Ballistic Coefficient Research Articles

A Systematic Research on Ballistic Characteristics of Aerial Ammunitions

Aviation has come a long way since its early days, and as technology has advanced, air vehicles have become even more advanced and effective, especially on the battlefield. In addition, in-depth research and discoveries in the field of aviation have a significant impact on the aviation industry, especially in the field of munitions. In this context, aerial ammunition is an important component of aviation and is widely used in combat. Because a malfunction that may occur during separation or premature detonation during separation from the aircraft may cause fatal effects on the crew. That’s why the bomb must be safely separated from the air vehicles. Modern bombs are therefore equipped with advanced safety features that guarantee a precise and safe separation from the aircraft before explosion. In addition, the determination of the ballistic coefficient according to the size of the desired effect reveals the importance of the choice of munition types. Otherwise, it will not be possible to achieve the desired level of target destruction. The aim of this study is to provide a comprehensive understanding of the basic characteristics of aerial munitions, including the composition and operation of generic aircraft bombs.

Drag augmentation for collision avoidance in LEO

Space debris proliferation in Low Earth Orbit (LEO) has heightened the urgency for effective Collision Avoidance Manoeuvres (CAMs). This work presents a pioneering framework aimed at devising a novel collision avoidance manoeuvre design for drag-augmentation small platforms. The framework facilitates the alteration of drag acceleration by adjusting the satellite’s ballistic coefficient through cross-sectional area changes. This approach generates controlled deviations in the nominal trajectory, offering a feasible solution for collision avoidance without necessitating thrusters or fuel consumption.The paper introduces an analytical method for propagating drag augmentation manoeuvres and applies it for collision avoidance studies purposes. The formulation followed to implement this manoeuvre within a numerical propagator is presented, as well as the optimisation process developed for the application of drag augmentation manoeuvres in collision avoidance scenarios. Real-world applications showcase the suitability of these approaches, confirming the use of drag augmentation manoeuvres to avoid collisions in LEO. Additionally, the requirements and boundaries of the strategy, including altitude restrictions and satellite-specific properties, are discussed.

Implementation of concavity over heat shield of a reentry vehicle in reducing aerodynamic heating

Excessive amount of aerodynamic heating is a major issue for all kinds of reentry vehicles. In the present computational study, the concave heat shield modification has been used on the existing Orion CEV design to reduce aerodynamic heating. The investigations have been conducted at three different Mach numbers of 3, 6, and 7 to understand the efficacy of the model from the supersonic to hypersonic range. It has been observed that the use of a concave heat shield helps in reducing the aerodynamic heating of the vehicle particularly at hypersonic speeds, and is found to be more effective as the speed increases. Furthermore, the modification caused a decrease of 6.31%, 6.27%, and 6.22% in the ballistic coefficient for Mach 3, 6, and 7, respectively, indicating an increase in the overall aerodynamic drag of the vehicle. As evident from the ballistic coefficient, a maximum of 6.71% increase in aerodynamic drag has been observed at Mach 3. The shock distance experienced by the vehicle is almost doubled for the modified geometry which eventually leads to higher heat dissipation area and thereby lower aerodynamic heating.

A Conceptual Modeling Approach for Performance of Magnetohydrodynamic Drag During Planetary Entry

Future higher-mass Mars missions present numerous engineering challenges and will require significant technological development, particularly of the entry, descent, and landing systems. One such development concept utilizes magnetohydrodynamic interaction with the plasma created during hypersonic planetary entry for energy generation, drag augmentation, and heat-flux mitigation. In this study, a performance estimation methodology for magnetohydrodynamic drag augmentation during Mars entry compatible with conceptual design is developed. A demonstrative investigation utilizing the developed methodology is then conducted, and simulated trajectory results are presented for various entry vehicles and magnetic field strengths. The study results show potential for significant magnetohydrodynamic drag augmentation during hypersonic entry at Mars, with calculated effective ballistic coefficient- reduction factors of up to 4, across entry vehicles ranging in mass from 70 MT to 4 MT. These results show that magnetohydrodynamic drag augmentation can have comparable impact to significant aeroshell diameter increases and also suggest that it could prove an effective form of drag-augmentation control authority by varying the applied magnetic field.

Analysis of Collision Avoidance Manoeuvres Using Aerodynamic Drag for the Flying Laptop Satellite

Collision avoidance is a topic of growing importance for any satellite orbiting Earth. Especially those satellites without thrusting capabilities face the problem of not being able to perform impulsive collision avoidance manoeuvres. For satellites in low Earth orbits, though, perturbing accelerations due to aerodynamic drag may be used to influence their trajectories, thus offering a possibility to avoid collisions without consuming propellant. Here, this manoeuvring option is investigated for the satellite Flying Laptop of the University of Stuttgart, which orbits the Earth at approximately 600km\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${600}\\,{\ extrm{km}}$$\\end{document}. In a first step, the satellite is aerodynamically analysed making use of the tool ADBSat. By employing an analytic equation from the literature, in-track separation distances can then be derived following a variation of the ballistic coefficient through a change in attitude. A further examination of the achievable separation distances proves the feasibility of aerodynamic collision avoidance manoeuvres for the Flying Laptop for moderate and high solar and geomagnetic activity. The predicted separation distances are further compared to flight data, where the principle effect of the manoeuvre on the satellite trajectory becomes visible. The results suggest an applicability of collision avoidance manoeuvres for all satellites in comparable and especially in lower orbits than the Flying Laptop, which are able to vary their ballistic coefficient.

Мathematical model for determining the design parameters of the aerodynamic elements of a deorbit system

The goal of this paper is to develop a mathematical model for choosing the design parameters of deorbit systems’ aerodynamic elements. To solve the problem of near-Earth space debris, it is proposed to deorbit used space objects. Low-Earth orbits are most clogged. Aerodynamic systems are among the most promising systems for space debris removal from low-Earth orbits. They are quite reliable and cheap, but they are sensitive to exposure to space factors. In this paper, aerodynamic systems are decomposed to identify their hierarchic structure, which has the following levels: a subsystem level, an element level, and a parameter level. Materials for the structural components of an aerodynamic element are analyzed. A set of design parameters for aerodynamic systems is formed and used in the development of a mathematical model for choosing the parameters of an aerodynamic element for deorbit systems of various classes: monoblock ones, frame inflatable ones, ones formed by transforming the structure of a space object into an aerodynamic system, and telescopic ones. The material thickness determination model accounts for shell exposure to the space vacuum, atomic oxygen, and excess pressure. It also accounts for errors in determining the ballistic coefficient of an aerodynamic system with a space debris object to be deorbited, the solar activity index, and the atomic oxygen density. The mathematical model for aerodynamic system parameter choice allows one to construct nomograms for determining the parameters of deorbit systems for space debris objects of various classes from their mass and orbit parameters.

Ballistic Coefficient Calculation Based on Optical Angle Measurements of Space Debris.

Atmospheric drag is an important factor affecting orbit determination and prediction of low-orbit space debris. To obtain accurate ballistic coefficients of space debris, we propose a calculation method based on measured optical angles. Angle measurements of space debris with a perigee height below 1400 km acquired from a photoelectric array were used for orbit determination. Perturbation equations of atmospheric drag were used to calculate the semi-major-axis variation. The ballistic coefficients of space debris were estimated and compared with those published by the North American Aerospace Defense Command in terms of orbit prediction error. The 48 h orbit prediction error of the ballistic coefficients obtained from the proposed method is reduced by 18.65% compared with the published error. Hence, our method seems suitable for calculating space debris ballistic coefficients and supporting related practical applications.

Testing of the N2O/HDPE Vortex Flow Pancake Hybrid Rocket Engine with Augmented Spark Igniter

The paper is part of the research aimed at determining if the vortex flow pancake (VFP) hybrid rocket engine is feasible as green in-space chemical propulsion. The objective of this study is to test an N2O/HDPE VFP hybrid ignited with N2O/C3H8 torch igniter. The N2O is used in self-pressurizing mode, which results in two-phase flow and varying inlet conditions, thus better simulating real in-space behavior. The study begins with characterizing the torch igniter, followed by hot-fire ignition tests of the VFP. The results allow for the improved design of the torch igniter and VFP hybrid. The axial regression rate ballistic coefficients are reported for the N2O/HDPE propellants in the VFP configuration.

Dynamic avoidance decision method for civil aircraft in a suborbital debris hazard zone.

Closing the static suborbital debris hazard zone method leads to low airspace resource utilization and long delays for civil aircraft, while the dynamic delineation of suborbital debris hazard zone method can solve the above phenomena. However, the existing research lacks the decision instruction for civil aircraft to avoid the dynamic suborbital debris hazard zone. To address the above problems, this paper creates probability ellipsoids of suborbital debris with different ballistic coefficients in the two-dimensional plane and use the divide-and-conquer algorithm for the dynamic delineation of the suborbital debris hazard zone. The suborbital debris hazard zone is extended outward by 10 km. Subsequently, the standard A* algorithm, the standard Lazy theta* algorithm, the improved Lazy theta* algorithm, and a flight path planning strategy are designed to avoid the suborbital debris hazard zone and provide safe dynamic avoidance commands for civil aircraft with fixed time intervals. The simulation results show that the average area of the dynamically delineated suborbital debris hazard zone is lower than the traditional static no-fly zone; the standard A* algorithm and improved Lazy theta* algorithm provides shorter flight path lengths and flight time and fewer waypoints in windless and windy conditions, respectively.

Mars orbit injection via aerocapture and low-thrust nonlinear orbit control

This research proposes a new strategy for Mars orbit injection, based on aerocapture and low-thrust nonlinear orbit control. The range of periapse altitudes that allow aerocapture is identified as a function of the hyperbolic excess velocity at Mars arrival, with reference to a large variety of atmospheric density profiles and different ballistic coefficients. This analysis proves that a safe periares altitudinal range leading to aerocapture in all atmospheric conditions does not exist. Three different correction maneuvers, aimed at avoiding both impact and escape, are identified. After the atmospheric arc, the spacecraft orbit exhibits large dispersions in terms of orbit elements. Therefore, the identification of an effective autonomous guidance strategy, capable of driving the spacecraft toward the desired operational orbit, is mandatory. To do this, low-thrust nonlinear orbit control is proposed as an effective option. A feedback law for the low-thrust direction and magnitude, with saturation of the thrust magnitude, is defined, and is proven to enjoy global stability properties. As a result, the spacecraft travels toward the operational orbit of interest, i.e. either (a) an areostationary orbit, (b) a quasi-synchronous inclined orbit, or (c) a low-altitude, sunsynchronous orbit. Monte Carlo simulations, with stochastic density profiles and uncertain initial conditions, point out that the strategy at hand is successful and allows reducing the overall propellant budget in comparison to direct orbit injection based on chemical propulsion. Moreover, the overall time of flight typically ranges from 45 to 140 days, and therefore it is much shorter than that required with the use of aerobraking. As a last advantage, low-thrust nonlinear orbit control allows achievement of a variety of operational orbits, with great accuracy.

Satellite Collision and Fragmentation Probabilities Using Radar-Based Size and Mass Estimates

Most conjunctions between Earth-orbiting satellites involve unknown objects, typically debris created by explosions or collisions. This study formulates methods to estimate probabilities of collision and fragmentation for such conjunctions, which depend on the estimated sizes and masses of the unknown objects. Analysis of radar cross-section (RCS) measurements provides estimated sizes, found to be accurate at the 90% confidence level to within a factor of 0.59 for potential underestimations and to within a factor of 3.1 for potential overestimations. For satellites that experience measurable atmospheric drag orbital perturbations, combining RCS data with orbit determination ballistic coefficients provides mass estimates accurate to within factors of 0.47 to 10.9 at the 90% confidence level. For satellites with perigee altitudes above 450 km, combining RCS data with solar radiation pressure coefficients provides mass estimates accurate to within factors of 0.44 to 5.6 at 90% confidence. The collision and fragmentation risk assessment formulation accounts for these size and mass estimation uncertainties. Specifically, conjunction collision probabilities formulated as statistically expected values account for the RCS-based size estimation uncertainties. Fragmentation probabilities, which measure the likelihood of producing more than a threshold number of collision fragments, account for both size and mass estimation uncertainties.

An analysis tool for collision avoidance manoeuvres using aerodynamic drag

Aerodynamic collision avoidance manoeuvres provide an opportunity for satellites in Low Earth Orbits to reduce the risk during close encounters. With rising numbers of satellites and objects in orbit, satellites experience close encounters more frequently. Especially those satellites without thrusting capabilities face the problem of not being able to perform impulsive evasive manoeuvres. For satellites in Low Earth Orbits, though, perturbing forces due to aerodynamic drag may be used to influence their trajectories, thus offering a possibility to avoid collisions. This work introduces a tool for the analysis of aerodynamic collision avoidance manoeuvres for satellites in circular Low Earth Orbits. Current space-weather data are employed to estimate the density the satellite encounters. Achievable in-track separation distances following a variation of the ballistic coefficient through a change in attitude are then derived by evaluating an analytical equation from literature. Considering additional constraints for the attitude, e.g., charging phases, and uncertainties in the used parameters, the influence of a manoeuvre on the conjunction geometry and the collision probability is examined. The university satellite Flying Laptop of the University of Stuttgart is used as an exemplary satellite for analysis, which show the general effectiveness of evasive manoeuvres employing aerodynamic drag. First manoeuvring strategies can be deducted and the influence of parameter uncertainties is assessed.

Studies of Satellite Position Measurements of LEO CubeSat to Identify the Motion Mode Relative to Its Center of Mass

This paper addresses the possibility of reconstructing motion relative to the center of mass of a low Earth orbit (LEO) nanosatellite of the CubeSat 3U standard using satellite position measurements (Two-Line Element Set (TLE)). This kind of task needs to be performed in the case where it is not possible to establish radio communication with the nanosatellite after it is launched into orbit. Therefore, it is important for the nanosatellite developers to develop some understanding of what is going on with the nanosatellite in order to be able to analyze the current situation after deployment. The study was carried out on the example of the aerodynamically stabilized SamSat-218D nanosatellite developed by the professors and students of Samara National Research University. SamSat-218D was launched into a near-circular orbit with an average altitude of 486 km on April 2016 during the first launch campaign from the Vostochny cosmodrome. Knowledge of CubeSat aerodynamics allows estimating the nature of its possible motion relative to the CubeSat center of mass by ballistic coefficient changes, evaluated with the use of satellite position measurements. The analysis showed that SamSat-218D performed spatial rotation with an angular velocity of more than two degree per second and had not stabilized aerodynamically by 2 March 2022, when it entered the atmosphere and was destroyed.

Aggregation Kinetics in Sedimentation: Effect of Diffusion of Particles

The aggregation kinetics of settling particles is studied theoretically and numerically using the advection–diffusion equation. Agglomeration caused by these mechanisms (diffusion and advection) is important for both small particles (e.g., primary ash or soot particles in the atmosphere) and large particles of identical or close size, where the spatial inhomogeneity is less pronounced. Analytical results can be obtained for small and large Péclet numbers, which determine the relative importance of diffusion and advection. For small numbers (spatial inhomogeneity is mainly due to diffusion), an expression for the aggregation rate is obtained using an expansion in terms of Péclet numbers. For large Péclet numbers, when advection is the main source of spatial inhomogeneity, the aggregation rate is derived from ballistic coefficients. Combining these results yields a rational approximation for the whole range of Péclet numbers. The aggregation rates are also estimated by numerically solving the advection–diffusion equation. The numerical results agree well with the analytical theory for a wide range of Péclet numbers (extending over four orders of magnitude).

Space Event and Outlier Detection Based on Expectation Maximization Algorithm

The United States provide Element Sets (ELSET) database in Two-Line Element (TLE) format for public use, which plays an important role in the inversion of atmospheric density in the thermosphere, ballistic coefficient estimation, early-warning and so on. Due to large uncertainties existing in the TLE generation process, space environment changes, and space events, ELSET database contains a large number of abnormal TLE data to be filtered, such as corrected TLE, orbital element outlier, and Bstar outlier. The existing methods to filter out the outliers lack general applicability and are very complicated, which are only applicable to a few space targets in certain orbit regions. To overcome the shortcomings of the existing methods, a filtering method is proposed based on Expectation Maximization (EM) algorithm employing a sliding window and polynomial fitting method, which can detect outliers for different orbital elements and space events. The research shows that the algorithm can effectively single out the outliers in TLE sequences and is suitable for all orbital debris.

Machine learning-based approach for ballistic coefficient estimation of resident space objects in LEO

The increasing number of Resident Space Objects poses a serious threat to the safe operation of satellites. Alongside with mitigation policies, it is fundamental to predict the trajectories of such objects which requires the accurate estimation of the physical characteristics that influence their orbits. An important role is played by the area-to-mass ratio, i.e., the ratio between the area exposed to the atmosphere/the Sun and the mass of the space object for the LEO/MEO and GEO region. Current literature proposes several approaches for the estimation of the area-to-mass ratio, ranging from semi-analytical to numerical methods. As regards the latter category, recent studies have focused on classification or regression algorithms for specific types of orbits (e.g., sun-synchronous, geostationary).In this context, this paper proposes a machine learning-based regression approach for the estimation of the ballistic coefficient (i.e., the product between the drag coefficient and the area-to-mass ratio) in Low Earth Orbit, covering a wide set of orbital parameters. Using a synthetic space catalogue, the performance of different types of machine learning techniques is evaluated and compared. A sensitivity analysis is carried out to analyse the effect on performance of the number of trainings, the propagation time, the number of objects of the training data set, and the frequency of the measurements. The applicability of the presented approach is tested and discussed using both real (i.e., based on publicly available catalogues of Two-Line Elements) and synthetic datasets.

기동모델이 변침기동 탄도탄 추적에 미치는 영향에 대한 고찰

This paper addresses the maneuvering ballistic target tracking problem for advanced missile defense systems. Based on the fact that the performance degradation of the existing tracking filters is mainly caused by the uncertainties in motion model of a ballistic target, an explicit maneuver model is introduced by utilizing a prior knowledge on the lift-induced drag characteristics. This model exploits the constraints among the ballistic coefficients, which enables us to design a tracking filter with more reliable target tracking performance in practice. Moreover, since the mismatch between our explicit ballistic target maneuver model and the real target motion leads to the bias of the residual sequence of the tracking filter, this property can also be used for target classification or recognition. Through simulation using a typical ballistic target tracking scenario, it is demonstrated that the proposed filter provides superior and reliable maneuvering ballistic target tracking performance.

Aerocapture Optimization Method with Lift–Drag Joint Modulation Suitable for Variable Structure Spacecraft

Aerocapture, the action of delivering a vehicle from a hyperbolic orbit to a planetary orbit by using the aerodynamic force, could potentially lower fuel consumption. By controlling the direction and size of the aerodynamic force, the vehicle can accurately enter the target orbit. This paper focuses on a preliminary study of the optimal trajectory for aerocapture on the basis of a novel flight control option, which considers lift and drag joint modulation so as to suit variable structure spacecraft. In the preliminary evaluation of such a flight control option, the aerocapture corridors under lift modulation and drag modulation and the influence of the ballistic coefficient on aerocapture were analyzed, demonstrating that joint modulation can achieve complementary advantages compared with pure lift modulation and drag modulation. Based on this flight control option, optimal aerocapture trajectories with different path constraints, target orbital constraints and control variable constraints were found. It bears noting that both the bank angle and the reference area were taken as control variables for lift modulation and drag modulation, respectively, during the atmospheric flight in the process of designing the optimal trajectories. The optimal results indicate that the flight control option with lift and drag joint modulation can greatly broaden the necessary conditions for aerocapture and extend the target orbital range.

Design of a deployable mechanism based on 7R-6R-double-loop units for mars decelerators

The increasing interest in decelerators utilized in Mars exploration has heightened the need for a decelerator with the function of deploying and a low ballistic coefficient. This paper designed a novel deployable mechanism based on 7R-6R double-loop units for Mars decelerators. First, this paper designed a new double-loop deployable unit coupled by a 7R loop and 6R loop through type synthesis based on line geometry. Then, the mobility of the mechanism was proven to be single by using screw theory. In addition, the singularity of the mechanism was investigated, which contains 3 singular configurations. Geometric conditions to avoid singular configurations were obtained in the singularity analysis. Finally, a scaled model utilized to verify the configuration and assemblability of the deployable unit was developed.

Characterization of the Fireballs Detected by All-sky Cameras in Romania

Some of the fields of research that have captured the persistent interest of both scientists and the general public are meteor phenomena. The main goal in the study of meteoroid impacts into Earth’s atmosphere is the recovery of the remnant matter after the ablation in the form of meteorites. This is a complementary approach, yet cheap alternative, to a sample return mission. Meteoroids are messengers since the time of the formation of the solar system due to the fact that they have preserved the same composition. The study of meteorites provides information regarding the chemical composition from which the planets formed. The increasing number of all-sky camera networks in recent years has resulted in a large set of events available for study. Thus, it is very important to use a method that determines whether the meteoroid could produce a meteorite or not. In this paper we study the meteors detected by the FRIPON network in Romania with the use of all-sky cameras. We focus on the events with noticeable deceleration (V f /V 0 < 0.8). We determine the ballistic coefficient α and the mass-loss parameter β for the selected sample. Based on this analysis the events are classified in three categories: (1) meteoroids that are likely to produce meteorites; (2) meteoroids that can possibly produce meteorites; (3) meteoroids that are unlikely to produce meteorites. The entry and final mass are determined for each event. From the recorded fireballs, we identified one possible meteorite dropper, and we analyzed its dynamical evolution.