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Postflight analysis including six degree of freedom trajectory digital simulation of Aerobee 350 sounding rocket behavior under large thrust misalignment
The Delta launch vehicle has experienced 153 successful launches since 1960 and 40 more are scheduled. Relying on up-to-date technology and proven flight hardware, the Delta vehicle has been used for low to high circular and geosynchronous transfer orbits, high elliptic probes, and lunar and planetary missions. A history of Delta launches and configuration modifications is presented, noting a 92-95% success rate and its cost effective role in reimbursable missions. Elements of mission planning such as feasibility studies (1-3 yrs), spacecraft restraints manuals, reference trajectories, preliminary mission analysis, detailed test objectives, range/safety studies, guided nominal trajectory, and mission specific studies are discussed. Trajectory shaping determines vehicle and spacecraft restraints, optimizes the trajectory, and maximizes the payload capabilities. Improvements in the Delta vehicle have boosted payloads from 100 to 2890 lbs., improving the price per pound ratio, as costs have risen, only by a factor of three. Current launch schedules extend well into 1985.
The Microwave Anisotropy Probe (MAP) is a Medium Class Explorers (MIDEX) mission produced in partnership between Goddard Space Flight Center (GSFC) and Princeton University. The main science objective of the MAP mission is to produce an accurate full-sky map of the cosmic microwave background temperature fluctuations anisotropy. MAP was launched from the Cape Canaveral Air Force Station Complex 17 aboard a Delta II 7425-10 expendable launch vehicle at exactly 19:46:46.183 UTC on June 30, 2001. The spacecraft received a nominal direct insertion by the Delta into a 185 km circular orbit. MAP was then maneuvered into a sequence of phasing loops designed to set up a lunar swingby (gravity-assisted acceleration) of the spacecraft onto a transfer trajectory to a Lissajous orbit about the Earth-Sun L2 point. The mission duration is approximately 27 months with 3 to 4 months of transfer time to the final mission orbit about L2. The MAP transfer orbit consisted of 3.5 phasing loops: the first loop has a 7-day period, the second and third loops have a 9-day period, and the last half loop has a 4-day period as illustrated in Figure 1, which also indicates the placement of maneuvers. A Pfinal correction maneuver was performed 18 hours after the last perigee to more closely achieve the targeted lissajous orbit. The lunar encounter or swingby took place approximately 30 days after launch. After the lunar encounter, the spacecraft will cruise for approximately 120 days before it arrives at L2. A Mid-Course Correction (MCC) maneuver was executed seven days after the swingby to further refine the trajectory. Once the MAP satellite is injected into the L2 Lissajous orbit, it will perform occasional stationkeeping maneuvers to maintain the Lissajous orbit for a minimum of two years (and a goal of four years). Because of its complex orbital characteristics, the mission provided a unique challenge to orbit determination (OD) support in many orbital regimes. Extensive trajectory error covariance analysis was performed to predict ephemeris accuracy for the OD process using a Bayesian least-squares technique. The orbit determination error analysis is essential for maneuver planning and maneuver recovery study. Several tracking scenarios were investigated for each phase of the mission. This paper provides a summary of the premission trajectory covariance error analysis, as well as actual real-time OD results. The use and impact of the various tracking stations, systems, and measurements will be discussed. Details of the operational OD support and the inferred OD accuracy will be presented, and the results will be compared to the premission covariance analysis, In addition, there will be a discussion of the challenges presented to OD support including delta-Vs at apogee as well as perigee, and effects due to spacecraft attitude mode, in light of their implications to the OD accuracy and covariance analysis.
A number of new aircraft concepts have recently been proposed which tightly couple the propulsion system design and operation with the overall vehicle design and performance characteristics. These concepts include propulsion technology such as boundary layer ingestion, hybrid electric propulsion systems, distributed propulsion systems and variable cycle engines. Initial studies examining these concepts have typically used a traditional decoupled approach to aircraft design where the aerodynamics and propulsion designs are done a-priori and tabular data is used to provide inexpensive look ups to the trajectory ana-ysis. However the cost of generating the tabular data begins to grow exponentially when newer aircraft concepts require consideration of additional operational parameters such as multiple throttle settings, angle-of-attack effects on the propulsion system, or propulsion throttle setting effects on aerodynamics. This paper proposes a new modeling approach that eliminated the need to generate tabular data, instead allowing an expensive propulsion or aerodynamic analysis to be directly integrated into the trajectory analysis model and the entire design problem optimized in a fully coupled manner. The new method is demonstrated by implementing a canonical optimal control problem, the F-4 minimum time-to-climb trajectory optimization using three relatively new analysis tools: Open M-DAO, PyCycle and Pointer. Pycycle and Pointer both provide analytic derivatives and Open MDAO enables the two tools to be combined into a coupled model that can be run in an efficient parallel manner that helps to cost the increased cost of the more expensive propulsion analysis. Results generated with this model serve as a validation of the tightly coupled design method and guide future studies to examine aircraft concepts with more complex operational dependencies for the aerodynamic and propulsion models.
The adoption of robust numerical optimization techniques in trajectory simulation programs has resulted in powerful design and analysis tools. These trajectory simulation/optimization programs are widely used, and a representative list includes the GTS system, the POST program, and newer collocation methods such as OTIS and FONPAC. All of these programs rely on optimization algorithms which require objective function and constraint gradient data during the iteration process. However, most trajectory optimization problems lack simple analytical expressions for these derivatives. In the general case a function evaluation involves integrating aerodynamic, propulsive, and gravity forces over multiple trajectory phases with complex control models. With the newer collocation methods, the integration is replaced by defect constraints and cubic approximations for the state. While analytic gradient expressions can sometimes be derived for trajectory optimization problems, the derivation is cumbersome, time consuming, and prone to mistakes. Fortunately, an alternate method exists for the gradient evaluation, namely finite difference approximations. In this paper some finite difference gradient techniques developed for use with the GTS system are presented. These techniques include methods for computing first and second partial derivatives of single and multiple sets of functions. A key feature of these methods is an error control mechanism which automatically adjusts the perturbation size to obtain accurate derivative values.
Small radius leading edges and nosetips were used to minimize wave drag in early hypervelocity vehicle concepts until further analysis demonstrated that extreme aerothermodynamic heating blunted the available thermal protection system materials. Recent studies indicate that ultra-high temperature composite (UHTC) materials are shape stable at temperatures approaching 3033 K and will be available for use as sharp leading edge components in the near future. Steady-state aerothermal performance constraints for UHTC components are presented in this paper to identify their non-ablating operational capability at altitudes from sea level to 90 km. An integrated design tool was developed to estimate these constraints. The tool couples aerothermodynamic heating with material response using commercial finite element analysis software and is capable of both steady-state and transient analysis. Performance during entry is analyzed by transient thermal analysis along the trajectory. The thermal load condition from the transient thermal analysis is used to estimate thermal stress. Applying the tool to UHTC materials shows that steady-state, non-ablating operation of a HfB2/SiC(A-7) (A-7) component is possible at velocities approaching Earth's circular orbital velocity of 7.9 km/s at altitudes approaching 70 km.
The bounded-impulse approach to low-thrust interplanetary trajectory optimization is widely used. In an effort to efficiently implement this approach using NASA’s OpenMDAO optimization software, the authors have implemented implicit formulations of the forward shooting/backwards-shooting methods commonly used in bounded-impulse models. These implicit approaches allow for vectorization of the underlying calculations which can significantly reduce runtime in interpreted languages. An implicit approach may be either converged by using an underlying nonlinear solver to converge the state propagation, or as a constraint in an optimizer-driven multiple-shooting approach. Significant computational efficiency gains are realized through the utilization of the modular approach to unified derivatives. Further computational efficiency is achieved by capitalizing on the sparsity of the constraint Jacobian matrix. This work demonstrates that a vectorized multiple-shooting approach for propagating a state-time history is superior in terms of computational efficiency as the number of segments in the state-propagation is increased.
Depressed Collector Design The microwave traveling wave tube (TWT) is used widely for space communications and high-power airborne transmitting sources. One of the most important features in designing a TWT is overall efficiency. Yet, overall TWT efficiency is strongly dependent on the efficiency of the electron beam collector, particularly for high values of collector efficiency. For these reasons, the NASA Glenn Research Center developed an optimization algorithm based on simulated annealing to quickly design highly efficient multistage depressed collectors (MDC's). Simulated annealing is a strategy for solving highly nonlinear combinatorial optimization problems. Its major advantage over other methods is its ability to avoid becoming trapped in local minima. Simulated annealing is based on an analogy to statistical thermodynamics, specifically the physical process of annealing: heating a material to a temperature that permits many atomic rearrangements and then cooling it carefully and slowly, until it freezes into a strong, minimum-energy crystalline structure. This minimum energy crystal corresponds to the optimal solution of a mathematical optimization problem. The TWT used as a baseline for optimization was the 32-GHz, 10-W, helical TWT developed for the Cassini mission to Saturn. The method of collector analysis and design used was a 2-1/2-dimensional computational procedure that employs two types of codes, a large signal analysis code and an electron trajectory code. The large signal analysis code produces the spatial, energetic, and temporal distributions of the spent beam entering the MDC. An electron trajectory code uses the resultant data to perform the actual collector analysis. The MDC was optimized for maximum MDC efficiency and minimum final kinetic energy of all collected electrons (to reduce heat transfer). The preceding figure shows the geometric and electrical configuration of an optimized collector with an efficiency of 93.8 percent. The results show the improvement in collector efficiency from 89.7 to 93.8 percent, resulting in an increase of three overall efficiency points. In addition, the time to design a highly efficient MDC was reduced from a month to a few days. All work was done in-house at Glenn for the High Rate Data Delivery Program. Future plans include optimizing the MDC and TWT interaction circuit in tandem to further improve overall TWT efficiency.
In recent years, there has been an increasing interest in space-qualified processors such as multi-core central processing units and graphics processing units that can withstand the adverse effects of space radiation. These processors can allow parallel programming to perform tasks that typically demand high computational power. One can study guidance schemes that can take advantage of these currently developing processors and provide more robust guidance. Software for Multi-model Autonomous Real-time Trajectories (SMART) guidance can identify robust trajectories by running an onboard Monte Carlo analysis. SMART guidance can take advantage of knowledge updates obtained from the onboard sensors, allowing it to consider the off-nominal cases that it would not typically encounter during the offline trajectory analysis. This work uses the SMART guidance for the powered divert at Mars simulation in Program to Optimize and Simulated Trajectories- II.
In recent years, there has been an increasing interest in space-qualified processors such as multi-core central processing units and graphics processing units that can withstand the adverse effects of space radiation. These processors can allow parallel programming to perform tasks that typically demand high computational power. One can study guidance schemes that can take advantage of these currently developing processors and provide more robust guidance. Software for Multi-model Autonomous Real-time Trajectories (SMART) guidance can identify robust trajectories by running an onboard Monte Carlo analysis. SMART guidance can take advantage of knowledge updates obtained from the onboard sensors, allowing it to consider the off-nominal cases that it would not typically encounter during the offline trajectory analysis. This work uses the SMART guidance for the powered divert at Mars simulation in Program to Optimize and Simulated Trajectories- II.
Three NASA centers: Marshall Space Flight Center (MSFC), Langley Research Center (LaRC), and Johnson Space Center (JSC) are currently involved in studying a family of single-stage- and two-stage-to-orbit (SSTO/TSTO) vehicles to serve as the next generation space transportation system (STS). A rocketed winged-body is the current focus. The configuration (WB001) is a vertically-launched, horizontally-landing system with circular cross-section. Preliminary aerodynamic data was generated by LaRC and is a combination of wind-tunnel data, empirical methods, and Aerodynamic Preliminary Analysis System-(APAS) generated values. JSC's efforts involve descent trajectory design, stability analysis, and flight control system synthesis. Analysis of WB001's static stability indicates instability in 'tuck' (C(sub mu) less than 0: Mach = 0.30, alpha greater than 3.25 deg; Mach = 0.60, alpha greater than 8.04), an unstable dihedral effects (C(sub l(beta)) greater than 0: Mach = 30,alpha less than 12 deg.; Mach = 0.60, alpha less than 10.00 deg.), and, most significantly, an unstable weathercock stability derivative, C(sub n(beta)), at all angles of attack and subsonic Mach numbers. Longitudinal trim solutions for Mach = 0.30 and 0.60 indicate flight path angle possibilities ranging from around 12 (M = 0.30) to slightly over 20 degrees at Mach = 0.60. Trim angles of attack increase from 6.24 at Mach 0.60 and 10,000 feet to 17.7 deg. at Mach 0.30, sea-level. Lateral trim was attempted for a design cross-wind of 25.0 knots. The current vehicle aerodynamic and geometric characteristics will only yield a lateral trim solution at impractical tip-fin deflections (approximately equal to 43 deg.) and bank angles (21 deg.). A study of the lateral control surfaces, tip-fin controllers for WB001, indicate increased surface area would help address these instabilities, particularly the deficiency in C(sub n(beta)), but obviously at the expense of increased vehicle weight. Growth factors of approximately 7 were determined using a design C(sub n(beta)) of 0.100/radian (approximate subsonic values for the orbiter).
Computer program for mission analysis of horizontal takeoff vehicle three dimensional trajectories
This report describes the approach and results of an end-to-end simulation to deflect a long-period comet (LPC) by using a rapid rendezvous spacecraft and laser ablation system. The laser energy required for providing sufficient deflection DELTA V and an analysis of possible intercept/rendezvous spacecraft trajectories are studied in this analysis. These problems minimize a weighted sum of the flight time and required propellant by using an advanced propulsion system. The optimal thrust-vector history and propellant mass to use are found in order to transfer a spacecraft from the Earth to a targeted celestial object. One goal of this analysis is to formulate an optimization problem for intercept/rendezvous spacecraft trajectories. One approach to alter the trajectory of the object in a highly controlled manner is to use pulsed laser ablative propulsion. A sufficiently intense laser pulse ablates the surface of a near-Earth object (NEO) by causing plasma blowoff. The momentum change from a single laser pulse is very small. However, the cumulative effect is very effective because the laser can interact with the object over long periods of time. The laser ablation technique can overcome the mass penalties associated with other nondisruptive approaches because no propellant is required to generate the DELTA V (the material of the celestial object is the propellant source). Additionally, laser ablation is effective against a wide range of surface materials and does not require any landing or physical attachment to the object. For diverting distant asteroids and comets, the power and optical requirements of a laser ablation system on or near the Earth may be too extreme to contemplate in the next few decades. A hybrid solution would be for a spacecraft to carry a laser as a payload to a particular celestial body. The spacecraft would require an advanced propulsion system capable of rapid rendezvous with the object and an extremely powerful electrical generator, which is likely needed for the propulsion system as well. The spacecraft would station-keep with the object at a small standoff distance while the laser ablation is performed.
The successful launch of the Parker Solar Probe (PSP) on August 12, 2018 with a Delta IV rocket and Star-48BV third stage has placed the spacecraft on a 7-year trajectory to study the Sun. The goals of PSP are to better characterize our solar environment and advance our understanding of the Sun at 9.86 Rs. A total of 42 trajectory correction maneuvers are planned. This paper documents trajectory correction maneuver analysis performed just prior to launch until just past the first solar encounter. The pre-launch analysis culminated in two final design cycles which analyzed 24 reference trajectories.
The design of the 1975 Viking lander is based, in part, upon performance optimization analyses and a requirement to maximize operational flexibility. The analysis technique is characterized by a graphical tradeoff approach found to be the most effective for evaluating lifting-entry trajectory performance. The analysis eliminates the constraint of a level flight trajectory and allows the lander to reach positive flight-path angles before parachute deployment. Updated Mars environmental knowledge and recent test results and design decisions are analysis factors. The entry-phase analysis indicates that a hypersonic lift-to-drag ratio of 0.18 and an entry flight-path-angle corridor of -15 to -19 deg satisfy the requirements of optimum performance (maximum payload and sufficient terrain height capability).
The General Mission Analysis Tool (GMAT) is a space trajectory optimization and mission analysis system developed by NASA and private industry in the spirit of the NASA Mission. GMAT contains new technology and is a testbed for future technology development. The goal of the GMAT project is to develop new space trajectory optimization and mission design technology by working inclusively with ordinary people, universities, businesses, and other government organizations, and to share that technology in an open and unhindered way. GMAT is a free and open source software system licensed under the NASA Open Source Agreement: free for anyone to use in development of new mission concepts or to improve current missions, freely available in source code form for enhancement or further technology development.
A variable-order, variable-step Taylor series integration algorithm was implemented in NASA Glenn's SNAP (Spacecraft N-body Analysis Program) code. SNAP is a high-fidelity trajectory propagation program that can propagate the trajectory of a spacecraft about virtually any body in the solar system. The Taylor series algorithm's very high order accuracy and excellent stability properties lead to large reductions in computer time relative to the code's existing 8th order Runge-Kutta scheme. Head-to-head comparison on near-Earth, lunar, Mars, and Europa missions showed that Taylor series integration is 15.8 times faster than Runge- Kutta on average, and is more accurate. These speedups were obtained for calculations involving central body, other body, thrust, and drag forces. Similar speedups have been obtained for calculations that include J2 spherical harmonic for central body gravitation. The algorithm includes a step size selection method that directly calculates the step size and never requires a repeat step. High-order Taylor series integration algorithms have been shown to provide major reductions in computer time over conventional integration methods in numerous scientific applications. The objective here was to directly implement Taylor series integration in an existing trajectory analysis code and demonstrate that large reductions in computer time (order of magnitude) could be achieved while simultaneously maintaining high accuracy. This software greatly accelerates the calculation of spacecraft trajectories. At each time level, the spacecraft position, velocity, and mass are expanded in a high-order Taylor series whose coefficients are obtained through efficient differentiation arithmetic. This makes it possible to take very large time steps at minimal cost, resulting in large savings in computer time. The Taylor series algorithm is implemented primarily through three subroutines: (1) a driver routine that automatically introduces auxiliary variables and sets up initial conditions and integrates; (2) a routine that calculates system reduced derivatives using recurrence relations for quotients and products; and (3) a routine that determines the step size and sums the series. The order of accuracy used in a trajectory calculation is arbitrary and can be set by the user. The algorithm directly calculates the motion of other planetary bodies and does not require ephemeris files (except to start the calculation). The code also runs with Taylor series and Runge-Kutta used interchangeably for different phases of a mission.
In order to support traffic management functions, such as mitigating traffic complexity, ground and airborne systems may benefit from preserving or optimizing trajectory flexibility. To help support this hypothesis trajectory flexibility metrics have been defined in previous work to represent the trajectory robustness and adaptability to the risk of violating safety and traffic management constraints. In this paper these metrics are instantiated in the case of planning a trajectory with the heading degree of freedom. A metric estimation method is presented based on simplifying assumptions, namely discrete time and heading maneuvers. A case is analyzed to demonstrate the estimation method and its use in trajectory planning in a situation involving meeting a time constraint and avoiding loss of separation with nearby traffic. The case involves comparing path-stretch trajectories, in terms of adaptability and robustness along each, deduced from a map of estimated flexibility metrics over the solution space. The case demonstrated anecdotally that preserving flexibility may result in enhancing certain factors that contribute to traffic complexity, namely reducing proximity and confrontation.