A linear theory of optimum low-thrust rendezvous trajectories.
Linear theory of optimum variable thrust rendezvous trajectories with power limit propulsion system
LINEAR EQUATION↗
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Interplanetary Trajectory Optimization with Powerlimited Propulsion Systems
A trajectory-optimization process is described in which the optimum thrust equations are derived using the calculus of variations. The magnitude of the thrust is constrained within an upper and a lower bound, but the thrust direction is arbitrary. This formulation allows both the constant-thrust program and the variable-thrust program to be considered. For the constant-thrust program, certain propulsion-system parameters are optimized for maximum final vehicle mass. This theory has been used to study interplanetary missions to Venus and Mars using a power-limited propulsion system. Both one-way and round trip rendezvous trajectories are considered. The analysis employs a two-body inverse-square force-field model of three dimensions. An iterative routine used to solve the two-point boundary-value problem is described in the Appendix.
TRAJECTORY↗
A Variational Method for the Optimization of Interplanetary Round-Trip Trajectories
The indirect method of the calculus of variations is used to optimize interplanetary round-trip trajectories for the case of a single, central, attracting body. The method of solution makes use of certain partial derivative properties of the Lagrangian multipliers associated with the Mayer formulation of the variational problem. This property of the multipliers allows the construction of mathematical expressions for certain other partial derivatives that must vanish when an optimum round trip has been found. These expressions are developed for the cases of propulsion systems using (1) fixed thrust and specific impulse or (2) variable thrust and constant exhaust jet power. Two numerical examples demonstrate how the analytical results may be applied to the solution of round-trip problems including (1) actual three-dimensional planetary positions and (2) planetocentric maneuvers.
VARIATIONAL CALCULUS↗
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.↗
Investigation of Recombination Processes In A Magnetized Plasma
Interplanetary travel requires propulsion systems that can provide high specific impulse (Isp), while also having sufficient thrust to rapidly accelerate large payloads. One such propulsion system is the Variable Specific Impulse Magneto-plasma Rocket (VASIMR), which creates, heats, and exhausts plasma to provide variable thrust and Isp, optimally meeting the mission requirements. A large fraction of the energy to create the plasma is frozen in the exhaust in the form of ionization energy. This loss mechanism is common to all electromagnetic plasma thrusters and has an impact on their efficiency. When the device operates at high Isp, where the exhaust kinetic energy is high compared to the ionization energy, the frozen flow component is of little consequence; however, at low Isp, the effect of the frozen flow may be important. If some of this energy could be recovered through recombination processes, and re-injected as neutral kinetic energy, the efficiency of VASIMR, in its low Isp/high thrust mode may be improved. In this operating regime, the ionization energy is a large portion of the total plasma energy. An experiment is being conducted to investigate the possibility of recovering some of the energy used to create the plasma. This presentation will cover the progress and status of the experiment involving surface recombination of the plasma.
Chavers, Greg↗
Momentum and Heat Flux Measurements in the Exhaust of VASIMR using Helium Propellant
Interplanetary travel requires propulsion systems that can provide high specific impulse (Isp), while also having sufficient thrust to rapidly accelerate large payloads. One such propulsion system is the Variable Specific Impulse Magneto-plasma Rocket (VASIMR), which creates, heats, and ejects plasma to provide variable thrust and Isp, designed to optimally meet the mission requirements. The fraction of the total energy invested in creating the plasma, as compared to the plasma's total kinetic energy, is an important factor in determining the overall system efficiency. In VASIMR, this 'frozen flow loss' is appreciable when at high thrust, but negligible at high Isp. The loss applies to other electric thrusters as well. If some of this energy could be recovered through recombination processes, and reinjected as neutral kinetic energy, the efficiency of VASIMR, in its low Isp/high thrust mode may be improved. An experiment is being conducted to investigate the possibility of recovering some of the energy used to create the plasma by studying the flow characteristics of the charged and neutral particles in the exhaust of the thruster. This paper will cover the measurements of momentum flux and heat flux in the exhaust of the VASIMR test facility using helium as the propellant where the heat flux is comprised of both kinetic and plasma recombination energy. The flux measurements also assist in diagnosing and verifying the plasma conditions in the existing experiment.
Chavers, D. Gregory↗
Computational analysis of liquid hypergolic propellant rocket engines
The combustion process in liquid rocket engines depends on a number of complex phenomena such as atomization, vaporization, spray dynamics, mixing, and reaction mechanisms. A computational tool to study their mutual interactions is developed to help analyze these processes with a view of improving existing designs and optimizing future designs of the thrust chamber. The focus of the article is on the analysis of the Variable Thrust Engine for the Orbit Maneuvering Vehicle. This engine uses a hypergolic liquid bipropellant combination of monomethyl hydrazine as fuel and nitrogen tetroxide as oxidizer.
Krishnan, A.↗
Computer experiments on ion beam deflection for thrust vector control.
Digital computer program for solution of space- charge-flow problem applied to design of thrustors with variable thrust vector, analyzing two ion- thrustor configurations with aid of computer
COMPUTER PROGRAM↗
Numerical analysis of bipropellant combustion in orbit maneuvering vehicle thrust chamber
The combustion and aerodynamic processes of liquid-liquid bipropellant; monomethylhydrazine and nitrogen tetroxide in the combustion chamber of a variable thrust engine (VTE) have been examined to assess the flow structure, combustion characteristics, and wall heat transfer under the simulated engine operations at two power levels. The Generalized Elliptic Multi-phase flow with Chemical reaction, Heat transfer and Interfacial Processes (GEM-CHIP) code and the Bipropellant Combustion (BICOMB) code, which is the GEMCHIP algorithm reformulated in the frame work of a body fitted coordinate system, have been used for the numerical study. Combustion flow structure with non-premixed type injection that simulates the impingement type injector is predicted and the results are compared with that of the premixed injector.
Chiu, H. H.↗
Advanced thrust chamber technology for in-space propulsion system
Two new concepts, the afterburning technique and the spray optimization method for the purpose of upgrading the combustion efficiency and C efficiency, are examined to assess the technical merits and hurdles that need to be resolved. Details of combustion and aerodynamic processes of monomethylhydrazine and nitrogen tetroxides in a toroidal shaped combustion chamber of a variable thrust engine, devised with a wall impingement cooling system and the secondary injection of an oxidizer from the chamber wall for an afterburning, are investigated for the selected secondary injection conditions. With an appropriate injection condition, the combustion efficiency was found to be almost 23 percent higher than that of an engine without afterburning.
Chiu, H. H.↗
The Diagnostics of the External Plasma for the Plasma Rocket
The plasma rocket is located at NASA Johnson Space Center. To produce a thrust in space. an inert gas is ionized into a plasma and heated in the linear section of a tokamak fusion device to 1 x 10(exp 4) - 1.16 x 10(exp 6)K(p= 10(exp 10) - 10(exp 14)/cu cm ). The magnetic field used to contain the plasma has a magnitude of 2 - 10k Gauss. The plasma plume has a variable thrust and specific impulse. A high temperature retarding potential analyzer (RPA) is being developed to characterize the plasma in the plume and at the edge of the magnetically contained plasma. The RPA measures the energy and density of ions or electrons entering into its solid angle of collection. An oscilloscope displays the ion flux versus the collected current. All measurements are made relative to the facility ground. A RPA is being developed in a process which involves the investigation of several prototypes. The first prototype has been tested on a thermal plasma. The knowledge gained from its development and testing were applied to the development of a RPA for collimated plasma. The prototypes consist of four equally spaced grids and an ion collector. The outermost grid is a ground. The second grid acts as a bias to repel electrons. The third is a variable v voltage ion suppressor. Grid four (inner grid) acts to repel secondary electrons, being biased equal to the first. Knowledge gained during these two stages are being applied to the development of a high temperature RPA Testing of this device involves the determination of its output parameters. sensitivity, and responses to a wide range of energies and densities. Each grid will be tested individually by changing only its voltage and observing the output from the RPA. To verify that the RPA is providing proper output. it is compared to the output from a Langmuir or Faraday probe.
Karr, Gerald R.↗
Nuclear Thermal Propulsion (NTP): A Proven Growth Technology for Human NEO/Mars Exploration Missions
The nuclear thermal rocket (NTR) represents the next "evolutionary step" in high performance rocket propulsion. Unlike conventional chemical rockets that produce their energy through combustion, the NTR derives its energy from fission of Uranium-235 atoms contained within fuel elements that comprise the engine s reactor core. Using an "expander" cycle for turbopump drive power, hydrogen propellant is raised to a high pressure and pumped through coolant channels in the fuel elements where it is superheated then expanded out a supersonic nozzle to generate high thrust. By using hydrogen for both the reactor coolant and propellant, the NTR can achieve specific impulse (Isp) values of ~900 seconds (s) or more - twice that of today s best chemical rockets. From 1955 - 1972, twenty rocket reactors were designed, built and ground tested in the Rover and NERVA (Nuclear Engine for Rocket Vehicle Applications) programs. These programs demonstrated: (1) high temperature carbide-based nuclear fuels; (2) a wide range of thrust levels; (3) sustained engine operation; (4) accumulated lifetime at full power; and (5) restart capability - all the requirements needed for a human Mars mission. Ceramic metal "cermet" fuel was pursued as well, as a backup option. The NTR also has significant "evolution and growth" capability. Configured as a "bimodal" system, it can generate its own electrical power to support spacecraft operational needs. Adding an oxygen "afterburner" nozzle introduces a variable thrust and Isp capability and allows bipropellant operation. In NASA s recent Mars Design Reference Architecture (DRA) 5.0 study, the NTR was selected as the preferred propulsion option because of its proven technology, higher performance, lower launch mass, versatile vehicle design, simple assembly, and growth potential. In contrast to other advanced propulsion options, no large technology scale-ups are required for NTP either. In fact, the smallest engine tested during the Rover program - the 25,000 lbf (25 klbf) "Pewee" engine is sufficient when used in a clustered engine arrangement. The "Copernicus" crewed spacecraft design developed in DRA 5.0 has significant capability and a human exploration strategy is outlined here that uses Copernicus and its key components for precursor near Earth object (NEO) and Mars orbital missions prior to a Mars landing mission. The paper also discusses NASA s current activities and future plans for NTP development that include system-level Technology Demonstrations - specifically ground testing a small, scalable NTR by 2020, with a flight test shortly thereafter.
Borowski, Stanley K.↗
Nuclear Thermal Rocket (Ntr) Propulsion: A Proven Game-Changing Technology for Future Human Exploration Missions
The NTR represents the next evolutionary step in high performance rocket propulsion. It generates high thrust and has a specific impulse (Isp) of approx.900 seconds (s) or more V twice that of today s best chemical rockets. The technology is also proven. During the previous Rover and NERVA (Nuclear Engine for Rocket Vehicle Applications) nuclear rocket programs, 20 rocket reactors were designed, built and ground tested. These tests demonstrated: (1) a wide range of thrust; (2) high temperature carbide-based nuclear fuel; (3) sustained engine operation; (4) accumulated lifetime; and (5) restart capability V all the requirements needed for a human mission to Mars. Ceramic metal cermet fuel was also pursued, as a backup option. The NTR also has significant growth and evolution potential. Configured as a bimodal system, it can generate electrical power for the spacecraft. Adding an oxygen afterburner nozzle introduces a variable thrust and Isp capability and allows bipropellant operation. In NASA s recent Mars Design Reference Architecture (DRA) 5.0 study, the NTR was selected as the preferred propulsion option because of its proven technology, higher performance, lower launch mass, simple assembly and mission operations. In contrast to other advanced propulsion options, NTP requires no large technology scale-ups. In fact, the smallest engine tested during the Rover program V the 25,000 lbf (25 klbf) Pewee engine is sufficient for human Mars missions when used in a clustered engine arrangement. The Copernicus crewed spacecraft design developed in DRA 5.0 has significant capability and a human exploration strategy is outlined here that uses Copernicus and its key components for precursor near Earth asteroid (NEA) and Mars orbital missions prior to a Mars landing mission. Initially, the basic Copernicus vehicle can enable reusable 1-year round trip human missions to candidate NEAs like 1991 JW and Apophis in the late 2020 s to check out vehicle systems. Afterwards, the Copernicus spacecraft and its 2 key components, now configured as an Earth Return Vehicle / propellant tanker, would be used for a short round trip (approx.18 - 20 months)/short orbital stay (60 days) Mars / Phobos survey mission in 2033 using a split mission approach. The paper also discusses NASA s current Foundational Technology Development activities and its pre-decisional plans for future system-level Technology Demonstrations that include ground testing a small (approx.7.5 klbf) scalable NTR before the decade is out with a flight test shortly thereafter.
Borowski, Stanley K.↗
Nuclear fusion powered Titan aircraft
This paper discusses a system for Titan exploration enabled by nuclear fusion power. Titan is one of the most interesting locations in the solar system with a thick atmosphere, surface oceans, under-ice oceans and complex terrain. This paper provides a conceptual design of a fusion-powered system to explore many parts of Titan and enable the use of high-power instruments. The design includes a fusion-powered orbital transfer vehicle and an electric Titan science aircraft. A Direct Fusion Drive (DFD) propulsive engine could bring a sizable spacecraft to Titan orbit in less than two years. A second fusion reactor, configured as a closed-loop power generator, would be used for an electric Titan science aircraft. Both reactors are based on the Princeton Field-Reversed Configuration (PFRC) concept which combines an FRC with a magnetic mirror. PFRC uses a novel radio-frequency plasma heating system and deuterium-helium-3 fuel. A lower temperature plasma flows around the closed-field FRC region removing the fusion products. In the DFD propulsive configuration, this secondary flow permits direct and variable thrust and exhaust velocity. The science aircraft would do a powered entry to Titan and then have the capability to fly anywhere on the moon at subsonic speeds. The DFD-powered transfer vehicle would allow the in-orbit transfer stage to change inclination as needed to cover different areas of the surface.
33 ADVANCED PROPULSION SYSTEMS↗
Time-optimal rendezvous for elliptic orbits
Time optimal rendezvous trajectories for variable thrust intercepting and orbiting space vehicles
Alfriend, K. T.↗
Chebychev Trajectory Optimization Program /CHEBYTOP/ Final report
Digital computer program for interplanetary trajectory optimization and variable thrust data
Hahn, D. W.↗
Minimum-time orbital rendezvous between neighboring elliptic orbits
Time optimal rendezvous maneuver between neighboring elliptic orbits, discussing propulsive jet system with variable thrust
Alfriend, K. T.↗
Two concepts for the reduction of payload attitude slewing times.
The concepts presented are particularly valuable in sounding rocket applications, where experiment data-gathering time above the atmosphere is measured in minutes per flight. One concept is a practical nonlinear control law for slewing a payload in one axis, with performance that approaches time-optimal as the uncertainty in angular acceleration approaches zero. The second concept is a practical transformation-of-coordinates system allowing slewing about an axis not coincident with any of the three control axes of the payload, so that the payload experiment axis may move along the great circle arc containing the initial and terminal target points. Implementation of both concepts is facilitated by the availability of variable-thrust cold-gas thrustors. Both concepts can result in significant reductions in slewing times compared with more conventional systems.
Riley, D. C.↗