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Comparison of a discrete steepest ascent method with the continuous steepest ascent method for optimal programing

A discrete steepest ascent method which allows controls which are not piecewise constant (for example, it allows all continuous piecewise linear controls) was derived for the solution of optimal programming problems. This method is based on the continuous steepest ascent method of Bryson and Denham and new concepts introduced by Kelley and Denham in their development of compatible adjoints for taking into account the effects of numerical integration. The method is a generalization of the algorithm suggested by Canon, Cullum, and Polak with the details of the gradient computation given. The discrete method was compared with the continuous method for an aerodynamics problem for which an analytic solution is given by Pontryagin's maximum principle, and numerical results are presented. The discrete method converges more rapidly than the continuous method at first, but then for some undetermined reason, loses its exponential convergence rate. A comparsion was also made for the algorithm of Canon, Cullum, and Polak using piecewise constant controls. This algorithm is very competitive with the continuous algorithm.

Childs, A. G.

Space shuttle: Aerodynamic characteristics of various MDAC space shuttle ascent configurations with parallel burn pressure-fed and SRM boosters. Volume 1: Tanks T1 and T2 ascent configurations

Various space shuttle ascent configurations were tested in a trisonic wind tunnel to determine the aerodynamic characteristics. The ascent configuration consisted of a NASA/MSC 040 orbiter in combination with various HO centerline tank and booster geometries. The aerodynamic interference between components of the space shuttle and the effect on the orbiter aerodynamics was determined. The various aerodynamic configurations tested were: (1) centerline HO tanks T1 and T2, (2) centerline HO tank T3, and (3) centerline HO tank H4.

Jarrett, T. W.

Asymmetrical booster ascent guidance and control system design study. Volume 2: SSFS math models - Ascent

The engineering equations and mathematical models developed for use in the space shuttle functional simulator (SSFS) are presented, and include extensive revisions and additions to earlier documentation. Definitions of coordinate systems used by the SSFS models and coordinate tranformations are given, along with documentation of the flexible body mathematical models. The models were incorporated in the SSFS and are in the checkout stage.

Williams, F. E.

Balloon Ascent: 3-D Simulation Tool for the Ascent and Float of High-Altitude Balloons

The BalloonAscent balloon flight simulation code represents a from-scratch development using Visual Basic 5 as the software platform. The simulation code is a transient analysis of balloon flight, predicting the skin and gas temperatures along with the 3-D position and velocity in a time and spatially varying environment. There are manual and automated controls for gas valving and the dropping of ballast. Also, there are many handy calculators, such as appropriate free lift, and steady-state thermal solutions with temperature gradients. The strength of this simulation model over others in the past is that the infrared environment is deterministic rather than guessed at. The ground temperature is specified along with the emissivity, which creates a ground level IR environment that is then partially absorbed as it travels upward through the atmosphere to the altitude of the balloon.

Farley, Rodger E.

Enabling Parametric Optimal Ascent Trajectory Modeling During Early Phases of Design

During the early phases of engineering design, the costs committed are high, costs incurred are low, and the design freedom is high. It is well documented that decisions made in these early design phases drive the entire design's life cycle. In a traditional paradigm, key design decisions are made when little is known about the design. As the design matures, design changes become more difficult -- in both cost and schedule -- to enact. Indeed, the current capability-based paradigm that has emerged because of the constrained economic environment calls for the infusion of knowledge acquired during later design phases into earlier design phases, i.e. bring knowledge acquired during preliminary and detailed design into pre-conceptual and conceptual design. An area of critical importance to launch vehicle design is the optimization of its ascent trajectory, as the optimal trajectory will be able to take full advantage of the launch vehicle's capability to deliver a maximum amount of payload into orbit. Hence, the optimal ascent trajectory plays an important role in the vehicle's affordability posture as the need for more economically viable access to space solutions are needed in today's constrained economic environment. The problem of ascent trajectory optimization is not a new one. There are several programs that are widely used in industry that allows trajectory analysts to, based on detailed vehicle and insertion orbit parameters, determine the optimal ascent trajectory. Yet, little information is known about the launch vehicle early in the design phase - information that is required of many different disciplines in order to successfully optimize the ascent trajectory. Thus, the current paradigm of optimizing ascent trajectories involves generating point solutions for every change in a vehicle's design parameters. This is often a very tedious, manual, and time-consuming task for the analysts. Moreover, the trajectory design space is highly non-linear and multi-modal due to the interaction of various constraints. Additionally, when these obstacles are coupled with The Program to Optimize Simulated Trajectories [1] (POST), an industry standard program to optimize ascent trajectories that is difficult to use, it requires expert trajectory analysts to effectively optimize a vehicle's ascent trajectory. As it has been pointed out, the paradigm of trajectory optimization is still a very manual one because using modern computational resources on POST is still a challenging problem. The nuances and difficulties involved in correctly utilizing, and therefore automating, the program presents a large problem. In order to address these issues, the authors will discuss a methodology that has been developed. The methodology is two-fold: first, a set of heuristics will be introduced and discussed that were captured while working with expert analysts to replicate the current state-of-the-art; secondly, leveraging the power of modern computing to evaluate multiple trajectories simultaneously, and therefore, enable the exploration of the trajectory's design space early during the pre-conceptual and conceptual phases of design. When this methodology is coupled with design of experiments in order to train surrogate models, the authors were able to visualize the trajectory design space, enabling parametric optimal ascent trajectory information to be introduced with other pre-conceptual and conceptual design tools. The potential impact of this methodology's success would be a fully automated POST evaluation suite for the purpose of conceptual and preliminary design trade studies. This will enable engineers to characterize the ascent trajectory's sensitivity to design changes in an arbitrary number of dimensions and for finding settings for trajectory specific variables, which result in optimal performance for a "dialed-in" launch vehicle design. The effort described in this paper was developed for the Advanced Concepts Office [2] at NASA Marshall Space Flight Center

Holt, James B.

The effects of different rates of ascent on the incidence of altitude decompression sickness

The effect of different rates of ascent on the incidence of altitude decompression sickness (DCS) was analyzed by a retrospective study on 14,123 man-flights involving direct ascent up to 38,000 ft altitude. The data were classified on the basis of altitude attained, denitrogenation at ground level, duration of stay at altitude, rest or exercise while at altitude, frequency of exercise at altitude, and ascent rates. This database was further divided on the basis of ascent rates into different groups from 1000 ft/min up to 53,000 ft/min. The database was analyzed using multiple correlation and regression methods, and the results of the analysis reveal that ascent rates influence the incidence of DCS in combination with the various factors mentioned above. Rate of ascent was not a significant predictor of DCS and showed a low, but significant multiple correlation (R=0.31) with the above factors. Further, the effects of rates below 2500 ft/min are significantly different from that of rates above 2500 ft/min on the incidence of symptoms (P=0.03) and forced descent (P=0.01). At rates above 2500 ft/min and up to 53,000 ft/min, the effects of ascent rates are not significantly different (P greater than 0.05) in the population examined while the effects of rates below 2500 ft/min are not clear.

Kumar, K. V.

Lunar Ascent and Rendezvous Trajectory Design

The Lunar Lander Ascent Module (LLAM) will leave the lunar surface and actively rendezvous in lunar orbit with the Crew Exploration Vehicle (CEV). For initial LLAM vehicle sizing efforts, a nominal trajectory, along with required delta-V and a few key sensitivities, is very useful. A nominal lunar ascent and rendezvous trajectory is shown, along with rationale and discussion of the trajectory shaping. Also included are ascent delta-V sensitivities to changes in target orbit and design thrust-to-weight of the vehicle. A sample launch window for a particular launch site has been completed and is included. The launch window shows that budgeting enough delta-V for two missed launch opportunities may be reasonable. A comparison between yaw steering and on-orbit plane change maneuvers is included. The comparison shows that for large plane changes, which are potentially necessary for an anytime return from mid-latitude locations, an on-orbit maneuver is much more efficient than ascent yaw steering. For a planned return, small amounts of yaw steering may be necessary during ascent and must be accounted for in the ascent delta-V budget. The delta-V cost of ascent yaw steering is shown, along with sensitivity to launch site latitude. Some discussion of off-nominal scenarios is also included. In particular, in the case of a failed Powered Descent Initiation burn, the requirements for subsequent rendezvous with the Orion vehicle are outlined.

Sostaric, Ronald R.

A study to evaluate STS heads-up ascent trajectory performance employing a minimum-Hamiltonian optimization strategy

A study was conducted to evaluate the performance implications of a heads-up ascent flight design for the Space Transportation System, as compared to the current heads-down flight mode. The procedure involved the use of the Minimum Hamiltonian Ascent Shuttle Trajectory Evaluation Program, which is a three-degree-of-freedom moment balance simulation of shuttle ascent. A minimum-Hamiltonian optimization strategy was employed to maximize injection weight as a function of maximum dynamic pressure constraint and Solid Rocket Motor burnrate. Performance Reference Mission Four trajectory groundrules were used for consistency. The major conclusions are that for heads-up ascent and a mission nominal design maximum dynamic pressure value of 680 psf, the optimum solid motor burnrate is 0.394 ips, which produces a performance enhancement of 4293 lbm relative to the baseline heads-down ascent, with 0.368 ips burnrate solid motors and a 680 psf dynamic pressure constraint. However, no performance advantage exists for heads-up flight if the current Solid Rocket Motor target burnrate of 0.368 ips is used. The advantage of heads-up ascent flight employing the current burnrate is that Space Shuttle Main Engine throttling for dynamic pressure control is not necessary.

Sinha, Sujit

Rocketdyne - Lunar Ascent Engine

The ascent engine was the last one from the moon, and I want to focus on the idea of redundancy and teams in regard to the engine. By teams, I mean teamwork - not just within Rocketdyne. It was teamwork within Rocketdyne; it was teamwork within Grumman; it was teamwork within NASA. These were all important elements leading to the successful development of the lunar excursion module (LEM) engine. Communication, rapid response, and cooperation were all important. Another aspect that went into the development of the ascent engine was the integration of technology and of lessons learned. We pushed all the above, plus technology and lessons learned, into a program, and that led to a successful result. One of the things that I like to think about - again in retrospect - is how it is very "in" now to have integrated product and process teams. These are buzzwords for teamwork in all program phases. That s where you combine a lot of groups into a single organization to get a job done. The ascent engine program epitomized that kind of integration and focus, and because this was the mid- to late-1960s; this was new ground for Rocketdyne, Grumman, and NASA. Redundancy was really a major hallmark of the Apollo Program. Everything was redundant. Once you got the rocket going, you could even lose one of the big F-1 engines, and it would still make it to orbit. And once the first stage separated from the rest of the vehicle, the second stage could do without an engine and still make a mission. This redundancy was demonstrated when an early Apollo launch shut down a J-2 second-stage engine. Actually, they shut down two J-2 engines on that flight. Even the third stage, with its single J-2 engine, was backed up because the first two stages could toss it into a recoverable orbit. If the third stage didn't work, you were circling the earth, and you had time to recover the command module and crew. Remember how on the Apollo 13 flight, there was sufficient system redundancy even when we lost the service module. That was a magnificent effort. TRW Inc. really ought to be proud of their engine for that. (See Slide 2, Appendix I) We had planned for redundancy; we had landed on the moon. However, weight restrictions in the architecture said, "You can t have redundancy for ascent from the moon. You've got one engine. It s got to work. There is no second chance. If that ascent engine doesn't work, you re stuck there." It would not have looked good for NASA. It wouldn't have looked good for the country. There was a letter written that President Richard Nixon would read if the astronauts got stuck on the moon, expressing how sorry we were and so forth. It was a scary letter, really. The ascent engine was an engine that had to work. (See Slide 3, Appendix I).

Harmon, Tim

Development of ASCENT Propellant Thrusters and Propulsion Systems

Since the 1960s, hydrazine technology has dominated the market of propulsion technology by providing reliable performance on a wide variety of spacecraft. Efforts to replace hydrazine with a higher-performance and safer alternative have engaged numerous emerging technologies in the industry to mature. ASCENT propellant, also known as AF-M315E, is an example of one such green propellant. Initially developed to provide a safer handling environment than hydrazine, ASCENT offers higher overall performance than a hydrazine equivalent by creating more heat during ignition. The next generation of propulsion technology, based on ASCENT propellant, produces a higher impulse and energy density, expanding the realm of applicable missions from LEO to GEO and beyond. Building on a strong background in small satellite technology and expertise in thermal and oxidation resistant materials, Plasma Processes began several thruster programs for variety of small satellite applications using ASCENT-based technology. Plasma Processes’ background expertise in thermal and oxidation resistant materials provides the necessary foundation to create ASCENT-based technology hardware.

Green Propellant

STS performance enhancements for a heads up ascent design

A method of increasing the STS (space transportation system) lift capability by flying the SSV (Space Shuttle vehicle) in a heads up attitude during the first stage atmospheric flight as opposed to the current heads down attitude is presented. The paper reveals that the STS lift capability and SRM (solid rocket motor) burnrate definition are sensitive to the magnitude and direction of normal aerodynamic force acting on the SSV during atmospheric ascent. The STS operational trajectory design angle of attack will permit increases in SRM burnrate definition and STS lift capability for the proposed heads up ascent when compared to the current heads down ascent. For a heads up ascent the SRM burnrate can be increased 7 percent with a corresponding 4000 lb increase in STS lift capability. A comparison of the heads up and heads down ascent reveals similar performance trades for changes in trajectory shaping parameters and SRM and SSME (Space Shuttle main engine) performance characteristics.

Millard, S. W.

A Terminal Area Analysis of Continuous Ascent Departure Fuel Use at Dallas/Fort Worth International Airport

Aircraft departing from the Dallas/Fort Worth International Airport (DFW) encounter vertical restrictions that prevent continuous ascent operations. The result of these restrictions are temporary level-offs at 10,000 feet. A combination of flow direction, specific Area Navigation (RNAV) route geometry, and arrival streams have been found to be the biggest factors in the duration and frequency of a temporary level-offs. In total, 20% of DFW departures are affected by these level-offs, which have an average duration of just over 100 seconds. The use of continuous descent approaches at DFW are shown to lessen the impact arrivals have on the departures and allow more continuous ascents. The fuel used in a continuous ascent and an ascent with a temporary level-off have been calculated using a fuel burn rate model created from a combination of actual aircraft track data, aircraft manufacturer flight operations manuals, and Eurocontrol's Base of Aircraft Data (BADA) simulation tool. This model represents the average aggregate burn rates for the current fleet mix at DFW. Continuous ascents would save approximately seven gallons of fuel out of 450 gallons used to climb to a cruise altitude of 31,000ft per departure.

Roach, Keenan

Evolution of Space Shuttle Range Safety (RS) Ascent Flight Envelope Design

Ascent flight envelopes are trajectories that define the normal operating region of a space vehicle s position from liftoff until the end of powered flight. They fulfill part of the RS data requirements imposed by the Air Force s 45th Space Wing (45SW) on space vehicles launching from the Eastern Range (ER) in Florida. The 45SW is chartered to protect the public by minimizing risks associated with the inherent hazards of launching a vehicle into space. NASA s Space Shuttle program has launched 130+ manned missions over a 30 year period from the ER. Ascent envelopes were delivered for each of those missions. The 45SW envelope requirements have remained largely unchanged during this time. However, the methodology and design processes used to generate the envelopes have evolved over the years to support mission changes, maintain high data quality, and reduce costs. The evolution of the Shuttle envelope design has yielded lessons learned that can be applied to future endevours. There have been numerous Shuttle ascent design enhancements over the years that have caused the envelope methodology to evolve. One of these Shuttle improvements was the introduction of onboard flight software changes implemented to improve launch probability. This change impacted the preflight nominal ascent trajectory, which is a key element in the RS envelope design. While the early Shuttle nominal trajectories were designed preflight using a representative monthly mean wind, the new software changes involved designing a nominal ascent trajectory on launch day using real-time winds. Because the actual nominal trajectory position was not known until launch day, the envelope analysis had to be customized to account for this nominal trajectory variation in addition to the other envelope components.

Brewer, Joan D.

Mars Ascent Vehicle Gross Lift-off Mass Sensitivities for Robotic Mars Sample Return

The Mars ascent vehicle is a critical element of the robotic Mars Sample Return (MSR) mission. The Mars ascent vehicle must be developed to survive a variety of conditions including the trans-Mars journey, descent through the Martian atmosphere and the harsh Martian surface environments while maintaining the ability to deliver its payload to a low Mars orbit. The primary technology challenge of developing the Mars ascent vehicle system is designing for all conditions while ensuring the mass limitations of the entry descent and landing system are not exceeded. The NASA In-Space Propulsion technology project has initiated the development of Mars ascent vehicle technologies with propulsion system performance and launch environments yet to be defined. To support the project s evaluation and development of various technology options the sensitivity of the Mars ascent vehicle gross lift-off mass to engine performance, inert mass, target orbits, and launch conditions has been completed with the results presented herein.

Dux, Ian J.

Constrained optimal ascent-flyback shuttle trajectories.

An optimal Space Shuttle ascent-flyback trajectory shaping capability is presented which is based on the accelerated gradient parameter optimization technique. A typical atmospheric flight branched optimization problem is analyzed which required the determination of 31 parameters. This parameter set includes the description of the vehicle attitude control angles for three branches of Shuttle flight: first stage ascent, second stage ascent, and first stage flyback. The important in-flight inequality constraints required to maintain the integrity of the vehicle are considered. Results indicate that for a launch into a 55 deg inclined ellipse, a 13% increase in payload can be realized by using optimal control in the first-stage ascent rather than the conventional gravity-turn steering.

Kamm, J. L.

Performance analysis of the ascent propulsion system of the Apollo spacecraft

Activities involved in the performance analysis of the Apollo lunar module ascent propulsion system are discussed. A description of the ascent propulsion system, including hardware, instrumentation, and system characteristics, is included. The methods used to predict the inflight performance and to establish performance uncertainties of the ascent propulsion system are discussed. The techniques of processing the telemetered flight data and performing postflight performance reconstruction to determine actual inflight performance are discussed. Problems that have been encountered and results from the analysis of the ascent propulsion system performance during the Apollo 9, 10, and 11 missions are presented.

Hooper, J. C., III