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Trajectory parameters for escaping from & braking into earth orbit utilizing single vehicle stage with high specific impulse
Minimum fuel multiple impulse orbital rendezvous for fixed transfer time near circular orbits
Optimal fixed-time impulsive transfer trajectories minimizing characteristic orbital velocity, determining sufficient conditions
Navigation aspects of a rendezvous mission to Deimos (the outer satellite of Mars) were examined using a modified Viking Monte Carlo error analysis program. Rendezvous is initiated by two-impulse transfer from an observation orbit cotangent with the orbit of Deimos. Television sightings of the satellite against a star background will allow a 20 km closest approach radius (R99) 99% of the time. This is well within the 100 km range of the terminal rendezvous radar. An additional delta-V capability of about 100 m/sec (above the nominal) must be allocated to account for the statistical nature of the mission. This delta-V requirement was found to be very sensitive to the level of satellite ephemeris error and maneuver execution error. The R99 on the other hand, is sensitive to the in-orbit DSN error and the maneuver execution error.
The Space Shuttle Main Propulsion System provides the impulse to transfer the reusable Orbiter of the Space Shuttle Transportation system and its payload from earth to earth orbit. Both cryogenic and solid rocket propulsion systems are utilized. The selected systems are characterized by (1) reusability wherever possible to reduce program cost, (2) design pressures, and other important design parameters, for the liquid propellant engine significantly higher than past programs for increased performance, and (3) advanced materials and manufacturing processes to withstand the extreme environments. The approaches for solution of these varied problems are emphasized.
Optimum three-impulse transfer from circular Earth parking orbit onto asymptotic velocity vector characteristic of Mars
Kantrowitz (1972) and Minovitch (1972) have proposed the use of laser sustained plasmas as a means to heat a rocket propellant. Recent studies of laser-powered propulsion have been directed toward the application of high-specific-impulse space propulsion systems for orbital transfer missions. Analyses of rocket performance relied heavily on the concept of the laser-supported combustion (LSC) wave. Raizer (1971) first drew the analogy between laser-sustained plasmas and combustion waves in an analysis. The Raizer model was later applied to hydrogen by Kemp and Root (1979). In connection with certain problems arising with the approach considered by Kemp and Root, the present investigation is concerned with a reexamination of the Raizer model. Attention is given to a numerical approach for the entire LSC wave in hydrogen, taking into account the incorporation of the proper boundary conditions far downstream of the wave.
A detailed model for the determination of ion propulsion system masses and performance is presented. The model divides the propulsion system into its component parts and provides mass scaling relationships for each part. In addition, the model is coupled to a detailed ion engine performance model to facilitate investigation of the impact of engine technology assumptions on the overall propulsion system mass and performance. The model is exercised to determine the optimum specific impulse for a selected earth orbit transfer mission.
The fuel optimal control problem arising in coplanar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) without plane change. The basic approach here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the coplanar aeroassisted HEO to LEO orbit transfer consists of three phases. In the first phase, the transfer begins with a deorbit impulse at HEO which injects the vehicle into a elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and drag modulation to satisfy heating constraints and to exit the atmosphere with the desired flight path angle and velocity so that the apogee of the exit orbit is the altitude of the desired LEO. Finally, the second impulse is required to circularize the orbit at LEO. The performance index is maximum final mass. Simulation results show that the coplanar aerocapture is quite different from the case where orbital plane changes are made inside the atmosphere. In the latter case, the vehicle has to penetrate deeper into the atmosphere to perform the desired orbital plane change. For the coplanar case, the vehicle needs only to penetrate the atmosphere deep enough to reduce the exit velocity so the vehicle can be captured at the desired LEO. The peak heating rates are lower and the entry corridor is wider. From the thermal protection point of view, the coplanar transfer may be desirable. Parametric studies also show the maximum peak heating rates and the entry corridor width are functions of maximum lift coefficient. The problem is solved using a direct optimization technique which uses piecewise polynomial representation for the states and controls and collocation to represent the differential equations. This converts the optimal control problem into a nonlinear programming problem which is solved numerically by using a modified version of NPSOL. Solutions were obtained for the described problem for cases with and without heating constraints. The method appears to be more robust than other optimization methods. In addition, the method can handle complex dynamical constraints.
The laser-driven rocket in which remotely generated laser power is used to heat propellant belongs basically to the class of specific-impulse limited propulsion systems if difficult missions are considered. It was previously established that trip time reaches a minimum as specific impulse is varied for payload transfers from low earth orbit to synchronous orbit and return via laser-driven rocket propulsion, the computations being based on the perigee-propulsion laser drive described by Minovitch (1972). The present study shows that such minimum occur for all missions and that optimum specific impulse is primarily determined by the mission difficulty. More generally, this optimum specific impulse maximizes payload kinetic energy achievable with a fixed jet power and propulsion time. A formula relating propulsion time parameter to payload ratio is obtained for estimating mission capabilities of laser-driven rockets.
Laser thermal propulsion (LTP) is studied for the case in which laser power is absorbed by a small very high-temperature plasma (about 20,000 K) and transferred to the remainder of the pure hydrogen propellant by radiation and mixing. This concept could lead to the realization of a lightweight orbital transfer vehicle propulsion system having a specific impulse in the range 1000-2000 s. Approximately 12 percent of the input power may be radiated to the thruster walls, and 15 percent of the total propellant flow must be heated to 20,000 K to provide a bulk temperature of 5000 K prior to expansion. Three principal research issues identified are: (1) conditions for hydrogen plasma ignition, (2) control of the plasma position within the laser beam, plasma stability, and plasma absorption efficiency, and (3) characterization of the mixing of the plasma and buffer flows.
Prime vector theory is used in analyzing a set of linear relative-motion equations - the Clohessy-Wiltshire (C/W) equations - to determine the criteria and necessary conditions for an optimal N-impulse trajectory. The analysis develops the analytical criteria for improving a solution by: (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of: (1) fixed-end conditions, two impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized renezvous problem.
Primer vector theory is used in analyzing a set of linear, relative-motion equations - the Clohessy-Wiltshire equations - to determine the criteria and necessary conditions for an optimal, N-impulse trajectory. Since the state vector for these equations is defined in terms of a linear system of ordinary differential equations, all fundamental relations defining the solution of the state and costate equations, and the necessary conditions for optimality, can be expressed in terms of elementary functions. The analysis develops the analytical criteria for improving a solution by (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of (1) fixed-end conditions, two-impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized rendezvous problem. A sequence of rendezvous problems is solved to illustrate the analysis and the computational procedure.
The problem of minimization of fuel consumption during the atmospheric portion of an aeroassisted, orbital transfer with plane change is addressed. The complete mission has required three characteristic velocities, a deorbit impulse at high earth orbit (HEO), a boost impulse at the atmospheric exit, and a reorbit impulse at low earth orbit (LEO). A performance index has been formulated as the sum of these three impulses. Application of optimal control principles has led to a nonlinear, two-point, boundary value problem which was solved by using a multiple shooting algorithm. The strategy for the atmospheric portion of the minimum-fuel transfer is to start initially with the maximum positive lift in order to recover from the downward plunge, and then to fly with a gradually decreasing lift such that the vehicle skips out of the atmosphere with a flight path angle near zero degrees.
The problem of minimization of fuel consumption during the atmospheric portion of an aeroassisted, orbital transfer with plane change is addressed. The complete mission has required three characteristic velocities, a deorbit impulse at high earth orbit (HEO), a boost impulse at the atmospheric exit, and a reorbit impulse at low earth orbit (LEO). A performance index has been formulated as the sum of these three impulses. Application of optimal control principles has led to a nonlinear, two-point, boundary value problem which was solved by using a multiple shooting algorithm. The strategy for the atmospheric portion of the minimum-fuel transfer is to start initially with the maximum positive lift in order to recover from the downward plunge, and then to fly with a gradually decreasing lift such that the vehicle skips out of the atmosphere with a flight path angle near zero degrees.
A nonlinear analysis is carried out for the optimal transfer between close near-circular noncoplanar orbits with no limit on time. The degeneracy of the linear analyses of Marec and Edelbaum is, thereby, removed and with the aid of a generalized Jacobi test, it is established that the minimum-impulse transfer requires, at most, three impulses. A field of extremals is generated in an orbit element space starting with the initial state and anticipated adjoint variables and integrating these variables by using the optimal thrust control law that maximizes the variational Hamiltonian. The nonoptimality of any four-impulse strategy is determined numerically by observing the reflection of every extremal from either an envelope (conjugate point test) or a switching surface on or before the application of the fourth impulse. This test is carried out in Regions I, II, and III of Marec, as well as the special transition region of Breakwell near the boundary of Region III.
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.