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Trajectory Design Enhancements to Mitigate Risk for the Transiting Exoplanet Survey Satellite (TESS)

The Transiting Exoplanet Survey Satellite (TESS) will employ a highly eccentric Earth orbit, in 2:1 lunar resonance, which will be reached with a lunar flyby preceded by 3.5 phasing loops. The TESS mission has limited propellant and several constraints on the science orbit and on the phasing loops. Based on analysis and simulation, we have designed the phasing loops to reduce delta-V (DV) and to mitigate risk due to maneuver execution errors. We have automated the trajectory design process and use distributed processing to generate and optimal nominal trajectories; to check constraint satisfaction; and finally to model the effects of maneuver errors to identify trajectories that best meet the mission requirements.

satellite↗

Dynamic Weather Routes: A Weather Avoidance Concept for Trajectory-Based Operations

The integration of convective weather modeling with trajectory automation for conflict detection, trial planning, direct routing, and auto resolution has uncovered a concept that could help controllers, dispatchers, and pilots identify improved weather routes that result in significant savings in flying time and fuel burn. Trajectory automation continuously and automatically monitors aircraft in flight to find those that could potentially benefit from improved weather reroutes. Controllers, dispatchers, and pilots then evaluate reroute options to assess their suitability given current weather and traffic. In today's operations aircraft fly convective weather avoidance routes that were implemented often hours before aircraft approach the weather and automation does not exist to automatically monitor traffic to find improved weather routes that open up due to changing weather conditions. The automation concept runs in real-time and employs two keysteps. First, a direct routing algorithm automatically identifies flights with large dog legs in their routes and therefore potentially large savings in flying time. These are common - and usually necessary - during convective weather operations and analysis of Fort Worth Center traffic shows many aircraft with short cuts that indicate savings on the order of 10 flying minutes. The second and most critical step is to apply trajectory automation with weather modeling to determine what savings could be achieved by modifying the direct route such that it avoids weather and traffic and is acceptable to controllers and flight crews. Initial analysis of Fort Worth Center traffic suggests a savings of roughly 50% of the direct route savings could be achievable.The core concept is to apply trajectory automation with convective weather modeling in real time to identify a reroute that is free of weather and traffic conflicts and indicates enough time and fuel savings to be considered. The concept is interoperable with today's integrated FMS/datalink. Auxiliary(lat/long) waypoints define a minimum delay reroute between current position and a downstream capture fix beyond the weather. These auxiliary waypoints can be uplinked to equipped aircraft and auto-loaded into the FMS. Alternatively, for unequipped aircraft, auxiliary waypoints can be replaced by nearby named fixes, but this could reduce potential savings. The presentation includes an overview of the automation approach and focuses on several cases in terms of potential savings, reroute complexity, best auxiliary waypoint solution vs. named fix solution, and other metrics.

McNally, B. David↗

Orbit Determination Toolbox

The Orbit Determination Toolbox is an orbit determination (OD) analysis tool based on MATLAB and Java that provides a flexible way to do early mission analysis. The toolbox is primarily intended for advanced mission analysis such as might be performed in concept exploration, proposal, early design phase, or rapid design center environments. The emphasis is on flexibility, but it has enough fidelity to produce credible results. Insight into all flight dynamics source code is provided. MATLAB is the primary user interface and is used for piecing together measurement and dynamic models. The Java Astrodynamics Toolbox is used as an engine for things that might be slow or inefficient in MATLAB, such as high-fidelity trajectory propagation, lunar and planetary ephemeris look-ups, precession, nutation, polar motion calculations, ephemeris file parsing, and the like. The primary analysis functions are sequential filter/smoother and batch least-squares commands that incorporate Monte-Carlo data simulation, linear covariance analysis, measurement processing, and plotting capabilities at the generic level. These functions have a user interface that is based on that of the MATLAB ODE suite. To perform a specific analysis, users write MATLAB functions that implement truth and design system models. The user provides his or her models as inputs to the filter commands. The software provides a capability to publish and subscribe to a software bus that is compliant with the NASA Goddard Mission Services Evolution Center (GMSEC) standards, to exchange data with other flight dynamics tools to simplify the flight dynamics design cycle. Using the publish and subscribe approach allows for analysts in a rapid design center environment to seamlessly incorporate changes in spacecraft and mission design into navigation analysis and vice versa.

Carpenter, James R.↗

NASA Tech Briefs, September 2013

Topics include: ISS Ammonia Leak Detection Through X-Ray Fluorescence; A System for Measuring the Sway of the Vehicle Assembly Building; Fast, High-Precision Readout Circuit for Detector Arrays; Victim Simulator for Victim Detection Radar; Hydrometeor Size Distribution Measurements by Imaging the Attenuation of a Laser Spot; Quasi-Linear Circuit; High-Speed, High-Resolution Time-to-Digital Conversion; Li-Ion Battery and Supercapacitor Hybrid Design for Long Extravehicular Activities; Ultrasonic Low-Friction Containment Plate for Thermal and Ultrasonic Stir Weld Processes; High-Powered, Ultrasonically Assisted Thermal Stir Welding; Next-Generation MKIII Lightweight HUT/Hatch Assembly; Centrifugal Sieve for Gravity-Level-Independent Size; Segregation of Granular Materials; Ion Exchange Technology Development in Support of the Urine Processor Assembly; Nickel-Graphite Composite Compliant Interface and/or Hot Shoe Material; UltraSail CubeSat Solar Sail Flight Experiment; Mechanism for Deploying a Long, Thin-Film Antenna From a Rover; Counterflow Regolith Heat Exchanger; Acquisition and Retaining Granular Samples via a Rotating Coring Bit; Very-Low-Cost, Rugged Vacuum System; Medicine Delivery Device With Integrated Sterilization and Detection; FRET-Aptamer Assays for Bone Marker Assessment, C-Telopeptide, Creatinine, and Vitamin D; Multimode Directional Coupler for Utilization of Harmonic Frequencies from TWTAs; Dual-Polarization, Multi-Frequency Antenna Array for use with Hurricane Imaging Radiometer; Complementary Barrier Infrared Detector (CBIRD) Contact Methods; Autonomous Control of Space Nuclear Reactors; High-Power, High-Speed Electro-Optic Pockels Cell Modulator; Covariance Analysis Tool (G-CAT) for Computing Ascent, Descent, and Landing Errors; Enigma Version 12; Micrometeoroid and Orbital Debris (MMOD) Shield Ballistic Limit Analysis Program; Spitzer Telemetry Processing System; Planetary Protection Bioburden Analysis Program; Wing Leading Edge RCC Rapid Response Damage Prediction Tool (IMPACT2); ISSM: Ice Sheet System Model; Automated Loads Analysis System (ATLAS); Integrated Main Propulsion System Performance Reconstruction Process/Models. Phoenix Telemetry Processor; Contact Graph Routing Enhancements Developed in ION for DTN; GFEChutes Lo-Fi; Advanced Strategic and Tactical Relay Request Management for the Mars Relay Operations Service; Software for Generating Troposphere Corrections for InSAR Using GPS and Weather Model Data; Ionospheric Specifications for SAR Interferometry (ISSI); Implementation of a Wavefront-Sensing Algorithm; Sally Ride EarthKAM - Automated Image Geo-Referencing Using Google Earth Web Plug-In; Trade Space Specification Tool (TSST) for Rapid Mission Architecture (Version 1.2); Acoustic Emission Analysis Applet (AEAA) Software; Memory-Efficient Onboard Rock Segmentation; Advanced Multimission Operations System (ATMO); Robot Sequencing and Visualization Program (RSVP); Automating Hyperspectral Data for Rapid Response in Volcanic Emergencies; Raster-Based Approach to Solar Pressure Modeling; Space Images for NASA JPL Android Version; Kinect Engineering with Learning (KEWL); Spacecraft 3D Augmented Reality Mobile App; MPST Software: grl_pef_check; Real-Time Multimission Event Notification System for Mars Relay; SIM_EXPLORE: Software for Directed Exploration of Complex Systems; Mobile Timekeeping Application Built on Reverse-Engineered JPL Infrastructure; Advanced Query and Data Mining Capabilities for MaROS; Jettison Engineering Trajectory Tool; MPST Software: grl_suppdoc; PredGuid+A: Orion Entry Guidance Modified for Aerocapture; Planning Coverage Campaigns for Mission Design and Analysis: CLASP for DESDynl; and Space Place Prime.

Source record↗

From Exploration Flight Test-1 to Artemis II--A NASA Langley's Orion Aerosciences Overview

The Orion Aerosciences program at NASA Langley has played a central role in advancing the aerodynamic and aeroheating prediction capabilities required for the Orion crew vehicle’s return from deep space. This presentation provides a technical overview of aerosciences contributions spanning Exploration Flight Test-1 (EFT-1), Artemis I, and the ongoing post-flight analysis of Artemis II. EFT-1 provided the first high-energy entry dataset for Orion, enabling critical validation of aerodynamic force and moment predictions, static and dynamic stability characteristics, and aeroheating environments at relevant flight Mach and Reynolds numbers. Flight-derived pressure data were used to refine the Flush Air Data System (FADS) methodology for atmospheric density reconstruction and to improve Best Estimated Trajectory (BET) solutions. The EFT-1 data also offered key insights into heat shield performance, including char layer recession, in-depth thermal response, and material retention behavior under flight conditions, informing updates to both thermal response models and uncertainty quantification practices. Building on EFT-1, Artemis I extended the database to true lunar-return conditions. Observations of heat shield performance, including localized char loss, bondline response, and recession variability, provided an unprecedented opportunity to reassess Thermal Protection System (TPS) and aeroheating modeling assumptions. Aerodynamic reconstruction efforts incorporated improved FADS calibration, enhanced atmospheric modeling, and refined force and moment databases to reduce trajectory and load uncertainties. Aeroheating comparisons between pre-flight predictions and flight data enabled targeted model updates, particularly in transitional flow environments and wake heating regions. For Artemis II, these lessons were systematically incorporated into the pre-flight prediction process. Updates included refined aerodynamic databases anchored to flight-validated corrections, improved density estimation and BET methodologies using enhanced database interpolation algorithm and FADS modeling, and revised aeroheating design environments informed by Artemis I material response observations. By the time of the workshop, Artemis II post-flight analysis will be underway, and preliminary findings will be presented where available, including early comparisons of aerodynamic reconstruction, atmospheric density estimation, and thermal protection system performance relative to updated predictions. Collectively, this body of work is a testament to the dedicated and multidisciplinary team whose sustained efforts have contributed to the program’s success and to the progressive maturation of Orion aerosciences modeling through numerical modeling, ground and flight data assimilation. The integrated advancement of aerodynamics, trajectory reconstruction, FADS-based density estimation, and aeroheating analysis has reduced predictive uncertainty and strengthened confidence for future crewed lunar and deep-space missions.

Orion↗

NASA Lewis Launch Collision Probability Model Developed and Analyzed

There are nearly 10,000 tracked objects orbiting the earth. These objects encompass manned objects, active and decommissioned satellites, spent rocket bodies, and debris. They range from a few centimeters across to the size of the MIR space station. Anytime a new satellite is launched, the launch vehicle with its payload attached passes through an area of space in which these objects orbit. Although the population density of these objects is low, there always is a small but finite probability of collision between the launch vehicle and one or more of these space objects. Even though the probability of collision is very low, for some payloads even this small risk is unacceptable. To mitigate the small risk of collision associated with launching at an arbitrary time within the daily launch window, NASA performs a prelaunch mission assurance Collision Avoidance Analysis (or COLA). For the COLA of the Cassini spacecraft, the NASA Lewis Research Center conducted an in-house development and analysis of a model for launch collision probability. The model allows a minimum clearance criteria to be used with the COLA analysis to ensure an acceptably low probability of collision. If, for any given liftoff time, the nominal launch vehicle trajectory would pass a space object with less than the minimum required clearance, launch would not be attempted at that time. The model assumes that the nominal positions of the orbiting objects and of the launch vehicle can be predicted as a function of time, and therefore, that any tracked object that comes within close proximity of the launch vehicle can be identified. For any such pair, these nominal positions can be used to calculate a nominal miss distance. The actual miss distances may differ substantially from the nominal miss distance, due, in part, to the statistical uncertainty of the knowledge of the objects positions. The model further assumes that these position uncertainties can be described with position covariance matrices. With these, and some additional simplifying assumptions, a closed-form solution for the probability of collision is obtained. This solution provides clear insights into how each of the independent parameters affects the probability of collision. It shows that for a given maximum probability of collision and prior knowledge of the objects position uncertainties and sizes, only knowledge of the nominal closest approach distance is required to make the launch/no launch decision. The model was completed and used for the mission assurance COLA analysis for the Cassini spacecraft, which was launched on a Titan IV/Centaur rocket on October 15, 1997. Although the model was specifically developed for the Cassini mission, it is clearly applicable for other launches as well. The effect of COLA closures on the launch window is shown. The bar represents the entire 140-min launch window on October 15, 1997; the blackened areas represent the loss of launch opportunities due to the potential for a collision with an orbiting object.

Bollenbacher, Gary↗

Modeling the Effects of Ice Accretion on the Low Pressure Compressor and the Overall Turbofan Engine System Performance

The focus of this study is on utilizing a mean line compressor flow analysis code coupled to an engine system thermodynamic code, to estimate the effects of ice accretion on the low pressure compressor, and quantifying its effects on the engine system throughout a notional flight trajectory. In this paper a temperature range in which engine icing would occur was assumed. This provided a mechanism to locate potential component icing sites and allow the computational tools to add blockages due to ice accretion in a parametric fashion. Ultimately the location and level of blockage due to icing would be provided by an ice accretion code. To proceed, an engine system modeling code and a mean line compressor flow analysis code were utilized to calculate the flow conditions in the fan-core and low pressure compressor and to identify potential locations within the compressor where ice may accrete. In this study, an "additional blockage" due to the accretion of ice on the metal surfaces, has been added to the baseline aerodynamic blockage due to boundary layer, as well as the blade metal blockage. Once the potential locations of ice accretion are identified, the levels of additional blockage due to accretion were parametrically varied to estimate the effects on the low pressure compressor blade row performance operating within the engine system environment. This study includes detailed analysis of compressor and engine performance during cruise and descent operating conditions at several altitudes within the notional flight trajectory. The purpose of this effort is to develop the computer codes to provide a predictive capability to forecast the onset of engine icing events, such that they could ultimately help in the avoidance of these events.

Veres, Joseph P.↗

Genesis Trajectory Design

The Genesis mission will launch in 2001, sending the spacecraft into a halo orbit about the Sun-Earth L1 point to collect and return solar wind samples to the Earth for analysis in 2003. One of the most constraining aspects of the mission design is the requirement to return to the designated landing site (the Utah Test and Training Range, UTTR) during daylight hours. The ongoing mission design has led the development of a family of solutions that characterize a broad range of conditions at Earth entry. Characterizing this family provides insight into the possible existence of additional trajectories while also helping to narrow the search space by indicating where additional solutions are unlikely to exist; this contributes to a more efficient utilization of mission design resources.

Bell, Julia L.↗

Block segmentation in feature space for realtime object detection in high granularity images

Computer vision has applications in object detection, image recognition and classification, and object tracking. One of the challenges of computer vision is the presence of useful information at multiple distance scales. Filtering techniques may sacrifice details at small scales in order to prioritize the analysis of large-scale features of the image. We present a strategy for coarse-graining multidimensional data while maintaining fine-grained detail for subsequent analysis. The algorithm is based on fixed-size block segmentation in the feature space. We apply this strategy to solve the long-standing challenge of detecting particle trajectories at the Large Hadron Collider in real time.

Computer vision↗

Failure Bounding And Sensitivity Analysis Applied To Monte Carlo Entry, Descent, And Landing Simulations

In the study of entry, descent, and landing, Monte Carlo sampling methods are often employed to study the uncertainty in the designed trajectory. The large number of uncertain inputs and outputs, coupled with complicated non-linear models, can make interpretation of the results difficult. Three methods that provide statistical insights are applied to an entry, descent, and landing simulation. The advantages and disadvantages of each method are discussed in terms of the insights gained versus the computational cost. The first method investigated was failure domain bounding which aims to reduce the computational cost of assessing the failure probability. Next a variance-based sensitivity analysis was studied for the ability to identify which input variable uncertainty has the greatest impact on the uncertainty of an output. Finally, probabilistic sensitivity analysis is used to calculate certain sensitivities at a reduced computational cost. These methods produce valuable information that identifies critical mission parameters and needs for new technology, but generally at a significant computational cost.

Gaebler, John A.↗

Recovery of Voyager Plasma Electron Observations at Jupiter

We will present our recovery of Voyager 1 and 2 plasma electron observations during their Jupiter flybys. The analysis is expected to be completed by the time of the Fall AGU 2023 Meeting and stored in Goddard’s Data Center and we will present new results never published before. The original summary data tapes and later data files at first appeared to be permanently lost but eventually located at the Massachusetts Institute of Technology, while data analysis results done at Goddard Space Flight Center, except for that published in journals, were permanently lost such as electron distribution functions, spacecraft trajectory and spacecraft attitude information. In addition to recovering the electron plasma observations (electron intensities and fluid parameters of the thermal and suprathermal electron populations, respectively), we use Spice Kernels for Voyager 1 and 2 trajectory and spacecraft attitude information, fortunately produced by NASA’s Jet Propulsion Laboratory. We will present new results of our work, originally funded under the Planetary Data Archiving, Restoration, and Tools (PDART) program but now being funded by the Internal Scientist Funding Model (ISFM) Exosphere Ionosphere Magnetospheres Modeling (EIMM) program at NASA Goddard Space Flight Center. If time permits, we will also present some of our recovery of the Voyager 2 Uranus plasma electron data and analysis similar to what was done for Jupiter.

E.C. Sittler Jr.↗

Recovery of Voyager Plasma Electron Observations at Jupiter

We will present our recovery of Voyager 1 and 2 plasma electron observations during their Jupiter flybys. The analysis is expected to be completed by the time of the Fall AGU 2023 Meeting and stored in Goddard’s Data Center and we will present new results never published before. The original summary data tapes and later data files at first appeared to be permanently lost but eventually located at the Massachusetts Institute of Technology, while data analysis results done at Goddard Space Flight Center, except for that published in journals, were permanently lost such as electron distribution functions, spacecraft trajectory and spacecraft attitude information. In addition to recovering the electron plasma observations (electron intensities and fluid parameters of the thermal and suprathermal electron populations, respectively), we use Spice Kernels for Voyager 1 and 2 trajectory and spacecraft attitude information, fortunately produced by NASA’s Jet Propulsion Laboratory. We will present new results of our work, originally funded under the Planetary Data Archiving, Restoration, and Tools (PDART) program but now being funded by the Internal Scientist Funding Model (ISFM) Exosphere Ionosphere Magnetospheres Modeling (EIMM) program at NASA Goddard Space Flight Center. If time permits, we will also present some of our recovery of the Voyager 2 Uranus plasma electron data and analysis similar to what was done for Jupiter.

E.C. Sittler Jr.↗

Modal analysis of the behavior of inertial particles in turbulence subjected to Stokes drag

The clustering of small heavy inertial particles subjected to Stokes drag in turbulence, which is the concern of present study, is known to be minimal at small and large Stokes number and substantial at St = $\textit{O}$(1). This nonmonotonic trend, which has been shown computationally and experimentally, is yet to be explained analytically. In this study, we obtain an analytical expression for the Lyapunov exponents that quantitatively predicts this trend. The sum of the exponents, which is the normalized rate of change of the signed volume of a small cloud of particles, is correctly predicted to be negative and positive at small and large Stokes numbers, respectively, asymptoting to $\textit{τQ}$ as $\textit{τ}$ → 0 and $τ^{–1/2}|Q|^{1/4}$ as $\textit{τ} → ∞$, where $\textit{τ}$ is the particle relaxation time and $\textit{Q(τ)}$ is the difference between the norm of the rotation- and strain-rate tensors computed along the particle trajectory, which remains negative at all $\textit{τ}$ in turbulent flows. Additionally, the trajectory crossing is predicted only in hyperbolic flows where Q < 0 for sufficiently inertial particles with a $\textit{τ}$ that scales with $|Q|^{–1/2}$. Following the onset of crossovers, a transition from clustering to dispersion is predicted correctly. We show these behaviors are not unique to three-dimensional isotropic turbulence and can be reproduced closely by a one-dimensional mono-harmonic flow, which appears as a fundamental canonical problem in the study of particle clustering. Analysis of this one-dimensional canonical flow shows that the rate of clustering, quantified as the product of the Lyapunov exponent and particle relaxation time, is bounded by –1/2, behaving with extreme nonlinearity in the hyperbolic flows and always remaining positive in the elliptic flows. Finally, this model problem also confirms that dispersion in a hyperbolic flow will occur only if particles' trajectory cross. These findings, which stem from our analysis, are corroborated by the direct numerical simulations.

42 ENGINEERING↗

Post2 End-to-End Descent and Landing Simulation for ALHAT Design Analysis Cycle 2

The ALHAT project is an agency-level program involving NASA centers, academia, and industry, with a primary goal to develop a safe, autonomous, precision-landing system for robotic and crew-piloted lunar and planetary descent vehicles. POST2 is used as the 6DOF descent and landing trajectory simulation for determining integrated system performance of ALHAT landing-system models and lunar environment models. This paper presents updates in the development of the ALHAT POST2 simulation, as well as preliminary system performance analysis for ALDAC-2 used for the testing and assessment of ALHAT system models. The ALDAC-2 POST2 Monte Carlo simulation results have been generated and focus on HRN model performance with the fully integrated system, as well performance improvements of AGNC and TSAR model since the previous design analysis cycle

Davis, Jody L.↗

Fairing Separation Analysis Using SepTOOL

This document describes the relevant equations programmed in spreadsheet software, SepTOOL, developed by ZIN Technologies, Inc. (ZIN) to determine the separation clearance between a launch vehicle payload fairing and remaining stages. The software uses closed form rigid body dynamic solutions of the vehicle in combination with flexible body dynamics of the fairing, which is obtained from flexible body dynamic analysis or from test data, and superimposes the two results to obtain minimum separation clearance for any given set of flight trajectory conditions. Using closed form solutions allows SepTOOL to perform separation calculations several orders of magnitude faster compared to numerical methods which allows users to perform real time parameter studies. Moreover, SepTOOL can optimize vehicle performance to minimize separation clearance. This tool can evaluate various shapes and sizes of fairings along with different vehicle configurations and trajectories. These geometries and parameters are inputted in a user friendly interface. Although the software was specifically developed for evaluating the separation clearance of launch vehicle payload fairings, separation dynamics of other launch vehicle components can be evaluated provided that aerodynamic loads acting on the vehicle during the separation event are negligible. This document describes the development of SepTOOL providing analytical procedure and theoretical equations whose implementation of these equations is not disclosed. Realistic examples are presented, and the results are verified with ADAMS (MSC Software Corporation) simulations. It should be noted that SepTOOL is a preliminary separation clearance assessment software for payload fairings and should not be used for final clearance analysis.

fairings↗

Real-time tracking and analysis of gas bubble dynamics in laser powder bed fusion using in-situ X-ray characterization and machine learning

Porosity defects remain a significant challenge in the laser powder bed fusion (LPBF) process, adversely affecting the mechanical properties and reliability of additively manufactured components. Here, this study investigates the real-time formation and trajectory of gas bubbles during LPBF of Al6061 alloy using advanced in-situ X-ray characterization and machine learning. The unsupervised Gaussian mixture model and particle tracking algorithm developed are able to precisely track and quantify the properties of gas bubbles and keyhole pores. Our analysis identified five distinct types of gas bubble formation and movement patterns, emphasizing the diverse origins and behaviors of these defects. It enables precise quantification of trajectories, velocities, and morphological changes of gas bubbles, offering a granular view of the subsurface dynamics within the melt pool. Additionally, we explored keyhole-induced pore dynamics, revealing the critical role of keyhole oscillation and collapse for the formation of both large and small gas pores. It defines four different regions of gas bubble movement within the melt pool, providing a clearer understanding of how local fluid dynamics affect pore behavior. The results underscore the importance of integrating in-situ experimental observation and automated machine learning to develop a more robust predictive model for defect formation in LPBF.

In-situ X-ray imaging↗

The Applicability of Unit Systems to High-Performance Computing Applications

Dimensional analysis is a key technique used to verify the soundness of scientific models. Most experts agree that engineering and scientific software would be made more reliable by integrating dimensional analysis in their type system. We explored how High Performance Computing (HPC) applications could integrate compile-time dimensional analysis. We started by investigating various implementation of unit systems for C++. Eventually, selecting the latest (and most advanced) one to apply to our test codes. We worked with code of increasing complexity, from a projectile trajectory calculation to the proxy-application Lulesh. This included our code, Springs-3D, which focuses on demonstrating language features while performing simple physic computations. Finally, our main contribution is a source-code analysis which extracts constraints on the dimension of all variables, functions, and constants in an application. This resulting system of equations is solved using the dimensions of a few of these objects. This analysis has the potential to greatly reduce the time spent performing dimensional analysis when refactoring application to use a representation of units.

97 MATHEMATICS AND COMPUTING↗

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.↗