Annotation: The main solid rocket motors of surface-to-air missiles and some short-range missiles have, as a rule, two operation modes – starting (augmented rating) and cruise (with decreased propellant consumption level). The methods to calculate intraballistic characteristics of such motors have a number of peculiarities, which set them apart from the methods of determining the characteristics of motors with constant propellant consumption level. The purpose of this article is to analyze such peculiarities, design methods, to find interrelation between the parameters of propellant consumption diagram, to determine the impact on the latter of motor design features and propellant characteristics. To achieve this goal, the method of analytical dependencies was developed. The equations obtained show that the required parameters of diagrams (including consumption-thrust characteristics difference between the starting and cruise modes) can be ensured due to varying either case diameter or propellant combustion rate or due to combined variation of these values. In practice, the cases are possible when for some reasons it does not seem possible to vary the case diameter or propellant combustion rate and the requirements to consumption diagram cannot be satisfied to the full extent. The task of motor developer in that case consists in determination of acceptable (alternative) propellant consumption diagrams that would be closest to required. The proposed method is based on calculation and construction of nomograms of dependencies of relative propellant consumption in cruse mode on relative time of starting leg at different propellant combustion rates and constant (required) case diameter and vice versa, at different values of case diameter and constant (available) propellant combustion rate. Using these nomograms, the rocket developer can determine the propellant consumption diagram acceptable for the rocket. In a number of cases, design limitations for separate main motor assemblies are imposed on consumption characteristic diagram that have an impact on its required parameters. The presented materials allow evaluating that impact and contain the proposals to remove it. The presented method allows quickly determining the conditions needed to fulfill required propellant combustion products consumption diagrams and in case of nonfulfillment of these conditions – allow presenting alternative options for selection of most acceptable one.

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.