Ballistic Coefficient Research Articles

Efficient Evaluation of Mars Entry Terminal State Based on Gaussian Process Regression

Trajectory optimization technology used for Mars entry is one of the key technologies for planetary exploration. Evaluation of the performance of the entry trajectory under conditions of complex atmospheric dynamics, various vehicular design parameters, and multiple constraints in the process of entry, are important issues pertaining to the design of trajectories. In this study, an efficient evaluation approach of the terminal state for Mars entry is proposed based on Gaussian process regression to evaluate the maximum terminal altitude for different entry velocities, terminal Mach numbers, and vehicular parameters. Additionally, the influences of entry flight-path angle, lift-drag ratio, and ballistic coefficient, on the maximum terminal altitude are analyzed. A genetic algorithm is used in the optimization solver to avoid local minima and to guarantee the data quality of the training samples used for Gaussian process regression. The mean function, kernel function, and hyperparameters are selected as the optimization parameters for Gaussian process regression to describe the correlation between samples, and the maximum terminal altitude prediction model is then established. Numerical simulations demonstrate that the proposed method can achieve the evaluation of more than 3000 group scenarios within tens of seconds with a mean relative error that is less than 4%.

Safety analysis for shallow controlled re-entries through reduced order modeling and inputs' statistics method

In recent years, the interest and demand for small satellites have grown exponentially. While in the past the end-of-life design for this type of spacecraft was often approximated or totally neglected, it has recently become increasingly important. Indeed, small spacecraft able to achieve advanced mission objectives are more frequently on the worldwide space agenda. They may contain components which might withstand the re-entry conditions and reach the ground. In addition, these spacecraft are usually limited to shallow re-entries which are more sensitive to atmospheric model uncertainties and thus have larger debris fields. The objective of this work is to provide a reliable and efficient statistical analysis to estimate the risk to aeronautic and maritime traffic as well as to ground based populations. A simple geometric safety assessment is proposed, based on the safety boxes concept introduced in the ESA Space Debris Mitigation Compliance Verification Guidelines. Correctly estimating the dimensions of a safety box and locating it over uninhabited regions, such as the oceans, guarantees a casualty risk below a prescribed value. Furthermore, by estimating the probability of debris landing outside the largest possible safety box within which there is a zero casualty risk, the maximum probability of control failure admissible for the mission can be estimated. This proposed safety analysis is achieved using two re-entry models of differing complexity. The high fidelity model includes both the aerodynamic and aerothermodynamic effects that occur during re-entry and is used to statistically characterize “high level’’ uncertain variables such as the ballistic coefficient and the demise altitude. The reduced order model is based on these high level variables and captures the spacecraft fragmentation behavior and its re-entry dynamics with significantly less computation time than the high fidelity model. Coupled with advanced statistical techniques designed to estimate very low probabilities such as the Inputs' Statistics Method, a reliable safety analysis can be conducted with a limited overall computational burden. The proposed safety analysis is applied to a fictitious 2U CubeSat mission that performs a controlled re-entry using the Drag De-orbit Device developed by the ADAMUS laboratory at the University of Florida.

Feasibility Assessment of Aerocapture for Future Titan Orbiter Missions

Numerical simulation is used to perform parametric analysis to assess the feasibility of aerocapture at Titan over arrival of , vehicle lift-to-drag ratio of 0–1, and vehicle ballistic coefficient of 90 and . Aerodynamic forces, peak heat rate, and total heat load are evaluated. It is shown that aerocapture at Titan requires a lifting vehicle with a minimum lift-to-drag ratio of 0.2 and an arrival of , an equivalent propulsive of about , which is higher than what is realistically possible. Results show that aerocapture requires different interplanetary trajectories from propulsive options, and aerocapture with a vehicle of lift-to-drag ratio of 0.3 enables an arrival of and higher. The peak heat rate is well within the capability of the state-of-the-art technologies of thermal protection system materials. In addition, the vehicle can achieve an inclination change up to 20 deg via an aerocapture maneuver.

Aerodynamics and flight mechanics activities for a suborbital flight test of a deployable heat shield capsule

MINI-IRENE is the Flight Demonstrator of IRENE, a new-concept capsule with a variable geometry, originally conceived by ASI to widen the range of available platforms to retrieve payloads and/or data from low Earth orbit. The main characteristics of IRENE is the “umbrella-like" deployable front structure that reduces the capsule ballistic coefficient, leading to acceptable heat fluxes, mechanical loads, stability and final descent velocity. Following the feasibility studies carried out since 2011, with also preliminary Thermal Protection System materials tests in plasma wind tunnels, the objective is now to design and build a Flight Demonstrator and a Ground Demonstrator to prove, with a suborbital flight and with a Plasma Wind Tunnel (PWT) test campaign, the functionality of the deployable heat shield. The Flight Demonstrator shall be included as a secondary payload in the interstage adapter of a VSB-30 launcher from ESRANGE, then ejected during the ascent phase of the payload section, perform a 15-min ballistic flight, re-enter the atmosphere and hit the ground. The Ground Demonstrator, representative of the Thermal Protection System of the Flight Demonstrator, shall be instead exposed to a heat flux similar to that expected for an atmospheric re-entry from low Earth orbit inside the SCIROCCO Plasma Wind Tunnel at CIRA. The paper, after a short description of the mission profile both for orbital and suborbital flights, focuses on the aerodynamics and flight mechanics activities held for the suborbital flight and PWT test campaigns.

State Prediction of High-speed Ballistic Vehicles with Gaussian Process

This paper proposes a new method of predicting the future state of a ballistic target trajectory. There have been a number of estimation methods that utilize the variations of Kalman filters, and the prediction of the future states followed the simple propagations of the target dynamic equations. However, these simple propagations suffered from no observation of the future state, so this propagation could not estimate a key parameter of the dynamics equation, such as the ballistic coefficient. We resolved this limitation by applying a data-driven approach to predict the ballistic coefficient. From this learning of the ballistic coefficient, we calculated the future state with the future ballistic parameter that differs over time. Our proposed model shows the better performance than the traditional simple propagation method in this state prediction task. The value of this research could be recognized as an application of machine learning techniques to the aerodynamics domains. Our framework suggests how to maximize the synergy by linking the traditional filtering aproaches and diverse machine learning techniques, i.e., Gaussian process regression, support vector regression and regularized linear regression.

A Study of the Reflection of Radio Waves from the Plasma Region on the Track behind an Axisymmetric Body Moving in the Earth’s Atmosphere

The results of numerical calculation of the dependences of the electron density, the eigenfrequency and the dielectric plasma permeability on the geometric parameters and the altitude of body motion in the near and far wake behind a thin conical body with a spherical nose blunting have been presented. The electron density maximum has been shown to be located in the region of the neck of the near wake behind the body, which determines the type of this region (supercritical or subcritical). This in turn affects the propagation of radio waves through this plasma region. A comparative analysis was performed for two different bodies with the same ballistic coefficient values. No characteristic distinctions were revealed in the values of electron density or the plasma eigenfrequency in the near and far wake behind these bodies. However, it has been shown that there are differences in the values of the distance from the bottom cross section to the neck of the near wake behind these bodies.

Design of Physically-based Virtual Cavity Simulation

In recent years, game and virtual reality contents using next-generation weapons have constantly been emerging. In the context of story development, the marks of the target's bullet are differently observed according to the unique characteristics of the rifle and bullets. There is also an example in which criminal traces are investigated by using forensic ballistics during criminal investigation. In this process, it is quite critical to recognize the relationship between the ballistic coefficient and the cavity due to the ballistic force. In this paper, we propose a physically-based cavity simulation that can enhance realism.

ESTIMATING THE IMPACT OF CARGO PARAMETERS AND EXTERNAL LOAD ON HELICOPTER CONTROLLABILITY

Within the problems solution of complex research in helicopter controllability, the reasons of changes controllability parameters when transporting cargo using external load have previously been identified. The next stage of research is to determine how concrete cargo parameters and external load as a whole, as well as their combination influence helicopter controllability parameters. The article contains research results of the cargo parameters and external load impact on static and dynamic controllability parameters. As a static characteristic of controllability the operation efficiency expressed by the maximal angular acceleration acquired by the helicopter in the case of throttle equal deviations at various flight velocities was considered. Time of the transient process was chosen as a dynamic characteristic with the observable parameter being the movement of the cyclic pitch. For cargo parameters, 16 combinations of ballistic coefficient and cargo mass were considered, while the external load parameter the cable length from 10 to 40 meters was chosen. According to completed simulation experiments, certain dependencies were found between controllability parameters and external cargo parameters and their various combinations. The analysis of the results showed that the dynamic characteristics are more appropriate for estimating the impact of cargo parameters on helicopter flying qualities, since such estimation fully defines the workload on a pilot. The acquired results may be applied to improve Flight Operations Manuals and Aviation Personnel Training Instructions.

The Restoration of Input Parameters of an Exterior Ballistic Solution by the Results of Body Movement Trajectory Measurement

Analyzing the results of ballistic experiments often brings up the problem of restoring the input computation parameters of the exterior ballistics of a body (the ballistic coefficient, the initial velocity, the environment temperature, the pressure, etc.) by the results of trajectory measurements (the reverse problem of exterior ballistics). It is found that without a priori information on unknown parameters, the problem in question cannot have a unique solution. We propose a procedure of solving the reverse problem with a priori information at hand; this procedure rests on the least-squares method and the maximum-likelihood method. An algorithm for solving the reverse problem is described in detail (the described algorithm implements the proposed procedure). We consider applying this procedure to the problem of restoring the initial departure conditions and atmospheric parameters, as well as to the problem of simultaneously determining the initial velocity of the body and its ballistic coefficient.

Influence of projectile ballistic coefficient dispersion on non-lethal and limited range weapons' tactical characteristics

Influence of projectile ballistic coefficient dispersion on non-lethal and limited range weapons' tactical characteristics

Drag-perturbed bounded relative trajectories in low Earth orbit: A semi-analytical approach

Although recent numerical studies have demonstrated the possibility to obtain entire families of bounded relative trajectories in the Earth zonal problem, it is still unclear whether such initial conditions can cope with mismodeled dynamics such as atmospheric drag, luni-solar attraction, and solar radiation pressure. In the attempt to deal with the dynamical perturbations caused by the Earth's atmosphere, this paper offers a semi-analytical approach that combines previous work developed by the authors with newly found analytical relationships describing the effects of drag on the nodal and sidereal periods of a satellite. It is shown that both of these quantities change in a secular fashion due to the variations in the semi-major axis of spacecraft. Nevertheless, bounded relative motion can be guaranteed over the course of several days by either initializing the satellites on the same invariant curve of a stroboscopic mapping or by design of appropriate ballistic coefficients. These conclusions are supported by numerical simulations that prove the feasibility of our approach for spacecraft formations in low Earth orbit.

Derivative-free Nonlinear Version of Extended Recursive Three-step Filter for State and Parameter Estimation during Mars Entry

Parameter uncertainties which may lead to divergence of traditional Kalman filters during Mars entry are investigated in this paper. To achieve high precision navigation, a Derivative-free Nonlinear version of an Extended Recursive Three-Step Filter (DNERTSF) is introduced, which suits nonlinear systems with arbitrary parameter uncertainties. A DNERTSF can estimate the state and the parameters simultaneously, and Jacobian and Hessian calculations are not necessary for this filter. Considering the uncertainties in atmosphere density, ballistic coefficient and lift-to-drag ratio, a numerical simulation of Mars entry navigation is carried out. Compared with the standard Unscented Kalman Filter (UKF), DNERTSF can effectively reduce the adverse effects of parameter uncertainties and achieve a high navigation accuracy performance, keeping position and velocity estimation errors at a very low level. In all, the DNERTSF in this paper shows good advantages for Mars entry navigation, providing a possible application for a future Mars pinpoint landing.

Kompjuterska simulacija spoljne balistike pištolja primenom dva različita zakona otpora vazduha (na primeru pištolja 7.62 mm TT)

A description of a pistol (rifle) cartridge often involves two ballistic coefficients that characterize its ballistic qualities with respect to various air resistance laws (ARLs). How close are the obtained ballistic trajectories with varied ARL specifications and what are the differences between them? How to evaluate ballistics if the ARLs are to be expressed in various mathematical forms? In this paper, the evaluation of external ballistics trajectories is given for two ARLs (the law brought in 1943 and the Siacci law). All the obtained results relate to the TT pistol with 7.62 × 25mm Tokarev cartridge. The paper also presents the answer to the question: how to calculate the ballistic trajectory if the ARL is expressed as a rational function, piecewise function or spline. For the 1943 ARL, a graphical interpretation of the function Cd (i, v) in the form of a surface is shown. This paper shows that, due to the selection of ballistic coefficients, it is possible to obtain sufficiently similar form of ballistic trajectories. A method of graphical comparison of external ballistic parameters is presented as well as the mathematical tools for quantitative analysis of a shape of ballistic curves. The difference between the two trajectories is proposed to be estimated using a relative error in regard to a selected ballistic parameter. Computer simulation considered for the 1943 and Siacci ARLs for the 7.62×25mm Tokarev cartridge indicates that the profiles of the function of instantaneous projectile velocity vs time of flight (TOF) had the greatest non-coincidence in relation to other ballistic parameters (e.g. horizontal range, height of the trajectory, etc.) The obtained maximum of the relative error was 0.8%. Its magnitude localizes at the point of impact.

Aerothermodynamic Studies on Low-Ballistic-Coefficient Mars Aerocapture Vehicle with Drag Modulation and Electric Propulsion

A Mars orbiter/lander mission using a micro-satellite (less than 100 kg at Mars arrival) with a deployable membrane aeroshell for the orbit insertion by the aerocapture and the electric propulsion for the trajectory maneuver was considered. The aerodynamic heating environment during the atmospheric flight was investigated solving the thermo-chemical nonequilibrium axi-symmetric Navier-Stokes equations around the spacecraft with the flare-shaped aeroshell. To obtain the appropriate amount of deceleration at the atmospheric pass, the drag modulation technique, in which the aeroshell is timely jettisoned from the spacecraft, was assumed. The hypersonic wind tunnel experiment successfully demonstrated that the backward jettison works well without significant time delay and attitude disturbance. Finally the corridor width for the entry path angle was estimated considering the ability of the orbit insertion, the peak aerodynamic heating, and the capability of the electric propulsion to raise the periapsis altitude. The combination of a low ballistic coefficient flight with the membrane aeroshell and an electric propulsion works well to acquire a finite width of the entry corridor for the aerocapture.

Constellation Phasing with Differential Drag on Planet Labs Satellites

A methodology is presented for the differential drag control of a large fleet of propulsionless satellites deployed in the same orbit. The controller places satellites into a constellation with specified angular offsets and zero relative speed. Time-optimal phasing is achieved by first determining an appropriate relative placement because the satellites are interchangeable. A second optimization problem is then solved as a large coupled system to find the drag command profile required for each satellite. The control authority is the available ratio of low-drag to high-drag ballistic coefficients of the satellites given realistic operational constraints. The controller is able to successfully phase constellations with up to 100 satellites in simulations. On-orbit performance of the controller is demonstrated by phasing Planet Labs’s Flock 2p constellation of 12 CubeSats, launched in June 2016, into a 510 km sun-synchronous orbit.

DETERMINATION OF THE BALLISTIC CHARACTERISTICS AND THE DAMAGING PROPERTIES OF SELF-MADE LOADING CARTRIDGES OF 7.62*39 CALIBER

In practice of forensic medicine and forensic ballistics there are quite often the cases of different types ofgunshot wounds infliction by atypical damaging elements which were used in illegal independent loading of cartridges to the rifle weapon. The purpose of the researches being performed - studying on a concrete example from criminalistics practice of damaging properties of 7.62 mm rifle bullets of type FMJBT (Full Metal Jacketed Boat Tail) which were used for loading by self-made way cartridges of 7.62 * 39 caliber. Originally, during natural tests in the conditions of a ballistic track the ballistic characteristics of the shot bullets and the value of their ballistic coefficient were established. At the following stage of researches the losses of kinetic energy of rifle bullets on punching blocks of ballistic plasticine with the thickness of 100-140 mm were determined. As a result of tests the character of formation of the damage channel in the thickness of biological tissues simulator is established at the stable and unstable movement of the bullets in the visco elastic medium. Besides, during the researches the values of the parameters necessary for calculations ofpenetration depth of the bullets into a fabric of biological object depending on their speed at the moment of hit in the target, were determined. In particular it was established that at unstable movement of an investigated bullet in thickness of the simulator the value of boundary speed amounts 138.1 m/s, and the value of the medium drag factor - 1.782. Using estimated values offlight speed of the bullets in the trajectory the values of depth wound channels in biological tissues were calculated and the conclusion was drawn on the guaranteed causing of penetrating wounds in all established distances of shooting. Thus, use of the methodfor estimation of damaging properties of investigated bullets, the criterion of which is the length of the wound channel and its boundary value was obviously demonstrated.

Mathematical Model of the Uncontrolled Bullet’s Motion in the Air with the Resistance Forces Assigned as Approximating Functions

Статья посвящена актуальной на сегодняшний день проблеме повышения кучности автоматической стрельбы короткими очередями. Особое внимание уделено описанию нового способа повышения кучности стрельбы, при котором пули с конструктивными особенностями двигаются по изменяющейся траектории в заданном направлении. Описываемый способ предполагает, что на некоторой дальности все три пули могут попасть в одну точку или обеспечить эффективный закон рассеивания, позволяющий кардинально повысить эффективность попадания пуль в цель и ее поражения. Это позволяет существенно повысить кучность стрельбы из штатных автоматов Калашникова известных калибров или перспективных автоматов, позволяющих применять и более мощные патроны. Основное содержание исследования составляет разработка математической модели движения пули в воздухе в трехмерном пространстве с силами сопротивления, заданными в виде аппроксимирующих функций. Значительное внимание уделяется определению сил сопротивления, действующих на пулю в потоке воздуха, без вычисления баллистических коэффициентов и способу их представления в математической модели для расчета траектории движения. На основе составленной в данной статье системы дифференциальных уравнений движения выполнен расчет внешней баллистики пули патрона 7Н6 и проанализированы относительные ошибки основных параметров траектории. В заключение представлены основные результаты выполненной работы и обосновывается необходимость расширения системы дифференциальных уравнений для изучения внешней баллистики более широкого диапазона пуль с различными конструктивными особенностями.

Modern Automated System for Evaluation of Movement Velocity of Firearm Bolt

Экспериментальное определение характеристик перемещений узлов автоматики чрезвычайно важно при проектировании стрелкового оружия. В статье предложен современный вариант реализации автоматизированной системы, предназначенной для измерения скорости перемещения затворной рамы стрелкового оружия. Проведен сравнительный анализ существующих методов и устройств для оценки линейных перемещений узлов стрелкового оружия, отмечены их недостатки. Выполнена оценка минимально необходимых характеристик регистрирующего устройства и осуществлен его выбор. Представлена структурная схема системы, описаны основные принципы ее работы. Созданная система во многом сходна с автоматизированными системами на основе световых экранов, применяемыми для оценки скорости, баллистического коэффициента и других параметров пуль и снарядов. Представлена форма сигналов, получаемых с фотоприемников и регистрируемых системой. Описаны возможности разработанного программного обеспечения: визуализация сигналов, получение статистической информации по серии выстрелов, сохранение всех результатов на жесткий диск компьютера. Созданная система позволяет определять среднюю скорость движения затворной рамы стрелкового оружия на участке измерительной базы в прямом и обратном направлении. При этом предлагаемый вариант реализации системы отличается сравнительно низкой стоимостью, простотой и компактностью.

Calibration of atmospheric density model using two-line element data

For satellites in orbits, most perturbations can be well modeled, however the inaccuracy of the atmospheric density model remains the biggest error source in orbit determination and prediction. The commonly used empirical atmospheric density models, such as Jacchia, NRLMSISE, DTM, and Russian GOST, still have a relative error of about 10%–30%. Because of the uncertainty in the atmospheric density distribution, high accuracy estimation of the atmospheric density cannot be achieved using a deterministic model. A better way to improve the accuracy is to calibrate the model with updated measurements. Twoline element (TLE) sets provide accessible orbital data, which can be used in the model calibration. In this paper, an algorithm for calibrating the atmospheric density model is developed. First, the density distribution of the atmosphere is represented by a power series expansion whose coefficients are denoted by the spherical harmonic expansions. Then, the useful historical TLE data are selected. The ballistic coefficients of the objects are estimated using the BSTAR data in TLEs, and the parameterized model is calibrated by solving a nonlinear least squares problem. Simulation results show that the prediction error is reduced using the proposed calibration algorithm.

Analysis of the dynamics of the deployed aerodynamic space tether system

An analysis of the motion of a deployed space system that consists of two end bodies connected by a tether has been considered. One of the bodies has a relatively large ballistic coefficient that ensures aerodynamic braking or the stabilization of the motion of the entire system in relatively low near-Earth orbits. The deployment of this system mainly occurs due to the action of aerodynamic forces. Several ways of deploying the system have been analyzed, including (1) the uncontrolled release of the tether with hardly any braking; (2) deployment with constant braking force; (3) the dynamic control law without feedback, when the resistance force varies according to a set program; (4) a kinematic control law with feedback when programs are set for varying the velocity and length of the tether release. To analyze the dynamics of the system, a mathematical model of motion has been constructed in which the motion of the end bodies relative to their centers of mass is taken into account.