Thrust Profile Research Articles

Impact of Solid Rocket Propellant Grain Manufacturing Limitations on Launch Vehicle Capability

It is examined if any limitations in existing solid rocket propellant grain manufacturing methods adversely affected the payload capability of recent space launch vehicles. It is seen if the transition from heavy, segmented metal rocket motor casings to lightweight monolith composite casings is possible without loss of ability to design and realize high-performance grain configurations using simple and safe methods. Considering payload fraction as the comparative performance metric, recently flown solid rocket-propelled, small-lift launch vehicles were surveyed and ranked. Solid rocket boosters of underperforming launch vehicles were investigated for manufacturing factors influencing payload fraction by comparing them to boosters of better-performing launch vehicles in their weight class. Relationships between payload fraction and the solid boosters’ mass fractions, casing construction, shape of thrust profile, propellant grain configuration and method employed to manufacture the grain were analysed. It is shown that those launch vehicles that did not possess or use the technology necessary to manufacture high-performance grain configurations like undercut finocyl in monolith composite casings ended up having boosters delivering poor thrust profiles with high inert mass ultimately leading to low payload fractions.

Effect of Using Fractals as Grain Configuration on the Performance of Solid Rocket Motors

Grain design is a very crucial consideration for determining the performance of solid propellant rocket motors. A rocket’s performance and combustion characteristics (thrust profile, chamber pressure variation, propellant mass flow rate, and sliver among other important performance parameters) depend very strongly on the grain configuration. We propose fractal shapes (Koch star, Koch snowflake, Gosper, and Cesaro) as new port geometries and theoretically predict their performance using simulations based on the fast-marching method implemented in the open-source software Open-Motor. The initial thrust for fractal geometry grains was found to be significantly higher than the commonly used industry standard BATES and Finosyl ports. The fractal grains also showed a significant decrease in sliver as compared to the Finocyl port that is generally used to increase performance as compared to the circular BATES ports. Especially, The Koch snowflake port had a drastically lower sliver. These new grain geometries proposed in this work can be used for applications in which low initiation and ignition times along with high initial thrust are crucial. Moreover, these geometries can improve the performance of the solid rocket motor (SRM) owing to their better regression characteristics which promise complete utilization of the entire grain web.

On‐demand microwave growth of porosity within a granular composite energetic material: Void formation via a dielectric loss phase change binder additive for propellant burning rate control

AbstractThis study demonstrates, for the first time ever, the ability to grow, in an on‐command fashion, porosity within a granular composite energetic material to effect a change in energy output rate. Specifically, the study investigates the change in burning rates of ammonium perchlorate composite propellants as a result of porosity created in situ via microwave field‐driven volatilization of the low boiling point binder additive, ethylene glycol. Theoretical mass densities were measured before and after microwave irradiation finding that the maximum observed %TMD change for tested propellants is 6 %. Propellants were burned at 1.72 MPa to 6.89 MPa pressures, finding that for all propellants, microwave irradiation produced a change in ballistic characteristics. Most propellant formulations demonstrate acceptable burning rate parameters for use within rocket motors; some exhibited a large change in their pressure exponent as well as slope breaks attributed to the onset of convective burning, while microwave irradiation produced no change in burning rate or density in reference propellants without the additive. Microwave heating simulation results are presented to gain insight into the thermal environment of the propellant during microwave irradiation. These results provide valuable insight into propellant formulations that can have their burning rates (and thus the thrust profile for motor grains) altered after casting via microwave irradiation.

Demonstration of dual-thrust capability in hybrid rockets using multi-layered tubular fuel grains

This study demonstrates the thrust modulation capabilities of a hybrid rocket motor employing a Multi-Layered Tubular (MLT) fuel grain. The MLT configuration involves arranging the fuel grains with distinct regression rates as layers. As combustion progresses, the regression rate changes based on the burning of each fuel layer, leading to variable thrust while maintaining a constant oxidizer flow rate. Variable-thrust fuel grains are suitable for diverse mission types, including employment in sounding rockets and cruise missiles, particularly those designed for anti-ship operations and missions wherein a boost-sustain thrust profile is required. The MLT fuel grains were designed for a boost-sustain phase thrust profile generally observed in missiles. Wax was used as a booster fuel, and wax with 20%EVA was used as a sustainer fuel. Two MLT configurations with different durations for the boost phase were demonstrated. During the tests, the boost-sustain phase was achieved successfully. However, a transition phase was observed while shifting from the boost to the sustain phase. The delay of the transition phase was observed to increase when the duration of the boost phase increased. The combined effect of axial variation of fuel regression rate and local mass flux is the reason for the transition phase. The Thrust Turn-Down Ratio (TDR) for Multi-Layered Tubular (MLT) fuel grains was calculated. At a web thickness (for booster fuel) of 4 mm, the TDR was approximately 1.23:1, and at a 5.5 mm web thickness, it was 1.28:1. Further, 20%Mg was added to the wax to increase the regression rate of booster fuel. The Wax/20%Mg fuel showed 41% and 14% improvement in regression rate and thrust, respectively. The TDR was improved marginally compared to pure wax-based MLT grain.

Controllable cone for horizontal landing on asteroids using a flexible probe

The recently proposed flexible probe for asteroids provides a novel scheme for landing on low-gravity surface. To understand the feasible initial condition of the flexible probe's horizontal landing trajectory under multiple constraints, a controllable cone is defined and investigated. The boundary of the controllable cone is calculated using a double-layer optimization method. In the inner-layer, the switching time of the thrust profile is fixed, and the boundary point is solved through a multi-constraint trajectory optimization problem that considers the influence caused by the flexible deformation. In the outer-layer, the switching time of the thrust profile is optimized to maximize the cone boundary. To improve the optimization efficiency, an adaptive interval is used to search the switching time. With the double-layer optimization method, the controllable cone boundaries can be generated for both a specific height and a three-dimensional space. The controllable cone of the flexible probe is simulated for the landing on asteroid 433 Eros, and the influence of the flexible deformation is also analyzed.

Lab-on-PCB solid propellant microthruster with multi-mode thrust capabilities.

In the realm of nano/microsatellite clustering, the demand for microthrusters is steadily growing. Solid propellant microthrusters, recognized for their lightweight build and structural simplicity, carry significant commercial promise. However, existing solid propellant microthrusters manufactured using MEMS technology encounter notable issues such as inconsistent thrust generation positions, limited thrust profiles, and issues related to productivity, scalability, and durability. In this study, we propose a novel shared-chamber solid-propellant microthruster design that consistently produces thrust at a designated position and accommodates multiple thrust modes. The components and fabrication of this thruster were developed using lab-on-printed-circuit-board (PCB) technology and PCB surface mount technology, showcasing enhanced structural stability, scalability, and potential for mass production. Our ignition and combustion experiments confirmed the repeatability of the unit operation, a fundamental feature of this innovative microthruster. Furthermore, we successfully implemented and evaluated the power mode for increased thrust and the continuous mode for prolonged operational duration. Integrating the lab-on-PCB-based shared-chamber solid propellant microthruster with propulsion and electronic control systems holds promising potential for future satellite missions.

Practical Methods of Optimizing the Maximum Range for Rockets

Range extension for artillery projectiles, rockets, and missiles is a problem of trajectory optimization based on a set of constraints aimed at maximizing the range as a measure of performance. Solid Rocket Motors (SRM) are rocket motors that use solid propellants. For higher engine efficiency and cost minimization, optimization of the engine is necessary, which implies a modification of the schematics of the engine. SRM optimization is currently a key topic in aerospace engineering research. Because some input data remain constant, others can be considered as variables, and their influence on the performance parameters of the rockets was investigated. In some investigations, the time until impact is an important performance parameter; in others, the range can be considered as the performance parameter to be optimized. In this study, pulsed solid propellant rocket motor technology was considered to demonstrate a feasible method for range extension. For the targeted optimization problem, the influence of the thrust profile along the launching angles was studied, and the results from the performed calculations were analyzed and discussed.

Effect of the nature of uncertainty on the optimization of collision avoidance maneuvers

With the soaring number of space debris, collision avoidance maneuvers have become crucial to ensure the safety of any operating satellite. In real-world scenario, the problem gets a little more complicated due to the presence of uncertainty in the values of the states of the space objects. Also, the uncertainty distribution assigned to a given state variable evolves over time. This paper studies the effects of linear and nonlinear propagation of the uncertainty distributions on the collision avoidance maneuver optimization. These different methods for error propagation lead to differing shapes and sizes of the error distribution, resulting in differing regions to be avoided during the encounter, thus resulting in different optimal Δv requirements. In the method using nonlinear propagation of uncertainty distribution, the uncertainty of the passive object is propagated using Monte Carlo samples while that of the operating spacecraft is evolved using Unscented Transform. The sigma points from the Unscented Transform of the operating spacecraft are required to lie outside the stretch of most of the debris uncertainty while implementing cumulative density function. This also results in defining a new probabilistic measure which is like a modified Mahalanobis distance but for a non-Gaussian distribution. The other approach uses linearly propagating the error covariances and a combined error ellipsoid to ensure the maintenance of a desired Mahalanobis distance of the hard body from the uncertainty distribution to ascertain safety. Both the approaches consider nonlinear state dynamics while incorporating the perturbing forces to find the optimal thrust profile and the corresponding steer angles. The approach implementing nonlinear propagation of uncertainty and using cumulative density to ensure that the sigma points of the satellite avoid the debris’ uncertainty distribution is found to require lower Δv compared to the other method while also representing the error propagation better. However, the method implementing linear propagation of uncertainty and using Mahalanobis distance of the hard body from the combined error distribution to frame the avoidance constraint proves to be computationally much faster.

Segmented Reconstruction of Low-Acceleration Orbital Maneuvers

This paper considers the problem of inferring the acceleration acting on a spacecraft in a near-circular orbit around a large planetary body when the acceleration is known to act in the along-track direction. A segmented approach is analyzed where the acceleration profile over a given period of time is approximated as a piecewise-constant profile. Noisy measurements of the spacecraft’s position are collected throughout the acceleration profile, from which the constant acceleration for each segment of the piecewise-constant profile can be inferred. The primary contribution of this work is an analytical approximation for the sensitivity of each measurement with respect to the constant acceleration of each segment. The resulting analytically approximated sensitivity matrix enables an analytical reconstruction of the acceleration profile given a numerically simulated reference trajectory. Applications of the segmented approach for thrust inference for both discontinuous and continuous thrust profiles are demonstrated. In particular, the reconstruction of a simulated thruster degradation profile over the course of 60 h is shown.

Adaptive Estimation of Distribution Algorithms for Low-Thrust Trajectory Optimization

A direct adaptive scheme is presented as an alternative approach for minimum-fuel low-thrust trajectory design in non-coplanar orbit transfers using fitness landscape analysis (FLA). The spacecraft dynamics is modeled with respect to modified equinoctial elements by considering orbital perturbations. Taking into account the timings of thrust arcs, the discretization nodes for thrust profile, and the solution of multi-impulse orbit transfer, a constrained continuous optimization problem is formed for low-thrust orbital maneuvers. An adaptive method within the framework of the estimation of distribution algorithms (EDA) is proposed, which aims at conserving the feasibility of the solutions within the search process. Several problem identifiers for low-thrust trajectory optimization are introduced, and the complexity of the solution domain is analyzed by evaluating the landscape feature of the search space via FLA. Two adaptive operators are proposed, which control the search process based on the need for exploration and exploitation of the search domain to achieve optimal transfers. The adaptive operators are implemented in the presented EDA and several perturbed and nonperturbed orbit transfer problems are solved. The results confirm the effectiveness and reliability of the proposed approach in finding optimal low-thrust transfer trajectories.

Trajectory optimization of rocket recovery based on Neural Network and Genetic Algorithm

After the completion of the launch mission, the soft landing recovery and reuse of the carrier rocket’s first-stage can effectively control the landing area to ensure safety and significantly reduce the cost of space launch transportation. The trajectory optimization of the whole process from the first section to the landing site is significant to fuel saving. In the entire process, the first-stage needs to go through three startup ignitions of course adjustment, power deceleration, and vertical landing. For this segmented fuel optimization problem, optimizing the thrust size and direction during three sections and the switching time between each section is necessary. Optimizing the vertical landing section is essential to ensure the accuracy of landing position and speed, which greatly complicates the whole process’s optimization. Therefore, the optimization process of the vertical landing is substituted by a neural network predictor, which is used to obtain the mapping relationship between the initial state of the vertical landing section and the fuel consumption of the segment. Besides, the thrust profiles of the first two startup sections are reasonably handled based on physical cognition. The combination of convex optimization and neural network successfully converted the multi-stage optimal control problem into a parameter optimization problem and solved it by a genetic algorithm. Optimization results were compared with the conventional method, which indicated its superiority.

Simulation-Based Prediction of Departure Aircraft Performance from Surveillance-like Data Using Neural Networks

Estimating the environmental impact of aviation, in terms of noise and emissions, requires accurate knowledge of flight parameters such as departure/arrival procedure, aircraft mass, thrust and flap settings. However, these parameters are not available from radar/ADS-B data, which are the main sources of multiple flight-specific information including aircraft position over time. This paper introduces a novel approach to estimating these parameters from radar/ADS-B data using three neural network models trained on flight simulator data for the Boeing 747-400 airplane. The models are tested on 2204 simulated flights that are not used for training and that are transformed into radar/ADS-B data formats. The models are capable of predicting the unknown parameters for the ADS-B data format, with the weight prediction error being 2.63% of maximum takeoff weight, the average R2 score for the thrust profile prediction being 89.90% and the flap setting profile having an average R2 score of 84.68%, while for the radar-like data format, the values are 2.11%, 95.74% and 88.24%, respectively. The predicted parameters can be used to improve the environmental impact assessment of individual flights and to support policy-making and management decisions. This approach is a proof of concept based on simulation data that will need to be validated on real data before being applied in practice.

The impact of changing fleet makeup on airline noise emission

With the advent of the Environmental Noise Directive (END) population level modelling of exposure to aircraft noise has increased within Europe. Present noise exposure legislation focuses on airports whereas the greatest potential to implement noise reduction technologies lies with the airlines and aircraft manufacturers. This work focuses on the modelling the noise emission of the fleet of Europe's largest airline by passenger numbers, Ryanair. The noise reduction achieved at a fleet level will be evaluated and the impact of changing fleet makeup assessed. The airline's current fleet consists of 409 Boeing 737-800 aircraft and 29 Airbus A320-232 aircraft, while 210 new Boeing 737-8200 max aircraft are on order. The new aircraft have a 40 % smaller footprint in the 85dB(A) noise contour during take-off than the existing 737-800. The 85dB(A) contour of 737-800 stretches out around 4.5km along the runway, while the contour of 737-8200 max was reduced to ca. 2.5km. This is achieved by implementing new winglet design and more efficient power units, which operate with lower fuel consumption (and thus lower aircraft weight), less carbon emissions, and lower noise emissions. The impact of this change to the fleet is evaluated using a representative airport modelled in SoundPLAN. Noise contours generated with SoundPLAN show the noise effects of the different aircraft types of the historic, current and future Ryanair fleet under realistic operating conditions. Different departure profiles are investigated, depending on the aircrafts weight, altitude, speed, and thrust profile. The generated noise contours provide an evidence base for decision making within the airline for investments aiming to reduce noise levels around airports. The potential for reducing population exposure to noise under the framework of the END is presented.

Thrust Integrated Trajectory Optimization for Multipulse Rocket Missiles Using Convex Programming

In this paper, a thrust integrated trajectory optimization algorithm for multipulse rocket missiles is proposed. Maximizing terminal velocity is selected as a performance index for achieving high maneuverability in the homing stage. To incorporate the optimization of thrust profile, thrust parameters are also considered as optimization variables with several thrust constraints such as impulse conservation and maximum/minimum thrust level. The original trajectory optimization problem is reformulated using new independent variables and timescale variables. This method simplifies the dynamics and makes the impulse conservation constraint disappear. Then, a control-affine system is established by defining the angle of attack and its square as new control inputs. The admissible input set is relaxed to a convex set, and mathematical proof is provided to show that the relaxation preserves the solution. The problem is discretized by applying a pseudospectral method for each subinterval. The solution is then obtained using sequential convex programming (SCP). A quadratic variable trust-region constraint is used for robust convergence of SCP. The proposed method robustly optimizes the thrust parameters and trajectory of the multipulse rocket missile within 1 s. Numerical simulation shows the feasibility and effectiveness of the proposed method.

Thrust profile optimisation for small inclination changes: a case study on LAPAN-A4

Inclination change manoeuvre is widely performed to correct the inclination to the desired value. However, inclination manoeuvres studied or performed so far assumed that the thrust profile is constant maximum. In fact, for inclination change manoeuvre, the satellite position in orbit affects the Δi/Δt efficiency and the manoeuvre will be best performed at nodes. This research investigated the optimum profile thrust for inclination change manoeuvre for small inclination changes only on a case study of LAPAN-A4 satellite. The optimisation involved several methods: using GMAT software and using genetic algorithm which is divided further into general and special perturbation. The results showed a good agreement that the most optimum thrust profile for this case is a constant maximum thrust profile.

Simulating Rocket Trajectory Using JSBSim and Optimal Thrust Profile for maximizing altitude of sounding rocket

Solid rocket boosters are commonly used for launching sounding rockets due to their simplicity and power-ness. The shape and geometry of the propellant grain determine the thrust-time profile which has a significant effect on rocket performance. In practical application, the thrust profile has three typical curves; regressive, neutral, and progressive. A great deal of studies has been focused on optimizing the trajectory based on various state variables in which the profile of the thrust-time curve was not among those variables. In this research, design variables were the thrust profile, the object function was maximizing the altitude subjected to constraints of a fixed amount of fuel. The trajectory was found by solving the equations of motion. For comparison purposes, the trajectory was also found using JSBSim, an open-source flight dynamic simulator. In the final results of the optimization process, the input thrust-time curve was evolved into an unusual shape, the letter “V” shaped. In this type of profile, the thrust curve starts regressively until reaches zero value at the middle of the burning time and then continues progressively until the end. This behavior can be satisfied only by two-stage boosters. Thus, these results show that two-stage boosters perform better than single-stage. The improvement is obtained by consuming the solid propellant more efficiently allowing fewer energy losses. This reason is added to the fact that two-stage boosters allow reducing the total masses due to the casste separation.

How Can Ablative Cooling in A Solid Propellant Rocket Engine Be Accurately Modelled in Order to Optimise Performance?

Abstract: This essay investigates the use of ablative cooling in solid propellant rocket engines. It begins by exploring the mechanisms by which ablation occurs. It then demonstrates how heat transfer to an ablator can be modelled, and how this can be used to find ablator recession rate and hence the necessary ablator thickness for a rocket engine. It does so by considering simplified mathematical models. These are then compared to the more complex models that have recently been developed. The different variables involved and how they might be used or calculated are discussed. The next section of the essay ties this theoretical knowledge and modelling into practical engineering use by considering the impact ablation has on performance. MATLAB is used to demonstrate how an expanding throat diameter of the nozzle can decrease thrust and specific impulse, and that this can greatly decrease payload capacities. Other variables involved in creating a thrust profile for a solid propellant rocket engine are considered. Finally, the essay will look at how to choose an optimal ablator. It goes through the universally desirable characteristics and uses the Space Shuttle SRMs as an example of disadvantages that may not initially be considered when selecting an ablator

Semi-Analytical Planetary Landing Guidance with Constraint Equations Using Model Predictive Control

With the deepening of planetary exploration, rapid decision making and descent trajectory planning capabilities are needed to cope with uncertain environmental disturbances and possible faults during planetary landings. In this article, a novel decoupling method is adopted, and the analytical three-dimensional constraint equations are derived and solved, ensuring real-time guidance computation. The three-dimensional motion modes and thrust profiles are analyzed and determined based on Pontryagin’s minimum principle, and a supporting semi-analytical reachability judgment method is presented, which can also be used to determine controllability. The algorithm is embedded in the model predictive control (MPC) framework, and several techniques are adopted to enhance stability and robustness, including thrust averaging, thrust correction after ignition, thrust reservation, and open-loop terminal guidance. Numerical simulations demonstrate that the proposed algorithm can guarantee real-time trajectory generation and meanwhile maintain considerable optimality. In addition, the MPC simulation shows that the algorithm can maintain a good accuracy under external disturbances.

Ascent trajectory design and optimization of a two-stage throttleable liquid rocket

This paper explores in detail the design and optimization of the ascent trajectory for a two-stage liquid rocket capable of providing variable thrust. Thrust and steering profiles play an essential role in designing a launch vehicle mission. Variable thrusting or throttling requirement arises in the thrust profile of a liquid rocket due to structural, aerodynamic and mission-related constraints. The current study investigates this aspect for two-stage liquid rockets, which deliver a 500 kg payload to 500 km circular orbit and 180×36000 km Geostationary Transfer Orbit (GTO). As payload mass is kept constant in both cases, the lift-off mass varies. The study found that for both missions mentioned earlier, the required variation of thrust (throttling) is in the range of 100% to 33% for the first stage to achieve an optimal trajectory. For the second stage, a considerable requirement for throttling is absent. Optimal trajectory with throttling capability reduced the lift-off mass of the launch vehicle for a mission to circular orbit by 41.6% and to the GTO by 16.3% compared to the constant thrusting cases. Also, a two-stage liquid rocket using semi cryogenic engines with variable thrusting capability and stage structural factors as low as 0.1 can replace a three-stage rocket which delivers the same payload to the 500 km circular orbit. Kulasekharapattinam and Sriharikota were the launch sites considered for the circular orbit and GTO. The study did not consider spent stage impact constraints. Canonical Differential Evolution based solver is used for global optimization. Thrust profile, steering profile and lift-off mass are the outputs of the optimization strategy.

Altitude Maximization for Small Subsonic Low-Power Unguided Rockets

This paper addresses the problem of maximizing the altitude that can be reached by small, unguided rockets propelled with low-thrust engines. A physical–mathematical model of a launcher device using exhaust gas recovery to increase the initial velocity of the rocket is presented. A case study related to a small-scale model used in amateur rocketry competitions is described. The analysis shows the constructive parameters of the piston launcher that optimize the performance of the rocket. The best thrust profile of the available motorizations, which potentially include delayed ignition of the sustainer, is identified, as well as the optimal distribution of the masses between the stages. Finally, the possibility of further increasing the initial velocity with a piston launcher through the use of retention mechanisms to increase the pressure in the tube or through the use of auxiliary gas generators is investigated. The results show the considerable performance benefits of using a piston launcher.