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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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At least 235 records · Page 13

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NASA NTRS1980

Primer vector theory applied to the linear relative-motion equations

Prime vector theory is used in analyzing a set of linear relative-motion equations - the Clohessy-Wiltshire (C/W) equations - to determine the criteria and necessary conditions for an optimal N-impulse trajectory. The analysis develops the analytical criteria for improving a solution by: (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of: (1) fixed-end conditions, two impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized renezvous problem.

Jezewski, D.↗

NASA NTRS1990

Singular perturbation analysis of AOTV-related trajectory optimization problems

The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality constraint was imposed on the full order AOTV point mass equations of motion, using a simple aerodynamic heating rate model.

Calise, Anthony J.↗

NASA NTRS2010

Optimizing Flight Departure Delay and Route Selection Under En Route Convective Weather

This paper presents a linear Integer Programming model for managing air traffic flow in the United States. The decision variables in the model are departure delays and predeparture reroutes of aircraft whose trajectories are predicted to cross weather-impacted regions of the National Airspace System. The model assigns delays to a set of flights while ensuring their trajectories are free of any conflicts with weather. In a deterministic setting, there is no airborne holding due to unexpected weather incursion in a flight s path. The model is applied to solve a large-scale traffic flow management problem with realistic weather data and flight schedules. Experimental results indicate that allowing rerouting can reduce departure delays by nearly 57%, but it is associated with an increase in total airborne time due to longer routes flown by aircraft. The computation times to solve this problem were significantly lower than those reported in the earlier studies.

Mukherjee, Avijit↗

NASA NTRS1974

A method for determining optimum re-entry trajectories

The Pontryagin Maximum Principle is used to formulate the problem of finding optimum atmospheric vehicular reentry trajectories. The optimization problem is that of minimizing an integral which is a function of the state and control variables. The vehicle's motion is assumed to be influenced by a gravitational force and an aerodynamic force. The problem is formulated and the necessary equations are developed simultaneously for three sets of Euler angles. Computational procedures are suggested so that numerical trajectories may be generated.

Reiter, W. F.↗

NASA NTRS1981

Motion of the angular momentum vector in body coordinates for torque-free dual-spin spacecraft

The motion of the angular momentum vector in body coordinates for torque free, asymmetric dual spin spacecraft without and, for a special case, with energy dissipation on the main spacecraft is investigated. Without energy dissipation, two integrals can be obtained from the Euler equations of motion. Using the classical method of elimination of variable, the motion about the equilibrium points (six for the general case) are derived with these integrals. For small nutation angle, theta, the trajectories about the theta = 0 deg and theta = 180 deg points readily show the requirements for stable motion about these points. Also the conditions needed to eliminate stable motion about the theta = 180 deg point as well as the other undesireable equilibrium points follow directly from these equations. For the special case where the angular momentum vector moves about the principal axis which contains the momentum wheel, the notion of 'free variable' azimuth angle is used. Physically this angle must vary from 0 to 2 pi in a circular periodic fashion. Expressions are thus obtained for the nutation angle in terms of the free variable and other spacecraft parameters. Results show that in general there are two separate trajectory expressions that govern the motion of the angular momentum vector in body coordinates.

Fedor, J. V.↗

NASA NTRS1990

The 4-D descent trajectory generation techniques under realistic operating conditions

NASA-Langley has been conducting and sponsoring research in airborne energy management for a number of years. During the course of this research, two fundamental techniques for the generation of 4D (fixed time) descent trajectories have emerged as viable candidates for advanced flight management systems. The first technique utilizes speed schedules of constant Mach number transitioning to constant calibrated airspeed chosen empirically to produce minimum fuel usage. The second technique computes cost optimized speed schedules of variable airspeed developed through application of optimal control theory. Both techniques have been found to produce reasonable and flyable descent trajectories. The formulation of the algorithms for each technique is evaluated and their suitability for operations in realistic conditions is discussed. Operational factors considered include: airplace speed, thrust, and altitude rate constaints; wind, temperature, and pressure variations; Air Traffic Control altitude, speed, and time constaints; and pilot interface and guidance considerations. Time flexibility, fuel usage, and airborne computational requirements were the primary performance measures.

Williams, David H.↗

NASA NTRS1980

Optimum reentry trajectories of a lifting vehicle

Research results are presented of an investigation of the optimum maneuvers of advanced shuttle type spacecraft during reentry. The equations are formulated by means of modified Chapman variables resulting in a general set of equations for flight analysis which are exact for reentry and for flight in a vacuum. Four planar flight typical optimum manuevers are investigated. For three-dimensional flight the optimum trajectory for maximum cross range is discussed in detail. Techniques for calculating reentry footprints are presented.

Chern, J. S.↗

DOE OSTI2025

Dynamics of McMillan mappings I. McMillan multipoles

In this article, we consider two dynamical systems: the McMillan sextupole and octupole integrable mappings, originally proposed by Edwin McMillan. Both represent the simplest symmetric McMillan maps, characterized by a single intrinsic parameter. While these systems find numerous applications across various domains of mathematics and physics, some of their dynamical properties remain unexplored. We aim to bridge this gap by providing a comprehensive description of all stable trajectories, including the parametrization of invariant curves, Poincaré rotation numbers, and canonical action–angle variables. In the second part, we establish connections between these maps and general chaotic maps in standard form. Our investigation reveals that the McMillan sextupole and octupole serve as first-order approximations of the dynamics around the fixed point, akin to the linear map and quadratic invariant (known as the Courant–Snyder invariant in accelerator physics), which represents zeroth-order approximations (referred to as linearization). Furthermore, we propose a novel formalism for nonlinear Twiss parameters, which accounts for the dependence of rotation number on amplitude. This stands in contrast to conventional betatron phase advance used in accelerator physics, which remains independent of amplitude. Notably, in the context of accelerator physics, this new formalism demonstrates its capability in predicting dynamical aperture around low-order resonances for flat beams, a critical aspect in beam injection/extraction scenarios.

43 PARTICLE ACCELERATORS↗

NASA NTRS1974

Analysis of a flare-director concept for an externally blown flap STOL aircraft

A flare-director concept involving a thrust-required flare-guidance equation was developed and tested on a moving-base simulator. The equation gives a signal to command thrust as a linear function of the errors between the variables thrust, altitude, and altitude rate and corresponding values on a desired reference flare trajectory. During the simulator landing tests this signal drove either the horizontal command bar of the aircraft's flight director or a thrust-command dot on a head-up virtual-image display of a flare director. It was also used as the input to a simple autoflare system. An externally blown flap STOL (short take-off and landing) aircraft (with considerable stability and control augmentation) was modeled for the landing tests. The pilots considered the flare director a valuable guide for executing a proper flare-thrust program under instrument-landing conditions, but were reluctant to make any use of the head-up display when they were performing the landings visually.

Middleton, D. B.↗

NASA NTRS1994

Multidisciplinary design optimization using genetic algorithms

Multidisciplinary design optimization (MDO) is an important step in the conceptual design and evaluation of launch vehicles since it can have a significant impact on performance and life cycle cost. The objective is to search the system design space to determine values of design variables that optimize the performance characteristic subject to system constraints. Gradient-based optimization routines have been used extensively for aerospace design optimization. However, one limitation of gradient based optimizers is their need for gradient information. Therefore, design problems which include discrete variables can not be studied. Such problems are common in launch vehicle design. For example, the number of engines and material choices must be integer values or assume only a few discrete values. In this study, genetic algorithms are investigated as an approach to MDO problems involving discrete variables and discontinuous domains. Optimization by genetic algorithms (GA) uses a search procedure which is fundamentally different from those gradient based methods. Genetic algorithms seek to find good solutions in an efficient and timely manner rather than finding the best solution. GA are designed to mimic evolutionary selection. A population of candidate designs is evaluated at each iteration, and each individual's probability of reproduction (existence in the next generation) depends on its fitness value (related to the value of the objective function). Progress toward the optimum is achieved by the crossover and mutation operations. GA is attractive since it uses only objective function values in the search process, so gradient calculations are avoided. Hence, GA are able to deal with discrete variables. Studies report success in the use of GA for aircraft design optimization studies, trajectory analysis, space structure design and control systems design. In these studies reliable convergence was achieved, but the number of function evaluations was large compared with efficient gradient methods. Applicaiton of GA is underway for a cost optimization study for a launch-vehicle fuel-tank and structural design of a wing. The strengths and limitations of GA for launch vehicle design optimization is studied.

Unal, Resit↗

NASA NTRS2017

Low-Thrust Many-Revolution Trajectory Optimization via Differential Dynamic Programming and a Sundman Transformation

Low-thrust trajectories about planetary bodies characteristically span a high count of orbital revolutions. Directing the thrust vector over many revolutions presents a challenging optimization problem for any conventional strategy. This paper demonstrates the tractability of low-thrust trajectory optimization about planetary bodies by applying a Sundman transformation to change the independent variable of the spacecraft equations of motion to the eccentric anomaly and performing the optimization with differential dynamic programming. Fuel-optimal geocentric transfers are shown in excess of 1000 revolutions while subject to Earths J2 perturbation and lunar gravity.

Aziz, Jonathan↗

NASA NTRS2017

Low-Thrust Many-Revolution Trajectory Optimization via Differential Dynamic Programming and a Sundman Transformation

Aziz, Jonathan D.↗

NASA NTRS2013

Sasquatch Footprint Tool

The Crew Exploration Vehicle Parachute Assembly System (CPAS) is the parachute system for NASA s Orion spacecraft. The test program consists of numerous drop tests, wherein a test article rigged with parachutes is extracted or released from an aircraft. During such tests, range safety is paramount, as is the recoverability of the parachutes and test article. It is crucial to establish an aircraft release point that will ensure that the article and all items released from it will land in safe locations. A new footprint predictor tool, called Sasquatch, was created in MATLAB. This tool takes in a simulated trajectory for the test article, information about all released objects, and atmospheric wind data (simulated or actual) to calculate the trajectories of the released objects. Dispersions are applied to the landing locations of those objects, taking into account the variability of winds, aircraft release point, and object descent rate. Sasquatch establishes a payload release point (e.g., where the payload will be extracted from the carrier aircraft) that will ensure that the payload and all objects released from it will land in a specified cleared area. The landing locations (the final points in the trajectories) are plotted on a map of the test range. Sasquatch was originally designed for CPAS drop tests and includes extensive information about both the CPAS hardware and the primary test range used for CPAS testing. However, it can easily be adapted for more complex CPAS drop tests, other NASA projects, and commercial partners. CPAS has developed the Sasquatch footprint tool to ensure range safety during parachute drop tests. Sasquatch is well correlated to test data and continues to ensure the safety of test personnel as well as the safe recovery of all equipment. The tool will continue to be modified based on new test data, improving predictions and providing added capability to meet the requirements of more complex testing.

Bledsoe, Kristin↗

NASA NTRS1983

Separation of time scales in aircraft trajectory optimization

Two methods for analyzing the time-scale properties of aircraft trajectory optimization problems are presented. Time-scale properties must be identified before solutions can be obtained by using singular perturbation methods. Both methods only require a knowledge of the state equations, the aircraft characteristics, and the bounds on the state and control variables. Although these methods give only rough estimates of time-scale separation, they do not require that an 'exact' optimal trajectory be known, as do the more rigorous methods, and they are an improvement on the ad hoc methods currently in use. The two methods are applied to an example problem for a high performance aircraft.

Ardema, M. D.↗

NASA NTRS1986

Plasmasphere formation in arbitrarily oriented magnetospheres

The formation of plasmaspheres in planetary magnetospheres with arbitrary orientations of the rotation and magnetic dipole axes is investigated. A traditional plasmasphere with closed orbits inside the plasmapause and open trajectories outside it only occurs for the limiting case of aligned rotation and dipole axes. A time-variable plasmapause exists if the rotation axis is perpendicular to the solar win flow direction. In any other case, no definite plasmapause exists. Solar wind-driven convection transports plasma throughout the magnetosphere with an effectiveness which increases as the orientation goes further from one of the two limiting cases of strict plasmapause formation. The present analysis is applied to earth and Uranus using the actual orientations of the rotation and dipole axes. Particle trajectories at earth deviate only slightly from those obtained with traditional models. Uranus has no plasmasphere, and plasma convects sunwards throughout the inner magnetosphere.

Selesnick, R. S.↗

NASA NTRS1991

Range optimization for a supersonic aircraft

Range optimal trajectories for an aircraft flying in the vertical plane are obtained from Pontryagin's Minimum Principle. Control variables are load factor n which appears nonlinearly in the equations of motion and throttle setting eta, which appears only linearly. Both controls are subject to fixed bounds, namely eta between values of 0 and 1 and absolute value of n not greater than n(max). Additionally, a dynamic pressure limit is imposed, which represents a first-order state-inequality constraint. For fixed flight time, fixed initial coordinates, and partially fixed final coordinates, the effect of the load factor limit absolute value of n not greater than n(max) is studied. Upon varying n(max), six different switching structures are obtained. All trajectories involve singular control along arcs with active dynamic pressure limit.

Seywald, Hans↗

NASA NTRS1994

Optimal Low Thrust Trajectories Using Differential Inclusion Concepts

A direct optimization method based on differential inclusion concepts has been developed and used to compute low thrust trajectories. This new formulation removes explicit control dependence from the problem statement thereby reducing the dimension of the parameter space of the resulting nonlinear programming problem. A simple example of a two-dimensional gravity-free trajectory involving a maximum velocity transfer to a rectilinear path is discussed. Three interplanetary trajectory examples, an Earth-Mars constant specific impulse transfer, and Earth-Jupiter constant specific impulse transfer, and an Earth-Venus-Mars variable specific impulse gravity assist, are also included. An analysis of the technique's performance is provided.

low↗

NASA NTRS2024

DAVINCI: Venus Atmospheric Model Comparisons

The Deep Atmosphere Venus Investigation of Noble gases, Chemistry, and Imaging(DAVINCI) mission aims to answer long-standing questions regarding Venus’ origin using Zephyr, an atmospheric descent probe. Zephyr will be the first probe to take high-resolution aerial photographs of a mountainous tesserae surface as it descends over the Alpha Regio highlands region, which has the oldest surfaces of Venus. The Zephyr’s descent trajectory that determines the touchdown in the Alpha Regio, which is crucial for the DAVINCI mission, depends on Venus’ atmospheric properties and winds. Unfortunately, the atmospheric data for Venus from previous missions is sparse. Therefore, it is essential to consider various atmospheric models and scenarios from past flight data to predict Zephyr’s flight performance, specifically landing ellipse. To this end, this work compares three atmospheric models: the Venus Global Reference Atmospheric Model (Venus-GRAM), the Venus Climate Database(VCD), and an empirical wind model developed by Ralph Lorenz for the DAVINCI trajectory simulation and modeling. This paper compares the mean and variations of different atmospheric properties and winds from these atmospheric models. In addition, this work combines the atmospheric properties and the wind variability from the Venus-GRAM with the winds from the Lorenz-based model to have more stressing Venus wind dispersions that allow for more conservative trajectory analysis. Furthermore, this work relies on the DAVINCI landing ellipse size as a metric to measure how robust the trajectory analysis will be to the change in the atmospheric properties and winds of the Venus atmosphere.

Pardha Sai Chadalavada↗