Some numerical results of geocentric low thrust trajectory optimization
Determination of optimum, coplanar, circle-to- circle, transfer trajectories for low thrust space vehicles in strong central force field
TRAJECTORY ANALYSIS↗
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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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End to End Optimization of a Mars Hybrid Transportation Architecture
NASA’s Mars Study Capability Team (MSCT) is developing a reusable Mars hybrid transportation architecture in which both chemical and solar electric propulsion systems are used in a single vehicle design to send crew and cargo to Mars. This paper presents a new integrated framework that combines Earth departure/arrival, heliocentric trajectory, Mars orbit reorientation, and vehicle sizing into a single environment and solves the entire mission from beginning to end in an effort to find a globally optimized solution for the hybrid architecture.
Qu, Min↗
Optimal guidance and propulsion control for transatmospheric vehicles
Problems associated with on-board trajectory optimization and with the synthesis of guidance laws are addressed for ascent to LEO of an air-breathing, single-stage-to-orbit vehicle. A multimode propulsion system is assumed which incorporates turbojet, ramjet, scramjet, and rocket engines. An energy-state approximation is applied to a four-state dynamic model for flight of a point mass over a spherical nonrotating earth. An algorithm for generating fuel-optimal climb profiles is derived via singular perturbation theory. This algorithm results from application of the minimum principle to a low-order dynamic model that includes general functional dependence on angle of attack and a normal component of thrust. Switching conditions are derived which, under appropriate assumptions, govern optimal transition from one propulsion mode to another. The use of bank angle to modulate the magnitude of the vertical component of lift is shown to improve the index performance. Numerical results illustrate the nature of the resulting fuel-optimal climb paths.
Corban, J. E.↗
Wind models for the NSTS ascent trajectory biasing for wind load alleviation
New concepts are presented for aerospace vehicle ascent wind profile biasing. The purpose for wind biasing the ascent trajectory is to provide ascent wind loads relief and thus decrease the probability for launch delays due to wind loads exceeding critical limits. Wind biasing trajectories to the profile of monthly mean winds have been widely used for this purpose. The wind profile models presented give additional alternatives for wind biased trajectories. They are derived from the properties of the bivariate normal probability function using the available wind statistical parameters for the launch site. The analytical expressions are presented to permit generalizations. Specific examples are given to illustrate the procedures. The wind profile models can be used to establish the ascent trajectory steering commands to guide the vehicle through the first stage. For the National Space Transportation System (NSTS) program these steering commands are called I-loads.
Smith, O. E.↗
Wind models for the NSTS ascent trajectory biasing for wind load alleviation
New concepts are presented for aerospace vehicle ascent wind profile biasing. The purpose for wind biasing the ascent trajectory is to provide ascent wind loads relief and thus decrease the probability for launch delays due to wind loads exceeding critical limits. Wind biasing trajectories to the the profile of monthly mean winds have been widely used for this purpose. The wind profile models presented give additional alternatives for wind biased trajectories. They are derived from the properties of the bivariate normal probability function using the available wind statistical parameters for the launch site. The analytical expressions are presented to permit generalizations. Specific examples are given to illustrate the procedures. The wind profile models can be used to establish the ascent trajectory steering commands to guide the vehicle through the first stage. For the National Space Transportation System (NSTS) program these steering commands are called I-loads.
Smith, O. E.↗
Determination of aerothermodynamic environment uncertainties with application to space shuttle vehicles
In an effort to minimize the cost of the thermal protection system (TPS) for space shuttles, an analysis is made of environmental uncertainties. The basic categories of these uncertainties include aerodynamic heating, trajectory dispersions, atmospheric variations, and vehicle attitude variations. Also discussed are TPS design sensitivity to environmental uncertainties, and uncertainty profiles. Preliminary results indicate moderate TPS cost for a high confidence level environment may be obtained.
Scottoline, C. A.↗
The 2006 Cape Canaveral Air Force Station Range Reference Atmosphere Model Validation Study and Sensitivity Analysis to the National Aeronautics and Space Administration's Space Shuttle
Atmospheric parameters are essential in assessing the flight performance of aerospace vehicles. The effects of the Earth's atmosphere on aerospace vehicles influence various aspects of the vehicle during ascent ranging from its flight trajectory to the structural dynamics and aerodynamic heatmg on the vehicle. Atmospheric databases charactenzing the wind and thermodynamic environments, known as Range Reference Atmospheres (RRA), have been developed at space launch ranges by a governmental interagency working group for use by aerospace vehicle programs. The National Aeronantics and Space Administration's (NASA) Space Shuttle Program (SSP), which launches from Kennedy Space Center, utilizes atmosphenc statistics derived from the Cape Canaveral Air Force Station Range Reference Atmosphere (CCAFS RRA) database to evaluate environmental constraints on various aspects of the vehlcle during ascent.
Decker, Ryan K.↗
Use of Smoothed Measured Winds to Predict and Assess Launch Environments
Since many of the larger launch vehicles are operated near their design limits during the ascent phase of flight to optimize payload to orbit, it often becomes necessary to verify that the vehicle will remain within certification limits during the ascent phase as part of the go/no-go review made prior to launch. This paper describes the approach used to predict Ares I-X launch vehicle structural air loads and controllability prior to launch which represents a distinct departure from the methodology of the Space Shuttle and Evolved Expendable Launch Vehicle (EELV) programs. Protection for uncertainty of key environment and trajectory parameters is added to the nominal assessment of launch capability to ensure that critical launch trajectory variables would be within the integrated vehicle certification envelopes. This process was applied by the launch team as a key element of the launch day go/no-go recommendation. Pre-launch assessments of vehicle launch capability for NASA's Space Shuttle and the EELV heavy lift versions require the use of a high-resolution wind profile measurements, which have relatively small sample size compared with low-resolution profile databases (which include low-resolution balloons and radar wind profilers). The approach described in this paper has the potential to allow the pre-launch assessment team to use larger samples of wind measurements from low-resolution wind profile databases that will improve the accuracy of pre-launch assessments of launch availability with no degradation of mission assurance or launch safety.
Cordova, Henry S.↗
Substantiation data for hypersonic cruise vehicle wing structure evaluation - Volume 1, sections 1-10
Trajectory, load, aerodynamic heating, materials, structural, and thermal analyses for hypersonic cruise vehicle wings
Davis, G. W.↗
Uncertainty Quantification of Expected Time-of-Arrival in UAV Flight Trajectory
One of the foremost requirements for accurate in-flight safety monitoring of autonomous unmanned aerial vehicles (UAVs) is tracking of their flight trajectory. Existing UAVs leverage autonomous flight functionalities based on trajectory generation algorithms developed in robotic applications such as polynomial or spline curves in order to facilitate kinematic smoothness, minimum vibrations and fuel efficiency. However in practice, the actual path may be subjected to unexpected local weather conditions, unexpected obstacles along the path or abrupt traffic changes in the low-altitude airspace resulting in large errors of the predicted time-of-arrival at way-points. In this study, an approach to quantify and propagate uncertainty in 4D trajectories is proposed. The paper presents a simple error interval propagation method based on the expected cruise speed of the UAV and its associated uncertainty. The uncertainty is then propagated in time to estimate reasonable confidence intervals on the times-of-arrival of the vehicle at each way-point as well as along the entire flight-path. The uncertainty propagation is demonstrated on a state-of-the-art trajectory generation algorithm based on non-uniform rational B-spline (NURBS) curves. Further, the effect of a stationary wind field is incorporated in the uncertainty propagation approach. The proposed method is implemented on synthetic and real data obtained from flight experiments with a small UAV.
Uncertainty Quantification↗
Augmenting Parametric Optimal Ascent Trajectory Modeling with Graph Theory
It has been well documented that decisions made in the early stages of Conceptual and Pre-Conceptual design commit up to 80% of total Life-Cycle Cost (LCC) while engineers know the least about the product they are designing [1]. Once within Preliminary and Detailed design however, making changes to the design becomes far more difficult to enact in both cost and schedule. Primarily this has been due to a lack of detailed data usually uncovered later during the Preliminary and Detailed design phases. In our current budget-constrained environment, making decisions within Conceptual and Pre-Conceptual design which minimize LCC while meeting requirements is paramount to a program's success. Within the arena of launch vehicle design, optimizing the ascent trajectory is critical for minimizing the costs present within such concerns as propellant, aerodynamic, aeroheating, and acceleration loads while meeting requirements such as payload delivered to a desired orbit. In order to optimize the vehicle design its constraints and requirements must be known, however as the design cycle proceeds it is all but inevitable that the conditions will change. Upon that change, the previously optimized trajectory may no longer be optimal, or meet design requirements. The current paradigm for adjusting to these updates is generating point solutions for every change in the design's requirements [2]. This can be a tedious, time-consuming task as changes in virtually any piece of a launch vehicle's design can have a disproportionately large effect on the ascent trajectory, as the solution space of the trajectory optimization problem is both non-linear and multimodal [3]. In addition, an industry standard tool, Program to Optimize Simulated Trajectories (POST), requires an expert analyst to produce simulated trajectories that are feasible and optimal [4]. In a previous publication the authors presented a method for combatting these challenges [5]. In order to bring more detailed information into Conceptual and Pre-Conceptual design, knowledge of the effects originating from changes to the vehicle must be calculated. In order to do this, a model capable of quantitatively describing any vehicle within the entire design space under consideration must be constructed. This model must be based upon analysis of acceptable fidelity, which in this work comes from POST. Design space interrogation can be achieved with surrogate modeling, a parametric, polynomial equation representing a tool. A surrogate model must be informed by data from the tool with enough points to represent the solution space for the chosen number of variables with an acceptable level of error. Therefore, Design Of Experiments (DOE) is used to select points within the design space to maximize information gained on the design space while minimizing number of data points required. To represent a design space with a non-trivial number of variable parameters the number of points required still represent an amount of work which would take an inordinate amount of time via the current paradigm of manual analysis, and so an automated method was developed. The best practices of expert trajectory analysts working within NASA Marshall's Advanced Concepts Office (ACO) were implemented within a tool called multiPOST. These practices include how to use the output data from a previous run of POST to inform the next, determining whether a trajectory solution is feasible from a real-world perspective, and how to handle program execution errors. The tool was then augmented with multiprocessing capability to enable analysis on multiple trajectories simultaneously, allowing throughput to scale with available computational resources. In this update to the previous work the authors discuss issues with the method and solutions.
Patrick D Dees↗
Research on Computational and Display Requirements for Human Control of Space Vehicle Boosters, Phase III. Part II - Computer Programs and Data Package Final Report, 1 Mar. - 31 Aug. 1967
Hybrid computer program for real time trajectory determination of human controlled space vehicle booster
REAL TIME↗
Alternate vehicles for engine/vehicle optimization
The space shuttle main engine, full flow staged combustion, integrated modular engine concept, split expander, and expander bleed rocket engine cycles were studied for use on Single-Stage-to-Orbit fully reusable vehicles. The vehicle uses vertical take-off and horizontal landing and liquid hydrogen rockets for propulsion. The PROPSIZE computer code was modified for use on the available computers. Vehicle sizing was done after trajectory optimization for various engine designs. The various rocket engine cycles were compared and it was found that the full flow staged combustion cycle had the lowest vehicle dry mass. The split expander cycle could have advantages in safety and cooling which could make it the preferred choice in some cases. Comparison to previous work with two-stage heavy-lift vehicles showed that the same ranking of the cycles was found for both vehicle concepts.
Venkatasubramanyam, G.↗
Design Considerations for Space Transfer Vehicles Using Solar Thermal Propulsion
The economical deployment of satellites to high energy earth orbits is crucial to the ultimate success of this nations commerical space ventures and is highly desirable for deep space planetary missions requiring earth escape trajectories. Upper stage space transfer vehicles needed to accomplish this task should ideally be simple, robust, and highly efficient. In this regard, solar thermal propulsion is particularly well suited to those missions where high thrust is not a requirement. The Marshall Space Flight Center is , therefore, currently engaged in defining a transfer vehicle employing solar thermal propulsion capable of transferring a 1000 lb. payload from low Earth orbit (LEO) to a geostationary Earth orbit (GEO) using a Lockheed launch vehicle (LLV3) with three Castors and a large shroud. The current design uses liquid hydrogen as the propellant and employs two inflatable 16 x 24 feet eliptical off-axis parabolic solar collectors to focus sunlight onto a tungsten/rhenium windowless black body type absorber. The concentration factor on this design is projected to be approximately 1800:1 for the primary collector and 2.42:1 for the secondary collector for an overall concentration factor of nearly 4400:1. The engine, which is about twice as efficient as the best currently available chemical engines, produces two pounds of thrust with a specific impulse (Isp) of 860 sec. Transfer times to GEO are projected to be on the order of one month. The launch and deployed configurations of the solar thermal upper stage (STUS) are depicted.
Emrich, William J.↗
Ares I-X Separation and Reentry Trajectory Analyses
The Ares I-X Flight Test Vehicle was launched on October 28, 2009 and was the first and only test flight of NASA s two-stage Ares I launch vehicle design. The launch was successful and the flight test met all of its primary and secondary objectives. This paper discusses the stage separation and reentry trajectory analysis that was performed in support of the Ares I-X test flight. Pre-flight analyses were conducted to assess the risk of stage recontact during separation, to evaluate the first stage flight dynamics during reentry, and to define the range safety impact ellipses of both stages. The results of these pre-flight analyses were compared with available flight data. On-board video taken during flight showed that the flight test vehicle successfully separated without any recontact. Reconstructed trajectory data also showed that first stage flight dynamics were well characterized by pre-flight Monte Carlo results. In addition, comparisons with flight data indicated that the complex interference aerodynamic models employed in the reentry simulation were effective in capturing the flight dynamics during separation. Finally, the splash-down locations of both stages were well within predicted impact ellipses.
Tartabini, Paul V.↗
Orion Exploration Flight Test 1 (EFT-1) Best Estimated Trajectory Development
The Orion Exploration Flight Test 1 (EFT-1) mission successfully flew on Dec 5, 2014 atop a Delta IV Heavy launch vehicle. The goal of Orions maiden flight was to stress the system by placing an uncrewed vehicle on a high-energy trajectory replicating conditions similar to those that would be experienced when returning from an asteroid or a lunar mission. The Orion navigation team combined all trajectory data from the mission into a Best Estimated Trajectory (BET) product. There were significant challenges in data reconstruction and many lessons were learned for future missions. The team used an estimation filter incorporating radar tracking, onboard sensors (Global Positioning System and Inertial Measurement Unit), and day-of-flight weather balloons to evaluate the true trajectory flown by Orion. Data was published for the entire Orion EFT-1 flight, plus objects jettisoned during entry such as the Forward Bay Cover. The BET customers include approximately 20 disciplines within Orion who will use the information for evaluating vehicle performance and influencing future design decisions.
Holt, Greg N.↗
Guidance on maneuvering flight paths for rotary wing aircraft
A synthesis procedure for on-line determination of variable speed trajectories in known winds between fixed way points is presented. The primary application is toward rotorcraft approach guidance, although the methodology can be directly applied to other types of vehicles and other problem areas. Trajectories are generated by appropriate combination of straight and turning flight segments to determine the horizontal ground track plus a vertical synthesis based on an energy rate approach. Perturbation equations and feedback laws for four-dimensional trajectory guidance are presented.
Slater, G. L.↗
Hyper-X Post-Flight 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 ight test data. Extended Kalman ltering 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 ltering routines. Additionally, smoothing algorithms have been implemented in which the nal 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 ight data.
Karlgaard, Christopher D.↗