Trajectory Parameters Research Articles

Discussion on the Automatic Design Method of Well Trajectory for Cluster Well Platform

Abstract Shale oil and gas and other unconventional oil and gas resources adopt the development mode of cluster well group to achieve economic benefit development. Cluster well groups have the characteristics of small spacing between wellheads and limited space, and generally adjust trajectory parameters by designing individual artificial Wells one by one to meet the needs of geological target hitting and anti-collision and circumnavigation. Trajectory design affects the whole body, and the change of trajectory of one well causes all Wells on the same platform to readjust design parameters, which seriously affects the design efficiency. Therefore, on the basis of summarizing the experience of manual trajectory design, combining classical path planning algorithm and global planning algorithm, an automatic trajectory design model is established. A* path optimization algorithm and ant colony algorithm are used to construct the routing strategy method and rule set, and adapt the efficient manual guidance strategy for different risk classifications to achieve efficient automatic routing. A cluster well trajectory automatic design and routing module has been developed. Automatic trajectory design tested 15 platforms, with an average time of 60s. The efficiency of trajectory design was greatly improved, and it has important guiding significance for the development of automated drilling technology.

Определение оптимальных параметров воздушного потока создаваемого пневмопогрузчиком уборочно-транспортного агрегата

The design of working bodies of a harvesting and transport unit (HTU) for hay collection is considered. The HTU consists of a hay pickup, a pneumatic loader and an assembly chamber. The process of filling the chamber was investigated, and the characteristics of the pneumatic loader ensuring high-quality performance of this process were determined. The main requirement for the pneumatic loader is the ability to create and maintain technological parameters – air flow rate at a corresponding air flow velocity. An analytical expression was obtained for the trajectory of a hay mass particle at the outlet of the loader depending on the air flow velocity and the angle to the horizontal. The relationship between this velocity and the parameters of the material particle flight trajectory and the dimensions of the assembly chamber was established. The optimal parameters of the velocity of 22-25 m/s correspond to the following overall dimensions: length – 5.0 m, height – up to 4.0 m.

Phytophthora zoospores display klinokinetic behaviour in response to a chemoattractant.

Microswimmers are single-celled bodies powered by flagella. Typical examples are zoospores, dispersal agents of oomycete plant pathogens that are used to track down hosts and infect. Being motile, zoospores presumably identify infection sites using chemical cues such as sugars, alcohols and amino acids. With high-speed cameras we traced swimming trajectories of Phytophthora zoospores over time and quantified key trajectory parameters to investigate chemotactic responses. Zoospores adapt their native run-and-tumble swimming patterns in response to the amino acid glutamic acid by increasing the rate at which they turn. Simulations predict that tuneable tumble frequencies are sufficient to explain zoospore aggregation, implying positive klinokinesis. Zoospores thus exploit a retention strategy to remain at the plant surface once arriving there. Interference of G-protein mediated signalling affects swimming behaviour. Zoospores of a Phytophthora infestans G⍺-deficient mutant show higher tumbling frequencies but still respond and adapt to glutamic acid, suggesting chemoreception to be intact.

Supporting the development of climate-resilient water safety plans through a risk-screening framework for drinking water source protection

ABSTRACT Climate change-induced impacts on water-quality challenge risk management of drinking water. Uncertainty around future changes and limited resources require approaches that enable prioritisation at regional or national scale for planning and adaptive intervention. This paper presents a framework for risk screening drinking water supplies, providing a staged approach to building the capacity for integrating climate change into risk management. The framework is applied to drinking water sources of the Scottish national drinking water provider, developing raw water trajectories for indicative water-quality parameters (water colour and Escherichia coli). It establishes baseline understanding of water-quality controls through multivariate statistical analysis. It incorporates climate and land-use change into the model using climate (UKCP18) and land-use projections. The results suggest potential higher organic carbon production in soils from increased production with higher temperature, combined with reduced dilution and drought effects from reductions in summer rainfall. For E. coli, risks arise through land-use change leading to potential agricultural intensification. The framework supports the targeted development of climate-resilient Water Safety Plans, prioritising systems most at risk of raw water-quality deteriorations. It emphasises source protection to maintain or improve regulatory compliance, minimise socioeconomic and environmental harms, and generate additional benefits.

Study on robot trajectory planning and coating thickness prediction for plasma spraying on complex surface

Plasma spraying techniques are commonly employed for the deposition of thermal barrier coatings (TBCs) due to their efficiency and cost-effectiveness. However, ensuring uniform coating thickness and quality on complex free-form surfaces poses significant challenges. This paper investigates the influence of spraying trajectory and related parameters (spraying distance, angle, velocity) on coating thickness distribution, addressing the need for simplified analysis among numerous variables affecting coating quality. Different from the predominantly existing research focusing on flat or rotationally symmetric substrates, this study delves into the planning of spray trajectories for free-form surfaces, which is crucial for industries dealing with complex components, such as turbine blades. Innovative optimization approaches are employed to refine spray trajectories and improve coating consistency. Through theoretical modeling, simulation and experimental validation, the impact of spray parameters on coating thickness was demonstrated. Both the mean and disperssion coefficient errors of the coating thickness, obtained by the theoretical prediction model and the spray experiments, are lower than 10 %. The normal spray trajectory makes the coatings more evenly distributed, and the coating uniformity is at least 50 % higher than that of the codirectional spraying. This research contributes to the optimization of plasma spraying processes, particularly on irregular surfaces, thereby facilitating the development of high-performance TBCs for industrial applications.

Ideal Time to Conduct a Pharmacokinetic Investigation After Delivery to Fully Capture the Effect of Pregnancy on Drug Exposure.

The World Health Organization is pushing to accelerate the study of new human immunodeficiency virus drugs in pregnant women. However, regulatory guidelines do not specify when to conduct pharmacokinetic studies in postpartum women. This knowledge gap carries the potential to jeopardize the outcomes and conclusions of clinical trials aiming to study the effect of pregnancy on drug exposure. We used physiologically based pharmacokinetic (PBPK) modeling along with clinical data to determine the time needed after delivery for drug exposure to return to prepregnancy levels. A literature review was conducted to collect physiological parameters of pregnant and postpartum women. Regression analyses were performed to derive equations describing the parameters trajectory throughout pregnancy and post partum to inform our PBPK model. Published pharmacokinetic data in pregnant and postpartum women were used for the model verification. The PBPK model was subsequently applied to investigate pharmacokinetic changes throughout pregnancy and post partum. In agreement with the clinical data the PBPK model was able to describe the different effects of pregnancy on drug exposure, with bictegravir showing the largest reduction in exposure (approximately 50%) during the third trimester while ritonavir and raltegravir showing the lowest (approximately 30%). The successfully verified PBPK model predicted that all evaluated antiretrovirals mostly return to prepregnancy exposure 4 weeks after delivery. Pharmacokinetic investigations on hepatically cleared drugs should not be conducted before the fifth week after delivery to fully characterize the effect of pregnancy on drug exposure. Because physiological changes remain after delivery, early measurements can underestimate the pregnancy effect on pharmacokinetics, leading to suboptimal dosing recommendations during pregnancy.

Multi-Trajectory Planning Control Strategy for Hydropower Plant Bridge Crane Based on Evaluation Algorithm

Currently, the research on crane trajectory planning mostly aims to, first, plan the trajectories of the crane and the trolley, and then to use a trial-and-error method or optimization algorithm to iteratively calculate the optimal trajectory parameters under the control of the optimal trajectory parameters to achieve the suppression of the swing angle. However, research on the fusion application of multi-trajectory planning algorithms is very rare. In addition, the existing methods are not suitable for the special operation control of hydropower plant bridge cranes. Based on the application scenario of hydropower plant bridge cranes, this paper proposes a comprehensive multi-trajectory control strategy based on the entropy weight technique for order preference, similarly to the ideal solution (TOPSIS) evaluation method. Specifically, the kinematic analysis of the crane is carried out and the trajectory evaluation index system is established. Secondly, under the walking constraint condition, four different trajectory planning algorithms are used to obtain the crane trajectory curve. In order to ensure the accuracy and comprehensiveness of the evaluation, the evaluation data are obtained through the Adams motion simulation platform. Finally, based on the entropy weight TOPSIS evaluation method, the optimal walking trajectory for each displacement is selected. The simulation and experimental results show that the evaluation method can select the optimal trajectory based on the motion characteristics of the trajectory algorithm in different displacement conditions, effectively reducing the load swing during the walking process of the crane and improving the positioning accuracy.

Nature and nurture in fussy eating from toddlerhood to early adolescence: findings from the Gemini twin cohort

BackgroundFood fussiness (FF) describes the tendency to eat a small range of foods, due to pickiness and/or reluctance to try new foods. A common behaviour during childhood, and a considerable cause of caregiver concern; its causes are poorly understood. This is the first twin study of genetic and environmental contributions to the developmental trajectory of FF from toddlerhood to early adolescence, and stability and change over time.MethodsParticipants were from Gemini, a population‐based British cohort of n = 4,804 twins born in 2007. Parents reported on FF using the Child Eating Behaviour Questionnaire ‘FF’ scale when children were 16 months (n = 3,854), 3 (n = 2,666), 5 (n = 2,098), 7 (n = 703), and 13 years old (n = 970). A mixed linear model examined the trajectory of FF, and a correlated factors twin model quantified genetic and environmental contributions to variation in and covariation between trajectory parameters. A longitudinal Cholesky twin model examined genetic and environmental influences on FF at each discrete age.ResultsWe modelled a single FF trajectory for all children, which was characterised by increases from 16 months to 7 years, followed by a slight decline from 7 to 13 years. All trajectory parameters were under strong genetic influence (>70%) that was largely shared, indicated by high genetic correlations. Discrete age analyses showed that genetic influence on FF increased significantly after toddlerhood (16 months: 60%, 95% CI: 53%–67%; 3 years: 83%; 81%–86%), with continuing genetic influence as indicated by significant genetic overlap across every age. Shared environmental influences were only significant during toddlerhood. Unique environmental influences explained 15%–26% of the variance over time, with some enduring influence from 5 years onwards.ConclusionsIndividual differences in FF were largely explained by genetic factors at all ages. Fussy eating also shows a significant proportion of environmental influence, especially in toddlerhood, and may, therefore, benefit from early interventions throughout childhood. Future work needs to refine the FF trajectory and explore specific trajectory classes.

Intelligent Trajectory Prediction Algorithm for Hypersonic Vehicle Based on Sparse Associative Structure Model

The Hypersonic Glide Vehicle (HGV) has become a focal point in military competitions among nations. Predicting the real-time trajectory of an HGV is of significant importance for aerospace defense interception and assessing enemy combat intentions. Existing prediction methods are limited by the need for large data samples and poor general applicability. To address these challenges, this paper presents a novel trajectory forecasting approach based on the Sparse Association Structure Model (SASM). The SASM can uncover the relationship among known data, transfer associative relationships to unknown data, and improve the generalization of the model. Firstly, a trajectory database is established for different maneuvering modes based on the six-degree-of-freedom motion equations and models of attack and bank angles of the HGV. Subsequently, three trajectory parameters are selected as prediction variables according to the maneuvering characteristics of the HGV. A parameters prediction model based on the SASM is then constructed to predict trajectory parameters. The SASM model demonstrates high accuracy and generalization in forecasting the trajectories of three different HGV types. Experimental results show a 50.35% reduction in prediction error and a 48.7% decrease in average processing time compared to the LSTM model, highlighting the effectiveness of the proposed method for real-time trajectory forecasting.

Dynamic modeling and trajectory optimization for the rigid-flexible coupled spacecraft with the free-floating manipulator and solar panels

The rigid-flexible coupled spacecraft, composed of flexible solar panels and a multilink manipulator, has gained prominence in on-orbit servicing due to rapid advancements in space technology. However, the intricate effects of rigid-flexible coupling pose significant challenges for dynamic modeling, trajectory planning, and control. This paper aims to develop general dynamic approaches for modeling and trajectory planning in such spacecraft, considering large deformations. The main distinguishing feature is the use of the referenced nodal coordinate formulation to accurately describe the large-deformed solar panels rather than directly treating them as disturbance for the free-floating system. Additionally, the common recursive model for the multilink manipulator is integrated into the same framework. The modal reduction method with modal derivatives techniques is employed to address geometric nonlinearity resulting from large deformations. Polynomial trajectory parameters with different performance characteristics are obtained by defining various optimization objectives. The coupling analysis is conducted based on an accurate reduced-order dynamic model, the results of which can be used for designing manipulator tasks. Coupling values are defined as the objective for trajectory optimization, offering advantages such as insensitivity to dynamic model accuracy and a fast optimization process. After validating the accuracy of the proposed dynamic model through simulations, the performances of different optimized trajectories are demonstrated using numerical examples.

A Direct Contour Control Method for Free-Form Surface Machining Trajectories Based on Coordinate Transformation

The requirement for high-speed and high-precision contouring with free-form surfaces in the CNC machining process is increasing. The contour error is an essential criterion for the quality of CNC machining. For the problem of contour error control, the present research is mainly based on position tracking, and the control method directly aiming at contour control has not been well studied. This paper proposed a new type of coordinate transformation-based direct contour control method (CT-DCC) for free-form surface machining trajectories. By real-time monitoring of the contour error and the foot point of the free-form parametric trajectory, the contouring task is decomposed into the contour error control task in the normal direction and the velocity control problem in the feed direction. Using coordinate transformation, the output commands of the two tasks are converted to the axial motion command. CT-DCC completely eliminates position tracking in the traditional control to achieve direct control of the contour error, which provides a new solution for the contour control problem of free-form surface machining. Both the axial velocity control and the axial torque control-based CT-DCC scheme were studied, and the two-axis and three-axis direct contour controllers were tested. The simulation and experiment results show the feasibility of the proposed method.

Generalized poisson regression for over-dispersed longitudinal count data

Abstract Longitudinal count data is a common type of discrete data in fields like medicine and social sciences. The Poisson regression model is an important method for analysing count data, and the standard Poisson regression model requires that the mean and variance of discrete count data are equal. However, longitudinal count data are often over-dispersed in practice, i.e., the variance of the data is greater than the mean. Besides, the degree of dispersion between the mean and variance of longitudinal count data varies over time. A generalized Poisson regression model based on joint modeling of the mean and dispersion parameters of over-dispersed longitudinal count data is proposed, which simultaneously describes the trajectories of longitudinal mean and dispersion parameters over time and explains how they are dependent on other covariates. The simulation results and real data analysis illustrate the accuracy and effectiveness of the proposed method.

Nonreciprocal conversion based on line trajectory near exceptional points

Spatio-temporal permittivity modulation can simultaneously impart wave vector and frequency shifts during an indirect photonic transition process where nonreciprocal responses are accomplished. Here, we combine the nonreciprocity with exceptional points (EPs) by employing line parameter trajectory to a spatio-temporally modulated waveguide. The instantaneous state evolutions on direction-dependent Riemann sheets are thus different in forward and backward directions. Light propagates through the structure is nonreciprocal. Forwardly, an arbitrary incident wave will convert to a combination of the two waveguide modes with same intensity. Backwardly, the waves almost entirely convert to one specific mode. The conversion efficiency is more than 80% and robust to the line design. The operating wavelength is in the telecommunications band, conducive to integration with other chips. Compared to the widely used loop path, the line path has the merit of easy preparation in experiments as only one parameter is changed. The research sheds light on the optical devices such as isolator and amplifier.

Research on the safety risks of microwave irradiation on motion balance perception in electric power environments

To the microwave irradiation safety hazards caused by the co-construction of towers in smart grids, this paper investigates the effects of microwave irradiation in the power environment on the biological motion balance perception function. Firstly, simulation of microwave signals in the electric power environment, i.e., low-frequency harmonics and high-frequency carriers, were realized by signal modulation and applied in four types of behavior testing scenarios. Then, determining rats as target organisms to replace workers and randomly dividing into groups in proportion: open field, rotating rod fatigue, beam walking and forced swimming. Configuring radar with various parameters to match the electric power irradiation scene and stimulate rats, monitoring the abnormal behavior by image processing module, including posture, motion trajectory, distance, and other features. The experimental result showed that exposed to microwaves induce rats motor ability decline, balance perception imbalance, together with paralysis within long-term exposure, and its locomotor activity, coordination, posture control and reaction time all exhibit varying degrees of weakening. These findings indicate that microwave irradiation in electric power environment may pose significant health and safety risks for worker.

Analysis and Verification on Buckling Mechanism of Spatial Tow Steering in Automated Fiber Placement

Automated fiber placement (AFP) enables the efficient and precise fabrication of complex-shaped aerospace composite structures with lightweight and high-performance properties. However, due to the excessive compression on the inner edge of the tow placed along the curved trajectory, the resulting defects represented by buckling and wrinkles in spatial tow steering can induce poor manufacturing accuracy and quality degradation of products. In this paper, a theoretical model of tow buckling based on the first-order shear deformation laminate theory, linear elastic adhesion interface and Hertz compaction contact theory is proposed to analyze the formation mechanism of the wrinkles and predict the formation of defects by solving the critical radius of the trajectory, and finite element analysis involving the cohesive zone modeling (CZM) is innovated to simulate the local buckling state of the steered tow in AFP. Additionally, numerical parametric studies and experimental results indicate that mechanical properties and geometric parameters of the prepreg, the curvature of the placement trajectory and critical process parameters have a significant impact on buckling formation, and optimization of process parameters can achieve effective suppression of placement defects. This research proposes a theoretical modeling method for tow buckling, and conducts in-depth research on defect formation and suppression methods based on finite element simulation and placement experiments.

Self-calibration method for geometric parameters based on feature point projection trajectories in Cone-beam Computed Laminography

Cone-beam computed laminography (CBCL) is an X-ray three-dimensional imaging method that is suitable for large plate-like objects. Geometric parameter calibration is crucial during CL imaging to prevent geometric artifacts in the reconstructed image. This study introduced a self-calibration method employing feature-point projection trajectories for CL geometric parameters. The method constructed point projection trajectory models for the system’s geometric parameters and optimized the best fit of these models to the characteristic point projection trajectories to solve for the geometric parameters of the system. Furthermore, this study examined the impact of the feature point location in the object coordinate system on the parameter calibration accuracy and reduced the required feature point locations from 11°to 4°using the alternating optimization algorithm. The imaging results demonstrated the ability of the method to achieve high-accuracy calibration of CL system geometric parameters, reducing the calibration error of the rotational axis tilt angle α from 1.1% to 0.08% while exhibiting resilience to noise. The proposed method enabled the calibration of all CL system geometric parameters without the model calibration, laying the groundwork for rectifying image geometric artifacts and enhancing CL imaging quality. Moreover, this method presents a novel approach for CT system geometric parameter calibration.

KINEMATIC PARAMETERS, PHYSICAL CHARACTERISTICS, AND CHEMICAL COMPOSITION OF SELECTED METEOR BODIES

Background. Meteoroids can reach the Earth and penetrate its atmosphere creating meteor phenomena. Kinematic parameters, physical characteristics, and chemical compositions of the observed meteor bodies provide information about the properties of their parent bodies — comets and asteroids. On the other hand, these parameters can reflect the physical conditions of meteor- oids staying in different parts of the Solar System and beyond. Methods. The meteor data analyzed in this work were obtained from observations using the automatical video and spectral meteor patrol (AVSMP) of the Institute of Astronomy of V. N. Karazin Kharkiv National University. The methods of meteor astronomy and spectroscopy make it possible to determine the kinematic parameters, physical properties, and chemical com- position of the meteoroids that we studied. Results. The paper presents the research results of meteors brighter than 0m that were recorded by the multi-stations method. These meteors also have spectral observations. For the selected 12 meteors, we obtained the coordinates of meteor radiants on the celestial sphere, the parameters of the atmospheric trajectories of meteor bodies, and the heliocentric orbital parameters of the observed meteoroids for the epoch (J2000). The extra-atmospheric masses of meteoroids were determined from photometric data. The identified emission lines detected in meteor spectra were analyzed. The software developed by the authors of this paper for me- teor spectra processing was used. Qualitative and quantitative analyses of the chemical composition of meteor bodies were carried out. During the quantitative analysis, the values of the relative intensities of the Fe I-15, Mg I-2, and Na I-1 lines were determined. Conclusions. Kinematic parameters and elements of heliocentric orbits presented in this work indicate that the observed me- teor bodies belong to meteor showers and their comets, such as Perseids, Leonids, and Southern Taurids. Some meteor bodies are sporadic. The calculated masses of meteoroids have some scatter of values, but they are generally consistent with observa- tions of other authors in the range of absolute values of the meteor brightness -2m…+1.5m. It was found that some of the studied meteor bodies are Fe-poor or Na-poor in their chemical composition.

Stability Analysis Method of a Hierarchical Control Structure Microgrid Based on a Small-Signal Model and Hopf Bifurcation Theory

To the oscillation and stability problem caused by multi-scale and broadband electromagnetic dynamics among many isomerized power electronic devices in a microgrid, a small-signal model of hierarchical control structure microgrid and stability analysis method based on oscillation trajectories are proposed. Moreover, a hierarchical control structure is used as the research object in microgrid, and the analysis is performed based on the small-signal model and Hopf bifurcation theory. First, the small-signal model of the hierarchical control structure microgrid is established, combining the dominant eigenvalue and participation factor analysis methods, to analyze the influence of the controller and related sensitive parameters on the dynamic performance of the system. Then, based on the small-signal model and Hopf bifurcation theory, a stability analysis method based on oscillation trajectories is proposed. The relationship between different oscillation modes and limit cycles in the microgrid system and the influence of the sag control parameter values on the oscillation trajectory and stability domain of the system are researched on. Combining Hopf bifurcation theory and oscillation trajectory to delineate the stable domain of parameter trajectories, the influence of secondary control on the system stability is analyzed under different oscillation trajectories and load disturbances, revealing the corresponding relationship between the state trajectories of different oscillation modes and system stability of a hierarchical control structure microgrid. Based on the proposed oscillating trajectories, the stability analysis method has sufficient universality for studying the impact of system stability, establishing the parameter selection standards for the design of microgrids. Finally, according to the verification results, the correctness and applicability of above methods are verified.

Mathematical analysis of successive approximation to identify the blood glucose regulation using picards iteration method

Diabetes affects millions of peoples all over the world, and the correct identification of Glucose of individuals affected with this disease, especially of those in early stages or in progression towards diabetes, remains an active area of research. This Picard’s Mathematical model is useful to identify the glucose-insulin interactions. In this system we used a couple of ordinary differential equations prevails as an important tool for interpreting data collected during an intravenous glucose tolerance test.(IVGTT). In this study we extract the solution to the Picard’s method and for identifying patient-specific parameters of glucose trajectories form IVGTT. As illustrated with patient data, our approach seems to have an edge over nearly an accurate approximate value using this method. Additionally, we also present an application of our method to prediction of the time to baseline glucose and calculation of glucose effectively, two quantities regarded as significant in diabetes diagnostics.

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.