Rocket Flight Research Articles

A functional fluorine (F)-containing oxidiser of nano-networked NH4CuF3 to improve the combustion efficiency of Al powder

Aluminium (Al) powder is the most common solid fuel component in metastable intermolecular composites (MICs). It is used in the field of propellants to provide energy for the flight of rockets and missiles. However, the passivation layer overlaying its surface hinders its energy release. Using fluorine (F)-containing oxidisers may etch the passivation layer, enabling Al to achieve a more direct redox process and improving its energy-release capacity. Herein, NH4CuF3, which has nano-network structure, was synthesised through the solvo-thermal method, and n-Al was filled into the nano-pore channels using a simple ultrasonic mixing method to form a new n-Al/NH4CuF3 MICs with excellent dispersion and interfacial contact. The thermal decomposition process of NH4CuF3 was investigated, and the results showed that NH4CuF3 could release hydrogen fluoride (HF) and ammonia (NH3) gaseous products. The passivation layer on the surface of the Al powder was etched by HF, and the abundance of gaseous products during the reaction of n-Al/NH4CuF3 Extended the combustion region. This can enhance air capture in the reaction system, minimise reaction sintering and aid in performing external work. Furthermore, n-Al/NH4CuF3 exhibits a lower onset reaction temperature, shorter ignition delay time and greater external work ability than n-Al/CuF2 and n-Al/CuO.

Ballistic Fitting Impact Point Prediction Based on Improved Crayfish Optimization Algorithm

To solve the problem of difficulty in predicting the impact point clearly and promptly during projectile flight, this paper proposes an improved ballistic-impact-point prediction method. A certain type of high-spinning tailed projectile is taken as the research object for online real-time landing point prediction research. This study comprehensively utilizes the real-time radar measurement data and the geomagnetic data measured by the bomb-carried geomagnetic sensor. It applies the four-degree-of-freedom ballistic model to predict the landing point. First, the roll angular velocity is calculated based on the geomagnetic data, after which the radar real-time measurement data are segmentally fitted using the improved crayfish algorithm. Then, the fitted parameters are substituted into the four-degree-of-freedom ballistic model. Finally, the C-K method is used to identify the aerodynamic parameters, and the identified aerodynamic parameters are used for fallout prediction. The simulation results show a small deviation between the predicted and actual impact points using the improved ballistic-impact-point prediction method.

MicroGravity Explorer Kit (MGX): An Open-Source Platform for Accessible Space Science Experiments

The study of microgravity, a condition in which an object experiences near-zero weight, is a critical area of research with far-reaching implications for various scientific disciplines. Microgravity allows scientists to investigate fundamental physical phenomena influenced by Earth’s gravitational forces, opening up new possibilities in fields such as materials science, fluid dynamics, and biology. However, the complexity and cost of developing and conducting microgravity missions have historically limited the field to well-funded space agencies, universities with dedicated government funding, and large research institutions, creating a significant barrier to entry. This paper presents the MicroGravity Explorer Kit’s (MGX) design, a multifunctional platform for conducting microgravity experiments aboard suborbital rocket flights. The MGX aims to democratize access to microgravity research, making it accessible to high school students, undergraduates, and researchers. To ensure that the tool is versatile across different scenarios, the authors conducted a comprehensive literature review on microgravity experiments, and specific requirements for the MGX were established. The MGX is designed as an open-source platform that supports various experiments, reducing costs and accelerating development. The multipurpose experiment consists of a Jetson Nano computer with multiple sensors, such as inertial sensors, temperature and pressure, and two cameras with up to 4k resolution. The project also presents examples of codes for data acquisition and compression and the ability to process images and run machine learning algorithms to interpret results. The MGX seeks to promote greater participation and innovation in space sciences by simplifying the process and reducing barriers to entry. The design of a platform that can democratize access to space and research related to space sciences has the potential to lead to groundbreaking discoveries and advancements in materials science, fluid dynamics, and biology, with significant practical applications such as more efficient propulsion systems and novel materials with unique properties.

Development of the BOLT-2 Roughness Experiment for Flight

A sounding rocket research flight called BOLT-2, which stands for Boundary Layer Turbulence 2, was initiated with the goal of studying hypersonic boundary-layer transition and turbulence. The BOLT-2 research vehicle is based on a three-dimensional geometry with concave surfaces and swept leading edges that provides two separate and distinct, also redundant, flowpaths for conducting measurements. One side of BOLT-2 is dedicated to smooth surface transition and turbulence, to better study the natural instability processes, whereas the other has been assigned to study forced transition and turbulence using discrete roughness trips. The present paper is intended to document the primary drivers and decisions made that lead up to finalizing the roughness-side experiment for the BOLT-2 flight.

Study of the payload extraction trajectory heavy class carrier rocket

Relevance. As the weight and complexity of the payload that needs to be launched into orbit increases, the relevance of rational trajectory selection to ensure maximum efficiency and minimum costs for delivering the payload to a given orbit increases. Rational choice of the trajectory of a heavy-class launch vehicle has a number of important practical applications. Firstly, it allows you to increase the payload capacity of the launch vehicle and reduce the cost of delivering payload to the target orbit. This is especially important in the context of the development of the space industry, when more and more companies and organizations are showing interest in launching their own satellites and other spacecraft in conditions of fierce economic competition. Choosing a rational trajectory for launching a payload into orbit will significantly reduce the cost of launches and make them available to a wider range of potential customers. Secondly, the choice of launch vehicle trajectory parameters is important for ensuring safety and minimizing risks during spacecraft launches. Thanks to the rational choice of trajectory, it is possible to reduce adverse impacts on the environment and eliminate the possibility of emergency situations associated with loss of control over the flight of the launch vehicle. Rational selection of launch vehicle trajectory parameters is a complex task that requires comprehensive research and consideration of various factors, such as aerodynamic parameters of the atmosphere, mass and characteristics of the payload (spacecraft), engine operating parameters, characteristics of the target orbit, features of the launch of the launch vehicle and many other factors. A more thorough and systematic study of the influence of these parameters will significantly improve the efficiency and reliability of launching spacecraft into orbit. Thus, the choice of rational parameters for the launch vehicle trajectory is a relevant and important topic for scientific research. Increasing the rocket's payload capacity, reducing the cost of delivering a spacecraft to a given orbit, and ensuring launch safety are tasks that depend on the chosen shape and parameters of the rocket's trajectory. Such research has important practical significance and can become the basis for the development of new technologies and methods in the space industry. The purpose of the study is to study and select rational parameters for the trajectory of a heavy-class launch vehicle when launching a payload. The main task is to determine the flight path parameters that will allow achieving maximum efficiency and accuracy in delivering the payload to a given orbit. To achieve the goal of the study, an analysis of various factors influencing the launch parameters of the spacecraft is required, such as the structural and aerodynamic characteristics of the rocket, the influence of aerodynamic factors and the Earth’s gravitational field on the flight path. Taking these factors into account, numerical calculations were carried out on the basis of a system of differential equations of motion using a computer program created in the MAPLE software package. Based on calculations, modeling of the shape and parameters of the launch vehicle flight path was carried out. Research results. During the study, the rational parameters of the trajectory of a heavy-class launch vehicle were selected. Calculations were carried out using numerical modeling of the parameters of payload launch trajectories, and an analysis of the resulting trajectories was carried out. Minimizing the rocket's flight time was identified as the main criterion for the rational choice of trajectory, which allows increasing launch efficiency and saving energy resources. An increase in payload mass and minimization of fuel consumption were adopted as additional criteria. Conclusion. The procedure for choosing rational parameters for the trajectory of a heavy-class launch vehicle proposed in this work will improve the delivery accuracy and reliability of spacecraft launches at the stage of ballistic analysis when designing rockets. The results of the study have practical significance for the development of future heavy-duty launch vehicle missions and improving the efficiency of space launches.

Моделювання інжекції газу в надзвукову частину сопла при газодинамічному регу-люванні вектора тяги

Solid-propellant rocket engines are simple in design, highly reliable, and able to store the propellant for a long time without its degradation. Their main feature is that the propellant is a mixture of a solid fuel and a solid oxidizer, thus ensuring a uniform combustion and a stable discharge of the combustion products. However, the combustion rate cannot be controlled, and the combustion cannot be stopped or restarted. This calls for efficient methods of thrust vector control. Gas-dynamic methods, such as a gas injection into the supersonic nozzle area, offer a required flight path control without complex high-power mechanical systems. The importance of this study lies in improving the accuracy and efficiency of rocket flight control, which is critical for today’s space and defense tasks. The numerical simulation of gas-dynamic control systems, in particular by an asymmetric gas injection, allows one to obtain detailed data on the flow behavior and optimize the design and operating conditions of the system. This study is concerned with a full-scale solid-propellant rocket engine with a gas-dynamic thrust vector control system based on the use of asymmetric forces that occur on the nozzle wall when the supersonic flow interacts with the injected transverse jets. To simulate the process in the Ansys Fluent software package, a geometric model of a nozzle with an asymmetric injection of the chamber gas into the supersonic area was developed. The injection flow rate was controlled by moving the valve flap. The simulation was carried out taking into account the temperature dependence of the main thermophysical gas parameters with consideration for dissociation processes by way of data approximation. The approximation was performed using piecewise polynomial functions. Nozzle flow patterns were obtained. The calculated results were compared with experimental test data and shown to be in satisfactory agreement with the lateral force measured during the fire bench tests of the prototype. From a practical point of view, the results obtained may be directly used to improve existing thrust vector control systems and develop new ones. This will improve rocket navigation accuracy, flight stability, and maneuverability, which is critical for complex space and defense tasks.

Rolling active load relief technology for launch vehicle bundled with common booster core in face

The aerodynamic interference forces and moments of different windward surfaces of a launch vehicle bundled with a common booster core in the face vary considerably. The servo mechanism is laid out to maximize the control capability of the rocket at a certain angle. The dominant surface of the rocket is determined by aerodynamic interference and control capability. For the problem of large interference and asymmetry during the flight of a nominal rocket, a rolling active load relief control law based on the optimization of the spatial interference vector is proposed. The direction with the largest spatial interference vector is obtained online by visual acceleration information. By adjusting the rolling program angle, the rocket will align the dominant face with the direction of the largest interference when flying through the windy area. And then, the rocket obtains a good control effect. The simulation results show that the control law proposed in this paper can effectively improve the adaptability of the rocket control in the case of sudden changes in wind direction. It achieves the purpose of reducing the static load of the rocket body structure during the flight.

Hypergravity Impact on Fertility of Apis mellifera carnica Queens – Case Study

The launch is considered the most stressful rocket flight stage due to the hypergravity occurrences. The possibility of using honey bees (Apis mellifera) as the extraterrestrial pollinator depends on their ability to reproduce correctly after experiencing hypergravity. The described study aims to verify the impact of a launching rocket’s acceleration on honey bee queen’s egg-laying behavior. Four artificially inseminated A. mellifera carnica queens were placed in the Human Training Centrifuge and given to the acceleration pattern of the launching Soyuz rocket. Next, the data on the number of food stores, eggs, larvae, and worker and drone pupae were collected from the test and control hives using the modified Liebefeld method. The pilot study results imply that accelerated queen’s egg-laying behavior may change twofold: limiting or maximizing the number of laid eggs, with the control queen egg-laying rate remaining stable for all samples. The number of drone pupae is greater for the test sample colonies, with its earlier appearance in the hive. No impact on overwintering success was observed. Authors indicate limitations of the results and a need to continue the study to verify the occurrence of anomalies potentially related to the examined factor.

Effects of microgravity on neural crest stem cells.

Exposure to microgravity (μg) results in a range of systemic changes in the organism, but may also have beneficial cellular effects. In a previous study we detected increased proliferation capacity and upregulation of genes related to proliferation and survival in boundary cap neural crest stem cells (BC) after MASER14 sounding rocket flight compared to ground-based controls. However, whether these changes were due to μg or hypergravity was not clarified. In the current MASER15 experiment BCs were exposed simultaneously to μg and 1 g conditions provided by an onboard centrifuge. BCs exposed to μg displayed a markedly increased proliferation capacity compared to 1 g on board controls, and genetic analysis of BCs harvested 5 h after flight revealed an upregulation, specifically in μg-exposed BCs, of Zfp462 transcription factor, a key regulator of cell pluripotency and neuronal fate. This was associated with alterations in exosome microRNA content between μg and 1 g exposed MASER15 specimens. Since the specimens from MASER14 were obtained for analysis with 1 week's delay, we examined whether gene expression and exosome content were different compared to the current MASER15 experiments, in which specimens were harvested 5 h after flight. The overall pattern of gene expression was different and Zfp462 expression was down-regulated in MASER14 BC μg compared to directly harvested specimens (MASER15). MicroRNA exosome content was markedly altered in medium harvested with delay compared to directly collected samples. In conclusion, our analysis indicates that even short exposure to μg alters gene expression, leading to increased BC capacity for proliferation and survival, lasting for a long time after μg exposure. With delayed harvest of specimens, a situation which may occur due to special post-flight circumstances, the exosome microRNA content is modified compared to fast specimen harvest, and the direct effects from μg exposure may be partially attenuated, whereas other effects can last for a long time after return to ground conditions.

A spectacular demonstration of energy transformation in an internal combustion engine

The structure and operating principle of a four-stroke internal combustion engine are usually demonstrated using the cut-away model of an internal combustion engine or its computer animation. However, by observing the operation of the engine mechanism, the understanding of the main essence, which consists of the transformation of thermal energy from the combustion of gasoline into the mechanical energy of the piston movement is lost. This work describes the demonstration of the ignition and combustion of the fuel mixture and the transformation of thermal energy generated by the combustion of gasoline into the mechanical energy of the piston. A paper rocket is used instead of a piston for the spectacle of the experiment. This demonstration does not leave anyone from the audience indifferent. The dependence of rocket flight height on the mass of burned gasoline was established.

Effects of microgravity and reduced atmospheric pressure on manufacturing photopolymer specimens

In-space manufacturing especially for external satellite structures has a huge potential to increase the packaging density of a satellite in launch configuration and enables large structures for advanced mission requirements. However, the processes and materials do have to withstand the harsh environmental conditions in space. These conditions have immediate effects on the manufacturing process as well as long-term effects on the structure manufactured in orbit. The experiments presented here are based on a photopolymer extrusion process by UV-radiation curing that is intended to be used as an in-space manufacturing technology. In order to understand the influence of reduced atmospheric pressure and microgravity on the process, we demonstrated the successful extrusion and curing of rod-shaped elements during a sounding rocket flight. Simultaneously, the same experiment was performed on the ground under normal gravity and ambient pressure. By comparing both groups of specimens, it was shown that the morphological artifacts and geometric deviations are more significant for the specimens manufactured during flight. This evaluation was performed by visual inspection, by comparison of the laser-scanned specimens with a reference model and by measuring and comparing the mass, length and diameter of the specimens. On a microscopic level, conducted by computer tomography, no influence of the reduced atmospheric pressure on the extrusion of the liquid photopolymer can be recognized as this was probably not low enough at the altitude reached by the rocket. As a result of this article, measures are proposed to avoid the morphological artifacts observed during the experiments and thus achieve higher accuracy and a resilient in-space manufacturing process.

Numerical–experimental study on the stability mechanism of tail slapping motion of supercavitation projectile

Tail slapping is considered to be a prominent mode for facilitating the movement of supercavitating projectiles underwater. Stability mechanism of the tail slapping and stability criterion of projectiles was numerically investigated in this paper. A numerical method was conducted to calculate the free flight of projectiles by combining the finite volume method, the mixture multiphase model, and a dynamic meshing scheme. The accuracy and applicability of the numerical calculation method are verified by experiments. Three typical stability modes of tail slapping motion, namely, stable, conditionally stable, and unstable, were identified through the free flight numerical simulations of projectiles with varying length-to-diameter ratios under different initial angular velocities. The stability criterion of projectiles was proposed, indicating that the tail slapping stability can be determined by analyzing the curve of the moment variation with the angle of attack at any velocity above 200 m/s. Furthermore, it was found that the stable projectiles possess inherent motion states that are exclusively determined by their structural features and are unaffected by the initial motion conditions.

Measurement model and accuracy analysis of parabolic ballistic projectile flight parameters based on random matrix

Measurement model and accuracy analysis of parabolic ballistic projectile flight parameters based on random matrix

Mathematical Model of Impact Projectile Flight Dynamics as an Element of its Digital Twin

This paper gives the analysis of the structure and characteristics of the mathematical model of the impact projectile’s flight dynamics. The model is designed for being used as an element of the projectile’s digital twin. The model is based on differential motion equations of a gyro-stabilized solid with an axisymmetric mass distribution. Different types of angle variables were chosen for describing aerodynamics and formulating equations of motion. Non-linear (considering the nutation angle) dependences for aerodynamic coefficients are proposed. They are created by applying proven scientific concepts and research methods in aerodynamics of axisymmetric body and by comparing with known numerical and experimental results obtained in exterior ballistics of gyro-stabilized aviation and artillery projectiles. Special aspects of initial conditions for angles and angular velocity were also studied. Since the impact projectile is considered as an axially symmetric body, its self-rotation angle is not of practical inte rest. Using algebraic manipulations, the differential equation for this angle was eliminated from the set of equations. This has made it possible to significantly reduce stiff of the remaining system of differential equations. The Dormand-Prince method is recommended as a method of numerical integration. The method of the eight-order (with seventh-order uncertainty estimate) allows getting the high accurate solution of the differential equations set under relatively small computing costs. The model allows computing the projectile trajectory under various initial conditions, including the flight with high nutation angles up to 87°—89°. As a result, there is a possibility to determine the nature of the interaction between impact projectiles and typical targets (ricochet, surface effect, after-penetration effect) within a wide range of approach angles to the target’s surface (skin) unattainable during the full-scale tests. The possibility of solving similar problems allows to recommend the designed model as an element of the impact projectile’s digital twin intended for testing its exterior ballistics on the digital (virtual) test range. All testing calculations and final modeling were made by using the "GNU Octave" computational software package.

СИЛА ТА МОМЕНТ СИЛИ МАГНУСА. ЇХ ВПЛИВ НА ДАЛЬНІСТЬ СТРІЛЬБИ 155-ММ СНАРЯДІВ

An important component of the main vector of aerodynamic forces and moments of the projectile is the force and moment from the Magnus force, which significantly affect the dynamics of the projectile flight. At the same time, the influence of the Magnus force and moment on the flight of projectiles has been studied relatively little, in addition, the leading scientists of Ballistic Research Laboratories (USA) published quantitative indicators achieved during its calculations, which do not fully meet the requirements for the accuracy of their determination. It is shown that the Magnus force and moment depend on the density of the air, the angular velocity of rotation and the velocity of the projectile, the lateral surface and diameter of the projectile, as well as the angle of its nutation. To evaluate the influence of the Magnus force and moment (their aerodynamic coefficients) on the range of the projectile, a difference method is used, which consists in solving the system of differential equations of spatial motion of a projectile so that changing the value of the aerodynamic coefficient results in a change in the value of the flight range. Numerical modeling of the dependence of the flight range of the 155-mm PF Assegai M2000 projectile and the 155-mm PF ERFB/BB projectile on the change in the magnitude of aerodynamic force and Magnus moment coefficients by 1 % was carried out. It is shown that the aerodynamic force coefficient of Magnus creates the largest errors in the range at the minimum charge, the deviation reaches – 0,005 %, the smallest at the maximum charge – 0,003 %. The largest error in the flight range of the projectile from the aerodynamic coefficient of the Magnus moment is observed at the minimum charge, the deviation reaches 0,6 % D; the effect on other charges leads to much smaller deviations, which are 1-3 orders of magnitude smaller compared to the minimum charge. The obtained results provide an opportunity to assess the required accuracy of determining the aerodynamic coefficients of the Magnus force and the moment of the Magnus force under different conditions of firing by artillery systems.

С этой ракеты начинался наш путь в «Тополиную рощу» (о проведении летных испытаний межконтинентальной баллистической ракеты РТ-2 на полигоне «Плесецк»)

In the first half of the 1960s, Special Design Bureau No. 1 created the RT-2 intercontinental ballistic missile. The use of the new missile in the Strategic Missile Forces was supposed to be part of the Separate Start type missile system. It was meant to be a worthy response to the American Minutemen. For the RT-2 rocket flight development tests, an experimental test base (technical and launch positions, command-measuring and computing complexes) and infrastructure facilities (roads, bridges) were created, fall fields and target fields were prepared, testing military units were formed, and personnel was trained. In 1966-68, flight tests of the RT-2 rocket were carried out as part of the 15P098 missile system. Although the RT-2 missile did not match the American Minutemen in terms of shooting accuracy and throw-weight, it was put into service and its modified version was on combat duty until 1994. The RT-2 became the first domestic solid-fuel intercontinental ballistic missile. An original layout and a new control system allowed it to “almost catch up” with the characteristics of Minuteman-2 and created the prerequisites for its further modernization. An excellent silo launcher, the best command post at that time, the first remote control and monitoring systems, and a small number of maintenance personnel made the system with these missiles one of the best in the Strategic Missile Forces at the beginning of the 1970s. The purpose of this article is to summarize information about the flight development tests of the RT-2 missile at the 53rd Research Test Site of the USSR Ministry of Defense (Mirny, Arkhangelsk Region). To achieve it, in addition to official documents and technical documentation, the author used information from the archives of testing military units and memories of participants in the events.

ВПЛИВ ПОЛЯРНОГО ТА ЕКВАТОРІАЛЬНОГО ДЕМПФУЮЧИХ МОМЕНТІВ СНАРЯДА НА ДАЛЬНІСТЬ ЙОГО ПОЛЬОТУ

A relevant and important issue in the calculation of projectile flight trajectories is the definition and presentation of the equatorial and polar damping moments in the system of differential equations of spatial motion of projectiles. It is shown that the damping moments are determined by the shape and orientation of the projectile, the nature of the flow, the type of boundary layer and its interaction with shock waves, the speed, the height of the projectile and its nutation angle. To evaluate the influence of the aerodynamic coefficients of the equatorial and polar damping moments (their aerodynamic coefficients) on the flight range of the projectile, the method of differences is used, which consists in solving the system of differential equations of the spatial motion of the projectile so that changing the value of the aerodynamic coefficient results in a change in the flight range. Numerical modeling of the dependence of the flight range of the 155-mm HE Assegai M2000 projectile on the change in the aerodynamic coefficients of the equatorial and polar damping moments by 1% was carried out. It is shown that the aerodynamic coefficient of the polar damping moment creates the largest errors in the range at the maximum and minimum charges, namely, at the maximum charge the error reaches 0.012%D, at the minimum charge – 0.01%D, the effect on intermediate charges is manifested in a much smaller form, and not exceeds the value of 0.005%D. The largest error in the flight range of the projectile from the aerodynamic coefficient of the equatorial damping moment is observed at the maximum charge, the deviation reaches 0.07%D, the smallest error at the minimum charge is 0.0001%D. The obtained results make it possible to estimate the required accuracy of determining the aerodynamic coefficients of the equatorial and polar damping moments under different firing conditions of artillery systems.

Weight optimization of 200 mm diameter rocket motor tube using finite element method

The lightweight design of the rocket motor tube is a critical requirement for enhancing the rocket's flight performance. This study assesses the impact of wall thickness, cap thickness, and fillet radius on structural strength and the optimization of rocket motor tube weight using the finite element method with the assistance of Ansys software. A total of 12 finite element model variations, utilizing Aluminium 6061-T6, were developed and subjected to a uniform internal operating pressure load of 10 MPa. The design includes wall thickness variations of 8 and 10 mm, cap thickness options of 25 and 30 mm, and fillet radius dimensions of 20, 25, and 30 mm, allowing for a comprehensive comparison to achieve the required minimum safety factor while minimizing structural weight. The research concludes that increasing the fillet radius is a more recommended approach compared to increasing wall thickness and cap thickness. The results indicate that Model 9, with wall thickness, cap thickness, and fillet radius dimensions of 10 mm, 25 mm, and 30 mm, respectively, is the optimal choice due to its lightweight construction.

Behavior of glioblastoma brain tumor stem cells following a suborbital rocket flight: reaching the “edge” of outer space

The emerging arena of space exploration has created opportunities to study cancer cell biology in the environments of microgravity and hypergravity. Studying cellular behavior in altered gravity conditions has allowed researchers to make observations of cell function that would otherwise remain unnoticed. The patient-derived QNS108 brain tumor initiating cell line (BTIC), isolated from glioblastoma (GBM) tissue, was launched on a suborbital, parabolic rocket flight conducted by EXOS Aerospace Systems & Technologies. All biologicals and appropriate ground controls were secured post-launch and transported back to our research facility. Cells from the rocket-flight and ground-based controls were isolated from the culture containers and expanded on adherent flasks for two weeks. In vitro migration, proliferation, and stemness assays were performed. Following cell expansion, male nude mice were intracranially injected with either ground-control (GC) or rocket-flight (RF) exposed cells to assess tumorigenic capacity (n = 5 per group). Patient-derived QNS108 BTICs exposed to RF displayed more aggressive tumor growth than the GC cells in vitro and in vivo. RF cells showed significantly higher migration (p < 0.0000) and stemness profiles (p < 0.01) when compared to GC cells. Further, RF cells, when implanted in vivo in the brain of rodents had larger tumor-associated cystic growth areas (p = 0.00029) and decreased survival (p = 0.0172) as compared to those animals that had GC cells implanted.

VERIFICATION OF THE MATHEMATICAL FLIGHT MODEL THE PROJECTILE AS A MODIFIED MODEL OF THE MATERIAL POINT

The analysis of mathematical models of the flight of projectiles has been carried out, it is shown that the nature of their provision varies depending on the degree of reliability of the representation of the real physical process of its flight by a mathematical model, the adequate consideration of certain forces (moments) acting on the projectile, as well as the level of information about external flight conditions. In the simplest mathematical model with three degrees of freedom, the projectile is considered as a material point that moves in the atmosphere under the influence of gravity and full aerodynamic force. The dynamics of projectile flight is most completely described by the mathematical model of the movement of a solid body with six degrees of freedom. In the intermediate model with four degrees of freedom, all aerodynamic forces are taken into account, the orientation of the projectile is characterized by taking into account the angle of nutation, and the kinetic energy of the rotational movement is taken into account through the angular velocity of the projectile around its axis of symmetry. The process of restori ng the coefficients of aerodynamic forces using the material point model does not provide the necessary accuracy and adequacy of the description of the projectile flight process; of the modified material point model is much simpler (the least complex) compared to the model of the motion of a rigid body with six degrees of freedom due to the smaller number of coefficients and differential equations included in its composition. The differential equations of the modified material point model are provided - the equation of motion of the center of mass and the equation of nutational oscillations of the projectile in scalar form; an assessment of its accuracy (adequacy) was carried out on the example of the 155-mm PF projectile M2000, one of the family of projectiles of the company Denel Naschem – Assegai M200X Series 155-mm Projectiles. A comparison of the characteristics of the 155-mm PF of the M2000 projectile calculated according to the 6DoF model and the modified material point model showed their high convergence; the error does not exceed 1%. Keywords: aerodynamic forces (moments), projectile, mathematical models, modified model, aerodynamic coefficients, simulation, accuracy, flight parameters.