Optimal transition from entry to cruising flight
Optimal angle of attack transition trajectories for space shuttle from atmospheric entry to cruising flight for conventional airport landing
Stengel, R. F.↗
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Further results on recurrent Lagrange multipliers for the low-thrust Earth-Jupiter transfer
Recurrent Lagrange multipliers coordinate transformation for optimal low thrust Earth- Jupiter trajectories
Fowler, W. T.↗
Navigation between the planets
Recent advances in spacecraft tracking, chronometry, ephemerides, and orbit and trajectory determinations are reviewed. Improvements in timekeeping are reviewed, as well as precision distance and range measurements; orbit determinations, trajectory-correction maneuvers, flight path optimization, and information provided by rotation of the tracking station with the earth's surface. Doppler and tropospheric wave propagation effects are dealt with. Nongravitational perturbations (solar radiation pressure, release of gases from the spacecraft, stochastic unmodeled accelerations and sequential estimation to cope with them), the effect of the target planet's gravitational field upon close approach, and navigation problems in the outer reaches of the solar system (TV data telemetered back for inertial navigation) are covered. By-products of the research include: refined data on the mass of planets, on planetary mass distributions, planet configurations, on physical properties of the atmospheres and ionospheres of planets, and opportunities for refined tests of gravitation and relativity theories and models.
Melbourne, W. G.↗
Methods used for Space Shuttle SRB thrust shape design
Optimization of the Space Shuttle trajectory is discussed with reference to the low acceleration profile required for Shuttle missions. Static tests of the nominal flight curve are described in terms of impulse requirements, vacuum thrust, and burn time. Attention is given to BARF (Burning Anomaly Rate Factor), and it is noted that mandrel fabrication is intended to include the flexibility to counter BARF, should it occur. Test results are presented in which both BARF and specific impulse are considered as independent variables. It was found that no erosive burning occurred, BARF did not occur, specific impulse was on the order of 265 sec, and flow anomalies in the star region produced head-to-aft stagnation pressure drops in excess of theoretical predictions. In other areas, good agreement is noted between theoretical prediction and empirical data.
Baker, J.↗
Disturbance-accommodating tracking maneuvers of flexible spacecraft
In this paper the problem of maneuvering a flexible spacecraft through a large angle is considered, where the disturbance-accommodating feedback control tracks a desired output state. The desired output state is provided from an open-loop solution for the linear system model. The components of the disturbance vector are assumed to be represented in terms of Fourier series. Closed-form solutions are provided for the Ricati, prefilter, state trajectory, and residual state trajectory equations which define the optimal control. Example maneuvers are presented where control-rate penalties have been included in the performance index for frequency-shaping, in order to smooth both the open- and closed-loop control commands.
Turner, J. D.↗
Practical methods for near-term piloted Mars missions
An evaluation is made of ways of using near-term technologies for direct and semidirect manned Mars missions. A notable feature of the present schemes is the in situ propellant production of CH4/O2 and H2O on the Martian surface in order to reduce surface consumable and return propellant requirements. Medium-energy conjunction class trajectories are shown to be optimal for such missions. Attention is given to the backup plans and abort philosophy of these missions. Either the Russian Energia B or U.S. Saturn VII launch vehicles may be used.
Zubrin, Robert M.↗
Geospace Magnetospheric Dynamics Mission
The Geospace Magnetospheric Dynamics (GMD) mission is designed to provide very closely spaced, multipoint measurements in the thin current sheets of the magnetosphere to determine the relation between small scale processes and the global dynamics of the magnetosphere. Its trajectory is specifically designed to optimize the time spent in the current layers and to minimize radiation damage to the spacecraft. Observations are concentrated in the region 8 to 40 R(sub E) The mission consists of three phases. After a launch into geostationary transfer orbit the orbits are circularized to probe the region between geostationary orbit and the magnetopause; next the orbit is elongated keeping perigee at the magnetopause while keeping the line of apsides down the tail. Finally, once apogee reaches 40 R(sub E) the inclination is changed so that the orbit will match the profile of the noon-midnight meridian of the magnetosphere. This mission consists of 4 solar electrically propelled vehicles, each with a single NSTAR thruster utilizing 100 kg of Xe to tour the magnetosphere in the course of a 4.4 year mission, the same thrusters that have been successfully tested on the Deep Space-1 mission.
Russell, C. T.↗
Advanced Electric Propulsion for RLV Launched Geosynchronous Spacecraft
Solar Electric Propulsion (SEP) when used for station keeping and final orbit insertion has been shown to increase a geostationary satellite's payload when launched by existing expendable launch vehicles. In the case of reusable launch vehicles or expendable launch vehicles where an upper stage is an expensive option, this methodology can be modified by using the existing on-board apogee chemical system to perform a perigee burn and then letting the electric propulsion system complete the transfer to geostationary orbit. The elimination of upper stages using on-board chemical and electric propulsion systems was thus examined for GEO spacecraft. Launch vehicle step-down from an Atlas IIAR to a Delta 7920 (no upper stage) was achieved using expanded on-board chemical tanks, 40 kW payload power for electric propulsion, and a 60 day elliptical to GEO SEP orbit insertion. Optimal combined chemical and electric trajectories were found using SEPSPOT. While Hall and ion thrusters provided launch vehicle step-down and even more payload for longer insertion times, NH3 arcjets had insufficient performance to allow launch vehicle step-down. Degradation levels were only 5% to 7% for launch step-down cases using advanced solar arrays. Results were parameterized to allow comparisons for future reusable launch vehicles. Results showed that for an 8 W/kg initial power/launch mass power density spacecraft, 50% to 100% more payload can be launched using this method.
Oleson, Steven↗
Simulation of electron beam formation and transport in a gas-filled electron-optical system with a plasma emitter
The results of computer simulations of the electron-optical system of an electron gun with a plasma emitter are presented. The simulations are performed using the KOBRA3-INP, XOOPIC, and ANSYS codes. The results describe the electron beam formation and transport. The electron trajectories are analyzed. The mechanisms of gas influence on the energy inhomogeneity of the beam and its current in the regions of beam primary formation, acceleration, and transport are described. Recommendations for optimizing the electron-optical system with a plasma emitter are presented.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Flight Testing of Terrain-Relative Navigation and Large-Divert Guidance on a VTVL Rocket
Since 2011, the Autonomous Descent and Ascent Powered-Flight Testbed (ADAPT) has been used to demonstrate advanced descent and landing technologies onboard the Masten Space Systems (MSS) Xombie vertical-takeoff, vertical-landing suborbital rocket. The current instantiation of ADAPT is a stand-alone payload comprising sensing and avionics for terrain-relative navigation and fuel-optimal onboard planning of large divert trajectories, thus providing complete pin-point landing capabilities needed for planetary landers. To this end, ADAPT combines two technologies developed at JPL, the Lander Vision System (LVS), and the Guidance for Fuel Optimal Large Diverts (G-FOLD) software. This paper describes the integration and testing of LVS and G-FOLD in the ADAPT payload, culminating in two successful free flight demonstrations on the Xombie vehicle conducted in December 2014.
ADAPT↗
Oscillatory Trajectories Applied to NASA's DF-7 Configuration
Analyses of oscillating trajectories were performed using the extensively analyzed NASA Dual Fuel Study Vehicle DF-7 that was designed for Mach 10 global reach reconnaissance/strike missions. (This vehicle was later modified to provide a vehicle design capable of both long-range hypersonic cruise and trajectory pull-up for launching an upper stage to deliver payload to orbit.) Study results indicate that oscillating trajectories result in reduced range, high g loading, higher peak heating, and more severe thermal gradients compared to steady-state cruise. These disadvantages plus the operational complexity of turning the engine off and on during each cycle, contribute to making oscillating trajectories undesirable for lifting-body configurations optimized for hypersonic cruise. Additionally, this study shows that technological advances would most likely benefit steady-state cruise trajectories greater than the oscillatory trajectories.
Moster, Gregory E.↗
Methodology and Results of the Near-Earth Object (NEO) Human Space Flight (HSF) Accessible Targets Study (NHATS)
Near-Earth Asteroids (NEAs) have been identified by the current administration as potential destinations for human explorers during the mid-2020s. While the close proximity of these objects' orbits to Earth's orbit creates a risk of highly damaging or catastrophic impacts, it also makes some of these objects particularly accessible to spacecraft departing Earth, and this presents unique opportunities for solar system science and humanity's first ventures beyond cislunar space. Planning such ambitious missions first requires the selection of potentially accessible targets from the growing population of nearly 7,800 NEAs. To accomplish this, NASA is conducting the Near-Earth Object (NEO) Human Space Flight (HSF) Accessible Targets Study (NHATS). Phase I of the NHATS was executed during September of 2010, and Phase II was completed by early March of 2011. The study is ongoing because previously undetected NEAs are being discovered constantly, which has motivated an effort to automate the analysis algorithms in order to provide continuous monitoring of NEA accessibility. The NHATS analysis process consists of a trajectory filter and a minimum maximum estimated size criterion. The trajectory filter employs the method of embedded trajectory grids to compute all possible ballistic round-trip mission trajectories to every NEA in the Jet Propulsion Laboratory (JPL) Small-Body Database (SBDB) and stores all solutions that satisfy the trajectory filter criteria. An NEA must offer at least one qualifying trajectory solution to pass the trajectory filter. The Phase II NHATS filter criteria were purposely chosen to be highly inclusive, requiring Earth departure date between January 1st, 2015 and December 31st, 2040, total round-trip flight time <= 450 days, stay time at the NEA >= 8 days, Earth departure C(sub 3) energy <= 60 km(exp 2)/s(exp 2), total mission delta-v <= 12 km/s (including an Earth departure maneuver from a 400 km altitude circular parking orbit), and a maximum atmospheric re-entry speed of 12 km/s. After determining which NEAs offer at least one trajectory solution meeting the criteria, the estimated size constraint is then imposed whereby those NEAs may only be considered NHATS- qualifying NEAs if their maximum estimated size is >= 30 m. This corresponds to an absolute magnitude H <= 26.5 with an assumed albedo p = 0:05. The following is a brief high-level summary of the Phase II study results. Of the 7,665 NEAs in the SBDB as of February 3rd, 2011, 765 NEAs passed the trajectory filter and yielded a total of 79,157,604 trajectory solutions. The trajectory solutions for each NEA are post-processed into Pork Chop Contour (PCC) plots which show total mission delta-v as a function of Earth departure date and total mission duration. Although the PCC plots necessarily compress a very multi-dimensional design space into a two-dimensional plot, they permit rapid assessment of the breadth and quality of an NEA's available Earth departure season and clearly indicate the regions of the trajectory design space which warrant further analysis and optimization. The PCC plot for the NEA with the greatest number of NHATS-qualifying trajectory solutions, 2000 SG-344, is shown. Of the 765 NEAs which passed the Phase II trajectory filter, a total of 590 NEAs also satisfied the further constraint of maximum estimated size >= 30 m. The distributions of osculating heliocentric orbital semi-major axis (a), eccentricity (e), and inclination (i), for those 590 NEAs are shown. Note that the semi-latus rectum used is equal to alpha (1-e(exp 2)). To further our understanding of round-trip trajectory accessibility dynamics, it is instructive to examine the distribution of the NHATS-Qualifying NEAs according to orbit classification. NEAs are grouped into four orbit families: Atiras (aphelion < 0.983 AU), Atens (aphelion > 0.983 AU, alpha < 1.0 AU), Apollos (perihelion < 1.017 AU, alpha > 1.0 AU), and Amors (1.017 < perihelion < 1.3 AU). Of the 765 NEAhich satisfied the NHATS trajectory criteria, none are Atiras, 193 are Atens (31% of known Atens), 456 are Apollos (11% of known Apollos), and 116 are Amors (4% of known Amors). While Apollos comprise 60% of the NEAs which pass the NHATS trajectory filter and Atens comprise only 25%, the percentages according to orbit family are perhaps more relevant. Note that only 11% of known Apollos passed the trajectory filter while 31% of known Atens passed. These simple statistics alone strongly suggest that Aten orbits possess features which tend to enhance their round-trip trajectory accessibility as compared to Apollos or Amors. This is significant because Atens' orbits cause them to spend considerable time in Earth's daytime sky, making them difficult to discover and track using ground-based observing assets. In this paper we will detail the NHATS analysis algorithms, present and analyze all NHATS results to date, and discuss aspects of HSF mission architecture design for future NEA missions.
Barbee, Brent↗
Ares I-X Test Flight Reference Trajectory Development
Ares I-X was the first test flight of NASA's Constellation Program's Ares I crew launch vehicle. Ares I is a two stage to orbit launch vehicle that provides crew access to low Earth orbit for NASA's future manned exploration missions. The Ares I first stage consists of a Shuttle solid rocket motor (SRM) modified to include an additional propellant segment and a liquid propellant upper stage with an Apollo J2X engine modified to increase its thrust capability. The modified propulsion systems were not available for the first test flight, thus the test had to be conducted with an existing Shuttle 4 segment reusable solid rocket motor (RSRM) and an inert Upper Stage. The test flight's primary objective was to demonstrate controllability of an Ares I vehicle during first stage boost and the ability to perform a successful separation. In order to demonstrate controllability, the Ares I-X ascent control algorithms had to maintain stable flight throughout a flight environment equivalent to Ares I. The goal of the test flight reference trajectory development was to design a boost trajectory using the existing RSRM that results in a flight environment equivalent to Ares I. A trajectory similarity metric was defined as the integrated difference between the Ares I and Ares I-X Mach versus dynamic pressure relationships. Optimization analyses were performed that minimized the metric by adjusting the inert upper stage weight and the ascent steering profile. The sensitivity of the optimal upper stage weight and steering profile to launch month was also investigated. A response surface approach was used to verify the optimization results. The analyses successfully defined monthly ascent trajectories that matched the Ares I reference trajectory dynamic pressure versus Mach number relationship to within 10% through Mach 3.5. The upper stage weight required to achieve the match was found to be feasible and varied less than 5% throughout the year. The paper will discuss the flight test requirements, provide Ares I-X vehicle background, discuss the optimization analyses used to meet the requirements, present analysis results, and compare the reference trajectory to the reconstructed flight trajectory.
Starr, Brett R.↗
Improving the performance of first- and last-mile mobility services through transit coordination, real-time demand prediction, advanced reservations, and trip prioritization
Socio-demographic trends and recent economic development patterns have resulted in travel behavior changes that call for more flexible and accessible public transit options. Because flexible transit services vary in scope, size, and service type, new data-informed methods are useful to optimize services based on the specific needs of local communities and riders. In this study, real-world demand and vehicle trajectory data were used to evaluate and optimize system performance for an existing first-mile–last-mile (FMLM) service in Robinson Township, PA. A general FMLM model for arbitrary demand and service supply was then developed to quantify system performance—both travel time costs and day-to-day reliability—for various operational polices considering spatio-temporal demand variation and transportation network dynamics. Heuristics were used for optimal real-time vehicle routing in sizable real-world networks accommodating various service types and scopes. In this case study, total user costs were reduced by 18.6% when rides were coordinated with mainline fixed-route transit. Predictive routing strategies were shown to marginally improve system performance under sparse and variable spatio-temporal demand. The case study also highlights potentially large travel time and user reliability improvements—reductions of 51% and 53.8%, respectively—when trip requests were made in advance of their desired pickup time. Finally, we show that travel time reliability can be improved for time-inflexible trips with trip prioritization without increasing total user costs. These results were stable to changes in demand density.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗
Minimum-fuel rescue trajectories for the Extravehicular Excursion Unit
The problem of determining minimum-fuel trajectories for rescuing astronauts or equipment which become separated from a Space Station is addressed. Using the Clohessy-Wiltshire equations of relative motion and assuming impulsive Delta-Vs, the minimum-fuel rescue problem is shown to be a parameter optimization problem. Minimum-fuel rescue trajectories are found for seventeen test cases using a recursive quadratic programming algorithm. The results are analyzed and general rules for astronaut rescue and equipment retrieval are developed.
Fowler, W. T.↗
Mission Design Strategies for Rendezvous and Servicing of Sun-Earth Libration Point Missions
With the launch of the James Webb Space Telescope (JWST) and future launches of the Roman Space Telescope (RST) and larger telescopes such as the proposed Habitable Worlds Observatory (HWO), the questions of where and how to rendezvous to enable servicing of these telescope missions arise. To aid in determining the allowable locations to rendezvous for servicing from a trajectory design approach, our previous research and analysis has shown feasible transfer trajectories between the Sun-Earth Libration L2 region (Quasi-Halo orbit) and the Earth Moon vicinity (Distant Retrograde Orbit (DRO), Quasi-Halo Orbit, Halo Orbit, and Near Rectilinear Halo Orbit (NRHO)), along with the related transfer constraints and the corresponding total fuel mass costs. We now focus on operational-like optimal scenarios for these transfers to complete a rendezvous to permit servicing at various Libration orbit locations. In this paper, we address how operational navigation and maneuver execution uncertainties impact the rendezvous timing and fuel mass (via ΔV). While optimization techniques are applied to ensure minimal ΔVs, we also analyze various transfer trajectory durations and rendezvous arrival geometries. The analysis presented includes dynamical system approaches and applies optimization through several tools including the Adaptive Trajectory Design (ATD) module as an initial guess, numerical computation using the General Mission Analysis Tool (GMAT) and Systems Tool Kit (STK) with higher fidelity perturbation modeling, and recently developed optimization tools that incorporate dynamical systems directly into the optimization process. Transfer trajectory options examined include a direct transfer from Earth versus departures from the previously examined Earth-Moon regime orbits, e.g. NRHOs and DROs. A return from Sun-Earth to lunar vicinity for a complete servicing after a rendezvous in Sun-Earth orbit is also considered. The resultant ΔV’s for each scenario is provided with discussions on various transfer trades, rendezvous considerations, and orbital limitations from the dynamical systems. A Poincare-like mapping of trajectory and rendezvous conditions categorize feasible and optimum transfer approaches, dependent on Sun-Earth orbit mission parameters. The focus of this research addresses questions for upcoming trades regarding servicing options for current and future Sun-Earth L1 and L2 missions. By doing a comprehensive analysis approach (dynamical systems + high fidelity optimization with true operational constraints), this paper will serve as a guide for mission architecture and operational trade considerations.
Maneuver Design↗
Optimal solar sail spiral to escape
A solar sail is being considered for various solar system missions, such as a comet rendezvous and a planetary sample return. Such missions might include a planetocentric escape or capture trajectory segment. This paper considers a method for calculating time optimal planetocentric solar sail spiral trajectories to near escape and orbit to orbit transfers. A number of examples illustrate trajectories generated with a computer program, SUNSPOT, based on this analysis.
Sackett, L. L.↗
Optimising response to an introduction of African swine fever in wild pigs
African swine fever virus (ASFv) is a virulent pathogen that threatens domestic swine industries globally and persists in wild boar populations in some countries. Persistence in wild boar can challenge elimination and prevent disease-free status, making it necessary to address wild swine in proactive response plans. In the United States, invasive wild pigs are abundant and found across a wide range of ecological conditions that could drive different epidemiological dynamics among populations. Information on the size of the control areas required to rapidly eliminate the ASFv in wild pigs and how this area should change with management constraints and local ecology is needed to optimize response planning. We developed a spatially explicit disease transmission model contrasting wild pig movement and contact ecology in two ecosystems in Southeastern United States. We simulated ASFv spread and determined the optimal response area (reported as the radius of a circle) for eliminating ASFv rapidly over a range of detection times (when ASFv was detected relative to the true date of introduction), culling capacities (proportion of wild pigs in the culling zone removed weekly) and wild pig densities. Large radii for response areas (14 km) were needed under most conditions but could be shortened with early detection (≤ 8 weeks) and high culling capacities (≥ 15% weekly). Under most conditions, the ASFv was eliminated in less than 22 weeks using optimal control radii, although ecological conditions with high rates of wild pig movement required higher culling capacities (≥ 10% weekly) for elimination within 1 year. The results highlight the importance of adjusting response plans based on local ecology and show that wild pig movement is a better predictor of the optimal response area than the number of ASFv cases early in the outbreak trajectory. Furthermore, our framework provides a tool for determining optimal control plans in different areas, guiding expectations of response impacts, and planning resources needed for rapid elimination.
59 BASIC BIOLOGICAL SCIENCES↗