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Lectures in Applied Mathematics. Volume 5 - Space Mathematics, Part 1

The present Proceedings should acquaint the reader with the current state of research on the behavior of nonpropulsive space vehicles, indicate the more pressing unsolved problems, and furnish examples of mathematical techniques which are currently useful. It is hoped that the reader will be stimulated to make contributions of his own, either in the way of developing better mathematical techniques, or finding more ingenious uses of existing ones.

Three-Body Problem↗

Free as a bird - A point of view

A number of ways are discussed in which ingenious people can further increase their enjoyment of experimenting in air (balloons, man-powered flight, etc.). For the lowest cost forms of flight, private sponsorship has been modestly successful. Much more could be done if people would not take themselves so seriously and always demand that advanced technology should serve some nationalistic or economic goals. For the society, the next step forward will perhaps originate if it is demonstrated to the government, manufacturers, and customers that private flying has become too costly due to those factors which limit the acquisition and introduction of new knowledge.

Burke, J. D.↗

Systems engineering studies of lunar base construction

Many ingenious concepts have been proposed for lunar base construction, but few systematic studies exist which relate time-consistent lunar base construction technologies and the choice of lunar base approach with the long-term SEI objectives - i.e., lunar indigenous base construction and Mars Exploration equipment development. To fill this gap, CSC has taken a two-pronged approach. First, the Center undertook basic geotechnical investigations of lunar soil, fabrication of a scale prototype of a lunar construction crane, a multi-robot construction team laboratory experiment, and a preliminary design of lunar base structures. Second, during Jun. and Jul. 1991 two lunar base construction systems engineering studies were accomplished - a 'near term lunar base' study, and a 'far-term lunar base' study. The goals of these studies were to define the major lunar base construction research problems in consistent technology/construction frameworks, and to define design requirements for construction equipment such as a lunar crane and a regolith mover. The 'near-term lunar base' study examined three different construction concepts for a lunar base comprised of pre-fabricated, pre-tested, Space Station Freedom-type modules, which would be covered with regolith shielding. Concept A used a lunar crane for unloading and transportation; concept B, a winch and cart; and concept C, a walker to move the modules from the landing site to the base site and assemble them. To evaluate the merits of each approach, calculations were made of mass efficiency measure, source mass, reliability, far-term base mass, Mars base mass, and base assembly time. The model thus established was also used to define the requirements for crane speed and regolith mover m(sup 3)/sec rates. A major problem addressed is how to 'mine' the regolith and stack it over the habitats as shielding. To identify when the cost of using indigenous lunar materials to construct the base exceeds the cost of development and delivery of the equipment for processing lunar materials, a study of construction of a candidate sintered regolith 'far term lunar base' was undertaken. A technique was devised for casting slabs of sintered (basaltic) regolith and assembling these into a hemispherical (or geodesic) dome. The major problem occurs with the inner liner. At 14.7 psi and 20 percent oxygen internal atmosphere, the entire structure is in tension, even with the regolith load. Also, another study has indicated that at 14.7 psi major resupply of air will be needed because of leakage, and astronauts may have to engage in extensive pre-breathing and post-breathing for extravehicular activity (EVA) tasks, thus detracting from useful mission work time. An alternative is to operate part of the base at, say, 5 psi and 70 percent oxygen, or to equip the astronauts with hard suits at 8.3 psi or greater. All of these choices directly influence base design and construction techniques.

Morgenthaler, George W.↗

An Optical Altitude Indicator for Night Landing

One of the most ingenious of the devices intended for use in night landing, especially emergency landing, is a very simple optical instrument known as the Jenkins night altitude indicator. The design and operation of this instrument, which allows a pilot to determine the altitude of the aircraft, is discussed. The author discusses various modifications and improvements that might be made to the instrument.

Warner, John A C↗

Ulysses log 1992

The Ulysses Log tells the story of some intriguing problems that we (=The Spacecraft Team) have encountered. Ulysses was launched on 6 Oct. 1990, and it made the fastest trip to Jupiter (8 Feb. 1992). It is presently going out of the ecliptic. This paper presents log entries from the following areas: (1) ingenious maneuvers; (2) telecommunication problems; and (3) surprises.

Perez, Raul Garcia↗

On the Generation of Turbulent Inflow Conditions for Boundary Layer Simulations

Turbulent flows that exhibit inhomogeneities in the streamwise direction pose a particular challenge to numerical simulation approaches due to the need to prescribe time-dependent turbulent inflow conditions. In most cases the flow downstream is more or less 'driven' by the conditions at the inlet, making it necessary to specify realistic turbulent fluctuations that are in equilibrium with the assumed mean flow. This requirement often dictates that the inflow data should satisfy the Navier-Stokes equations, which in turn implies that an independent simulation be used to generate them. Detailed simulations for the purpose of creating inflow conditions can be costly and thus certain levels of approximation are desirable. In this paper we shall focus on an approximate yet accurate method for generating inflow conditions for spatially-developing boundary layer simulations. The proposed method is essentially a simplification of the method of Spalart and Leonard (1985), who devised an ingenious transformation that allows for the calculation of spatially evolving boundary layers in conjunction with periodic boundary conditions applied in the streamwise direction. While this method is elegant and highly accurate, it is more complicated than is necessary for the purpose of generating inflow data. A few key approximations are used in this work to arrive at a 'modified Spalart method' that is very easy to implement and efficient to use. The new method is shown to yield results that compare well with the computations of Spalart (1988). When used as a means of generating inflow data, the modified Spalart method is shown to be superior to existing approaches.

Lund, T. S.↗

Holographic Optical Data Storage

Although the basic idea may be traced back to the earlier X-ray diffraction studies of Sir W. L. Bragg, the holographic method as we know it was invented by D. Gabor in 1948 as a two-step lensless imaging technique to enhance the resolution of electron microscopy, for which he received the 1971 Nobel Prize in physics. The distinctive feature of holography is the recording of the object phase variations that carry the depth information, which is lost in conventional photography where only the intensity (= squared amplitude) distribution of an object is captured. Since all photosensitive media necessarily respond to the intensity incident upon them, an ingenious way had to be found to convert object phase into intensity variations, and Gabor achieved this by introducing a coherent reference wave along with the object wave during exposure. Gabor's in-line recording scheme, however, required the object in question to be largely transmissive, and could provide only marginal image quality due to unwanted terms simultaneously reconstructed along with the desired wavefront. Further handicapped by the lack of a strong coherent light source, optical holography thus seemed fated to remain just another scientific curiosity, until the field was revolutionized in the early 1960s by some major breakthroughs: the proposition and demonstration of the laser principle, the introduction of off-axis holography, and the invention of volume holography. Consequently, the remainder of that decade saw an exponential growth in research on theory, practice, and applications of holography. Today, holography not only boasts a wide variety of scientific and technical applications (e.g., holographic interferometry for strain, vibration, and flow analysis, microscopy and high-resolution imagery, imaging through distorting media, optical interconnects, holographic optical elements, optical neural networks, three-dimensional displays, data storage, etc.), but has become a prominent am advertising, and security medium as well. The evolution of holographic optical memories has followed a path not altogether different from holography itself, with several cycles of alternating interest over the past four decades. P. J. van Heerden is widely credited for being the first to elucidate the principles behind holographic data storage in a 1963 paper, predicting bit storage densities on the order of 1/lambda(sup 3) with source wavelength lambda - a fantastic capacity of nearly 1 TB/cu cm for visible light! The science and engineering of such a storage paradigm was heavily pursued thereafter, resulting in many novel hologram multiplexing techniques for dense data storage, as well as important advances in holographic recording materials. Ultimately, however, the lack of such enabling technologies as compact laser sources and high performance optical data I/O devices dampened the hopes for the development of a commercial product. After a period of relative dormancy, successful applications of holography in other arenas sparked a renewed interest in holographic data storage in the late 1980s and the early 1990s. Currently, with most of the critical optoelectronic device technologies in place and the quest for an ideal holographic recording medium intensified, holography is once again considered as one of several future data storage paradigms that may answer our constantly growing need for higher-capacity and faster-access memories.

Timucin, Dogan A.↗

Tool for Movable Ceiling

The Bendix Corp., with the help of NASA's Kennedy Space Center, developed a tool to equalize tensions in the 150 cables of the ceiling. This inexpensive tool used in concert halls was developed first for elevator and crane cables used to lift heavy space vehicles. University of Akron's performing arts hall has been developed to shrink and expand to accommodate audiences as large as 3,000 and as small as 900. Once the hall has been sound tuned, various positions of this ingenious ceiling and related acoustic curtains may be called into play immediately by pushing buttons on a control console programmed previously. With the touch of a finger before an event, a technician may condition the hall for chamber music, symphony, or theater.

Source record↗

A TRMM-Calibrated Infrared Technique for Global Rainfall Estimation

The development of a satellite infrared (IR) technique for estimating convective and stratiform rainfall and its application in studying the diurnal variability of rainfall on a global scale is presented. The Convective-Stratiform Technique (CST), calibrated by coincident, physically retrieved rain rates from the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR), is applied over the global tropics during 2001. The technique is calibrated separately over land and ocean, making ingenious use of the IR data from the TRMM Visible/Infrared Scanner (VIRS) before application to global geosynchronous satellite data. The low sampling rate of TRMM PR imposes limitations on calibrating IR-based techniques; however, our research shows that PR observations can be applied to improve IR-based techniques significantly by selecting adequate calibration areas and calibration length. The diurnal cycle of rainfall, as well as the division between convective and stratiform rainfall will be presented. The technique is validated using available data sets and compared to other global rainfall products such as Global Precipitation Climatology Project (GPCP) IR product, calibrated with TRMM Microwave Imager (TMI) data. The calibrated CST technique has the advantages of high spatial resolution (4 km), filtering of non-raining cirrus clouds, and the stratification of the rainfall into its convective and stratiform components, the latter being important for the calculation of vertical profiles of latent heating.

Negri, Andrew J.↗

A TRMM-Calibrated Infrared Technique for Global Rainfall Estimation

This paper presents the development of a satellite infrared (IR) technique for estimating convective and stratiform rainfall and its application in studying the diurnal variability of rainfall on a global scale. The Convective-Stratiform Technique (CST), calibrated by coincident, physically retrieved rain rates from the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR), is applied over the global tropics during summer 2001. The technique is calibrated separately over land and ocean, making ingenious use of the IR data from the TRMM Visible/Infrared Scanner (VIRS) before application to global geosynchronous satellite data. The low sampling rate of TRMM PR imposes limitations on calibrating IR- based techniques; however, our research shows that PR observations can be applied to improve IR-based techniques significantly by selecting adequate calibration areas and calibration length. The diurnal cycle of rainfall, as well as the division between convective and ~ t i f m rainfall will be presented. The technique is validated using available data sets and compared to other global rainfall products such as Global Precipitation Climatology Project (GPCP) IR product, calibrated with TRMM Microwave Imager (TMI) data. The calibrated CST technique has the advantages of high spatial resolution (4 km), filtering of non-raining cirrus clouds, and the stratification of the rainfall into its convective and stratiform components, the latter being important for the calculation of vertical profiles of latent heating.

Negri, Andrew J.↗

Bioinspired engineering of exploration systems for NASA and DoD

A new approach called bioinspired engineering of exploration systems (BEES) and its value for solving pressing NASA and DoD needs are described. Insects (for example honeybees and dragonflies) cope remarkably well with their world, despite possessing a brain containing less than 0.01% as many neurons as the human brain. Although most insects have immobile eyes with fixed focus optics and lack stereo vision, they use a number of ingenious, computationally simple strategies for perceiving their world in three dimensions and navigating successfully within it. We are distilling selected insect-inspired strategies to obtain novel solutions for navigation, hazard avoidance, altitude hold, stable flight, terrain following, and gentle deployment of payload. Such functionality provides potential solutions for future autonomous robotic space and planetary explorers. A BEES approach to developing lightweight low-power autonomous flight systems should be useful for flight control of such biomorphic flyers for both NASA and DoD needs. Recent biological studies of mammalian retinas confirm that representations of multiple features of the visual world are systematically parsed and processed in parallel. Features are mapped to a stack of cellular strata within the retina. Each of these representations can be efficiently modeled in semiconductor cellular nonlinear network (CNN) chips. We describe recent breakthroughs in exploring the feasibility of the unique blending of insect strategies of navigation with mammalian visual search, pattern recognition, and image understanding into hybrid biomorphic flyers for future planetary and terrestrial applications. We describe a few future mission scenarios for Mars exploration, uniquely enabled by these newly developed biomorphic flyers.

Space Flight↗

Limits to randomness in paleobiologic models: the case of Phanerozoic species diversity

The question of how random, or unconstrained, paleobiologic models should be is examined with a case study: Signor's (1982, 1985) inverse calculation of levels of marine species diversity through the Phanerozoic. His calculation involved an ingenious model that estimated species numbers and species abundances in the world oceans of the past by correcting known numbers of fossil species for variations in sedimentary rocks available for sampling and in effort paleontologists might devote to sampling. The model proves robust to changes in possible shapes of species-abundance distributions, but it is sensitive to alterations in the assumption that paleontologists collect fossils at random. If it is assumed that ease of collecting varies with age of sediment (with the Cenozoic offering easy sampling) or that paleontologists tend to seek out rarer fossils, results of the inverse calculation change. In particular, the magnitude of the calculated Cenozoic diversity increase always declines from the factor of about seven as originally reported to something considerably smaller. This leaves open the problem of the magnitude of Cenozoic increase in marine species diversity, awaiting better empirical data and, perhaps, more exacting models, random or otherwise.

Non-NASA Center↗

Learning to Control Advanced Life Support Systems

Advanced life support systems have many interacting processes and limited resources. Controlling and optimizing advanced life support systems presents unique challenges. In particular, advanced life support systems are nonlinear coupled dynamical systems and it is difficult for humans to take all interactions into account to design an effective control strategy. In this project. we developed several reinforcement learning controllers that actively explore the space of possible control strategies, guided by rewards from a user specified long term objective function. We evaluated these controllers using a discrete event simulation of an advanced life support system. This simulation, called BioSim, designed by Nasa scientists David Kortenkamp and Scott Bell has multiple, interacting life support modules including crew, food production, air revitalization, water recovery, solid waste incineration and power. They are implemented in a consumer/producer relationship in which certain modules produce resources that are consumed by other modules. Stores hold resources between modules. Control of this simulation is via adjusting flows of resources between modules and into/out of stores. We developed adaptive algorithms that control the flow of resources in BioSim. Our learning algorithms discovered several ingenious strategies for maximizing mission length by controlling the air and water recycling systems as well as crop planting schedules. By exploiting non-linearities in the overall system dynamics, the learned controllers easily out- performed controllers written by human experts. In sum, we accomplished three goals. We (1) developed foundations for learning models of coupled dynamical systems by active exploration of the state space, (2) developed and tested algorithms that learn to efficiently control air and water recycling processes as well as crop scheduling in Biosim, and (3) developed an understanding of the role machine learning in designing control systems for advanced life support.

Subramanian, Devika↗

An Overview of Autogyros and The McDonnell XV-1 Convertiplane

This report and its lengthy appendix first reviews early autogyro history. The period from Juan de la Cierva's invention in the early1920s through to the U. S. Army Air Corps' choice, in 1943, of the helicopter instead of the more fully developed autogyro, is examined from a technical point of view. With this historical background in hand, simple aerodynamic technology for rotors, wings, propeller, and fuselages is provided for reference. The McDonnell XV-1 convertiplane development and its program are discussed in detail, with particular emphasis on the wind tunnel and flight testing that was accomplished with two prototype aircraft in the early 1950s. The tip drive rotor system with its ingeniously designed hub was well suited to high speed rotorcraft. The configuration was conceived by Kurt Hohenemser and Fred Dubloff. Many photographs taken of the XV-1 stored at Fort Rucker are included in this report's appendix.

Harris, Franklin D.↗

Active Management of Flap-Edge Trailing Vortices

The vortex hazard produced by large airliners and increasingly larger airliners entering service, combined with projected rapid increases in the demand for air transportation, is expected to act as a major impediment to increased air traffic capacity. Significant reduction in the vortex hazard is possible, however, by employing active vortex alleviation techniques that reduce the wake severity by dynamically modifying its vortex characteristics, providing that the techniques do not degrade performance or compromise safety and ride quality. With this as background, a series of experiments were performed, initially at NASA Langley Research Center and subsequently at the Berlin University of Technology in collaboration with the German Aerospace Center. The investigations demonstrated the basic mechanism for managing trailing vortices using retrofitted devices that are decoupled from conventional control surfaces. The basic premise for managing vortices advanced here is rooted in the erstwhile forgotten hypothesis of Albert Betz, as extended and verified ingeniously by Coleman duPont Donaldson and his collaborators. Using these devices, vortices may be perturbed at arbitrarily long wavelengths down to wavelengths less than a typical airliner wingspan and the oscillatory loads on the wings, and hence the vehicle, are small. Significant flexibility in the specific device has been demonstrated using local passive and active separation control as well as local circulation control via Gurney flaps. The method is now in a position to be tested in a wind tunnel with a longer test section on a scaled airliner configuration. Alternatively, the method can be tested directly in a towing tank, on a model aircraft, a light aircraft or a full-scale airliner. The authors believed that this method will have significant appeal from an industry perspective due to its retrofit potential with little to no impact on cruise (devices tucked away in the cove or retracted); low operating power requirements; small lift oscillations when deployed in a time-dependent manner; and significant flexibility with respect to the specific devices selected.

Greenblatt, David↗

Insect-Inspired Flight Control for Unmanned Aerial Vehicles

Flight-control and navigation systems inspired by the structure and function of the visual system and brain of insects have been proposed for a class of developmental miniature robotic aircraft called "biomorphic flyers" described earlier in "Development of Biomorphic Flyers" (NPO-30554), NASA Tech Briefs, Vol. 28, No. 11 (November 2004), page 54. These form a subset of biomorphic explorers, which, as reported in several articles in past issues of NASA Tech Briefs ["Biomorphic Explorers" (NPO-20142), Vol. 22, No. 9 (September 1998), page 71; "Bio-Inspired Engineering of Exploration Systems" (NPO-21142), Vol. 27, No. 5 (May 2003), page 54; and "Cooperative Lander-Surface/Aerial Microflyer Missions for Mars Exploration" (NPO-30286), Vol. 28, No. 5 (May 2004), page 36], are proposed small robots, equipped with microsensors and communication systems, that would incorporate crucial functions of mobility, adaptability, and even cooperative behavior. These functions are inherent to biological organisms but are challenging frontiers for technical systems. Biomorphic flyers could be used on Earth or remote planets to explore otherwise difficult or impossible to reach sites. An example of an exploratory task of search/surveillance functions currently being tested is to obtain high-resolution aerial imagery, using a variety of miniaturized electronic cameras. The control functions to be implemented by the systems in development include holding altitude, avoiding hazards, following terrain, navigation by reference to recognizable terrain features, stabilization of flight, and smooth landing. Flying insects perform these and other functions remarkably well, even though insect brains contains fewer than 10(exp -4) as many neurons as does the human brain. Although most insects have immobile, fixed-focus eyes and lack stereoscopy (and hence cannot perceive depth directly), they utilize a number of ingenious strategies for perceiving, and navigating in, three dimensions. Despite their lack of stereoscopy, insects infer distances to potential obstacles and other objects from image motion cues that result from their own motions in the environment. The concept of motion of texture in images as a source of motion cues is denoted generally as the concept of optic or optical flow. Computationally, a strategy based on optical flow is simpler than is stereoscopy for avoiding hazards and following terrain. Hence, this strategy offers the potential to design vision-based control computing subsystems that would be more compact, would weigh less, and would demand less power than would subsystems of equivalent capability based on a conventional stereoscopic approach.

Thakoor, Sarita↗

Why Space Technology Needs More Non-Traditional Chemical Engineers – From the Perspective of a NASA Chemical Engineering Student

Final document is attached. With planetary missions and deep space gateway on the horizon, humankind is entering a new era of space exploration. Manned mission durations will be longer than any previous flight, resupply capabilities are limited, and system robustness is more imperative than ever. Traditional space systems, especially in the realm of carbon dioxide removal and water remediation, are large in size, mass, energy consumption, and number of mechanical moving parts prone to failure. Non-traditional space exploration needs non-traditional technology solutions. Organizational psychologist Adam Grant is well-known for his studies on originality and how non-conformists can move the world. In the words of Adam Grant, "to become original, you have to try something new, which means accepting some measure of risk." As chemical engineers, we shouldn't let that measure of risk stop us from considering ingenious technology. As a part of the new generation of engineers at NASA, I believe we need a paradigm shift in space technology for this new era of exploration.

Rogers, Tanya↗

Virtual Project Management Challenge

Technical knowledge is essential to the work done by NASA practitioners. So it may be surprising to learn that the most ingenious and elegant solutions to project challenges often arise not from a specific technical discipline perspective, but from a systems-focused mindset. While technical discipline expertise is a critical component of project success, sometimes the simplest resolution to a problem involves a systems-wide solution. Because of this, encouraging a systems mentality among project team members can be a powerful tool in mitigating risk and eliminating threats. Join us for an exploration of the critical ways in which a systems engineering and integration perspective can enhance project management efforts. Presenter Bo Bejmuk is the former Space Shuttle Orbiter Program Director and manager of Sea Launch Program operations and development for Boeing. He recently served as Chairman of the Standing Review Board for the NASA Constellation Program. Moderator Ramien Pierre is from NASA's Academy for Program/Project and Engineering Leadership (APPEL).

Bo Bejmuk↗