach. The proposed method can be implemented in the following cases: – Computations for spacecraft GACC functioning effectiveness assessing t in various conditions, performed at stages of a longterm and operational planning of its resources employing; – Prospective composition spacecraft GACC evaluation capacity and advanced spacecraft control technology studies; – The study of various kinds of requirements for both in general (GACC) and in particular (spacecraft); – Justification trends in spacecraft GACC development and improvement. Keywords: Ground Automatic Control Complex, spacecraft, efficiency, technology management cycle 

Medical purpose instruments, systems and products  
The paper discusses mathematical modeling, analysis and parameters selection of ultrasonic interaction with a spaceman’s injured bone tissue to accelerate its regeneration during longterm missions. The authors developed a mathematical model of ultrasonic interaction with multilayer system of a biological human tissue based on reflection of the mechanical ultrasonic energy at the boundaries, such as “soft tissue — cortical bone tissue”, “cortical tissue — trabecular bone tissue”, “trabecular bone tissue — bone marrow tissue”. Mechanical ultrasonic elastic stresses of biological cells in the bone tissue such as displacement amplitude (deformation) and shear forces on the cells of cortical bone that stimulate regeneration of the cortical bone tissue without causing cells destruction and cellular organelles were computed. The temperature gradients in the cortical bone were computed to evaluate thermal effects of ultrasound on biological cells. Finally, the recommended parameters of ultrasonic exposure for accelerated regeneration of a spaceman’s cortical bone tissue: intensity of ultrasonic source: I_{0} = 0,05 — 0,1 W/cm^{2}, the oscillation frequency f = 0,02 — 0,1 MHz, the duration of continuous exposure shall not exceed 10 minutes were elaborated. Moreover, the weight of a spacecraft lifesupport system will not be increased as the ultrasonic device is already a part of the medical and technical equipment onboard the orbital station. The presented study is the first one to offer implementation of ultrasound with the parameters selected to accelerate a spaceman injured bone tissues regeneration during longterm missions. Keywords: frequency, intensity of ultrasonic waves, bone tissue, longterm space missions 

Radio engineering and communication  
Antennas, SHFdevices and technologies  
Frequencyscan array antennas (FSAA) are widely used in airspace surveillance radars and air trafficcontrol systems. In most cases, these antennas present a planar equidistant array of linear emitters connected to the traveling wave multichannel power divider (PD). PD is based on couplers, connected in series with sinuous delay line (DL). It is well known that sharp increasing of PD input voltage to standingwave ratio (VSWR) on the frequency corresponding to beamforming near broadside is a significant disadvantage of such antennas. The reason for this is the inphase addition of large quantity of even low reflections from periodic discontinuities: couplers and DL bends. This effect, which leads to a significant gain reduction and unacceptable distortions of directional pattern, is called a “broadside impact” in technical literature. Currently, to eliminate the broadside impact, the method, based on integer odd number of quarterwavelength in DL shift between all of even and odd discontinuities was proposed. This paper presents the simulation results obtained using the algorithm, realized in MathCAD. The algorithm was designed for FSAA PD input VSWR evaluation at a certain reflection level from periodic discontinuities and amplitudephase distribution (APD) forming in frequencyscan plane. During the simulation it has been established that the aforementioned elimination method have a disadvantage, i. e. occurrence of broadside impact in the lower and upper operating frequency range when wideangle scanning with pattern at a relative bandwidth of more than a few percent was implemented. Thus, the new method, which was designed for complete elimination of broadside impact, is proposed. It is based on automated iterative search procedure of electrical lines lengths connected between the couplers and DL bends. The iterative convergence condition search procedure is defined by PD input VSWR lowest possible value, which achieved in operating frequency range at a certain reflection level from discontinuities. Reasonability of transition from PD series circuit to seriesparallel circuit with wideangle scanning implementation in a relative bandwidth of more than 5% was analyzed. Thus, the main practical result of research concludes in FSAA broadside impact complete elimination possibility and, respectively, operating frequency range and scanning sector expansion without reducing the antenna gain requirements. Keywords: frequencyscan array antenna, frequency scanning, pattern, traveling wave power divider, broadside impact, simulation modeling 

With reference of constantly growing demand for radar installations of new generation implementation, the issue of meeting the strict requirements to SHFdevices becomes quite topical. Filters play one of the key roles practically in every navigation or communication system. The main functions of the filters consist in ensuring: ‒ passband in the specified frequency band; ‒ necessary suppression level; − low level of insertion losses; − specified amplitudefrequency response. The main purpose of the research is consists in comparison of influence of heterogeneity (capaciti character) on filter skirt. Two ways of setting of the waveguide filter has been presented. The presented paper focuses on studying the procedure of waveguide SFRfilter of Ka waveband tuning. The filter key parameters while tuning are as follows: its characteristic conformance to specification requirements and total tuning time, which is especially uptodate at mass production. To ensure these parameters at conventional tuning metal screws are used. These screws present a nonuniformity (of capacitive type) for cavity links matching adjustment. The presented study suggests innovative solution in this sphere, which consists in metal screws substitution by fluoroplastic ones. It is associated with some key specifics of this material. It is noteworthy that in the framework of this research thermo and vibrostrength test were carried out. These tests present an important criterion, warranting the features stability of the tuned unit. The assumption that by material substitution we will manage not only cut the time of waveguide filter tuning, but also ensure the more qualitative frequency response were substantiated experimentally. Moreover, while working on this problem the accessory for convenience in this procedure realization was developed. Thus, the presented work presents complex comparison of the obtained parameters, complexity and time component of the two variants of waveguide filters tuning procedure.Keywords: waveguide bandpass filter, microwave filter of KA of range, filter tuning, implementation of dielectric elements for waveguide filter fine tuning, device for filter setup, nonuniformity effect on resonator links coordination 

Radiolocation and radio navigation  
The article is devoted to the problem of the rational quality definition of the GLONASS system pseudo satellites and to the problem of optimization of their location relating to the runway for supplying better accuracy of the aircraft positioning on the final landing stage. The article presents the optimization criterion based on the minimization of the vertical geometrical factor both in a preset point and lengthwise the glide path. The difficulty in solving the problem is in a constant change of a geometrical factor due to the satellite moving relating to a user. The problem of optimization has been solved during a period of time which is equal to a period of orbital movement satellites GLONASS frequency with an hour discreteness. In this case we get a set of pseudo satellites locations which are optimal for a certain chosen moment of time. The method of finding the only positioning of pseudo satellites among others offered is based on the creation of the histogram of the latitude and longitude coordinates. To define the optimal pseudo satellites location, certain algorithms are drawn up which are based on the method of a direct search ( by HookJeeves) and a no rigid polygon (by NelderMid). The comparison of results got by both methods proved the adequacy of found solutions. To conduct the research a program complex LabView was created. It has got the module of orbital movement GLONASS imitation which works on the base of the functioning almanac of the system. The data out of this almanac are the characteristics of a nautical session in a set point of any preset period of time. And the data out of the optimization module that implements certain algorithms are the coordinates of optimal position pseudolites points. On the bases of the carried research there is a benefit in the average value of geometric factor both lengthwise the glide path and certain points provided in case of the pseudolites optimal position. The Influence of the number of optimal position pseudolites on the vertical geometric factor value in a zone of the airdrome was researched. It was proved that for the vertical geometric factor minimization and the zone increase, within provided minimum value, the use of more than three pseudolites is not rational. Keywords: pseudolite, glide path, geometric factor, GLONASS orbit group, math modelling, allocation optimisation 

Informatics, computation engineering and management  
System analysis, control and data processing  
Rapid development of multicopters became possible due to the popularity of MEMS technologies, brushless engines and highcapacity lithiumpolymer batteries. Multicopters are widely used in unprofessional aviamodelling, military and civil tasks because the construction is very easytouse. In spite of this multicopters don’t have the ability of windmilling and glide landing therefore multicopter are damaged easily. Seminatural modelling helps us to reduce risk of damage, decrease time and increase the efficiency of developing UAVs. Seminatural modelling have the maximum accord with fullsize UAV. Seminatural modelling system of multicopters consists of two parts: modelling system and computing center. Computing center computes math model of multicopter and environment, visualizes the results of math modelling, registers parameters of math model and modelling system. Modelling system controls the multicopter in math model, makes the dynamical similarity of the system, simulates of navigation system, visualizes the environment of modelling. Computing center consists of multicopter math model, environment math model, visualization system, registration system. Modelling system consists of Stewart platform with six degrees of freedom, collimation system, imitator of navigation system (GPS, barometer, compass), quadcopters CPU. Equations of math model compute in Matlab/Simulink system. Model of environment is used from Matlab/Simulink system and simulates wind, gravity and atmosphere. Registration system registers parametres of math model, parameters of Stewart platform, navigation parameters of quadcopters CPU and navigational parameters of collimation system. Stewart platform with six degrees of freedom consists of Arduino Mega, 6 servos and some peripheral devices. Quadrotor CPU stands on Stewart platform and rotate on it. Besides it Quadrotor CPU control the math model through the signals to the brushless motors. Imitator of navigation system simulates the parametres and transmits it to the quadrotor CPU. Collimation system makes the image of environment for modelling the optical systems. As the result the article shows the structure of seminatural modelling system for the modelling of control system of quadrotor and optical system. Keywords: seminatural modeling, seminatural modelling system, unmanned aerial vehicle, multicopter, quadcopter 

Computing machinery, complexes and computer networks  
This work set and solved the problem of unmanned aerial vehicles (UAVs) computing power sharing to ensure reliable identification of a number of objects, employing neuron network identification. The main requirement imposed on a group of neural networks’ joint operation is related to incorrect detection of objects in complicated cases, when this probability in a single network is sufficiently great. The authors found the conditions, which fulfillment defines the possibility of forming a group of neural networks, solving the problem of detection of any degree of complexity and returning a wrong answer with the probability not exceeding the preset small value. Theoretical justification of neural networks’ joint operation organization is based on evolutionary solutions adjustment method. On its first stage populations of separate neuron networks solutions were formed, and possible answers were generated, where the room was left for discarding the answer. At the second and subsequent stages the exchange of variants was carried out, and neuron networks, which «discarded» the answer, select, in their judgement, the right answers from proposed answers, or refuse to answer again. This iteration process continues until the majority of neuron networks give coinciding answers. It is quite clear that this answer ca be of three types: <<right>>, <<wrong>> or <<cannot decide>>. The probability values of such answers depend on the number neural networks in the group, problem complexity, initial probabilities of right and wrong answers generation by single neuron networks, and of probabilities of right or wrong selection of foreign answers at the stages of solutions adjustment. To obtain analytical solution of the set problem of defining conditions which fulfillment a group of neuron networks goes wrong with the probability not exceeding the preset small value, the authors employed the result of Condorcet jury theorem and Rasch model. The authors proved the theorem on inconsistent solution of a problem of arbitrary complexity, obtained by a group of neuron networks, probability tending to zero, as well as the theorem on limit value of existence problems’ complexity, which cannot obtain the proper solutions with the preset probability. The judgement was exercised, that the proved theorems bear universal character and can be implemented to the group of natural intellectual objects, such as performing the task on context scientific citation number building in complicated cases. The paper describes “errorfree” objects detection technology by a UAVs group. Preliminary processing of images under detection was carried out according to the algorithm presented in [11]. Computer simulation of images detection by a group of neural networks confirmed the workability of the approach under discussion and allowed draw inferences on probability value of correct objects detection significant increase in simple cases, and reduce practically to zero the probability value of incorrect detection. Keywords: correct decision making probability, detection, network decision making system, unmanned aerial vehicles, neural network, evolutionary solutions adjustment method, Rasch model, context detection 

Mathematica modeling, numerical technique and program complexes  
The paper tackles the problem of railway cargo transportation planning and organizing. Oriented multigraph of a train traffic energy efficient strategies and a set of this multigraph permitted paths, i. e. a set of normative threads of a train schedule, are put under consideration. Nonoriented conflict graph is determined on the set of train schedule normative threads, associated with a monotonous Boolean function. The paper envisages the problem of creating a conflictfree set of train schedules, reduced to the monotonous Boolean function maximum upper zero search. The conflictfree schedule threads herein should ensure the specified volume of transportation. For this purpose, conditions of amount of traffic provision should be met, given by correspondence matrix. The transportation plan for the available set of locomotives is formed based on nonconflict set of the graph normative thread sets. A problem of locomotives’ assignment and movement is formulated for the transportation plan, which optimizes the number of completed transportation assignments, a number of used locomotives and a number of «empty runnings». The graphcombinatorial problem of subgraph nodes of oriented graph of transportations dependencies coverage by oriented paths. The abovementioned criteria herein are formulated in terms of the determined coverage properties. The algorithmic diagram. The main results of the research consist in mathematical formulation of the problem of optimal assignments of locomotives and its reducingtion to the dual graphcombinatorial problem, which solution structure is offered. The obtained results could find an application for solving practical problems on railway transportations optimization with regard to the required fleet of locomotives and its utilization ratio. Keywords: assignments of locomotives, algorithm, optimization 