METHODOLOGY AND PROGRAM COMPLEX OF RESEARCH OF LONGITUDINAL STATIC SUSTAINABILITY OF SCREENPLANE AT THE DESIGN STAGE

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Introduction. Design of wing-in-ground effect vehi- cles (WIG vehicles) with pre-determined stability and controllability characteristics is a complex and topical task. The requirements of their stability and controllability are more demanding as compared to the design standards of other aircraft with comparable aerodynamic character- istics, such as airplanes. That is determined by the de- mands of flight safety, as WIG vehicles fly at a high speed and quite close to the water or ground surface. WIG-craft handling qualities (either set initially or speci- fied by an automatic flight monitoring system) must pro- vide fine control of flight and the craft’s specified align- ment with the underlying surface within the given flight envelope. Besides, WIG vehicles’ aerodynamic character- istics (aerodynamic coefficients and their derivatives) depend on the distance of the given distinguished point of the craft (in this paper - the center of mass) from the un- derlying surface, and on the position of the center of mass as the point of the aircraft rotation. Unlike with airplanes, here the range of significant influence of these factors corresponds to the main operational range of WIG vehi- cles’ flight parameters. It is difficult to overestimate the importance of solving the problem of specifying the sta- bility and controllability characteristics of the craft at the preliminary design stage, as the correction of design er- rors in aerodynamic configuration of the aircraft can’t be fully completed at subsequent design stages. That is why the article deals with the problem so urgent for the devel- opment of aircraft engineering. Subject of research. The purpose is to work out methods and a packet of computer programs for assessing the WIG vehicle static stability at the stage of preliminary design using mathematical modeling and method studies. These can help to assess the applicability of the methods and programs offered for WIG-craft aerodynamic design. Note: the ideology of mathematical modeling of WIG vehicle flight dynamics this paper is based on is acquired from Ref. [1], the aerodynamics and motion designations and parameter structuring are specified in accordance with Ref. [1-3]. It is known that an aircraft (WIG vehicle, airplane, etc.) is statically stable with respect to one of the parame- ters, if its changing causes force factors (forces or mo- ments) that tend to eliminate the increment of this pa- rameter. Longitudinal static stability specifically shows itself in longitudinal motion, i. e. when the aircraft is moving along its own symmetry plane. This paper defines the longitudinal static stability of WIG vehicle as the static stability of its two parameters: the angle of attack (pitch) and the altitude of flight above the ground-effect plane (distance). The longitudinal stability characteristics of a WIG vehicle is determined by two groups of factors. The first group is determined by the aerodynamic and mass configuration of the aircraft. The second group includes the initial flight mode parameters, the center of mass location, the flying weight and other variable parameters [3-5]. Calculation methods of longitudinal stability pa- rameters. Characteristics of the program packet. A lot of works are devoted to solving the problem of providing WIG-craft stability in longitudinal motion, the most essential being the works of R. D. Irodov and V. I. Zhu- kov [6; 7]. They offer a criterial approach to WIG vehicle stability assessment based on the analysis of the angle of attack and distance from the ground-effect plane. It should be noted that in most works devoted to the assessment of WIG vehicle stability, including those published abroad, the same approach is either applied or developed (Ref. [8-10]). In this paper, two approaches are used to evaluate WIG static stability in longitudinal motion. The first is based on the theoretical propositions of Ref. [6]. This paper analyses the basic system of equations describ- ing WIG vehicle longitudinal motion, which does not dif- fer in form from the equations used for airplane parame- ters calculations and is in the same form as in Ref. [1; 3]: dV = g(n dt xа dθ g - sin θ), Aerodynamic characteristics are presented as a mathe- matical model, describing dependences of aerodynamic coefficients on the parameters of flight and WIG vehicle dt = V (nyа - cos θ), , d 2J = Mz dt2 Iz dh = Vsin θ. dt Here g - is free fall acceleration; nxа and nyа (1) - tanconfiguration based on multidimensional approximation of data by exponential polynomials. The derivatives of aerodynamic coefficients with respect to the given pa- rameters are determined by methods of numerical differ- entiation. The second approach is classic for the aircraft of airplane type, where longitudinal static stability is es- sentially understood as stability with respect to the angle gential and normal high-speed overload respectively; t - time; V - true airspeed (in case of the absence of airflow velocity along the underlying surface); θ - flight path slope angle; J - pitch angle; h - flight altitude (relative distance from the ground-effect plane, distance from the aircraft’s center of mass to the ground-effect plane); M z - longitudinal moment. With certain assumptions, the terms of aperiodic and y y oscillation stability of WIG vehicle were obtained. As on the cruiser flight modes ch < 0, ca > 0 (lift coefficient derivatives according to the distance and the angle of at- tack respectively), the stability criteria can be described as: of attack in low-speed longitudinal motion; it also de- pends on the center-of-gravity positioning of the aircraft [1-3]. In this case, the aircraft is stable under condition of dmz < 0 . The simplified approach is dictated by the d a necessity of WIG- craft’s static stability evaluation when it moves out of (or with negligible) wing-in-ground effect. Application of the first approach at a considerable dis- tance from the effect plane often gives rather contradic- tory results of stability evaluation. Besides, certain exam- ples of analysis of some aerodynamic configurations bring to conclusion that in several cases the simplified (second) approach to longitudinal stability evaluation within the total range of distances from the underlying cya =cya ГП < 0; cya =cya ГП < 0, (2) surface is enough. In this case stability evaluation is made when the following conditions coincide: ma < 0 и mh < 0 ya where c ГП - lift coefficient for stable horizontal flight; (with no condition cya = const z z set up). mz - WIG vehicle longitudinal moment coefficient. WIG If the criteria ma < 0 and mh < 0 are not synchronized, z z z z vehicle is regarded as stable when ma < 0 or mh < 0 it means that the aerodynamic configuration of WIG vehi- (longitudinal moment coefficient derivatives mz with cle doesn’t provide its longitudinal static stability. MatLab system and its Guide application are used as respect to the angle of attack α and distance h respec- tively) when cya = const = cya ГП . In accordance with this approach to evaluation of WIG craft static stability the following mathematical algorithm of derivatives calculation was worked out a mathematical modelling platform, allowing to work out original applications for Windows. Aerobatic 1.0 program application was made on this basis (fig. 2). The program presents a multi-window structure inter- face, which allows step-by-step problem solving: m a = dmz z d a cya =cya ГП z и mh = dmz dh cya =cya ГП (fig. 1). 1. Formation of aerodynamic characteristics database for the aircraft under study. Stating the special task for analysis (when it is necessary to analyse several inde- On the block diagram fig. 1: xT - current center of mass location of the aircraft under consideration; h - specified relative distance from the ground-effect plane; cya - specified lift coefficient for stable horizontal flight; a ГП - angle of attack for horizontal flight with the speci- fied parameters; hГП - relative distances calculated with corresponding value of cya ; mz - longitudinal moment coefficient calculated for corresponding to the angle of attack and the distance in horizontal flight ( a ГП и h ГП ). The complex of aerodynamic characteristics is determined with the help of ANSYS software packet. To estimate the range of kinematics parameters of ANSYS applicability to solving the given problems and the reli- ability of the results the model yields, a methodical research was done based on comparing the results of the calculations with the experimental data and modelling results obtained in researches of other authors [11-13]. pendent configurations or configurations derived one from the other) (fig. 3). 2. Analysis of the aircraft aerodynamic characteristics using visualization methods and mathematical modelling of its aerodynamics by means of data processing, calcula- tion of secondary aerodynamic characteristics and deriva- tive aerodynamic coefficients within the given working process [1]. 3. Stating the succession of calculations and initial data (fig. 4.) The program allows to calculate and make mathematical experiments both within the program and using other external software (for example, an optimiza- tion program packet). 4. Analysis of modelling results based on multi-variant presentation of results in numerical terms along with visualization methods, including the analysis of separate configuration components within the range of generalized results (for example, within stability criteria values). Methods and results of longitudinal stability esti- mation. The subject of research is a non-standard WIG vehicle configuration. The given configuration is of two load-carrying surfaces mounted one behind the other in a tandem (fig. 5). The front wing - trapezoidal, swept at the leading edge, flat, of a relatively thing section - makes a small rigging angle of incidence with the longitudinal axis of the aircraft. The back wing - with a straight leading edge, swept back at the trailing edge - has a considerable rigging angle and is of an anhedral wing angle. The back wing is dome-shaped, and its trailing edge lies in the same plane. The horizontal tail of rectangular form is mounted in this configuration with a considerable elevation as to the load-carrying system of front and back wings. ma calculation z mh calculation z Fig. 1. Block diagram of ma и mh calculation when c = const z z ya Рис. 1. Блок-схема расчета ma и mh для случая c = const z z ya Fig. 2. Aerobatic 1.0 starting window Рис. 2. Стартовое окно программы Aerobatic 1.0 Fig. 3. Window of the analyzed object choice Рис. 3. Окно выбора объекта исследования Fig. 4. The main processing window for calculation and feeding the initial data 845 Рис. 4. Основное управляющее окно порядка выполнения расчетов и задания исходных данных It should be noted that ma и h parameters for the z m z set configuration are determined by the flight parameters and the center of mass location. Here the character of de- pendence of longitudinal moment coefficient on the angle of attack mz (a) and distance mz (h ) differs qualitatively (fig. 6, 7). We can conclude that the sign of the derivative ma in case c = const is specifically determined by the the necessity of implementation of both conditions. The given setting can be used as an instrument of modelling quality control and is illustrated by the data of fig. 9. However, the application of stability criteria (2) at dis- tances greater than 1 (at distances of low wing-in-ground effect influence on WIG vehicle aerodynamic characteris- tics) doesn’t correspond to the results of using the simplified approach based on the stability criterion z ya o rder of mz (a) variation in “corr ection” of the distance ma < 0 . z The representation of the static stability conditions h . “Correction” of the distance h is determined by the in the form [5] is more informative from the point of view necessity to keep cya = const when changing the angle of WIG vehicle aerodynamic configuration analysis: of attack α. The increase of the angle of attack α (increase xFh - xFa < 0 , (3) of cya ) demands the corresponding increase of the dis- tance h (decrease of c ). This setting can be illustrated where xFh , xFa are the angle-of-attack and distance foci ya by the following example (fig. 8). Setting the lift coeffi- cient cya = 0.56 (the diagram above) results in the longicoordinates. The results of basic configuration modelling of the load-carrying system are shown in fig. 10. It is obvious tudinal moment coefficient mz increase with the angle of that the location of the distance focus xFh doesn’t depend attack α increase (the diagram below). This can be ex- on the center of mass location. The location of the angleplained by the fact that the increase rate of mz due to the of-attack focus xFa considerably depends on the center of unavoidable “correction” of distance h (its increase) is higher than the decrease rate of mz due to the increase of the angle of attack α. For the example given mz (a) > 0 , mass location, as it is the WIG vehicle rotation point. The rotation point location determines the WIG vehicle atti- tude to the underlying surface when the angle of attack (and the aerodynamic characteristics) are changed. In a that means that the WIG vehicle is statically unstable in certain sense, the model data bring to conclusion that the longitudinal motion when cya = 0.56 . The results of the modelling outline the static stability and instability ranges of WIG vehicle (fig. 9). The range of parameters within which the stability of WIG vehicle can be sustained is limited both by extreme aft and for- ward center-of-gravity position. Stability is provided within a narrow range of center-of-gravity and flight pa- rameters. Application of stability criteria in the form (2), considering that the implementation of one of the conditions - ma < 0 or mh < 0 - is enough, logically results in WIG vehicle’s center-of gravity location control does not allow effective influence on the aircraft stability in longitudinal motion and specifically on the range of stable modes of flight. However, the position of the center of mass can have a significant effect on the range of WIG vehicle static stability in respect to the angle of attack, which in turn determines the parameters of the aircraft perturbed motion. z z Fig. 5. General configuration in cross-section Рис. 5. Общий вид компоновки в плане Fig. 6. Dependence of longitudinal moment coefficient on the angle of attack mz (a) for varied distances h (extreme forward center - of-gravity) Рис. 6. Зависимость коэффициента продольного момента от угла атаки mz (a) для различных отстояний h (центровка - предельно передняя) Fig. 7. Dependence of longitudinal moment coefficient mz (h ) on the distance h for varied angles of attack α (extreme forward center - of-gravity) Рис. 7. Зависимость коэффициента продольного момента mz (h ) от отстояния h для различных углов атаки α (центровка - предельно передняя) Conclusion. It is obvious that the analysis of the WIG vehicle longitudinal static stability alone based on the criterial approach has a rather conventional practical significance for several reasons. First, the problem of determining the best (optimal, rational, etc.) relative position of the center of mass, foci of the angle of attack and distance, even when the requirements of static stability are fulfilled, remains a subject of investigation and of scientific publications’ argument (examples in [8-10]. Second, perturbed motion of WIG vehicle with the relatively intensive change of distance and, accord- ingly, change of aerodynamic characteristics and parame- ters, including static stability (fig. 10) result in the neces- sity of solving the stability evaluation problem using simulation models of WIG vehicle flight dynamics with reference to non-stationary constituents of aerodynamic characteristics [14]. Third, we have to point out that pres- ently the paradigm of WIG vehicle flight control in ground-effect mode is in itself the subject of research and argument, also including the performance of automatic control and stability control systems [15]. As an example, there are attempts to find the proof for the concept of con- trolling WIG vehicle flight altitude by changing its velocity. As a rule, here every specified altitude of WIG vehicle’s flight corresponds to a certain horizontal flight velocity (in the absence of active control of the angle of attack and, consequently, on condition that cya = const ). Nevertheless, the offered methodology, software, and the corresponding modelling results allow to evaluate the WIG vehicle static stability even at the stage of prelimi- nary design plan, to outline the range of applicable con- struction and configuration factors. Fig. 8. The example of the derivative m a calculation when cy = const z a Рис. 8. Пример расчета производной m a для случая cy = const z a Fig. 9. Areas of longitudinal static instability (dark grey) with respect to criteria cya =cya ГП < 0 and cya =cya ГП < 0 (above) and dmz < 0 and d a dmz < 0 dh in the distance and relative center-of-mass location coordinates Рис. 9. Области продольной статической неустойчивости (обозначены темным цветом) по критериям cya =cya ГП < 0 и cya =cya ГП < 0 (верхние графики) и dmz < 0 и d a dmz < 0 dh в координатах отстояния и относительного положения центра масс Fig. 10. Dependence of the distance foci locations xFh and of the angle of attack xF a on the distance h and the center of mass location XT = 1.69673 : 1 - XT = 0.7653; 2 - XT = 0.99803; 3 - XT = 1.2313; 4 - XT = 1.46403; 5 - XT = 1.69673; 6 - XT = 1.9293 Рис. 10. Зависимость положений фокусов по отстоянию xFh и углу атаки xF a от отстояния h и положения центра масс XT = 1,69673 : 1 - XT = 0,7653; 2 - XT = 0,99803; 3 - XT = 1,2313; 4 - XT = 1,46403; 5 - XT = 1,69673; 6 - XT = 1,9293

About the authors

J. F. Vshivkov

Irkutsk State University

1, Karl Marx Str., Irkutsk, 664003, Russian Federation

S. M. Krivel

Irkutsk State University

Email: krivel66@mail.ru
1, Karl Marx Str., Irkutsk, 664003, Russian Federation

References

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