Annotation: The scientific and methodological propositions for the designing single-stage guided missiles with the solid rocket motors for advanced multiple launch rocket systems are defined. The guided missiles of multiple launch rocket system are intended for delivering munitions to the given spatial point with required and specified kinematic motion parameters at the end of flight. The aim of the article is an analysis of the development trends of the guided missiles with the solid rocket motors for the multiple launch rocket systems, identifying the characteristics and requirements for the flight trajectories, design parameters, control programs, overall dimensions and mass characteristics, structural layout and aerodynamic schemes of missiles. The formalization of the complex task to optimize design parameters, trajectory parameters and motion control programs for the guided missiles capable of flying along the ballistic, aeroballistic or combined trajectories is given. The complex task belongs to a problem of the optimal control theory with limitations in form of equa lity, inequality and differential constraints. To simplify the problem, an approach to program forming is proposed for motion control in the form of polynomial that brings the problem of the optimal control theory to a simpler problem of nonlinear mathematical programming. When trajectory parameters were calculated the missile was regarded as a material point of variable mass and the combined equations for center-of-mass motion of the guided missile with projections on axes of the terrestrial reference system were used. The structure of the mathematical model was given along with the calculation sequence of the criterion function that was used for determination of the optimal parameters, programs and characteristics. The mathematical model of the guided missile provides adequate accuracy for design study to determine depending on the main design parameters: overall dimensions and mass characteristics of the guided missile in general and its structural comp onents and subsystems; power, thrust and consumption characteristics of the rocket motor; aerodynamic and ballistic characteristics of the guided missile. The developed methodology was tested by determining design and trajectory parameters, overall dimensions and mass characteristics, power and ballistic characteristics of two guided missiles with wings for advanced multiple launch rocket systems produced by the People’s Republic of China, using the limited amount of information available in the product catalog.

Annotation: The high demands for the flow rate and thrust characteristics specified for the modern solid-propellant rocket motors (SRM) under the strict mass and overall dimensions constraints require high level of mass fraction of propellant. And in the process of propellant grain combustion, erosive burning often takes place (increase of propellant burning rate depending on combustion products flow rate along the grain channel). This may play both negative (off-design increase of chamber pressure) and positive role (for example, increasing the launch thrust-to-weight ratio of the rocket). It is typical of the main SRMs of various rocket systems (multiple launch rocket systems, anti-aircraft guided missiles, tactical missiles, boosters). This paper proposes a methodology for calculating the internal ballistic characteristics of a solid propellant rocket motor under erosive burning, which is relatively time and resource consuming. The methodology is based on equidistant model of propellant grain combustion, where grain is divided lengthwise into a number of intervals. For any point of time during the engine operation, burning area and port area of each interval are calculated, taking into account erosive impact on each interval; total burning area is the sum of all intervals burning areas. Gas flow rate in each interval of the grain channel is calculated using gas-dynamic equations. The motor mass flow rate is a mass input sum of all the intervals; and the burning rate in each interval is estimated with proper erosion factor. The combustion chamber pressure had been calculated for four erosive burning models proposed by different authors. All the models showed convergence with the experimental SRM test data sufficient for engineering estimate (in particular, for maximum chamber pressure and combustion time). Selected as a result erosive burning model may be used to design new motors with solid propellants similar in chemical composition, and the model parameters are to be further customized using the test specimens.

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: The main scientific and methodological propositions for designing single-stage guided missiles with main solid rocket motors that are intended for delivering payload to the given spatial point with required and specified kinematic motion parameters are defined. The aim of the article is to develop methodology for the early design phase to improve the basic characteristics of guided missiles, including formalization of complex problem to optimize design parameters, trajectory parameters and motion control programs for guided missiles capable of flying along the ballistic, aeroballistic or combined trajectories. The task is defined as a problem of the optimal control theory with limitations in form of equality, inequality and differential constraints. An approach to program forming is proposed for motion control in the form of polynomial that brings the problem of the optimal control theory to a simpler problem of nonlinear mathematical programming. When trajectory parameters were calculated the missile was regarded as material point of variable mass and the combined equations for center-of-mass motion of the guided missile with projections on axes of the terrestrial reference system were used. The structure of the mathematical model was given along with the calculation sequence of criterion functional that was used for optimization of design parameters, control programs and basic characteristics of the guided missile. The mathematical model of the guided missile provides adequate accuracy for design study to determine: overall dimensions and mass characteristics of the guided missile in general and its structural components and subsystems; power, thrust and consumption characteristics of the main engine; aerodynamic and ballistic characteristics of the guided missile. The developed methodology was tested by solving design problems. Applications of the developed program were studied to present the research results in a user-friendly form.

Annotation: The main phases of formation and development of solid motor engineering are presented. The basic technical problems are considered, solution of which allowed building the main motors and dispensing motors with high performance level and highly-effective rocket systems on their basis

Annotation: In the phase of designing and developmental testing of short-range missiles with main solid rocket motors, the necessity arises of quick evaluation of propulsion system power characteristics, in particular, determination of specific thrust pulse value and scatter. The use of hypothesis of specific thrust constancy (weak dependence of vacuum thrust pulse on pressure and temperature) allows to considerably simplify the procedure of SRM specific thrust pulse evaluation, thus increasing the efficiency of SRM design calculations and the speed of test results processing, and in some cases, even to considerably reduce the test scope.