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At least 217 records · Page 12

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NASA NTRS1980

Calculation of Water Drop Trajectories to and About Arbitrary Three-Dimensional Bodies in Potential Airflow

Calculations can be performed for any atmospheric conditions and for all water drop sizes, from the smallest cloud droplet to large raindrops. Any subsonic, external, non-lifting flow can be accommodated; flow into, but not through, inlets also can be simulated. Experimental water drop drag relations are used in the water drop equations of motion and effects of gravity settling are included. Seven codes are described: (1) a code used to debug and plot body surface description data; (2) a code that processes the body surface data to yield the potential flow field; (3) a code that computes flow velocities at arrays of points in space; (4) a code that computes water drop trajectories from an array of points in space; (5) a code that computes water drop trajectories and fluxes to arbitrary target points; (6) a code that computes water drop trajectories tangent to the body; and (7) a code that produces stereo pair plots which include both the body and trajectories. Code descriptions include operating instructions, card inputs and printouts for example problems, and listing of the FORTRAN codes. Accuracy of the calculations is discussed, and trajectory calculation results are compared with prior calculations and with experimental data.

Norment, H. G.↗

NASA NTRS1980

Utilization of multi-body trajectories in the Sun-Earth-Moon system

An overview of three uncommon trajectory concepts for space missions in the Sun-Earth-Moon System is presented. One concept uses a special class of libration-point orbits called 'halo orbits.' It is shown that members of this orbit family are advantageous for monitoring the solar wind input to the Earth's magnetosphere, and could also be used to establish a continuous communications link between the Earth and the far side of the Moon. The second concept employs pretzel-like trajectories to explore the Earth's geomagnetic tail. These trajectories are formed by using the Moon to carry out a prescribed sequence of gravity-assist maneuvers. Finally, there is the 'boomerang' trajectory technique for multiple-encounter missions to comets and asteroids. In this plan, Earth-swingby maneuvers are used to retarget the original spacecraft trajectory. The boomerang method could be used to produce a triple-encounter sequence which includes flybys of comets Halley and Tempel-2 as well as the asteroid Geographos.

Farquhar, R. W.↗

NASA NTRS1980

Near-comet trajectory design

The Halley Flyby/Tempel 2 Rendezvous mission requires not only a new spacecraft design and a new propulsion system (the Solar Electric Propulsion System), but it also requires new approaches to the trajectory and the mission design. Because of the feebleness of Tempel 2 gravitation and because of the presence of various other competing forces, a realization and/or preservation of a spacecraft trajectory about the comet is characteristically different from that about a more massive body. This paper surveys, compares, and evaluates the significance of various forces acting on the spacecraft in the vicinity of the comet. The range of variations and uncertainties inherent in modeling of these forces are also discussed. Then, a number of different types of trajectories relevant to the design of the Tempel 2 exploration are depicted and examined. These include short-arc trajectories, near-comet short- and long-term orbits, and comet-landing trajectories.

Jones, J. B.↗

NASA NTRS1980

Application of an advanced trajectory optimization method to ramjet propelled missiles

The mission performance characteristics of ramjet-propelled missiles are highly dependent upon the trajectory flown. Integration of the trajectory profile with the ramjet propulsion system performance characteristics to achieve optimal missile performance is very complex. Past trajectory optimization methods have been extremely problem dependent and require a high degree of familiarity to achieve success. A general computer code (CTOP) has been applied to ramjet-powered missiles to compute open-loop optimal trajectories. CTOP employs Chebyshev polynomial representations of the states and controls. This allows a transformation of the continuous optimal control problem to one of parameter optimization. With this method, the trajectory boundary conditions are always satisfied. State dynamics and path constraints are enforced via penalty functions. The presented results include solutions to minimum fuel-to-climb, minimum time-to-climb, and minimum time-to-target intercept problems.

Paris, S. W.↗

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 NTRS1987

Quasi-steady flight to quasi-steady flight transition in a windshear - Trajectory guidance

The control (via the angle of attack) of the vertical flight of an aircraft taking off at maximum power in a horizontal wind shear with downdraft is investigated analytically. Optimal trajectories to recover the initial path inclination or to recover quasi-steady flight (the relative values of the velocity, path inclination, and angle of attack) are derived using a Chebyshev approach and shown to be nearly identical in the shear but divergent after the shear. These results are then applied to construct a trajectory-guidance control comprising a variable-gamma guidance scheme for the shear trajectory, a constant-gamma guidance scheme for the immediate postshear trajectory, and a constant-rate-of-climb guidance scheme for the aftershear trajectory. Numerical results demonstrating the near-optimal performance of the control are presented in tables and graphs.

Miele, A.↗

NASA NTRS1988

Optimization and guidance of landing trajectories in a windshear

The problem of the optimization and guidance of landing trajectories in the presence of a windshear is considered with emphasis on abort landing and penetration landing. For abort landing, optimal trajectories are determined by minimizing the peak value of the altitude drop. For penetration landing, optimal trajectories are determined by minimizing a performance index measuring the deviation of the altitude of the flight trajectory from that of the nominal trajectory, with touchdown path inclination, touchdown velocity tolerance, and touchdown distance tolerance specified.

Miele, A.↗

NASA NTRS1990

The effect of interplanetary trajectory options on a manned Mars aerobrake configuration

Manned Mars missions originating in low Earth orbit (LEO) in the time frame 2010 to 2025 were analyzed to identify preferred mission opportunities and their associated vehicle and trajectory characteristics. Interplanetary and Mars atmospheric trajectory options were examined under the constraints of an initial manned exploration scenario. Two chemically propelled vehicle options were considered: (1) an all propulsive configuration, and (2) a configuration which employs aerobraking at Earth and Mars with low lift/drag (L/D) shapes. Both the interplanetary trajectory options as well as the Mars atmospheric passage are addressed to provide a coupled trajectory simulation. Direct and Venus swingby interplanetary transfers with a 60 day Mars stopover are considered. The range and variation in both Earth and Mars entry velocity are also defined. Two promising mission strategies emerged from the study: (1) a 1.0 to 2.0 year Venus swingby mission, and (2) a 2.0 to 2.5 year direct mission. Through careful trajectory selection, 11 mission opportunities are identified in which the Mars entry velocity is between 6 and 10 km/sec and Earth entry velocity ranges from 11.5 to 12.5 km/sec. Simulation of the Earth return aerobraking maneuver is not performed. It is shown that a low L/D configuration is not feasible for Mars aerobraking without substantial improvements in the interplanetary navigation system. However, even with an advanced navigation system, entry corridor and aerothermal requirements restrict the number of potential mission opportunities. It is also shown that for a large blunt Mars aerobrake configuration, the effects of radiative heating can be significant at entry velocities as low as 6.2 km/sec and will grow to dominate the aerothermal environment at entry velocities above 8.5 km/sec. Despite the additional system complexity associated with an aerobraking vehicle, the use of aerobraking was shown to significantly lower the required initial LEO weight. In comparison with an all propulsive mission, savings between 19 and 59 percent were obtained depending upon launch date.

Braun, Robert D.↗

NASA NTRS1989

Optimal trajectories for the aeroassisted flight experiment

The optimal trajectories of the aeroassisted flight experiment (AFE) spacecraft are analyzed in a three-dimensional space using the full system of six ODEs describing the atmospheric pass. The optimal trajectories are computed for two possible transfers: indirect ascent to a 178 NM perigee via a 197 NM apogee and direct ascent to a 178 NM apogee. For each transfer, two cases are investigated: (1) the bank angle is continuously variable, and (2) the trajectory is divided into segments along which the bank angle is constant. It is shown that the optimal trajectories for both cases coalesce into a two subarc trajectory, with the bank angle constant in each subarc. It is also shown that, during the atmospheric pass, the peak values of the changes of the orbital inclination and the longitude of the ascending node are nearly zero.

Miele, A.↗

NASA NTRS1989

MIDAS - Mission design and analysis software for the optimization of ballistic interplanetary trajectories

A patched conic trajectory optimization program MIDAS is described that was developed to investigate a wide variety of complex ballistic heliocentric transfer trajectories. MIDAS includes the capability of optimizing trajectory event times such as departure date, arrival date, and intermediate planetary flyby dates and is able to both add and delete deep space maneuvers when dictated by the optimization process. Both powered and unpowered flyby or gravity assist trajectories of intermediate bodies can be handled and capability is included to optimize trajectories having a rendezvous with an intermediate body such as for a sample return mission. Capability is included in the optimization process to constrain launch energy and launch vehicle parking orbit parameters.

Sauer, Carl G., Jr.↗

NASA NTRS1989

The International Cometary Explorer comet encounter and earth-return trajectory

ICE experienced a successful encounter with Comet Giacobini-Zinner on September 11, 1985. The comet-intercept trajectory, earth-return trajectory, and two cases of a possible 2014 capture trajectory are presented. Also, the essential propulsive trajectory correction maneuvers and the projected August 10, 2014 lunar swingby maneuver are discussed. The targeting methodology used for designing the trajectories is also discussed.

Roberts, Craig E.↗

NASA NTRS1991

Querying databases of trajectories of differential equations 2: Index functions

Suppose that a large number of parameterized trajectories (gamma) of a dynamical system evolving in R sup N are stored in a database. Let eta is contained R sup N denote a parameterized path in Euclidean space, and let parallel to center dot parallel to denote a norm on the space of paths. A data structures and indices for trajectories are defined and algorithms are given to answer queries of the following forms: Query 1. Given a path eta, determine whether eta occurs as a subtrajectory of any trajectory gamma from the database. If so, return the trajectory; otherwise, return null. Query 2. Given a path eta, return the trajectory gamma from the database which minimizes the norm parallel to eta - gamma parallel.

Grossman, Robert↗

NASA NTRS1990

Optimization and guidance of trajectories for coplanar, aeroassisted orbital transfer

Guidance trajectories for coplanar aeroassisted orbital transfer (AOT) from high earth orbit to LEO are presently optimized under the assumption of trajectory control during its endoatmospheric phase by alpha-dependent lift coefficient. Optimal trajectories are first computed by minimizing the total velocity impulse required for AOT; attention is then given to guidance trajectories capable of approximating such key properties of the optimal trajectories as minimum altitude, exit velocity, and exit path inclination, in real time. A switch is made from target-altitude guidance to target path inclination-guidance according to the velocity depletion required for optimum flight.

Miele, A.↗

NASA NTRS1991

Trajectory and navigation system design for robotic and piloted missions to Mars

Future Mars exploration missions, both robotic and piloted, may utilize Earth to Mars transfer trajectories that are significantly different from one another, depending upon the type of mission being flown and the time period during which the flight takes place. The use of new or emerging technologies for future missions to Mars, such as aerobraking and nuclear rocket propulsion, may yield navigation requirements that are much more stringent than those of past robotic missions, and are very difficult to meet for some trajectories. This article explores the interdependencies between the properties of direct Earth to Mars trajectories and the Mars approach navigation accuracy that can be achieved using different radio metric data types, such as ranging measurements between an approaching spacecraft and Mars orbiting relay satellites, or Earth based measurements such as coherent Doppler and very long baseline interferometry. The trajectory characteristics affecting navigation performance are identified, and the variations in accuracy that might be experienced over the range of different Mars approach trajectories are discussed. The results predict that three sigma periapsis altitude navigation uncertainties of 2 to 10 km can be achieved when a Mars orbiting satellite is used as a navigation aid.

Thurman, S. W.↗

NASA NTRS1991

Common Lunar Lander (CLL) trajectory analysis

Common Lunar Lander trajectory analysis is presented in viewgraph format. Trajectory requirements, trajectory characteristics, trajectory timeline, and alternate trajectory advantages and disadvantages are given.

Wagner, Lynn A., Jr.↗

NASA NTRS1991

Trajectory and navigation system design for robotic and piloted missions to Mars

Thurman, S. W.↗

NASA NTRS1992

Trajectories to the outer planets using aero-gravity assist flybys of Venus and Mars

The trajectory concept used here is to flyby Venus and then Mars with moderately high speeds expecting to use both gravity and aeroassisted (wave rider) turns in the atmospheres of the planets in order to form fast trajectories to the planets beyond Jupiter. The first part of the paper contains a description of the development of earth-Venus-Mars trajectories yielding the required speeds at Mars in the interval 2001 to 2015. The second part consists in identifying cases in which Mars is at the proper longitude for each target and obtaining trajectories. Trajectories to Saturn, Uranus, Neptune, and Pluto have been found.

Bender, David F.↗

NASA NTRS1992

An investigation into critical aspects of a new form of low energy lunar transfer, the Belbruno-Miller trajectories

This paper documents an integrated Belbruno-Miller (B-M) trajectory and its corresponding injection period. The B-M trajectories use Weak Stability Boundaries (WSB) resulting from four-body perturbative dynamics between the earth, moon, sun, and spacecraft to significantly reduce maneuver requirements for lunar transfer. It is determined that the presented nominal trajectory has a viable 4-day injection period considering maneuver constraints. The nominal B-M trajectory produces saving varying from 150 m/s to 222 m/s over traditional Hohmann means thus pointing to the practical utility of the WSB method. Energy savings are extracted at the price of extended flight time of approximately 6-months. Usefulness of this procedure was recently dramatized by the Japanese spacecraft Hiten when it arrived a the moon on October 2, 1991 following its entry into B-M trajectory on April 25, 1991.

Krish, V.↗