Academic literature on the topic 'Launch Vehicle Model'

The controller design for reusable launch vehicles is challenging due to enormous amounts of model parameter uncertainties and atmospheric disturbances. This paper first derives six-degree-of-freedom model of a reusable launch vehicle with atmospheric disturbances. Next, four kinds of atmospheric disturbances are introduced and wind models are established respectively. For attitude control of the reusable launch vehicle, a nonsingular terminal sliding mode controller is designed with stability guaranteed. Finally, simulation results show a satisfactory performance for the attitude tracking of the reusable launch vehicle with atmospheric disturbances.

The launch vehicle industry has long been considered a pioneering industry in systems engineering. Launch vehicles are large complex systems that require a methodical multi-disciplinary approach to design, build, and launch. Launch vehicles are used to deliver payloads—such as humans, robotic science missions, or national security payloads—to desired locations in space. Previous research has identified deficient or underperforming systems engineering as a leading contributor to launch vehicle failures. Launch vehicle failures can negatively affect national security, the economy, science, and society, thus highlighting the importance of understanding the factors that influence systems engineering in launch vehicle organizations in the United States. The purpose of this study was to identify and evaluate the relationships between organizational factors and systems engineering process performance. Structural equation modeling was used to develop a model of the relationships of these factors and test hypotheses. The results showed that organizational commitment, top management support, the perceived value of systems engineering, and systems engineering support significantly influence systems engineering process performance in the launch vehicle industry. Implications of this study for improving the performance of systems engineering in launch vehicle organizations are discussed.

Safety of the up-to-date rocket and space complexes remains a topical problem for the developers of rocket and space technology. The integral component of this problem along with the safety of operations during launch vehicle ground pre-launch processing is organization of flight safety. The basic task of this rocket and space complexes safety component is to prevent or minimize serious consequences in case of launch vehicle failure in the flight leg, after all such accidents can cause damage to the population and facilities (including personnel and facilities of the ground complex), located along the flight paths. It is shown that the flight safety assurance of the launch vehicle is based on the experience of combat missile systems. Flight safety during the launch vehicle launches is provided by laying flight paths through sparsely populated (unpopulated) territories and using special onboard flight safety systems. This system limits the size of impact zones of emergency launch vehicle and its debris by emergency engine shutdown. Recently flight safety process is organized based on the acceptable risk concept. It is based on a risk assessment for the ground-based facilities and people, and it should not exceed the established standards. Such approach requires development and upgrading of the mathematical models of risk assessment in case of launch vehicle failure in the flight phase. Formation of the risk-oriented approach to flight safety in Yuzhnoye SDO is shown. Key moment in this process is to develop the separate structural unit, which started working on rocket and space complexes flight safety assurance and analysis. The basic model for assessing the risks of damage to facilities and people is analyzed, using the maximum impact zone of an emergency launch vehicle, which is realized in case of loss of control and flight safety system activation. The main directions of the basic model improvement are shown, which led to the development of a number of new original models of flight safety assessment in the Yuzhnoye SDO. First of all, the developed models take into account the flight safety system specifics, which are used to equip the launch vehicles, developed by Yuzhnoye SDO: criteria of activation, blocking of the engine emergency shutdown in the initial flight phase and Fe functional. Such models allow to take into account the different nature of emergency situations in the launch vehicle flight phase and ways of their representation, representation of the damage areas of facilities in the form of convex polygons, possible fragmentation of the emergency launch vehicle at the free- fall leg etc. The developed models have found wide application in the practice of assessing flight safety indicators in the Yuzhnoye SDO projects. Key words: launch vehicle; acceptable risk; launch vehicle failure in the flight phase; flight safety system; emergency launch vehicle impact zone; risk of damage to facilities; collection risk.

Launch vehicles suffer from severe base heating during ascents. To predict launch vehicle base heat flux, the computational fluid dynamics (CFD) tools are widely used. The selection of the turbulence model determines the numerical simulation results of launch vehicle base heating, which may instruct the thermal protection design for the launch vehicle base. To assess performances, several Reynolds-averaged turbulence models have been investigated for the base heating simulation based on a four-nozzle launch vehicle model. The finite-rate chemistry model was used for afterburning. The results showed that all the turbulence models have provided nearly identical mean flow properties at the nozzle exit. Menter’s baseline (BSL) and shear stress transport (SST) models have estimated the highest collision pressure and have best predicted base heat flux compared to the experiment. The Spalart-Allmaras (SA) model and the renormalization group (RNG) model have performed best in temperature estimation, respectively, in around r/rb=0~0.2 and r/rb=0.6~1. The realizable k‐ε (RKE) model has underestimated the reverse flow and failed to correctly reflect the recirculation in the base region, thus poorly predicted base heating. Among all the investigated turbulence models, the BSL and SST models are more suitable for launch vehicle base heating simulation.

At present, most small satellites are delivered as hosted payloads on large launch vehicles. Considering the current technological development, constellations of small satellites can provide a broad range of services operating at designated orbits. To achieve that, small satellite customers are seeking cost-effective launch services for dedicated missions. This paper deals with performance and cost assessments of a set of launch vehicle concepts based on a solid propellant rocket engine (S-50) under development by the Institute of Aeronautics and Space (Brazil) with support from the Brazilian Space Agency. Cost estimation analysis, based on the TRANSCOST model, was carried out taking into account the costs of launch system development, vehicle fabrication, direct and indirect operation cost. A cost-competitive expendable launch system was identified by using three S-50 solid rocket motors for the first stage, one S-50 engine for the second stage and a flight-proven cluster of pressure-fed liquid engines for the third stage. This launch system, operating from the Alcantara Launch Center, located at 2 ∘ 20’ S, would deliver satellites from the 500 kg class in typical polar missions with a specific transportation cost of about US$39,000 per kilogram of payload at a rate of 12 launches per year, in dedicated missions. At a low inclined orbit, vehicle payload capacity increased, decreasing the specific transportation cost to about 32,000 US$/kg. Cost analysis also showed that vehicle development effort would claim 781 work year, or less than 80 million dollars. Vehicle fabrication accounted for 174 work year representing less than 23 million dollars per unit. The launch system based on the best concept would, therefore, deploy small satellite constellations in cost-effective dedicated launches, 224 work year per flight, from the Alcantara Launch Center in Brazil.

Abstract In order to accurately analyze the effect of a shock wave on a missile launch vehicle as a whole and on its components when the launch vehicle is at a medium or long distance from the detonation center, a simulation method based on the empirical algorithm and numerical analysis was carried out in this study. The method significantly reduced the computational cost while ensuring computational accuracy. Based on the simulation method, a finite element model for a typical missile launch vehicle was established that consisted of 2.5 million elements. Based on the structured arbitrary Lagrangian-Eulerian method and the fluid-structure coupling algorithm, it took the model only a few hours to simulate the second-level physical process. Next, a shock wave load model was built with a 2000 kg TNT equivalent detonation condition, and the degree of damage to the launch vehicle within 25–45 m from the detonation center was analyzed. The results showed that the joint action of the shock wave overpressure and the dynamic pressure was the main source of damage. Specifically, the missile launcher, the cab, and the fuel tank were the key vulnerable parts. The effective damage radius of the 2000 kg TNT equivalent detonation to the missile launch vehicle was 35 m.

Introduction. A constant increase in the amount of space debris already constitutes a significant threat to satellites in nearEarth orbits, starting with the trajectory of their launch vehicle injection. Problem Statement. Design and development of various modern methods of protection against space debris requires knowledge of the statistical characteristics of the distribution of the kinematic parameters of the simultaneous motion of a launch vehicle injecting satellite and a group of space debris objects in the area of its trajectory. Purpose. Development of a mathematical model of a launch vehicle rendezvous with a group of observable orbital debris while injecting a satellite into near-earth orbits with an altitude of up to 2100 km and an inclination from 45 to 90 degrees. Materials and Methods. The following methods are used in the research: analysis, synthesis, comparison, simulation modeling, statistical processing of experimental results, approximation, correlation analysis, and the least squares method. Results. The simultaneous motion of a launch vehicle and a group of space debris objects has been studied. The distributions of relative distance, relative velocity, angle of encounter, and moments of time of approach of a launch vehicle to a group of the observed space debris at a relative distance of less than 5 km have been obtained. The dependence of the average rendezvous concentration on the distribution of space debris across the average altitude of the orbit and the inclination of the target orbit of the launch vehicle has been determined. The dependence of the average probability of rendezvous in the launch on the inclination of the target orbit, the number of orbital debris, and the relative distance of the rendezvous has been determined. Conclusions. The obtained mathematical model of rendezvous of a launch vehicle with a group of observed orbital debris can be used while designing means of cleaning the near-Earth space and systems to protect modern satellite launch vehicles from orbital debris. In addition, the results of the research can be used to assess the impact of unobserved orbital debris on the flight of a launch vehicle.

Introduction. A constant increase in the amount of space debris already constitutes a significant threat to satellites in nearEarth orbits, starting with the trajectory of their launch vehicle injection. Problem Statement. Design and development of various modern methods of protection against space debris requires knowledge of the statistical characteristics of the distribution of the kinematic parameters of the simultaneous motion of a launch vehicle injecting satellite and a group of space debris objects in the area of its trajectory. Purpose. Development of a mathematical model of a launch vehicle rendezvous with a group of observable orbital debris while injecting a satellite into near-earth orbits with an altitude of up to 2100 km and an inclination from 45 to 90 degrees. Materials and Methods. The following methods are used in the research: analysis, synthesis, comparison, simulation modeling, statistical processing of experimental results, approximation, correlation analysis, and the least squares method. Results. The simultaneous motion of a launch vehicle and a group of space debris objects has been studied. The distributions of relative distance, relative velocity, angle of encounter, and moments of time of approach of a launch vehicle to a group of the observed space debris at a relative distance of less than 5 km have been obtained. The dependence of the average rendezvous concentration on the distribution of space debris across the average altitude of the orbit and the inclination of the target orbit of the launch vehicle has been determined. The dependence of the average probability of rendezvous in the launch on the inclination of the target orbit, the number of orbital debris, and the relative distance of the rendezvous has been determined. Conclusions. The obtained mathematical model of rendezvous of a launch vehicle with a group of observed orbital debris can be used while designing means of cleaning the near-Earth space and systems to protect modern satellite launch vehicles from orbital debris. In addition, the results of the research can be used to assess the impact of unobserved orbital debris on the flight of a launch vehicle.

Abstract In the process of launch vehicle multidisciplinary design optimization, aerodynamic calculation takes a long time, which affects the overall design cycle. In order to solve the above problems, based on the idea of machine learning, this paper constructs the surrogate model of relevance vector machine and calculates the aerodynamic coefficients of launch vehicles quickly. Firstly, the aerodynamic model of launch vehicle is established, and the orthogonal design method is used to generate test sample points. Then, the aerodynamic coefficients of the sample points are calculated by using Fluent software, and the training data of the surrogate model are obtained. On this basis, the relevance vector machine model is trained with training data, generating correlation vector machine agent model. Finally, the calculation accuracy of the surrogate model is evaluated by simulation, and the feasibility and validity of the method are verified.

This study investigates the use of a Model Reference Adaptive Control (MRAC) direct approach to solve the attitude control problem of an Expendable Launch Vehicle (ELV) during its boost phase of flight. The adaptive autopilot design is based on Lyapunov Stability Theory and provides a useful means for controlling the ELV in the presence of environmental and dynamical uncertainties. Several different basis functions are employed to approximate the nonlinear parametric uncertainties in the system dynamics. The control system is designed so that the desire dresponse to a reference model would be tracked by the closed-loop system. The reference model is obtained via the feedback linearization technique applied to the nonlinear ELV dynamics. The adaptive control method is then applied to a representative ELV longitudinal motion, specifically the 6th flight of Atlas-Centaur launch vehicle (AC-6) in 1965. The simulation results presented are compared to that of the actual AC-6 post-flight trajectory reconstruction. Recommendations are made for modification and future applications of the method for several other ELV dynamics issues, such as control saturation, engine inertia, flexible body dynamics, and sloshing of liquid fuels.
M.S.A.E.
Department of Mechanical, Materials and Aerospace Engineering
Engineering and Computer Science
Aerospace Engineering MSAE

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2002.
Includes bibliographical references (p. 188-189).
During the boost phase of ascent, winds have a significant impact on a launch vehicle's angle of attack, and can induce large structural loads on the vehicle. Traditional methods for mitigating these loads involve measuring the winds prior to launch and designing trajectories to minimize the vehicle angle of attack (a). The current balloon-based method of collecting wind field information produces wind profiles with significant uncertainty due to the inherent time delays associated with balloon measurement procedures. Managing the mission risk caused by these uncertain wind measurements has always been important to control system designers. This thesis will describe a novel approach to managing structural loads through the combination of a Light Detection and Ranging (LIDAR) wind sensor, and Model Predictive Control (MPC). LIDAR wind sensors can provide near real-time wind measurements, significantly reducing wind uncertainty at launch. MPC takes full advantage of this current wind information through a unique combination of proactive control, constraint integration and tuning flexibility. This thesis describes the development of two types of MPC controllers, as well as a baseline controller representative of current control methods used by industry. A complete description of Model Predictive Control theory and derivation of the necessary control matrices is included. The performance of each MPC controller is compared to that of the baseline controller for a wide range of wind profiles from both the Eastern and Western U.S. Test Ranges. Both MPC controllers are shown to provide reductions of greater than 50% in a, Qa and structural bending moments. In addition, the effects of wind measurement delays and uncertainty on the performance of each controller are investigated.
by Andrew Allen Martin.
S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2002.
Includes bibliographical references (p. 235-236).
The space industry plans to develop new reusable launch vehicles. The new vehicles will need advanced, new guidance and control systems. Since 1996 Draper Laboratory has been developing the next generation guidance and control for reusable launch vehicles in which guidance and control is integrated into one correlated system. Draper's research of integrated guidance and control originated with a single loop multivariable control scheme using time-invariant linear quadratic regulator theory. The research has since evolved into the use of model predictive control theory. The main focus of this thesis is the theory and design of model predictive control for entry of aerospace vehicles. The goal is to develop design criteria and guidelines explaining how to select the model predictive control parameters: prediction horizon, simulation rates, and weighting matrices. A secondary goal is to tightly couple an onboard trajectory generation algorithm with the model predictive controller to improve tracking performance and robustness. Favorable tracking is achieved through two model predictive control architectures, which are discussed. The first architecture has an inner loop stability augmentation system with model predictive control used as an outer loop. The second architecture replaces the inner and outer loops with a single model predictive controller. The two architectures demonstrate the flexibility of model predictive control to adapt to new vehicles; the model predictive control may be used to augment an existing inner loop or may be used as a stand-alone controller. The design focuses primarily on the architecture without a stability augmentation system.
by Robert C. LePome, II.
S.M.

La conception de lanceurs est un problème d’optimisation multidisciplinaire dont l’objectif est de trouverl’architecture du lanceur qui garantit une performance optimale tout en assurant un niveau de fiabilité requis.En vue de l’obtention de la solution optimale, les phases d’avant-projet sont cruciales pour le processus deconception et se caractérisent par la présence d’incertitudes dues aux phénomènes physiques impliqués etaux méconnaissances existantes sur les modèles employés. Cette thèse s’intéresse aux méthodes d’analyse et d’optimisation multidisciplinaire en présence d’incertitudes afin d’améliorer le processus de conception de lanceurs. Trois sujets complémentaires sont abordés. Tout d’abord, deux nouvelles formulations du problème de conception ont été proposées afin d’améliorer la prise en compte des interactions disciplinaires. Ensuite, deux nouvelles méthodes d’analyse de fiabilité, permettant de tenir compte d’incertitudes de natures variées, ont été proposées, impliquant des techniques d’échantillonnage préférentiel et des modèles de substitution. Enfin, une nouvelle technique de gestion des contraintes pour l’algorithme d’optimisation ”Covariance Matrix Adaptation - Evolutionary Strategy” a été développée, visant à assurer la faisabilité de la solution optimale. Les approches développées ont été comparées aux techniques proposées dans la littérature sur des cas tests d’analyse et de conception de lanceurs. Les résultats montrent que les approches proposées permettent d’améliorer l’efficacité du processus d’optimisation et la fiabilité de la solution obtenue
Launch vehicle design is a Multidisciplinary Design Optimization problem whose objective is to find the launch vehicle architecture providing the optimal performance while ensuring the required reliability. In order to obtain an optimal solution, the early design phases are essential for the design process and are characterized by the presence of uncertainty due to the involved physical phenomena and the lack of knowledge on the used models. This thesis is focused on methodologies for multidisciplinary analysis and optimization under uncertainty for launch vehicle design. Three complementary topics are tackled. First, two new formulations have been developed in order to ensure adequate interdisciplinary coupling handling. Then, two new reliability techniques have been proposed in order to take into account the various natures of uncertainty, involving surrogate models and efficient sampling methods. Eventually, a new approach of constraint handling for optimization algorithm ”Covariance Matrix Adaptation - Evolutionary Strategy” has been developed to ensure the feasibility of the optimal solution. All the proposed methods have been compared to existing techniques in literature on analysis and design test cases of launch vehicles. The results illustrate that the proposed approaches allow the improvement of the efficiency of the design process and of the reliability of the found solution

This work focuses on tracking launch vehicles with multiple radar sites and proposes a data fusion strategy based on the Covariance Intersection (CI) method. At each site, multiple models are embedded in a Kalman filter or locally estimate position, velocity, and acceleration using a de-biased measurement transformation from spherical to cartesian coordinates. The estimation of position, velocity, and acceleration of moving object based on radar measurements is critical in applications such as air traffic control, surveillance systems, and orbital vehicles launching among many others. However, this work will focus on the conditions observed at Alcântara Launch Center, where two radars located at distinct sites provide the trajectory coverage. All simulations presented herein make use of actual data obtained from a VS30 sounding rocket launch at Alcântara Launch Center in February, 2000. Impact point prediction is also assessed, and considers uncertainties inferred form the computed covariance matrix, culminating in an ellipsoidal impact area with a given impact probability.

O sistema de controle por alocação dos pólos com filtro foi utilizado para controlar a atitude de um modelo de veículo lançador de satélites. Com este intuito, foram confeccionados um modelo e uma base de fixação que permite a movimentação nos três graus de liberdade. Utilizando a resposta à entrada degrau em conjunto com um sistema de controle PID obtido de forma empírica para estabilizar o sistema, as características da planta foram identificadas e então o sistema de controle por alocação de pólos foi projetado. Este sistema apresentou uma oscilação em torno da referência com amplitude menor do que 0,5° e tempo de pico para a entrada degrau na ordem de 2,17 segundos. Um segundo controlador PID foi projetado de forma analítica para se obter uma referência, porém apresentou resposta com características inferiores ao controlador por alocação de pólos. Os dois sistemas de controle projetados conseguem manter o modelo estável mesmo quando um dos motores é desligado.
Pole placement control system with filter was implemented to control the attitude of a satellite launch vehicle model. With this purpose, a model and a fixing base with three degrees of freedom was made. Utilizing the system response to step input with PID controller empirically designed to stabilize the system, the model characteristics were identified and the pole placement control system was designed. This system oscillated around the reference with amplitude smaller than 0.5° and peak time around 2.17 seconds. Another PID controller was designed analytically for reference, however the pole placement controller had better response characteristics than the PID controller. Both controllers can stabilize the system even when one engine is shut off.

A launch vehicle experiences intense acoustic loading in the initial phase of its lift-off due to the noise generated by the rocket exhaust. This affects the launch vehicle structure in addition to sensitive payloads and may result in their failure. The launch vehicle structure has to be specially stiffened to withstand such loading which adversely affects its payload capabilities. Therefore, the mitigation of the lift-off acoustic environment of the launch vehicle is of utmost importance. At lift-off, the components of launch environment such as the launch platform and jet blast deflector contribute to the intense acoustic loads experienced by the launch vehicle by either reflecting the noise generated by the rocket jet exhaust or by creating additional sources of noise. Though the effect of jet blast deflector shape on the acoustic loading has been extensively investigated, contributions from other launch structures such as the launch platform are often ignored. The present work attempts to characterize the acoustic behaviour of the launch platform by simulating a scaled down launch vehicle environment at lift-off, inside an anechoic chamber. The lift-off scenario was simulated by allowing jets from single and twin jet launch vehicle models to impinge on flat plates with and without cut-outs, at varying lift-off distances. The results from the acoustic measurements carried out in the near and far-field of the launch vehicle models show that the presence of the cut-outs have significant effect on the near-field acoustics of the launch vehicle at low lift-off distances(L/De). The acoustic field in the vicinity of the launch vehicle is found to be considerably lower than that obtained when jets impinged on solid flat plates without cut-outs. The influence of the cut-outs, diminishes at higher L/De, when a large fraction of the jet, in addition to flowing through the cut-outs, impinges on the launch platform. The study also explores a new concept of including perforations in the launch platform as a means to attenuate the its contribution to the acoustic levels experienced by the launch vehicle. The inclusion of perforations in the launch platform, decreased the surface area of the launch platform available for jet impingement at higher L/De, thereby reducing the acoustic levels experienced by the launch vehicle at these lift-off distances. The perforated launch platform is found to be effective even with the presence of jet blast deflector, all the way up to 16 nozzle diameters after lift-off. Flow visualizations using schlieren technique indicate that the effectiveness of the perforations stem from the fact that they reduce the strength of the flow features such as wall jets and fountain flow - that are characteristic of jet impingement. The thesis brings out the significant contribution to the lift-off noise from a typical launch platform and the role of flow features like the wall jets and the fountain flow towards noise generation. It is shown that an attenuation of about 4-5 dB can be achieved at L/De>8 by perforating the platform. An optimal design of the launch platform incorporating the perforations can considerably reduce the acoustic loading of the launch vehicle thereby increasing its payload capabilities and ensuring its safety.

Stability is an important criterion in the design and performance of launch vehicles. Present day launch vehicles have become more and more flexible due to the constraints of weight reduction, necessarily imposed for enhanced performance of the vehicle. Due to higher flexibility, the launch vehicle stability becomes a concern. Instability in the launch vehicles has been noticed due to three major sources: thrust, aerodynamic forces and combustion induced instabilities. Instability in the launch vehicles may pose problem to the structural integrity leading to structural failure or it may lead to the deviation in the trajectory of the vehicle. Several structural failures of launch vehicles due to instabilities have been reported in the literature. The prediction of the structural response due to various excitations such as thrust and aerodynamic loading is essential to identify any failure scenarios and to limit the vibrations transmitted to the payload. Therefore, determination of dynamic and stability characteristics of a launch vehicle under the influence of different parameters, is of vital importance. Disciplines such as, flight mechanics (dynamics), structural dynamics, aerodynamics, propulsion, guidance and control are closely related in the design and analysis of launch vehicles. Typically, flight mechanics, guidance and control problems consider a rigid vehicle for modeling and simulation purposes. The disciplines of structural dynamics and aeroelasticity consider a flexible vehicle. In order to bring in the effect of flexibility on the flight dynamics of the launch vehicle, structural dynamics and aeroelasticity aspects need to be effected. The preliminary design of a new launch vehicle requires inputs from different disciplines and parametric studies are required to finalise the vehicle configuration. The study of the effect of different parameters on the dynamics and stability of launch vehicles is required. In this context, there is a need to develop an integrated approach that provides tools for the design and analysis of a launch vehicle. The availability of integrated modeling and simulation tools will reduce the requirement of costly prototype development and testing. In the present thesis, an attempt has been made to develop a numerical tool to conduct parametric studies for launch vehicle dynamics and stability. The developed tool is suitable for prediction of onset of instabilities under the influence of different parameters. The approach developed in this thesis is also well suited for specialized analysis of problems involving vertical launch, stage separation, engine shutdown and internal stress wave propagation related to structural integrity. Stability problems due to thrust and the aerodynamic forces (aeroelastic stability) in the launch vehicles/ missiles have been reported in the literature. Most of these works have modeled the vehicle as a beam or by using discrete degrees of freedom. In these works, the effect of thrust or aerodynamic forces on the flexible body modes is investigated and it is shown that the instability may occur in one of the bending modes due to change in the parameters such as thrust or aerodynamic forces. Traditionally, the dynamic characteristics are obtained in a body-fixed coordinate system, whereas the prediction of trajectory (rigid body dynamics) is carried out in an inertial frame of reference. Only few works have addressed the coupling of the rigid body motion and the flexible body dynamics of a vehicle. But these works also, do not consider the total derivative of displacements with respect to an inertial frame of reference. When the integrated equations of motion are derived in an inertial frame of reference, the rigid body motion and the elastic displacements are highly coupled. In this thesis, the rigid body motion and the flexible body dynamics is studied in an inertial frame of reference. The flexible body dynamics of the moving vehicle is studied in an inertial frame of reference, including velocity induced curvature effects, which have not been considered so far in the published literature. A detailed mechanics based model is developed to analyze the problem of structural instabilities in launch vehicles. Coupling among the rigid-body modes, the longitudinal vibrational modes and the transverse vibrational modes due to asymmetric lifting-body cross-section are considered. The model also incorporates the effects of aerodynamic forces and the propulsive thrust of the vehicle. The propulsive thrust is considered as a follower force. The model is one-dimensional, and it can be employed to idealized slender vehicles with complex shapes. The governing differential equations along with the boundary conditions are derived using Extended Hamilton’s principle. Subsequently, the modeling of the propulsive thrust and the aerodynamic forces are included in the formulation. In the literature, the propulsive thrust has generally been modeled as a follower force applied at the nozzle end. Few of the works in the literature have modeled the combustion process in the solid rocket motor and the liquid propellant engine in detail. This is required to understand the combustion induced instabilities. In the present thesis, the propulsive thrust is considered as a follower force and few of the combustion parameters affecting the thrust are considered. In the literature, the modeling of the aerodynamic forces acting on a launch vehicle has been carried out using general purpose computational fluid dynamics (CFD) codes or by using empirical methods. CFD codes are used to obtain the pressure and the shear stress distribution on the vehicle surface by the solution of Navier Stokes/ Euler equations. The empirical methods have been used to obtain the distributed aerodynamic forces acting on the vehicle. The aerodynamic forces are expressed in terms of distributed aerodynamic coefficients. In the present work, the modeling of the aerodynamic forces has been carried out in two different ways: using a CFD package and by using empirical methods. The stability of a system can be studied by determining the system response with time. Eigenvalue analysis is another tool to investigate the stability of a linear system. To study the stability characteristics of the system using eigenvalue analysis, a computational framework has been developed. For this purpose, the finite element discretization of the system is carried out. Further to that, two different methods are utilized for finite element discretization of the vehicle structure: Fourier Transform based Spectral Finite Element method (SFEM) and an hp Finite Element method (FEM). The conventional FEM is a versatile tool for modeling complicated structures and to obtain the solution of the system of equations for a variety of forcing functions. The SFEM is more suitable for obtaining the solution for simple 1D and 2D structures subjected to shock and transient loads, having high frequency content. In this thesis, the spectral finite element model is developed for a vehicle subjected to the propulsive thrust and the aerodynamic forces. Prediction of instability using SFEM, means solving a nonlinear eigenvalue problem. Standard computer codes or routines are not available for solving a nonlinear eigenvalue problem. A computer code has been written to solve the nonlinear eigenvalue problem using one of the algorithms available in the literature. An hp finite element model is also developed for launch vehicle. The finite element stiffness and damping matrices due to the thrust, the aerodynamic forces and the rigid body velocity and acceleration are derived using Lagrange’s equations of motion. A standard linear eigenvalue problem and a polynomial eigenvalue problem is formulated for determination of instability regimes of the vehicle. It is important to understand the influence of different parameters such as thrust, velocity, angle of attack etc. on the stability of a launch vehicle. Parametric studies are important during the preliminary design phase of a vehicle to identify the instability regimes. The design parameters can be changed to reduce the possibility of instabilities. Numerical simulations are carried out to determine the unstable regimes of a slender launch vehicle for propulsive thrust and velocity as the parameters, neglecting the aerodynamic forces. Comparison between the results based on a Fourier spectral finite element model and a hp finite element model are carried out. Phenomenon of static instability (divergence) and dynamic instability (flutter) are observed. Determination of mode shapes of the vehicle is important for deciding the placement of sensors and actuators on the vehicle. In this context, eigenvectors (mode shapes) for different end thrust and speed are analyzed. Further, numerical simulations are also carried out to determine the instabilities in a slender launch vehicle considering the combined effects of propulsive thrust, aerodynamic forces and mass variation. The finite element model simulation results for aeroelastic effects are compared with the published literature. Stability of a vehicle is analysed for velocity (free stream Mach number) as a parameter, at maximum propulsive thrust, including the effect of aerodynamic forces and mass variation. Phenomenon of static instability (divergence) and dynamic instability (flutter) are observed. With the increase in the Mach number, branching (splitting) and merging of the modes is observed. At higher Mach numbers, divergence and flutter are observed in different modes simultaneously. Numerical simulations are carried out for a typical nosecone launch vehicle configuration to analyse the aeroelastic stability at two different Mach numbers using empirical aerodynamic data. The phenomenon of flow separation and reattachment is observed at the cone-cylinder junction. The stability of a typical vehicle under propulsive thrust and aerodynamic forces is investigated using CFD derived aerodynamic data. The aerodynamic pressure and shear stress distribution for a launch vehicle are obtained from the CFD analysis. The effect of different parameters such as combustion chamber pressure, tip mass and slenderness ratio on the stability of a vehicle is studied. In the later part of the thesis, solution methodology for the time domain response for a coupled axial and transverse motion of a vehicle is developed. The axial responses (displacements and velocities) of a typical vehicle subjected to axial thrust are determined using direct integration of the equations of motion. The axial displacements due to two different thrust histories are compared. The axial velocities with time at different locations are determined. The time domain and the frequency domain responses for a representative vehicle subjected to a transverse shock force are determined using Spectral Finite Element method (SFEM). The system of equations for a coupled axial and transverse motion of a vehicle is developed. Numerical simulations are carried out to determine the coupled axial and transverse response of a vehicle subjected to axial and transverse forces. The coupling of rigid body motion with the elastic displacements is illustrated. The thesis is comprised of seven chapters. The first chapter gives a detailed introduction to launch vehicles and covers literature survey of launch vehicle dynamics and stability. The dynamics and stability related aspects of flexible structures are also discussed. In chapter 2, a detailed mathematical model of a slender launch vehicle is developed to analyze the problem of structural instabilities. Chapter 3 deals with the finite element discretization of the vehicle structure using two different methods: Fourier spectral finite element method and an hp finite element method. In chapters 4 and 5, numerical simulations are carried out to determine the instabilities in a slender launch vehicle considering the effects of propulsive thrust, aerodynamic forces and mass variation. In chapter 6, solution methodology for the time domain response for a coupled axial and transverse motion of a vehicle is developed. The last chapter gives the conclusions and the future scope of work. To summarize, this thesis is a comprehensive document, that not only describes some detailed mathematical models for launch vehicle stability studies, but also presents the effect of aerodynamic, propulsion and structural loads on the launch vehicle stability. Linear stability analysis of a representative vehicle is carried out for prediction of onset of the instabilities under the influence of different parameters such as velocity, thrust, combustion factors etc. The correlation between the stability analysis and the time domain response is established. In short, the matter presented in this thesis can serve as a useful design aide for those working in the launch vehicle design.

Stability is an important criterion in the design and performance of launch vehicles. Present day launch vehicles have become more and more flexible due to the constraints of weight reduction, necessarily imposed for enhanced performance of the vehicle. Due to higher flexibility, the launch vehicle stability becomes a concern. Instability in the launch vehicles has been noticed due to three major sources: thrust, aerodynamic forces and combustion induced instabilities. Instability in the launch vehicles may pose problem to the structural integrity leading to structural failure or it may lead to the deviation in the trajectory of the vehicle. Several structural failures of launch vehicles due to instabilities have been reported in the literature. The prediction of the structural response due to various excitations such as thrust and aerodynamic loading is essential to identify any failure scenarios and to limit the vibrations transmitted to the payload. Therefore, determination of dynamic and stability characteristics of a launch vehicle under the influence of different parameters, is of vital importance. Disciplines such as, flight mechanics (dynamics), structural dynamics, aerodynamics, propulsion, guidance and control are closely related in the design and analysis of launch vehicles. Typically, flight mechanics, guidance and control problems consider a rigid vehicle for modeling and simulation purposes. The disciplines of structural dynamics and aeroelasticity consider a flexible vehicle. In order to bring in the effect of flexibility on the flight dynamics of the launch vehicle, structural dynamics and aeroelasticity aspects need to be effected. The preliminary design of a new launch vehicle requires inputs from different disciplines and parametric studies are required to finalise the vehicle configuration. The study of the effect of different parameters on the dynamics and stability of launch vehicles is required. In this context, there is a need to develop an integrated approach that provides tools for the design and analysis of a launch vehicle. The availability of integrated modeling and simulation tools will reduce the requirement of costly prototype development and testing. In the present thesis, an attempt has been made to develop a numerical tool to conduct parametric studies for launch vehicle dynamics and stability. The developed tool is suitable for prediction of onset of instabilities under the influence of different parameters. The approach developed in this thesis is also well suited for specialized analysis of problems involving vertical launch, stage separation, engine shutdown and internal stress wave propagation related to structural integrity. Stability problems due to thrust and the aerodynamic forces (aeroelastic stability) in the launch vehicles/ missiles have been reported in the literature. Most of these works have modeled the vehicle as a beam or by using discrete degrees of freedom. In these works, the effect of thrust or aerodynamic forces on the flexible body modes is investigated and it is shown that the instability may occur in one of the bending modes due to change in the parameters such as thrust or aerodynamic forces. Traditionally, the dynamic characteristics are obtained in a body-fixed coordinate system, whereas the prediction of trajectory (rigid body dynamics) is carried out in an inertial frame of reference. Only few works have addressed the coupling of the rigid body motion and the flexible body dynamics of a vehicle. But these works also, do not consider the total derivative of displacements with respect to an inertial frame of reference. When the integrated equations of motion are derived in an inertial frame of reference, the rigid body motion and the elastic displacements are highly coupled. In this thesis, the rigid body motion and the flexible body dynamics is studied in an inertial frame of reference. The flexible body dynamics of the moving vehicle is studied in an inertial frame of reference, including velocity induced curvature effects, which have not been considered so far in the published literature. A detailed mechanics based model is developed to analyze the problem of structural instabilities in launch vehicles. Coupling among the rigid-body modes, the longitudinal vibrational modes and the transverse vibrational modes due to asymmetric lifting-body cross-section are considered. The model also incorporates the effects of aerodynamic forces and the propulsive thrust of the vehicle. The propulsive thrust is considered as a follower force. The model is one-dimensional, and it can be employed to idealized slender vehicles with complex shapes. The governing differential equations along with the boundary conditions are derived using Extended Hamilton’s principle. Subsequently, the modeling of the propulsive thrust and the aerodynamic forces are included in the formulation. In the literature, the propulsive thrust has generally been modeled as a follower force applied at the nozzle end. Few of the works in the literature have modeled the combustion process in the solid rocket motor and the liquid propellant engine in detail. This is required to understand the combustion induced instabilities. In the present thesis, the propulsive thrust is considered as a follower force and few of the combustion parameters affecting the thrust are considered. In the literature, the modeling of the aerodynamic forces acting on a launch vehicle has been carried out using general purpose computational fluid dynamics (CFD) codes or by using empirical methods. CFD codes are used to obtain the pressure and the shear stress distribution on the vehicle surface by the solution of Navier Stokes/ Euler equations. The empirical methods have been used to obtain the distributed aerodynamic forces acting on the vehicle. The aerodynamic forces are expressed in terms of distributed aerodynamic coefficients. In the present work, the modeling of the aerodynamic forces has been carried out in two different ways: using a CFD package and by using empirical methods. The stability of a system can be studied by determining the system response with time. Eigenvalue analysis is another tool to investigate the stability of a linear system. To study the stability characteristics of the system using eigenvalue analysis, a computational framework has been developed. For this purpose, the finite element discretization of the system is carried out. Further to that, two different methods are utilized for finite element discretization of the vehicle structure: Fourier Transform based Spectral Finite Element method (SFEM) and an hp Finite Element method (FEM). The conventional FEM is a versatile tool for modeling complicated structures and to obtain the solution of the system of equations for a variety of forcing functions. The SFEM is more suitable for obtaining the solution for simple 1D and 2D structures subjected to shock and transient loads, having high frequency content. In this thesis, the spectral finite element model is developed for a vehicle subjected to the propulsive thrust and the aerodynamic forces. Prediction of instability using SFEM, means solving a nonlinear eigenvalue problem. Standard computer codes or routines are not available for solving a nonlinear eigenvalue problem. A computer code has been written to solve the nonlinear eigenvalue problem using one of the algorithms available in the literature. An hp finite element model is also developed for launch vehicle. The finite element stiffness and damping matrices due to the thrust, the aerodynamic forces and the rigid body velocity and acceleration are derived using Lagrange’s equations of motion. A standard linear eigenvalue problem and a polynomial eigenvalue problem is formulated for determination of instability regimes of the vehicle. It is important to understand the influence of different parameters such as thrust, velocity, angle of attack etc. on the stability of a launch vehicle. Parametric studies are important during the preliminary design phase of a vehicle to identify the instability regimes. The design parameters can be changed to reduce the possibility of instabilities. Numerical simulations are carried out to determine the unstable regimes of a slender launch vehicle for propulsive thrust and velocity as the parameters, neglecting the aerodynamic forces. Comparison between the results based on a Fourier spectral finite element model and a hp finite element model are carried out. Phenomenon of static instability (divergence) and dynamic instability (flutter) are observed. Determination of mode shapes of the vehicle is important for deciding the placement of sensors and actuators on the vehicle. In this context, eigenvectors (mode shapes) for different end thrust and speed are analyzed. Further, numerical simulations are also carried out to determine the instabilities in a slender launch vehicle considering the combined effects of propulsive thrust, aerodynamic forces and mass variation. The finite element model simulation results for aeroelastic effects are compared with the published literature. Stability of a vehicle is analysed for velocity (free stream Mach number) as a parameter, at maximum propulsive thrust, including the effect of aerodynamic forces and mass variation. Phenomenon of static instability (divergence) and dynamic instability (flutter) are observed. With the increase in the Mach number, branching (splitting) and merging of the modes is observed. At higher Mach numbers, divergence and flutter are observed in different modes simultaneously. Numerical simulations are carried out for a typical nosecone launch vehicle configuration to analyse the aeroelastic stability at two different Mach numbers using empirical aerodynamic data. The phenomenon of flow separation and reattachment is observed at the cone-cylinder junction. The stability of a typical vehicle under propulsive thrust and aerodynamic forces is investigated using CFD derived aerodynamic data. The aerodynamic pressure and shear stress distribution for a launch vehicle are obtained from the CFD analysis. The effect of different parameters such as combustion chamber pressure, tip mass and slenderness ratio on the stability of a vehicle is studied. In the later part of the thesis, solution methodology for the time domain response for a coupled axial and transverse motion of a vehicle is developed. The axial responses (displacements and velocities) of a typical vehicle subjected to axial thrust are determined using direct integration of the equations of motion. The axial displacements due to two different thrust histories are compared. The axial velocities with time at different locations are determined. The time domain and the frequency domain responses for a representative vehicle subjected to a transverse shock force are determined using Spectral Finite Element method (SFEM). The system of equations for a coupled axial and transverse motion of a vehicle is developed. Numerical simulations are carried out to determine the coupled axial and transverse response of a vehicle subjected to axial and transverse forces. The coupling of rigid body motion with the elastic displacements is illustrated. The thesis is comprised of seven chapters. The first chapter gives a detailed introduction to launch vehicles and covers literature survey of launch vehicle dynamics and stability. The dynamics and stability related aspects of flexible structures are also discussed. In chapter 2, a detailed mathematical model of a slender launch vehicle is developed to analyze the problem of structural instabilities. Chapter 3 deals with the finite element discretization of the vehicle structure using two different methods: Fourier spectral finite element method and an hp finite element method. In chapters 4 and 5, numerical simulations are carried out to determine the instabilities in a slender launch vehicle considering the effects of propulsive thrust, aerodynamic forces and mass variation. In chapter 6, solution methodology for the time domain response for a coupled axial and transverse motion of a vehicle is developed. The last chapter gives the conclusions and the future scope of work. To summarize, this thesis is a comprehensive document, that not only describes some detailed mathematical models for launch vehicle stability studies, but also presents the effect of aerodynamic, propulsion and structural loads on the launch vehicle stability. Linear stability analysis of a representative vehicle is carried out for prediction of onset of the instabilities under the influence of different parameters such as velocity, thrust, combustion factors etc. The correlation between the stability analysis and the time domain response is established. In short, the matter presented in this thesis can serve as a useful design aide for those working in the launch vehicle design.

AbstractAerodynamic force plays an important role in the flight of space launch vehicles. Therefore, obtaining accurate aerodynamic characteristics is the basis and prerequisite for establishing an aerodynamic model and designing a vehicle with excellent characteristics.

Abstract The flow field around generic space launch vehicles with hot exhaust plumes is investigated numerically. Reynolds-Averaged Navier-Stokes (RANS) simulations are thermally coupled to a structure solver to allow determination of heat fluxes into and temperatures in the model structure. The obtained wall temperatures are used to accurately investigate the mechanical and thermal loads using Improved Delayed Detached Eddy Simulations (IDDES) as well as RANS. The investigated configurations feature cases both with cold air and hot hydrogen/ water vapour plumes as well as cold and hot wall temperatures. It is found that the presence of a hot plume increases the size of the recirculation region and changes the pressure distribution on the nozzle structure and thus the loads experienced by the vehicle. The same effect is observed when increasing the wall temperatures. Both RANS and IDDES approaches predict the qualitative changes between the configurations, but the reattachment location predicted by IDDES is up to 7% further upstream than that predicted by RANS. Additionally, the heat flux distribution along the nozzle and base surface is analysed and shows significant discrepancies between RANS and IDDES, especially on the nozzle surface and in the base corner.

AbstractIncreasing complex space missions require launch vehicles to be with greater load-carrying capacity, better orbit injection accuracy and higher reliability. Such demands also cause the increased complexity of the vehicle, leading to a higher probability of fault, especially for the propulsion system. To remedy this issue, an advanced and robust ascent guidance capable of fault-tolerant is critical for the success of mission. Iterative guidance method [1] (IGM) and powered explicit guidance [2] (PEG) are two commonly used methods for the ascent phase of launch vehicles. These two guidance methods work well in the nominal condition and can adapt to many off-nominal conditions [3]. However, they lack of strong adaptive capacity, which cannot guarantee the reliability when the dynamic model or parameters change significantly. Alternatively, numerical approaches based on the optimal control theory may be the better choice. The existing algorithms can be divided into direct methods and indirect methods. Using the indirect methods, the guidance problem is transformed into Hamilton two-point boundary value problems [4] (TPBVP), but the solving process of this Hamilton two-point boundary value problem is complicated and highly sensitive to the initial guess. Using the direct method, the guidance problem is transformed into a nonlinear programming problem [5] (NLP). However, solving such problem is extremely computational intensive, which is difficult to meet the real-time requirement for online application.

Active transportation can play an important role in promoting more physically active and positive public health outcomes. While walking and biking provide significant physical health benefits, their modal share remains low. As a new form of micromobility service, shared e-scooters can enhance the suite of options available in cities to promote active transportation and fill in the gaps when walking or biking are not preferred. Although e-scooters show potential as a mode of transportation, it is unclear whether people will adopt the technology for everyday use. Furthermore, shared micromobility (e.g., electric scooters) is gaining attention as a complementary mode to public transit and is expected to offer a solution to access/egress for public transit. However, few studies have analyzed integrated usage of shared e-scooters and public transit systems while using panel data to measure spatial and temporal characteristics. This study aims to examine the adoption and frequency of shared e-scooter usage and provide policy implementation. To do so, the researchers launched a survey in the Chicago region in late 2020 and collected a rich data set that includes residents’ sociodemographic details and frequency of shared e-scooter use. To characterize the frequency, the researchers used an ordered probit structure. The findings show that respondents who are male, low income, Millennials and Generation Z, or do not have a vehicle are associated with a higher frequency of shared e-scooter use. Furthermore, this study utilizes shared e-scooter trips for a 35-day measurement period from 10 shared e-scooter operators in Chicago, where the researchers used a random-parameter negative binomial modeling approach to analyze panel effects. The findings highlight the critical role of spatial and temporal characteristics in the integration of shared e-scooters with transit.