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All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Constrained optimum trajectories with specified range

The characteristics of optimum fixed-range trajectories whose structure is constrained to climb, steady cruise, and descent segments are derived by application of optimal control theory. The performance function consists of the sum of fuel and time costs, referred to as direct operating costs (DOC). The state variable is range-to-go and the independent variable is energy. In this formulation a cruise segment always occurs at the optimum cruise energy for sufficiently large range. At short ranges (500 n. mi. and less) a cruise segment may also occur below the optimum cruise energy. The existence of such a cruise segment depends primarily on the fuel flow vs thrust characteristics and on thrust constraints. If thrust is a free control variable along with airspeed, it is shown that such cruise segments will not generally occur. If thrust is constrained to some maximum value in climb and to some minimum in descent, such cruise segments generally will occur. The performance difference between free thrust and constrained thrust trajectories has been determined in computer calculations for an example transport aircraft.

Erzberger, H.↗
NASA NTRSDate not supplied

New Developments in Retropropulsion Testing for Mars Entry, Descent and Landing

NASA’s plans for landing human-scale payloads on Mars in the next decade require that retrorockets be used to decelerate the atmospheric entry vehicle continuously from supersonic conditions through soft touchdown. Conventional Mars entry vehicle architectures that include a single parachute for supersonic-to-subsonic descent are not scalable to the sizes needed to land humans on Mars (~20 metric tons). The major aerosciences risks are the uncertainties in predicting aerodynamic stability and performance during powered free-flight and landing. These risks are influenced partially by current limitations in relevant data and testing methods. Consequently, trajectory simulations currently depend on unvalidated powered descent and landing aerodynamics models. NASA engineers have identified gaps in testing methods that, if addressed, would improve the ability to validate these models. There are gaps in capabilities to test multi-engine hot-gas retropropulsion systems in US wind tunnels. This is partially due to the successful use of parachutes as decelerators for human spaceflight at Earth and for the entire Mars lander program to date. Retropulsion test data historically and to this day are limited to using high pressure air jets, at comparatively low temperatures,as engine plume simulants on subscale wind tunnel models. Additionally, the ability to directly measure aerodynamic interference force and moments is limited by existing flow-through balance capabilities. This paper briefly covers historical and recent test data, and identifies new ground test techniques as a means to provide more relevant test data for powered flight and landing aerodynamic model validation.These techniques include using heated inert gases as a substitute for combustion products, additively manufactured 6-component flow-through force and moment balances, and off-body quantitative diagnostic measurements.

Retropropulsion↗
NASA NTRS2013

Mars Science Laboratory Entry Descent and Landing Simulation Using DSENDS

The most recent planetary science mission to Mars is Mars Science Laboratory (MSL) with the Curiosity rover, launched November 26, 2011 and landed at Gale Crater on August 6, 2012. This spacecraft was the first use at Mars of a complete closed-loop Guidance Navigation and Control (GN&C) system, including guided entry with a lifting body that greatly reduces dispersions during the Entry, Descent and Landing (EDL) phase to achieve a 25 km x 20 km landing error relative to the selected Gale Crater landing target. In order to confirm meeting the above landing criteria, high-fidelity simulation of the EDL phase is required. The tool used for 6DOF EDL trajectory verification analysis is Dynamics Simulator for Entry, Descent and Surface landing (DSENDS), which is a high-fidelity simulation tool from JPLs Dynamics and Real-Time Simulation Laboratory for the development, test and operations of aero-flight vehicles. DSENDS inherent capability is augmented for MSL with project-specific models of atmosphere, aerodynamics, sensors and thrusters along with GN&C flight software to enable high-fidelity trajectory simulation. This paper will present the model integration and independent verification experience of the JPL EDL trajectory analysis team.

Mars↗
NASA NTRS1974

Apollo lunar descent guidance

Apollo lunar-descent guidance transfers the Lunar Module from a near-circular orbit to touchdown, traversing a 17 deg central angle and a 15 km altitude in 11 min. A group of interactive programs in an onboard computer guide the descent, controlling altitude and the descent propulsion system throttle. A ground-based program pre-computes guidance targets. The concepts involved in this guidance are described. Explicit and implicit guidance are discussed, guidance equations are derived, and the earlier Apollo explicit equation is shown to be an inferior special case of the later implicit equation. Interactive guidance, by which the two-man crew selects a landing site in favorable terrain and directs the trajectory there, is discussed. Interactive terminal-descent guidance enables the crew to control the essentially vertical descent rate in order to land in minimum time with safe contact speed. The altitude maneuver routine uses concepts that make gimbal lock inherently impossible.

Klumpp, A. R.↗
NASA NTRS2015

High Altitude Venus Operations Concept Trajectory Design, Modeling and Simulation

A trajectory design and analysis that describes aerocapture, entry, descent, and inflation of manned and unmanned High Altitude Venus Operation Concept (HAVOC) lighter-than-air missions is presented. Mission motivation, concept of operations, and notional entry vehicle designs are presented. The initial trajectory design space is analyzed and discussed before investigating specific trajectories that are deemed representative of a feasible Venus mission. Under the project assumptions, while the high-mass crewed mission will require further research into aerodynamic decelerator technology, it was determined that the unmanned robotic mission is feasible using current technology.

Lugo, Rafael A.↗
NASA NTRS1983

Nimbus 7 total ozone mapping spectrometer (TOMS) data during the Gap, France, ozone intercomparisons of June 1981

The Nimbus 7 Total Ozone Mapping Spectrometer (TOMS) data over Europe have been processed for 2 days of the ozone sensor intercomparison balloon campaign in June 1981 at Gap, France. The June 19 TOMS map shows an elongated ozone maximum (about 400 D.U) extending in a NW-SE direction across central Europe and an ozone minimum (300 D.U.) in the central Atlantic. This pattern produces a 12 D.U. decrease along the balloon trajectory from the fist ascent to the second descent. On June 26 a much smaller ozone maximum (400 D.U.) is centered in northern France with its main axis running in a SW-NE direction. The total ozone contours tend to lie parallel to the balloon trajectory so that the total ozone during the flight is nearly constant.

Krueger, A. J.↗
NASA NTRSDate not supplied

Trajectory Simulation Using Multi Model Monte Carlo with Python (MXMCPy)

EDL (Entry, Descent and Landing) is the process from a vehicle approaching a surface to landing on it, such as a Mars rover approaching the planet before landing. POST2 (Program to Optimize Simulated Trajectories 2) is Langley’s primary EDL simulation tool and is used NASA-wide for simulations. POST2 can generate highly accurate results by running a precise, but time consuming, Monte Carlo (MC) simulation hundreds or thousands of times. Though POST2 can produce highly accurate results, it can take unrealistic time spans to generate these results, which has created a need to speed up the simulations. The new NASA software MXMCPy offers various ways to speed up the simulations while getting just as precise results. Instead of running high-precision POST2 simulations many times for traditional MC, MXMCPy can run fewer high-precision POST2 simulations and many less precise POST2 simulations and merge the results. MXMCPy contains 30+ different methods which will each suggest different allocations between model precision levels, which result in results of varying precision based on the POST2 simulation. I created Python and Bash code to automate the 5 steps of MXMCPy’s application to POST2. I also tested the precision of traditional Monte Carlo simulations to MXMCPy aided simulations and found that MXMCPy can achieve substantially more precise solutions at the same computer runtime. I learned Test Driven Development (TDD), a software programming workflow which involves writing computer-automated tests before writing the code which is being tested. These tests are ran every time the code is changed and they can find glitches in the code much quicker than a human can. This programming workflow saved me a lot of time because the automated tests could tell me exactly where the code had stopped working. I plan on using this software development method for future academic and professional software projects. I have greatly enjoyed my work at NASA, so I have been applying to NASA internships and Pathways positions. In addition, I plan on applying what I have learned about Test Driven Development to my computer science courses next semester

James Warner↗
NASA NTRS1988

LANDER program manual: A lunar ascent and descent simulation

LANDER is a computer program used to predict the trajectory and flight performance of a spacecraft ascending or descending between a low lunar orbit of 15 to 500 nautical miles (nm) and the lunar surface. It is a three degree-of-freedom simulation which is used to analyze the translational motion of the vehicle during descent. Attitude dynamics and rotational motion are not considered. The program can be used to simulate either an ascent from the Moon or a descent to the Moon. For an ascent, the spacecraft is initialized at the lunar surface and accelerates vertically away from the ground at full thrust. When the local velocity becomes 30 ft/s, the vehicle turns downrange with a pitch-over maneuver and proceeds to fly a gravity turn until Main Engine Cutoff (MECO). The spacecraft then coasts until it reaches the requested holding orbit where it performs an orbital insertion burn. During a descent simulation, the lander begins in the holding orbit and performs a deorbit burn. It then coasts to pericynthion, where it reignites its engines and begins a gravity turn descent. When the local horizontal velocity becomes zero, the lander pitches up to a vertical orientation and begins to hover in search of a landing site. The lander hovers for a period of time specified by the user, and then lands.

Source record↗
NASA NTRS2013

Mars Science Laboratory Entry Descent and Landing Simulation Using DSENDS

The most recent planetary science mission to Mars was Mars Science Laboratory (MSL) with the Curiosity rover, launched November 26, 2011 and landed at Gale Crater on August 6, 2012. This spacecraft was the first use at Mars of a complete closed-loop Guidance Navigation and Control (GN&C) system, including guided entry with a lifting body that greatly reduces dispersions during the Entry, Descent and Landing (EDL) phase to achieve a 25 km X 20 km landing error relative to the selected Gale Crater landing target. In order to confirm meeting the above landing criteria, high-fidelity simulation of the EDL phase is required. The tool used for 6DOF EDL trajectory verification analysis is Dynamics Simulator for Entry, Descent and Surface landing (DSENDS), which is a high-fidelity simulation tool from JPLs Dynamics and Real-Time Simulation Laboratory for the development, test and operations of aero-flight vehicles. DSENDS inherent capability is augmented for MSL with project-specific models of atmosphere, aerodynamics, sensors and thrusters along with GN&C flight software to enable high-fidelity trajectory simulation. This paper will present the model integration and independent verification experience of the JPL EDL trajectory analysis team.

Burkhart, P. Daniel↗
NASA NTRS1982

Optimal short-range trajectories for helicopters

An optimal flight path algorithm using a simplified altitude state model and a priori climb cruise descent flight profile was developed and applied to determine minimum fuel and minimum cost trajectories for a helicopter flying a fixed range trajectory. In addition, a method was developed for obtaining a performance model in simplified form which is based on standard flight manual data and which is applicable to the computation of optimal trajectories. The entire performance optimization algorithm is simple enough that on line trajectory optimization is feasible with a relatively small computer. The helicopter model used is the Silorsky S-61N. The results show that for this vehicle the optimal flight path and optimal cruise altitude can represent a 10% fuel saving on a minimum fuel trajectory. The optimal trajectories show considerable variability because of helicopter weight, ambient winds, and the relative cost trade off between time and fuel. In general, reasonable variations from the optimal velocities and cruise altitudes do not significantly degrade the optimal cost. For fuel optimal trajectories, the optimum cruise altitude varies from the maximum (12,000 ft) to the minimum (0 ft) depending on helicopter weight.

Slater, G. L.↗
NASA NTRS1979

Viking Navigation: Introduction

The design, control, and reconstruction of the flight paths of all four Viking vehicles is presented. The specification of requirements on the flight hardware is described along with the navigation strategies, procedures, operational software, and the inflight navigation. Features of the Viking navigation discussed include the precise determination of the spacecraft trajectories, prediction of the trajectories, design of the propulsive maneuvers required to effect the necessary trajectory changes, and calculation of the Lander descent guidance parameters.

Oneil, W. J.↗
NASA NTRS2019

Human Mars Entry, Descent and Landing Architecture Study: Deployable Decelerators

NASA’s Entry, Descent and Landing Architecture Study uses a trajectory simulation framework to evaluate various technologies and concepts of operations for human scale EDL at Mars. The study results inform agency technology investments. This paper summarizes the design assumptions and analysis of two deployable entry concepts performed in Phase 2 of the study. The entry concepts include a rigid deployable called the Adaptable Deployable Entry Placement Technology and an inflatable concept called the Hypersonic Inflatable Aerodynamic Decelerator. This paper describes the concept operations of these vehicles to deliver a 20-metric ton payload to the surface of Mars. Details of vehicle design and flight performance are summarized along with results of analysis on the aft body heating and its effect on the payload. Finally, recommended technology investments based on the results are presented.

Dwyer Cianciolo, Alicia↗
NASA NTRS2008

Lagrangian Trajectory Modeling of Lunar Dust Particles

Apollo landing videos shot from inside the right LEM window, provide a quantitative measure of the characteristics and dynamics of the ejecta spray of lunar regolith particles beneath the Lander during the final 10 [m] or so of descent. Photogrammetry analysis gives an estimate of the thickness of the dust layer and angle of trajectory. In addition, Apollo landing video analysis divulges valuable information on the regolith ejecta interactions with lunar surface topography. For example, dense dust streaks are seen to originate at the outer rims of craters within a critical radius of the Lander during descent. The primary intent of this work was to develop a mathematical model and software implementation for the trajectory simulation of lunar dust particles acted on by gas jets originating from the nozzle of a lunar Lander, where the particle sizes typically range from 10 micron to 500 micron. The high temperature, supersonic jet of gas that is exhausted from a rocket engine can propel dust, soil, gravel, as well as small rocks to high velocities. The lunar vacuum allows ejected particles to travel great distances unimpeded, and in the case of smaller particles, escape velocities may be reached. The particle size distributions and kinetic energies of ejected particles can lead to damage to the landing spacecraft or to other hardware that has previously been deployed in the vicinity. Thus the primary motivation behind this work is to seek a better understanding for the purpose of modeling and predicting the behavior of regolith dust particle trajectories during powered rocket descent and ascent.

Lane, John E.↗
DOE OSTI2020

Annihilation-to-nothing: a quantum gravitational boundary condition for the Schwarzschild black hole

The interior of a static Schwarzschild metric can be written in terms of two functions, similar to some models of anisotropic cosmology. With a suitable choice of canonical variables, we solve the Wheeler-DeWitt equation (WDW) inside the horizon of a Schwarzschild black hole. By imposing classicality near the horizon, and requiring boundedness of the wave function, we get a rather generic solution of the WDW equation, whose steepest-descent solution, i.e., the ridge of the wave function, coincides nicely with the classical trajectory. However, there is an ambiguity in defining the arrow of time which leads to two possible interpretations—(i) if there is only one arrow of time, one can infer that the steepest-descent of the wave function follows the classical trajectory throughout: coming from the event horizon and going all the way down to the singularity, while (ii) if there are two different arrows of time in two separate regimes, it can be inferred that the steepest-descent of the wave function comes inwards from the event horizon in one region while it moves outwards from the singularity in the other region, and there exists an annihilation process of these two parts of the wave function inside the horizon. Additionally, adopting the second interpretation could shed light on the information loss paradox: as time goes on, probabilities for histories that include black holes and singularities decay to zero and eventually only trivial geometries dominate.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRSDate not supplied

Tailored Arrival Manager Plan for ecoD 2020

TAM is an automated approach to ensuring safe separation while maximizing throughput and efficiency; as currently conceived, it would serve as an ATC tool. TAM relies on NASA’s Autoresolver technology to compute trajectory-based arrival solutions that provide separation assurance while maximizing airspace and airport capacity utilization. In addition, TAM enables optimized profile descents that minimize altitude level offs and speed interruptions. Importantly, TAM trajectory clearances are intended for delivery to the flight deck through datacomm rather than voice-based communications. Once received on the flight deck, TAM solutions can be auto-loaded into a Flight Management System (FMS) for precision guidance and control along the intended arrival trajectory.

Richard A Coppenbarger↗
NASA NTRS2020

Pterodactyl: The Development and Performance of Guidance Algorithms for a Mechanically Deployed Entry Vehicle

Pterodactyl is a NASA Space Technology Mission Directorate (STMD) project focused on developing a design capability for optimal, scalable, Guidance and Control (G&C) solutions that enable precision targeting for Deployable Entry Vehicles (DEVs). This feasibility study is unique in that it focuses on the rapid integration of targeting performance analysis with structural & packaging analysis, which is especially challenging for new vehicle and mission designs. This paper will detail the guidance development and trajectory design process for a lunar return mission, selected to stress the vehicle designs and encourage future scalability. For the five G&C configurations considered, the Fully Numerical Predictor-Corrector Entry Guidance (FNPEG) was selected for configurations requiring bank angle guidance and FNPEG with Uncoupled Range Control (URC) was developed for configurations requiring angle of attack and sideslip angle guidance. Successful G&C configurations are defined as those that can deliver payloads to the intended descent and landing initiation point, while abiding by trajectory constraints for nominal and dispersed trajectories.

Johnson, Breanna J.↗
NASA NTRS1983

Optimal short range trajectories for helicopters

An optimal flight path algorithm using a simplified altitude state model and an apriori climb-cruise-descent flight profile has been developed and applied to determine minimum fuel and minimum cost trajectories for a helicopter flying a fixed range trajectory. The performance model is based on standard flight manual data and is such that on-line trajectory optimization is feasible with a relatively small computer. The results show that the optimal flight path and optimal cruise altitude can represent a 10 percent fuel saving on a minimum fuel trajectory. The optimal trajectories show considerable variability due to helicopter weight, ambient winds and the relative cost trade-off between time and fuel. In general, 'reasonable' variations from the optimal velocities and cruise altitudes do not significantly degrade the optimal cost.

Slater, G. L.↗
NASA NTRS1986

A time-based concept for terminal-area traffic management

An automated air-traffic-management concept that has the potential for significantly increasing the efficiency of traffic flows in high-density terminal areas is discussed. The concept's implementation depends on techniques for controlling the landing time of all aircraft entering the terminal area, both those that are equipped with on-board four-dimensional (4D) guidance systems as well as those aircraft types that are conventionally equipped. The two major ground-based elements of the system are a scheduler which assigns conflict-free landing times and a profile descent advisor. Landing time provided by the scheduler is uplinked to equipped aircraft and translated into the appropriate 4D trajectory by the-board flight-management system. The controller issues descent advisories to unequipped aircraft to help them achieve the assigned landing times. Air traffic control simulations have established that the concept provides an efficient method for controlling various mixes of 4D-equipped and unequipped, as well as low- and high-performance, aircraft. Piloted simulations of profiles flown with the aid of advisories have verified the ability to meet specified descent times with prescribed accuracy.

Erzberger, Heinz↗