Annotation: Substantiation of the research tools has been performed as a part of methodology development for the air and missile defense system. The problem under consideration is very complex due to the multifactorial nature of the research object, its qualitative variety and manifold structure, incomplete definition of the problem statement. Furthermore, the ability of modern technologies to produce different arms systems, which are capable of carrying out same class tasks, considerably increases the risk of making not the best decisions. Based on this, as well as taking into account the sharp increase in the cost of weaponry, the considered problem is classified as an optimization one that should be solved through the theory of operations research. In this theory, such task is viewed as a mathematical problem, and mathematical simulation is the basic method of research. The main types of mathematical models, their areas of application have been considered as a part of the analysis. The classification of mathematical models has been indicated according to the scale of reproduced operations, purpose, and goal orientation. Quantitative and qualitative correlation of forces has been accepted as the efficiency criterion, which determines a goal orientation of the model. The problems related to this have been shown. In particular, searching for the compromise between simplicity of the mathematical model and its adequacy to the research object is among these problems. Two of the basic approaches to principles of the military operation model construction and its assessment have been considered. The first is implemented through modeling of the combat operations. The second approach is based on the assumption that different armament types can be compared based on their contribution to the outcome of the operation, and on the possibility to assign «a weighting coefficient» named as a combat potential to each of these types. The modern level of problem solving related to this method has been shown. The reasonability of its application in the considered task, including the definition of forces correlation of the opposing parties, has been substantiated. The basic regulations of the construction concept of the required mathematical model and tools for its research have been formulated based on the analysis results: the assigned problem should be solved by analytical methods through the theory of operations research; the analytical model is the most acceptable conception of the analyzed level of the military operation; the synthesis of the model should be based on the idea of a combat potential. At the same time, it should be taken into account that the known approach to the definition of forces correlation, which uses the combat potential method, has a number of essential limitations, including the methodological ones. Therefore, within the bounds of further research, this approach requires the development both in terms of improving the reliability of the single assessment and in terms of giving the system qualities to the synthesized mathematical model.

Annotation: In the present-day rocket engineering, the liquid rocket engines with pump feed system have gained wide acceptance. As a rule, the pumps used in liquid rocket engines are screw-axifugal. The screw serves to increase pressure upstream of the axifugal wheel, thus ensuring its cavitation-free operation. The screws used in the screw-axifugal pumps of liquid rocket engines may be of two types: with constant and variable step. The screws with constant step are easier to calculate, profile and manufacture as compared to the screws with variable step. As known from the literature, the use of the screw with variable step increases power characteristics of the screw-axifugal pump. The purpose of investigation is comparative analysis of cavitation and power characteristics of the following high-speed low-consumption screw-axifugal pumps of liquid rocket engines with jointed screws, screws of constant and variable step:  RD868 engine oxidizer and fuel pumps;  RD859 engine fuel pumps;  RD861K engine fuel pumps. Besides, the analysis has been made of the impact of design features and geometrical dimensions of the screws with variable and constant step on power characteristics of the screw-axifugal high-speed lowconsumption pumps of liquid rocket engines. Special attention has been given to the analysis of anticavitation properties of the pumps with screws of variable step and pumps with jointed screws. Based on the results of investigation, it has been ascertained that when using the joint screws and screws with variable step instead of the screws with constant step in the high-speed low-consumption screw-axifugal pumps of liquid rocket engines, the pump delivery head increases from 0.65 to 3.83%, the efficiency increases up to 1.7%. The use of jointed screw and screw of variable step as compared with the screw of constant step does not have any impact on cavitation properties of low-consumption crew-axifugal pumps of liquid rocket engines.