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: This paper describes the firing rig test of the solid rocket motor, fastened to the rig in order to measure the thrust level. It is shown that when the motor enters the steady-state mode, the rig with solid rocket motor starts experiencing mechanical oscillations due to the sudden thrust build-up. Motion of the oscillating system is studied under the impact of the linearly or suddenly increasing impulse load. Mechanical oscillations damping is considered on the basis of the viscous friction model. Procedure of the analytical modeling of the damped oscillations is suggested for the complex pattern of the loading variations, based on the fundamental principle of superposition, according to which the motor displacement during the oscillating motion is considered as sum of displacements due to the impact of the impulsive, sudden and linearly increasing loadings. This procedure simulates different time variations of thrust as motor enters the steady-state mode. Oscillating motion with parameters of the oscillating system and thrust change with time option have been simulated as they were realized during the firing rig tests of one of the solid rocket motors. Simulated and experimental (thrust sensor readings) curves of the elastic force were compared, which showed the qualitative and quantitative conformity of the suggested model of oscillations to the actual oscillations of the solid rocket motor, installed in the rig during the firing rig test. Values of the initial thrust, initial impulse and other simulation parameters were updated, adjusting the simulated curve of the elastic force to the experimental one. It was concluded that simulation of the elastic oscillations of the solid rocket motor in the rig using the suggested analytical model will enable more reliable definition of the initial thrust of the motor and its time behavior, impulse loading due to the separation of the plug and used elements that separate with it. Application of the suggested procedure of motor oscillations simulation in the phase of rig design will enable more detailed prediction of the occurring processes as well as the estimation of parameters of the individual elements, units and rig as a whole.

Annotation: When accomplishing the task of spacecraft orbital injection, the necessity arises of main engine multiple ignitions and consequently, long pauses between the ignitions are possible. As the propellant during pauses between ignitions is in the conditions of practically full absence of gravitation and can freely move over entire tank volume taking practically any spatial position, to ensure main engine guaranteed ignition the necessity arises to move the propellant into pre-start position. The propellant is moved to the supply lines by way of creating longitudinal acceleration which is done using inertial continuity ensuring means (thrusters). The time of full liquid displacement from one position into another is the most important parameter having an impact on propellant amount in the tanks and accordingly, on power characteristics of a stage. The theoretical calculations of hydrodynamic processes are connected with considerable mathematical difficulties caused by complexity of solving hydrodynamic problems of determination of liquid flowing with free surface taking into account surface tension of the liquid and many other geometrical, kinematic, and dynamic factors. Therefore, the most reliable data from solving these problems are currently obtained only on model hydrodynamic stands where it is possible to model liquid behavior in tanks in the conditions of variable gravitation. The paper presents the authors-developed procedure of calculating the full time required for propellant components deposition during rocket’s apogee stage flight and the procedure of selecting the modeling parameters (scale, time, and acсeleration) to ensure development testing in the conditions of limited test stand base. The use of the proposed procedure allows (in initial phase of launch vehicle development) determining the full time required to perform deposition with sufficient accuracy and thus optimizing the propellant mass required for operation of inertial continuity ensuring system, which in its turn, will allow increasing the payload mass to be injected.