DEVELOPMENT OF A TRAJECTORY-CORRECTION PROPULSION SYSTEM FOR SPACECRAFT
Mariner a midcourse and approach trajectory correction propulsion system for space vehicles
MARINER A PROGRAM↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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AN APPLICATION OF TIME OPTIMAL CONTROL TO A FLEXIBLE LAUNCH VEHICLE
Application of time optimal control to a flexible launch vehicle - pitch controller
TRAJECTORY CONTROL↗
Closed-Loop Simulation Study of the Ares I Upper Stage Thrust Vector Control Subsystem for Nominal and Failure Scenarios
As a replacement to the current Shuttle, the Ares I rocket and Orion crew module are currently under development by the National Aeronautics and Space Administration (NASA). This new launch vehicle is segmented into major elements, one of which is the Upper Stage (US). The US is further broken down into subsystems, one of which is the Thrust Vector Control (TVC) subsystem which gimbals the US rocket nozzle. Nominal and off-nominal simulations for the US TVC subsystem are needed in order to support the development of software used for control systems and diagnostics. In addition, a clear and complete understanding of the effect of off-nominal conditions on the vehicle flight dynamics is desired. To achieve these goals, a simulation of the US TVC subsystem combined with the Ares I vehicle as developed. This closed-loop dynamic model was created using Matlab s Simulink and a modified version of a vehicle simulation, MAVERIC, which is currently used in the Ares I project and was developed by the Marshall Space Flight Center (MSFC). For this report, the effects on the flight trajectory of the Ares I vehicle are investigated after failures are injected into the US TVC subsystem. The comparisons of the off-nominal conditions observed in the US TVC subsystem with those of the Ares I vehicle flight dynamics are of particular interest.
Chicatelli, Amy↗
A Multi-Disciplinary Analysis Framework for the Design of Small Launch Vehicles
Between the years of 1995 and 2014 the number of small satellites (1-500 kg) went up from 20 to 180. [1] Out of the 180 launched in 2014 66% were Nano satellites (1-10 kg). [1] With this trend of smaller satellites, one would expect a rise in number of small launch vehicles (SLVs are defined by capability to carry 1-100 kg to orbit), but this has not happened: [3] only 8% of all small satellites are launched on SLVs and the others become secondary payloads on regular launch vehicles. [1] This results in small satellites being placed into either suboptimal orbits or waiting for launch schedules to align with bigger launches, resulting in long waiting times. Dedicated SLVs could improve the responsiveness of small satellite launches, but SLV design is complicated by the large architecture space needed to be explored in order to find efficient and affordable designs. The SLV architecture trade space contains many discrete options, e.g. solid vs. liquid fuels, air launch vs. ground launch, number of stages, etc. [2][3] Performing detailed analysis for all the options at once would be prohibitive. Thus, a sizing environment/framework that is capable of providing necessary information for conceptual-level trade studies and can rapidly explore the vast SLV architecture space is necessary. The framework, illustrated in Figure 1, consists of four disciplines central to the sizing and synthesis of launch vehicles: propulsion, aerodynamics, structures, and trajectory. For the aerodynamics and trajectory disciplines, Missile DATCOM and POST2 are used, respectively. The propulsion and structures disciplines are represented in the framework with tools developed at ASDL Georgia Tech. For propulsion, the Solid Motor Analysis Code (SMAC) is a physics-based conceptual design tool for solid rocket motors. SMAC is capable of geometric burn simulation, ballistic analysis, and prediction of thrust performance. [4] For structures, Launch Vehicle Structural Analysis (LVSA) tool is a physics-based tool that focuses on structural dynamic analysis with sizing capability. These tools are integrated into the framework illustrated in Figure 1 with the corresponding connections described in Table 1. The process flow is as follows: first, SMAC sizes insulation and calculates maximum operating pressures for each vehicle stage. The MEOP and insulation thickness values from SMAC are fed to LVSA which then utilizes this information to size the motor casing. This creates a feedback loop between LVSA and SMAC that converges on the radius available for fuel, casing, and insulation thickness. Once the stage sizing is converged on SMAC creates an engine deck that is passed to POST2. Next, the data from SMAC and LVSA goes into Missile DATCOM which generates an aerodynamics database for POST2. Finally, POST2 performs a targeting optimization while maximizing the payload mass to orbit. Within the framework, POST2 is automated in order to be robust to a wide variety of possible designs by performing a Monte Carlo simulation over the initialization vector of the POST2 optimization variables. To demonstrate the capability of this framework, a sample problem of exploring the design space of an SLV capable of placing satellites into a low Earth orbit (inclination=47 deg, 196.5 by 211.3 nm) is used. This sample problem is a ground-launched SLV consisting of four in-line SRM stages. The multidisciplinary design analysis (MDA) environment is utilized to explore a design space consisting of 22 continuous and 12 discrete variables, shown by Table 1 by blocks 1,2,3. Running a full factorial design of experiments (DOE) would have been prohibitively expensive even with this reduced design space, thus a space filling design with 3,502 and then additional expansion of 2,602 cases was used. The first DOE consisted of 3,502 cases, and all of the variables were varied. These input variables are listed in blocks 1, 2, and 3 in Table 1. Most of the variables are propulsion related with stage lengths determining the delta-V split of the SLV. The expansion consisted of 2,602 cases, and the continuous variables were set to be equal to the most promising designs from the sizing of first DOE. For each set of continuous variables, the discrete variables (grain type, star points, and propellant) were to varied. The results of the DOE can be seen in Figure 2; each of the points in this plot represents a closed launch vehicle that reaches the targeted orbit. For each of the cases, there is information on flown trajectory, structural, and propulsion properties of the SLV. For example, Figure 3 shows changes in altitude and velocity with time for a particular case. The right side of Figure 3 clearly shows the coasting (slow decrease) and burning phases (sharp increase) of the SLV mission. LV mass is positively correlated with the optimized payload mass to orbit because heavier LVs carry more fuel and thus have more stored chemical energy. Furthermore, for any given payload mass to orbit, the most efficient design would result in the smallest LV. The results as visualized in Figure 2 shows this tradeoff, and the Pareto frontier of the efficient designs can be seen along the dotted line. Figure 2 can be divided into regions with the lowest mass vehicles corresponding to the minimum bound on radius, and the highest mass vehicles corresponding to the maximum bound on radius. Within a mass region, the discrete variables, such as propellant type and propellant grain arrangement, have the most effect on payload mass. This paper presents an MDA framework that can perform an automated physics-based sizing of SLV designs and a corresponding methodology to utilize the MDA to explore the design space of SLVs. The proposed methodology was applied to a perform a design space exploration for a four stage SLV. The outputs show the expected pareto frontier forming and provide detailed information about the SLV performance and staging. Using the produced data, it will be possible to select a set of pareto optimal designs that can then be further explored in subsequent design cycles. This demonstration shows that automated design space exploration should be used in the early phase design of future SLV concepts.
Nikita S Birbasov↗
Enabling Parametric Optimal Ascent Trajectory Modeling During Early Phases of Design
During the early phases of engineering design, the costs committed are high, costs incurred are low, and the design freedom is high. It is well documented that decisions made in these early design phases drive the entire design's life cycle. In a traditional paradigm, key design decisions are made when little is known about the design. As the design matures, design changes become more difficult -- in both cost and schedule -- to enact. Indeed, the current capability-based paradigm that has emerged because of the constrained economic environment calls for the infusion of knowledge acquired during later design phases into earlier design phases, i.e. bring knowledge acquired during preliminary and detailed design into pre-conceptual and conceptual design. An area of critical importance to launch vehicle design is the optimization of its ascent trajectory, as the optimal trajectory will be able to take full advantage of the launch vehicle's capability to deliver a maximum amount of payload into orbit. Hence, the optimal ascent trajectory plays an important role in the vehicle's affordability posture as the need for more economically viable access to space solutions are needed in today's constrained economic environment. The problem of ascent trajectory optimization is not a new one. There are several programs that are widely used in industry that allows trajectory analysts to, based on detailed vehicle and insertion orbit parameters, determine the optimal ascent trajectory. Yet, little information is known about the launch vehicle early in the design phase - information that is required of many different disciplines in order to successfully optimize the ascent trajectory. Thus, the current paradigm of optimizing ascent trajectories involves generating point solutions for every change in a vehicle's design parameters. This is often a very tedious, manual, and time-consuming task for the analysts. Moreover, the trajectory design space is highly non-linear and multi-modal due to the interaction of various constraints. Additionally, when these obstacles are coupled with The Program to Optimize Simulated Trajectories [1] (POST), an industry standard program to optimize ascent trajectories that is difficult to use, it requires expert trajectory analysts to effectively optimize a vehicle's ascent trajectory. As it has been pointed out, the paradigm of trajectory optimization is still a very manual one because using modern computational resources on POST is still a challenging problem. The nuances and difficulties involved in correctly utilizing, and therefore automating, the program presents a large problem. In order to address these issues, the authors will discuss a methodology that has been developed. The methodology is two-fold: first, a set of heuristics will be introduced and discussed that were captured while working with expert analysts to replicate the current state-of-the-art; secondly, leveraging the power of modern computing to evaluate multiple trajectories simultaneously, and therefore, enable the exploration of the trajectory's design space early during the pre-conceptual and conceptual phases of design. When this methodology is coupled with design of experiments in order to train surrogate models, the authors were able to visualize the trajectory design space, enabling parametric optimal ascent trajectory information to be introduced with other pre-conceptual and conceptual design tools. The potential impact of this methodology's success would be a fully automated POST evaluation suite for the purpose of conceptual and preliminary design trade studies. This will enable engineers to characterize the ascent trajectory's sensitivity to design changes in an arbitrary number of dimensions and for finding settings for trajectory specific variables, which result in optimal performance for a "dialed-in" launch vehicle design. The effort described in this paper was developed for the Advanced Concepts Office [2] at NASA Marshall Space Flight Center
Holt, James B.↗
NASA’s Space Launch System: Launch Capability for Lunar Exploration and Transformative Science
Excitement is building for the first launch of NASA’s Space Launch System (SLS), a unique exploration asset for the agency’s Artemis lunar program as well as for a new generation of science missions. SLS is designed for an array of missions beyond Earth’s orbit. The flexible system, which can be configured for Orion, cargo or Orion with co-manifested payload missions, offers high escape velocities to send more mass to deep space destinations. When configured with an 8.4 m-diameter fairing, SLS offers unmatched payload volume for human exploration and science missions. The initial Block 1 variant will insert at least 26 metric tons (t) to trans-lunar injection (TLI) and the more powerful Block 1B vehicle will launch 34-37 t to TLI using a new-development upper stage. Much of the initial SLS Block 1 vehicle is complete, including the upper stage and payload section, the core stage, engines and the solid rocket boosters. The first mission, Artemis I, launching from modernized and upgraded facilities at Kennedy Space Center (KSC), will be an uncrewed test flight of SLS, Orion and ground processing, with a primary objective of testing Orion’s heat shield at lunar re-entry velocity. Artemis I will have accommodations for 13 6U CubeSat payloads. These CubeSat missions will be deployed along the upper stage disposal trajectory after Orion separates from the vehicle. A rare opportunity for CubeSats to be deployed beyond low Earth orbit (LEO), Artemis I CubeSat missions range from searching for hydrogen and other volatiles on the lunar South Pole to studying the acceleration mechanisms of solar and interplanetary particles from a heliocentric trajectory. With manufacturing of the initial vehicle complete, fabrication and procurement is progressing for the second flight of SLS and Orion, Artemis II. Also an SLS Block 1 and Orion flight launching from KSC, Artemis II will mark the return of American astronauts to deep space with a lunar flyby-free return trajectory mission. With the Artemis III flight, NASA has the goal to land the first woman and the next man on the Moon. Infrastructure beyond SLS will be required for this effort, including elements of the lunar Gateway as well as lunar rovers, landers and additional commercially supplied launch services. SLS, as the only vehicle with the capability to lift 26 t of mass to TLI in its initial Block 1 variant, will remain a key component of this new-era exploration program. Future variants – Block 1B and Block 2 –will lift 34-45 t to TLI. This paper will discuss the status of testing and integration for the Artemis I vehicle, manufacturing progress for the second vehicle and the manifest outlook for primary, co-manifested and secondary payloads in the current deep space exploration environment.
Creech, Stephen D.↗
Applying Motion Constraints Based on Test Data
MSC ADAMS is a simulation software that is used to analyze multibody dynamics. Using user subroutines, it is possible to apply motion constraints to the rigid bodies so that they match the motion profile collected from test data. This presentation describes the process of taking test data and passing it to ADAMS using user subroutines, and uses the Morpheus free-flight 4 test as an example of motion data used for this purpose. Morpheus is the name of a prototype lander vehicle built by NASA that serves as a test bed for various experimental technologies (see backup slides for details) MSC.ADAMS"TM" is used to play back telemetry data (vehicle orientation and position) from each test as the inputs to a 6-DoF general motion constraint (details in backup slides) The MSC.ADAMS"TM" playback simulations allow engineers to examine and analyze flight trajectory as well as observe vehicle motion from any angle and at any playback speed. This facilitates the development of robust and stable control algorithms, increasing reliability and reducing development costs of this developmental engine The simulation also incorporates a 3D model of the artificial hazard field, allowing engineers to visualize and measure performance of the developmental autonomous landing and hazard avoidance technology ADAMS is a multibody dynamics solver. It uses forces, constraints, and mass properties to numerically integrate equations of motion. The ADAMS solver will ask the motion subroutine for position, velocity, and acceleration values at various time steps. Those values must be continuous over the whole time domain. Each degree of freedom in the telemetry data can be examined separately; however, linear interpolation of the telemetry data is invalid, since there will be discontinuities in velocity and acceleration.
Burlone, Michael↗
A Collaborative Analysis Tool for Thermal Protection Systems for Single Stage to Orbit Launch Vehicles
Presented is a design tool and process that connects several disciplines which are needed in the complex and integrated design of high performance reusable single stage to orbit (SSTO) vehicles. Every system is linked to every other system and in the case of SSTO vehicles with air breathing propulsion, which is currently being studied by the National Aeronautics and Space Administration (NASA); the thermal protection system (TPS) is linked directly to almost every major system. The propulsion system pushes the vehicle to velocities on the order of 15 times the speed of sound in the atmosphere before pulling up to go to orbit which results high temperatures on the external surfaces of the vehicle. Thermal protection systems to maintain the structural integrity of the vehicle must be able to mitigate the heat transfer to the structure and be lightweight. Herein lies the interdependency, in that as the vehicle's speed increases, the TPS requirements are increased. And as TPS masses increase the effect on the propulsion system and all other systems is compounded. To adequately determine insulation masses for a vehicle such as the one described above, the aeroheating loads must be calculated and the TPS thicknesses must be calculated for the entire vehicle. To accomplish this an ascent or reentry trajectory is obtained using the computer code Program to Optimize Simulated Trajectories (POST). The trajectory is then used to calculate the convective heat rates on several locations on the vehicles using the Miniature Version of the JA70 Aerodynamic Heating Computer Program (MINIVER). Once the heat rates are defined for each body point on the vehicle, then insulation thicknesses that are required to maintain the vehicle within structural limits are calculated using Systems Improved Numerical Differencing Analyzer (SINDA) models. If the TPS masses are too heavy for the performance of the vehicle the process may be repeated altering the trajectory or some other input to reduce the TPS mass. The problem described is an example of the need for collaborative design and analysis. Analysis tools are being developed to facilitate these collaborative efforts. RECIPE is a cross-platform application capable of hosting a number of engineers and designers across the Internet for distributed and collaborative engineering environments. Such integrated system design environments allow for collaborative team design analysis for performing individual or reduced team studies. The analysis tools mentioned earlier are commonly run on different platforms and are usually run by different people. To facilitate the larger number of potential runs that may need to be made, RECIPE connects the computer codes that calculate the trajectory data, heat rate data, and TPS masses so that the output from each tool is easily transferred to the model input files that need it. This methodology is being applied to solve launch vehicle thermal design problems to shorten the design cycle, and enable the project team to evaluate design options. Results will be presented indicating the effectiveness of this as a collaborative design tool.
Alexander, Reginald A.↗
Study of thermal protection requirements for a lifting body entry vehicle suitable for near-earth missions Final report
Reentry and abort trajectory analyses, and thermal protection requirements for lifting body entry vehicles
THERMAL PROTECTION↗
Hyper-X Mach 10 Trajectory Reconstruction
This paper discusses the formulation and development of a trajectory reconstruction tool for the NASA X-43A/Hyper-X high speed research vehicle, and its implementation for the reconstruction and analysis of flight test data. Extended Kalman filtering techniques are employed to reconstruct the trajectory of the vehicle, based upon numerical integration of inertial measurement data along with redundant measurements of the vehicle state. The equations of motion are formulated in order to include the effects of several systematic error sources, whose values may also be estimated by the filtering routines. Additionally, smoothing algorithms have been implemented in which the final value of the state (or an augmented state that includes other systematic error parameters to be estimated) and covariance are propagated back to the initial time to generate the best-estimated trajectory, based upon all available data. The methods are applied to the problem of reconstructing the trajectory of the Hyper-X vehicle from data obtained during the Mach 10 test flight, which occurred on November 16th 2004.
Karlgaard, Christopher D.↗
Computer program trajectory optimization by explicit numerical methods
Computer program using numerical methods that calculates minimum time for space vehicle to meet its mission with optimum trajectory, and can maximize option if burning time is fixed
COMPUTER PROGRAM↗
Flight Evaluation of Center-TRACON Automation System Trajectory Prediction Process
Two flight experiments (Phase 1 in October 1992 and Phase 2 in September 1994) were conducted to evaluate the accuracy of the Center-TRACON Automation System (CTAS) trajectory prediction process. The Transport Systems Research Vehicle (TSRV) Boeing 737 based at Langley Research Center flew 57 arrival trajectories that included cruise and descent segments; at the same time, descent clearance advisories from CTAS were followed. Actual trajectories of the airplane were compared with the trajectories predicted by the CTAS trajectory synthesis algorithms and airplane Flight Management System (FMS). Trajectory prediction accuracy was evaluated over several levels of cockpit automation that ranged from a conventional cockpit to performance-based FMS vertical navigation (VNAV). Error sources and their magnitudes were identified and measured from the flight data. The major source of error during these tests was found to be the predicted winds aloft used by CTAS. The most significant effect related to flight guidance was the cross-track and turn-overshoot errors associated with conventional VOR guidance. FMS lateral navigation (LNAV) guidance significantly reduced both the cross-track and turn-overshoot error. Pilot procedures and VNAV guidance were found to significantly reduce the vertical profile errors associated with atmospheric and airplane performance model errors.
Williams, David H.↗
An Expert System-Driven Method for Parametric Trajectory Optimization During Conceptual Design
During the early phases of engineering design, the costs committed are high, costs incurred are low, and the design freedom is high. It is well documented that decisions made in these early design phases drive the entire design's life cycle cost. In a traditional paradigm, key design decisions are made when little is known about the design. As the design matures, design changes become more difficult in both cost and schedule to enact. The current capability-based paradigm, which has emerged because of the constrained economic environment, calls for the infusion of knowledge usually acquired during later design phases into earlier design phases, i.e. bringing knowledge acquired during preliminary and detailed design into pre-conceptual and conceptual design. An area of critical importance to launch vehicle design is the optimization of its ascent trajectory, as the optimal trajectory will be able to take full advantage of the launch vehicle's capability to deliver a maximum amount of payload into orbit. Hence, the optimal ascent trajectory plays an important role in the vehicle's affordability posture yet little of the information required to successfully optimize a trajectory is known early in the design phase. Thus, the current paradigm of optimizing ascent trajectories involves generating point solutions for every change in a vehicle's design parameters. This is often a very tedious, manual, and time-consuming task for the analysts. Moreover, the trajectory design space is highly non-linear and multi-modal due to the interaction of various constraints. When these obstacles are coupled with the Program to Optimize Simulated Trajectories (POST), an industry standard program to optimize ascent trajectories that is difficult to use, expert trajectory analysts are required to effectively optimize a vehicle's ascent trajectory. Over the course of this paper, the authors discuss a methodology developed at NASA Marshall's Advanced Concepts Office to address these issues. The methodology is two-fold: first, capture the heuristics developed by human analysts over their many years of experience; and secondly, leverage the power of modern computing to evaluate multiple trajectories simultaneously and therefore enable the exploration of the trajectory's design space early during the pre- conceptual and conceptual phases of design. This methodology is coupled with design of experiments in order to train surrogate models, which enables trajectory design space visualization and parametric optimal ascent trajectory information to be available when early design decisions are being made.
Dees, Patrick D.↗
Overview of the Space Launch System Transonic Buffet Environment Test Program
Fluctuating aerodynamic loads are a significant concern for the structural design of a launch vehicle, particularly while traversing the transonic flight environment. At these trajectory conditions, unsteady aerodynamic pressures can excite the vehicle dynamic modes of vibration and result in high structural bending moments and vibratory environments. To ensure that vehicle structural components and subsystems possess adequate strength, stress, and fatigue margins in the presence of buffet and other environments, buffet forcing functions are required to conduct the coupled load analysis of the launch vehicle. The accepted method to obtain these buffet forcing functions is to perform wind-tunnel testing of a rigid model that is heavily instrumented with unsteady pressure transducers designed to measure the buffet environment within the desired frequency range. Two wind-tunnel tests of a 3 percent scale rigid buffet model have been conducted at the Langley Research Center Transonic Dynamics Tunnel (TDT) as part of the Space Launch System (SLS) buffet test program. The SLS buffet models have been instrumented with as many as 472 unsteady pressure transducers to resolve the buffet forcing functions of this multi-body configuration through integration of the individual pressure time histories. This paper will discuss test program development, instrumentation, data acquisition, test implementation, data analysis techniques, and several methods explored to mitigate high buffet environment encountered during the test program. Preliminary buffet environments will be presented and compared using normalized sectional buffet forcing function root-meansquared levels along the vehicle centerline.
Piatak, David J.↗
Power and Propulsion Element (PPE) Spacecraft Reference Trajectory Document
This document captures example reference trajectories for the PPE including a reference delivery orbit and orbit maintenance, an example cislunar orbit transfer and end-of-mission (EOM) disposal trajectory. The flexibility of electric propulsion offers, by its low thrust nature, multiple different trajectory options to transfer from one orbit to another. The trajectories captured in this document are representative examples of a low thrust transfer from the NRHO and to multiple cislunar orbits. This document provides a consistent set of data from mission design to be used in the design of the vehicle capable of flying the trajectory described. The data in this document will be used to create conference papers. In order to do so, we are ending this document through for external release.
Melissa L Mcguire↗
An overview of the current state of the art optimization used for trajectory design in the GTS system
The high cost of delivering payloads to orbit demands that launch vehicles be flown in an optimal and reliable manner. Thus, computer simulated trajectories are optimized to obtain maximum vehicle payload capability or a maximum amount of reserve fuel, subject to design constraints. The Generalized Trajectory Simulation (GTS) system developed at The Aerospace Corporation is capable of simulating and optimizing trajectories for a wide variety of boost and reentry problems. Optimization is an integral part of the GTS system. This has resulted in progressive use of optimization. Additionally, the flexibility of the GTS system allows optimum trade studies to be conducted and complicated missions to be designed. This paper describes the integrated and flexible nature of the optimization software in the GTS system. Special features of the NLP2 and NLP3 optimization codes are described. Post optimality, parameter sensitivity analysis and the automatic scaling capability in the GTS system are also described.
Beltracchi, Todd J.↗
Collaborative Analysis Tool for Thermal Protection Systems for Single Stage to Orbit Launch Vehicles
Presented is a design tool and process that connects several disciplines which are needed in the complex and integrated design of high performance reusable single stage to orbit (SSTO) vehicles. Every system is linked to every other system and in the case of SSTO vehicles with air breathing propulsion, which is currently being studied by the National Aeronautics and Space Administration (NASA); the thermal protection system (TPS) is linked directly to almost every major system. The propulsion system pushes the vehicle to velocities on the order of 15 times the speed of sound in the atmosphere before pulling up to go to orbit which results high temperatures on the external surfaces of the vehicle. Thermal protection systems to maintain the structural integrity of the vehicle must be able to mitigate the heat transfer to the structure and be lightweight. Herein lies the interdependency, in that as the vehicle's speed increases, the TPS requirements are increased. And as TPS masses increase the effect on the propulsion system and all other systems is compounded. To adequately determine insulation masses for a vehicle such as the one described above, the aeroheating loads must be calculated and the TPS thicknesses must be calculated for the entire vehicle. To accomplish this an ascent or reentry trajectory is obtained using the computer code Program to Optimize Simulated Trajectories (POST). The trajectory is then used to calculate the convective heat rates on several locations on the vehicles using the Miniature Version of the JA70 Aerodynamic Heating Computer Program (MINIVER). Once the heat rates are defined for each body point on the vehicle, then insulation thickness that are required to maintain the vehicle within structural limits are calculated using Systems Improved Numerical Differencing Analyzer (SINDA) models. If the TPS masses are too heavy for the performance of the vehicle the process may be repeated altering the trajectory or some other input to reduce the TPS mass.
Alexander, Reginald Andrew↗