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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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NASA NTRS1971

An analysis and comparison of several trajectory optimization methods

The sensitivities of the convergence characteristics of the methods to initially assumed parameters and trial solution, convergence times, computer logic, and storage requirements are discussed. Numerical comparison of the convergence characteristics is made by considering a minimum time, low thrust, Earth-Mars transfer trajectory. A modified quasi-linearization method reduces convergence time by approximately 70% when compared with the generalized Newton-Raphson method and allows the terminal boundary to be specified by a general function of the problem variables. A uniquely specified and easily determined, time dependent weighting matrix for the gradient techniques accelerates the shaping of the optimal control program and improves the convergence characteristics during the terminal iterations. Convergence envelopes, indicating how sensitive the convergence characteristics are to initially assumed parameters, are plotted for the perturbation and quasi-linearization methods. Several iteration schemes are proposed which increase the size of the convergence envelopes and decrease the sensitivity of the method to initially assumed parameters.

Lewallen, J. M.↗
NASA NTRS1972

On reconstructing trajectories in the Venus lower atmosphere

A Monte Carlo technique was utilized in order to demonstrate the feasibility of processing in situ measurements of temperature, pressure, and molecular weight. The technique assumes that the lower atmosphere of Venus obeys the ideal gas law and the hydrostatic equation. Time correlations are assumed to exist in the data. It is shown that the errors in trajectory reconstruction are due mostly to noise in the data rather than to inaccuracies in the numerical technique.

Argentiero, P.↗
NASA NTRS1972

Optimal ascent trajectories of a two stage space shuttle vehicle

The effects of aerodynamic lift on the performance capability of a two stage space shuttle are discussed. The performance program uses three degrees of freedom to describe the trajectory of a point mass moving over the rotating earth. Two cases of ascent modes are described and compared. It is concluded that significant improvements in performance through the use of lift appear to be configuration dependent, and for this reason cannot be generalized for all spacecraft configurations.

Wilson, R. A.↗
NASA NTRS1972

A comparison of optimal and noise-abatement trajectories of a tilt-rotor aircraft

The potential benefits of flight path control to optimize performance and/or reduce the noise of a tilt-rotor aircraft operating in the takeoff and landing phases of flight are investigated. A theoretical performance-acoustic model is developed and then mathematically flown to yield representative takeoff and landing profiles. Minimum-time and minimum-fuel trajectories are compared to proposed noise-abatement profiles to assess the reductions in annoyance possible through flight path control. Significant reductions are feasible if a nearly vertical-takeoff flight profile is flown near the landing site; however, the time expended and fuel consumed increase.

Schmitz, F. H.↗
NASA NTRS1972

Goddard trajectory determination subsystem: Mathematical specifications

The mathematical specifications of the Goddard trajectory determination subsystem of the flight dynamics system are presented. These specifications include the mathematical description of the coordinate systems, dynamic and measurement model, numerical integration techniques, and statistical estimation concepts.

Wagner, W. E.↗
NASA NTRS1971

Optimal boost trajectories for the shuttle vehicle.

Solutions of the optimal boost problem for the MSC April 1970 base line shuttle vehicle show significant payload increases may be achieved by flying optimal pitch profiles. Results consistent with aerodynamic and acceleration constraints indicate payload gains of approximately 2.0 per cent of the total injected weight may be achieved. This corresponds to a real payload increase of about 20 per cent. Trajectory parameters for optimal launches under various conditions and a standard gravity turn launch are presented along with a brief discussion of the problem modeling and assumptions. The data are used to support a number of observations and conclusions and to provide some insight into the methods by which payload gains are achieved.

Sullivan, H. C.↗
NASA NTRS1972

Estimating trajectory correction requirements for the Outer Planets Grand Tour missions.

The estimation of trajectory correction requirements for the Outer Planets Grand Tour (OPGT) missions poses a unique and many-faceted problem for the systems analyst. In this paper the navigation concept for the OPGT is developed and illustrated. The limiting accuracies and performance of the combined radio/onboard optical system are examined. The combined orbit determination system is characterized by its accuracy and by its system risks. Such considerations are included with the statistical combination of maneuver estimates to produce preliminary delta V estimates for the planned OPGT missions.

Friedman, L. D.↗
NASA NTRS1972

Optimal trajectories between Earth and Mars in their true planetary orbits.

The optimal transfers from Earth to Mars and from Mars to Earth, considering the actual planetary orbits, are presented as functions of the corresponding idealized Hohmann transfers. The numerically exact two-impulse optimal trajectories are given in graphical form for all possible Hohmann windows. The two-impulse transfers which are absolute optimals and those for which a third impulse provides the absolute optimal are delineated. These data are designed to provide all the information necessary for quick orbit calculations for preliminary Martian mission analysis. In this form, they are as easy to use as the standard Hohmann transfer approximations and provide much greater accuracy.

Gravier, J. P.↗
NASA NTRS1972

Maximum noise abatement trajectories.

Minimum noise annoyance trajectories for developing STOL operation procedures are obtained by modulating five control variables in two dimensions. The performance index is formulated such that it explicitly assigns the same relative importance to thrust as it does to distances between discrete listeners and the aircraft. However, using a steepest descent optimization program, results indicate that it is preferable to keep the thrusters at their maximum value to minimize the integrated annoyance rather than to reduce thrust which would lower the instantaneous annoyance. Thrust decreases below its bound only when the instantaneous noise at a listener is limited.

Zeldin, S.↗
NASA NTRS1972

N-burn optimal analytic trajectories.

Derivation of N-burn analytic solutions for propellant-optimal transfer trajectories of a vehicle in a vacuum between arbitrary boundary conditions. Variational changes in the desired boundary conditions are expressed, in general, in terms of variational changes in the control vector and in the initial state vector. All coefficient matrices are computed recursively in terms of the analytic matrices established from the subarcs of the N-burn solution. The solution is applicable to shuttle ascent (exoatmospheric), rendezvous, and deorbit problems. Consideration is also given to state-variable and control-variable inequality constraints.

Jezewski, D. J.↗
NASA NTRS1972

Generation of NEP heliocentric trajectory data

A study, designed to generate representative nuclear electric propulsion data for rendezvous missions to the comet Encke using the variational calculus program HILTOP, is presented. Other purposes of the study include a comparison of the HILTOP data with equivalent data generated with QUICKTOP program and to propose approaches for storing and subsequently accessing the optimum trajectory and performance data in the QUICKLY program.

Horsewood, J. L.↗
NASA NTRS1973

Tracking and data system support for the Pioneer project. Volume 1: Pioneer 10-prelaunch planning through second trajectory correction, 4 December 1969 - 1 April 1972

The tracking and data system support of the launch, near-earth, and deep space phases of the Pioneer 10 mission, which sent a Pioneer spacecraft into a flyby of Jupiter that would eventually allow the spacecraft to escape the solar system is discussed. The support through the spacecraft's second trajectory correction is reported. During this period, scientific instruments aboard the spacecraft registered information relative to interplanetary particles and fields, and radiometric data generated by the network continued to improve knowledge of the celestial mechanics of the solar system. In addition to network support activity detail, network performance and special support activities are covered.

Siegmeth, A. J.↗
NASA NTRS1973

Mission objectives and trajectories

The present state of the knowledge of asteroids was assessed to identify mission and target priorities for planning asteroidal flights in the 1980's and beyond. Mission objectives, mission analysis, trajectory studies, and cost analysis are discussed. A bibliography of reports and technical memoranda is included.

Source record↗
NASA NTRS1973

Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 1: Technical discussion

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical solution to the problem on N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The derivation of the second-order solution is summarized by showing the essential steps, some in functional form. The general asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-earth, and interplanetary solutions. The results show that the accuracies of the asymptotic solutions range from an order of magnitude better than conic approximations to that of numerical integration itself. Also, since no iterations are required, the asymptotic boundary value solutions are obtained in a fraction of the time required for comparable numerically integrated solutions. The subject of minimizing the second-order error is discussed, and recommendations made for further work directed toward achieving a uniform accuracy in all applications.

Lancaster, J. E.↗
NASA NTRS1973

Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 2: Derivations of second-order asymptotic boundary value solutions

Previously published asymptotic solutions for lunar and interplanetery trajectories have been modified and combined to formulate a general analytical solution to the problem of N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The complete derivation of the second-order solution, including the application of a regorous matching principle, is given. It is shown that the outer and inner expansions can be matched in a region of order mu to the alpha power, where 2/5 alpha 1/2, and mu (the moon/earth or planet/sun mass ratio) is much less than one. The second-order asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-Earth, and interplanetary solutions. Each is presented as an explicit analytical solution which does not require iterative steps to satisfy the boundary conditions. The complete derivation of each solution is shown, as well as instructions for numerical evaluation. For Vol. 1, see N73-27738.

Lancaster, J. E.↗

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