Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “engineered form”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,729 records · Page 96
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Fuel-rich, catalytic reaction experimental results

Future aeropropulsion gas turbine combustion requirements call for operating at very high inlet temperatures, pressures, and large temperature rises. At the same time, the combustion process is to have minimum pollution effects on the environment. Aircraft gas turbine engines utilize liquid hydrocarbon fuels which are difficult to uniformly atomize and mix with combustion air. An approach for minimizing fuel related problems is to transform the liquid fuel into gaseous form prior to the completion of the combustion process. Experimentally obtained results are presented for vaporizing and partially oxidizing a liquid hydrocarbon fuel into burnable gaseous components. The presented experimental data show that 1200 to 1300 K reaction product gas, rich in hydrogen, carbon monoxide, and light-end hydrocarbons, is formed when flowing 0.3 to 0.6 fuel to air mixes through a catalyst reactor. The reaction temperatures are kept low enough that nitrogen oxides and carbon particles (soot) do not form. Results are reported for tests using different catalyst types and configurations, mass flowrates, input temperatures, and fuel to air ratios.

Rollbuhler, R. James↗
NASA NTRS1991

Fuel-rich, catalytic reaction experimental results

Future aeropropulsion gas turbine combustion requirements call for operating at very high inlet temperatures, pressures, and large temperature rises. At the same time, the combustion process is to have minimum pollution effects on the environment. Aircraft gas turbine engines utilize liquid hydrocarbon fuels which are difficult to uniformly atomize and mix with combustion air. An approach for minimizing fuel related problems is to transform the liquid fuel into gaseous form prior to the completion of the combustion process. Experimentally obtained results are presented for vaporizing and partially oxidizing a liquid hydrocarbon fuel into burnable gaseous components. The presented experimental data show that 1200 to 1300 K reaction product gas, rich in hydrogen, carbon monoxide, and light-end hydrocarbons, is formed when flowing 0.3 to 0.6 fuel to air mixes through a catalyst reactor. The reaction temperatures are kept low enough that nitrogen oxides and carbon particles (soot) do not form. Results are reported for tests using different catalyst types and configurations, mass flowrates, input temperatures, and fuel to air ratios.

Rollbuhler, Jim↗
NASA NTRS1991

Flux-vector splitting algorithm for chain-rule conservation-law form

A flux-vector splitting algorithm with Newton-Raphson iteration was developed for the 'full compressible' Navier-Stokes equations cast in chain-rule conservation-law form. The algorithm is intended for problems with deforming spatial domains and for problems whose governing equations cannot be cast in strong conservation-law form. The usefulness of the algorithm for such problems was demonstrated by applying it to analyze the unsteady, two- and three-dimensional flows inside one combustion chamber of a Wankel engine under nonfiring conditions. Solutions were obtained to examine the algorithm in terms of conservation error, robustness, and ability to handle complex flows on time-dependent grid systems.

Shih, T. I.-P.↗
NASA NTRS1992

Vertical regolith shield wall construction for lunar base applications

Lunar bases located on the lunar surface will require permanent protection from radiation and launch ejecta. This paper outlines a method of providing physical protection using lunar regolith that is constructed in situ as a modular vertical wall using specially devised methods of containment and construction. Deployable compartments, reinforced with corner struts, are elevated and filled by a moving gantry. The compartments interlock to form a stable wall. Different wall heights, thicknesses, and plan configurations are achieved by varying the geometry of the individual compartments, which are made from woven carbon fibers. Conventional terrestrial structural engineering techniques can be modified and used to establish the structural integrity and performance of the wall assembly.

Kaplicky, Jan↗
NASA NTRS1993

Los Alamos studies of the Nevada test site facilities for the testing of nuclear rockets

The topics are presented in viewgraph form and include the following: Nevada test site geographic location; location of NRDA facilities, area 25; assessment program plan; program goal, scope, and process -- the New Nuclear Rocket Program; nuclear rocket engine test facilities; EMAD Facility; summary of final assessment results; ETS-1 Facility; and facilities cost summary.

Hynes, Michael V.↗
NASA NTRS1996

Extruded Self-Lubricating Solid For High-Temperature Use

"EX-212" denotes high-density extruded form of composite solid material self-lubricating over wide range of temperatures. Properties equal or exceed those of powder-metallurgy version of this material. Developed for use in advanced engines at high temperatures at which ordinary lubricants destroyed.

Sliney, H. E.↗
NASA NTRS1999

Tissue Engineered Skeletal Myofibers can Directly "Sense" Gravitational Force Changes

Long-term manned space flight requires a better understanding of skeletal muscle atrophy resulting from microgravity. Atrophy most likely results from changes at both the systemic level (e.g. decreased circulating growth hormone, increased circulating glucocorticoids) and locally (e.g. decreased myofiber resting tension). Differentiated skeletal myofibers in tissue culture have provided a model system over the last decade for gaining a better understanding of the interactions of exogenous growth factors, endogenous growth factors, and muscle fiber tension in regulating protein turnover rates and muscle cell growth. Tissue engineering these cells into three dimensional bioartificial muscle (BAM) constructs has allowed us to extend their use to Space flight studies for the potential future development of countermeasures. Embryonic avian muscle cells were isolated and BAMs tissue engineered as described previously. The myoblasts proliferate and fuse into aligned postmitotic myofibers after ten to fourteen days in vitro. A cylindrical muscle-like structure containing several thousand myofibers is formed which is approximately 30 mm in length, 2-3 mm in diameter, and attached at each end. For the Space Shuttle experiments, the BAMs were transferred to 55 mL bioreactor cartridges (6 BAMs/cartridge). At Kennedy Space Center, the cartridges were mounted in two Space Tissue Loss (STL) Modules (three to four cartridges per Module) and either maintained as ground controls or loaded in a Mid-Deck locker of the Space Shuttle. The BAM cartridges were continuously perfused during the experiment at 1.5 mL/ min with tissue culture medium. Eighteen BAMs were flown for nine days on Mission STS66 while eighteen BAMs served as ground controls. The complete experiment was repeated on Mission STS77 with twenty four BAMs in each group. BAMs could be maintained in a healthy state for at least 30 days in the perfusion bioreactor cartridges. The BAM muscle fibers directly detected both the loss of gravity and the reloading effects of 1 x g. While total cellular metabolism and total protein degradation rates were not altered during 9 to 10 days in Space, protein synthesis rates were significantly reduced and resulted in significant myofiber atrophy compared to ground controls. One g reloading of the flight muscle cells post-flight significantly increased protein synthesis rates and the synthesis rates of myosin heavy chain, fibronectin, and collagen. Tissue cultured muscle cells can directly "sense" changes in gravity and provide a valid model to begin the study of countermeasures. Based on our ground based experiments, and the experiments of others, growth hormone and/or insulin-like growth factors are attractive protein therapeutics which may assisting attenuating skeletal muscle wasting in space. Our laboratory is developing a new cell-based delivery system for this and other potential therapeutic factors for attenuating muscle and bone wasting.

Vandenburgh, Herman H.↗
NASA NTRS2007

NTREES Testing and Operations Status

Nuclear Thermal Rockets or NTR's have been suggested as a propulsion system option for vehicles traveling to the moon or Mars. These engines are capable of providing high thrust at specific impulses at least twice that of today's best chemical engines. The performance constraints on these engines are mainly the result of temperature limitations on the fuel coupled with a limited ability to withstand chemical attack by the hot hydrogen propellant. To operate at maximum efficiency, fuel forms are desired which can withstand the extremely hot, hostile environment characteristic of NTR operation for at least several hours. The simulation of such an environment would require an experimental device which could simultaneously approximate the power, flow, and temperature conditions which a nuclear fuel element (or partial element) would encounter during NTR operation. Such a simulation would allow detailed studies of the fuel behavior and hydrogen flow characteristics under reactor like conditions to be performed. Currently, the construction of such a simulator has been completed at the Marshall Space Flight Center, and will be used in the future to evaluate a wide variety of fuel element designs and the materials of which they are fabricated. This present work addresses the operational status of the Nuclear Thermal Rocket Element Environmental Simulator or NTREES and some of the design considerations which were considered prior to and during its construction.

Emrich, Bill↗
NASA NTRS2010

Corrosion-Resistant Container for Molten-Material Processing

In a carbothermal process, gaseous methane is passed over molten regolith, which is heated past its melting point to a temperature in excess of 1,625 C. At this temperature, materials in contact with the molten regolith (or regolith simulant) corrode and lose their structural properties. As a result, fabricating a crucible to hold the molten material and providing a method of contact heating have been problematic. Alternative containment approaches use a large crucible and limit the heat zone of the material being processed, which is inefficient because of volume and mass constraints. Alternative heating approaches use non-contact heating, such as by laser or concentrated solar energy, which can be inefficient in transferring heat and thus require higher power heat sources to accomplish processing. The innovation is a combination of materials, with a substrate material having high structural strength and stiffness and high-temperature capability, and a coating material with a high corrosion resistance and high-temperature capability. The material developed is a molybdenum substrate with an iridium coating. Creating the containment crucible or heater jacket using this material combination requires only that the molybdenum, which is easily processed by conventional methods such as milling, electric discharge machining, or forming and brazing, be fabricated into an appropriate shape, and that the iridium coating be applied to any surfaces that may come in contact with the corrosive molten material. In one engineering application, the molybdenum was fashioned into a container for a heat pipe. Since only the end of the heat pipe is used to heat the regolith, the container has a narrowing end with a nipple in which the heat pipe is snugly fit, and the external area of this nipple, which contacts the regolith to transfer heat into it, is coated with iridium. At the time of this reporting, no single material has been found that can perform the functions of this combination of materials, and other combinations of materials have not proven to be survivable to the corrosiveness of this environment. High-temperature processing of materials with similar constituencies as lunar regolith is fairly common. The carbo-thermal process is commonly used to make metallurgical-grade silicon for the semiconductor and solar-cell industries.

Stern, Theodore G.↗
NASA NTRS2016

Compatibility Assessment Tool

In support of ground system development for the Space Launch System (SLS), engineers are tasked with building immense engineering models of extreme complexity. The various systems require rigorous analysis of pneumatics, hydraulic, cryogenic, and hypergolic systems. There are certain standards that each of these systems must meet, in the form of pressure vessel system (PVS) certification reports. These reports can be hundreds of pages long, and require many hours to compile. Traditionally, each component is analyzed individually, often utilizing hand calculations in the design process. The objective of this opportunity is to perform these analyses in an integrated fashion with the parametric CADCAE environment. This allows for systems to be analyzed on an assembly level in a semi-automated fashion, which greatly improves accuracy and efficiency. To accomplish this, component specific parameters were stored in the Windchill database to individual Creo Parametric models based on spec control drawings. These parameters were then accessed by using the Prime Analysis within Creo Parametric. MathCAD Prime spreadsheets were created that automatically extracted these parameters, performed calculations, and generated reports. The reports described component compatibility based on local conditions such as pressure, temperature, density, and flow rates. The reports also determined component pairing compatibility, such as properly sizing relief valves with regulators. The reports stored the input conditions that were used to determine compatibility to increase traceability of component selection. The desired workflow for using this tool would begin with a Creo Schematics diagram of a PVS system. This schematic would store local conditions and locations of components. The schematic would then populate an assembly within Creo Parametric, using Windchill database parts. These parts would have their attributes already assigned, and the MathCAD spreadsheets could begin running through database parts to determine which components would be suited for specific locations within the assembly. This eliminates a significant amount of time from the design process, and makes initial analysis assessments more accurate. Each component that would be checked for a location within the assembly would generate a report, showing whether the component was compatible. These reports could be used to generate the PVS report without the need to perform the same analysis multiple times. This process also has the potential to be expanded upon to further automate PVS reports. The integration of software codes or macros could be used to automatically check through hundreds of parts for each location on the schematic. If the software could recognize which type of component would be necessary for each location, it is possible that simply starting the macro could completely choose all the components needed for the schematic, and in turn the system. This would save many hours of work initially selecting components, which could end up saving money. Overall, this process helps to automate initial component selections for PVS systems to fit local design specifications. These selections will automatically generate reports showing how the design criteria are met by the specific component that was chosen. These reports will contribute to easier compilation of the PVS certification reports, which currently take a great amount of time and effort to produce.

Egbert, James Allen↗
NASA NTRS2023

Trades, Architecture, and Design of the Joint Augmented Reality Visual Informatics (Joint AR) Product

Future expeditions will enable exploration and study of the planetary surfaces of the Moon and Mars by performing extravehicular activity (EVA) operations. Present-day International Space Station (ISS) EVA operations require an intricate and tight choreography of crew, space suits, tools, systems, and flight teams to plan, train, and execute with limited advanced informatics. Additionally, EVA operations, aside from the Apollo Lunar surface missions, have predominately focused on maintenance and construction tasks where success criteria are clearly measurable. However, future exploration missions expect to enable crew to carry out scientific objectives in increasingly Earth-independent ways. In this paper, the Joint Augmented Reality Visual Informatics System (Joint AR) characterizes the design space for developing a modular augmented reality (AR) device for a spacesuit form factor that can support crew decision-making for EVA. This paper highlights the project’s experience with a product-focused management style and use-case centered systems engineering approach to iteratively design, build, and test. The Joint AR product features were defined via trade studies and market analysis of previous EVA display efforts, various AR components such as optics, commercial AR systems, light engines, data interfaces, graphics engine software and analog test beds. We outline the defining architectural design decisions, including safety criticality considerations, suit mounting interfaces, computer architectures, and partnership contracting mechanisms. The outcomes of these studies, architecture decisions, and management requirements result in a recommended design which is the Joint AR product. We discuss the evolution, development of these system components, and what work remains. We hope to share a unified understanding of various design decisions and how they impact the future of crew members’ access to data during Lunar and Martian EVAs. This ongoing effort can enable a community-wide discovery process toward realizing necessary AR features and capabilities for future missions.

Augmented Reality↗
DOE OSTI2024

The phycosphere and its role in algal biofuel production

Oleaginous microalgae have become a focus for large-scale biofuel production due to their ability to accumulate large quantities of lipids. However, production is currently limited by cost and predation. At present, algal biofuel cultivation is optimized through starvation, supplementing media with nutrients, or genetic engineering; these methods can often be costly with little to no increase in lipid production or the culture’s defense. Investigating the phycosphere of algal-bacterial interactions may overcome these current barriers to large-scale production. The phycosphere of algal-bacterial interactions have formed over millions of years through mutualistic and symbiotic relationships and can provide a more direct source of nutrients compared to adding the nutrients in bulk. The most promising of these interactions include the production of phytohormones and quorum signaling compounds that alter the behaviors of the consortia. Phytohormones can improve algal growth rates, lipid production, and stress resistance. Quorum signaling could create consortia capable of warding off invaders—such as rotifers—while self-regulating and altering behavior based on population density. Mechanisms within the algal phycosphere present many opportunities for the development of novel engineering strategies to further improve algal lipid production and operational costs. This review outlines previous preliminary phycosphere research as well as posing possible opportunities to be pursued in future biofuel production.

09 BIOMASS FUELS↗
NASA NTRS2015

A Vehicle Management End-to-End Testing and Analysis Platform for Validation of Mission and Fault Management Algorithms to Reduce Risk for NASA's Space Launch System

The development of the Space Launch System (SLS) launch vehicle requires cross discipline teams with extensive knowledge of launch vehicle subsystems, information theory, and autonomous algorithms dealing with all operations from pre-launch through on orbit operations. The characteristics of these systems must be matched with the autonomous algorithm monitoring and mitigation capabilities for accurate control and response to abnormal conditions throughout all vehicle mission flight phases, including precipitating safing actions and crew aborts. This presents a large complex systems engineering challenge being addressed in part by focusing on the specific subsystems handling of off-nominal mission and fault tolerance. Using traditional model based system and software engineering design principles from the Unified Modeling Language (UML), the Mission and Fault Management (M&FM) algorithms are crafted and vetted in specialized Integrated Development Teams composed of multiple development disciplines. NASA also has formed an M&FM team for addressing fault management early in the development lifecycle. This team has developed a dedicated Vehicle Management End-to-End Testbed (VMET) that integrates specific M&FM algorithms, specialized nominal and off-nominal test cases, and vendor-supplied physics-based launch vehicle subsystem models. The flexibility of VMET enables thorough testing of the M&FM algorithms by providing configurable suites of both nominal and off-nominal test cases to validate the algorithms utilizing actual subsystem models. The intent is to validate the algorithms and substantiate them with performance baselines for each of the vehicle subsystems in an independent platform exterior to flight software test processes. In any software development process there is inherent risk in the interpretation and implementation of concepts into software through requirements and test processes. Risk reduction is addressed by working with other organizations such as S&MA, Structures and Environments, GNC, Orion, the Crew Office, Flight Operations, and Ground Operations by assessing performance of the M&FM algorithms in terms of their ability to reduce Loss of Mission and Loss of Crew probabilities. In addition, through state machine and diagnostic modeling, analysis efforts investigate a broader suite of failure effects and detection and responses that can be tested in VMET and confirm that responses do not create additional risks or cause undesired states through interactive dynamic effects with other algorithms and systems. VMET further contributes to risk reduction by prototyping and exercising the M&FM algorithms early in their implementation and without any inherent hindrances such as meeting FSW processor scheduling constraints due to their target platform - ARINC 653 partitioned OS, resource limitations, and other factors related to integration with other subsystems not directly involved with M&FM. The plan for VMET encompasses testing the original M&FM algorithms coded in the same C++ language and state machine architectural concepts as that used by Flight Software. This enables the development of performance standards and test cases to characterize the M&FM algorithms and sets a benchmark from which to measure the effectiveness of M&FM algorithms performance in the FSW development and test processes. This paper is outlined in a systematic fashion analogous to a lifecycle process flow for engineering development of algorithms into software and testing. Section I describes the NASA SLS M&FM context, presenting the current infrastructure, leading principles, methods, and participants. Section II defines the testing philosophy of the M&FM algorithms as related to VMET followed by section III, which presents the modeling methods of the algorithms to be tested and validated in VMET. Its details are then further presented in section IV followed by Section V presenting integration, test status, and state analysis. Finally, section VI addresses the summary and forward directions followed by the appendices presenting relevant information on terminology and documentation.

Trevino, Luis↗
NASA NTRS2001

An Algorithm for Interactive Modeling of Space-Transportation Engine Simulations: A Constraint Satisfaction Approach

In this research we have developed an algorithm for the purpose of constraint processing by utilizing relational algebraic operators. Van Beek and others have investigated in the past this type of constraint processing from within a relational algebraic framework, producing some unique results. Apart from providing new theoretical angles, this approach also gives the opportunity to use the existing efficient implementations of relational database management systems as the underlying data structures for any relevant algorithm. Our algorithm here enhances that framework. The algorithm is quite general in its current form. Weak heuristics (like forward checking) developed within the Constraint-satisfaction problem (CSP) area could be also plugged easily within this algorithm for further enhancements of efficiency. The algorithm as developed here is targeted toward a component-oriented modeling problem that we are currently working on, namely, the problem of interactive modeling for batch-simulation of engineering systems (IMBSES). However, it could be adopted for many other CSP problems as well. The research addresses the algorithm and many aspects of the problem IMBSES that we are currently handling.

Mitra, Debasis↗
DOE OSTI2023

Bio-fuel effects and seasonal fuel property variations related to abnormal combustion occurrences observed in the field

Since 2015, the automotive industry has regularly observed sharp increases in customer complaints of poor driveability and increased warranty claims during the months of September and October. These persistent seasonal complaint increases have been tracked to occur from increased abnormal combustion events that coincide with the seasonal transition from summer to winter fuel volatility, beginning on September 15th annually. The Reid Vapor Pressure (RVP) of gasoline during this seasonal transition has been found to be the primary property attributed to this annual issue. It’s hypothesized that an increase in volatile butanes and pentanes from advanced petroleum recovery techniques and hydrofracking production has hastened the transition from summer to winter fuel volatility in the marketplace, rather than the gradual increase of the RVP over time as historically intended. At worst, mid-winter fuel, with an RVP ranging from 12 to 16 psi, depending on location in the U.S., enters the market while ambient temperatures can still be above average for the winter season. This combination of high volatility fuel with unseasonably warm weather will increase fuel system flash boiling, injector spray cavitation, and spray collapse inside the engine’s combustion chamber, ultimately linking fuel property variations to abnormal engine combustion processes. This CRADA program will investigate these known knowledge gaps by coupling with two national laboratories, Oak Ridge National Laboratory, and the National Renewable Energy Laboratory to employ both unique tools and expertise throughout the industry to provide the insight, knowledge, and data critical to understand the observed interactions. Overall findings of this work are that fuel wall retention increased SPI proportionally, and fuels with an increased distillation (i.e. energy fraction) above the wall temperature increased fuel retention. Likewise fuels with increased enthalpy of vaporization (HoV) increased fuel retention proportional to the temperature reduction from the HoV (~13K reduction in this work). Thus, fuel with increased HoV and increased fuel distillation above the linear temperature also exhibited increased SPI rates. Fuel with high RVP did exhibit increased fuel spray collapse form spray imaging measurements, but in SPI testing the high volatility of these fuels at the tested conditions did not necessarily increase SPI rates despite exhibiting increased spray collapse in injector imaging and increased spray-wall impingement measured in fired engine testing. It was also found that spray imaging showed collapse was possible at throttled conditions, but this was not relevant to high boost pressures relevant to SPI conditions, however, under transient load and or speed encountered in real-world operation fuel spray collapse could affect fuel retention and real-world SPI that were not probed in the automated high load test sequence of this work.

09 BIOMASS FUELS↗
DOE OSTI2023

Prospects for engineering Ralstonia eutropha and Zymomonas mobilis for the autotrophic production of 2,3-butanediol from CO 2 and H 2

The decarbonization of the chemical industry and a shift toward circular economies because of high global CO 2 emissions make CO 2 an attractive feedstock for manufacturing chemicals. Moreover, H 2 is a low-cost and carbon-free reductant because technologies such as solar-driven electrolysis and supercritical water (scH 2 O) gasification enable sustainable production of molecular hydrogen (H 2 ). We review the recent advances in engineering Ralstonia eutropha, the representative species of "Knallgas" bacteria, for utilizing CO 2 and H 2 to autotrophically produce 2,3-butanediol (2,3-BDO). This assessment is focused on state-of-the-art approaches for splitting H 2 to supply energy in the form of ATP and NADH to power cellular reactions and employing the Calvin-Benson-Bassham cycle for CO 2 fixation. Major challenges and opportunities for application and future perspectives are discussed in the context of developing other promising CO 2 and H 2 -utilizing microorganisms, exemplified by Zymomonas mobilis.

42 ENGINEERING↗
NASA NTRS2006

Calculation of Free-Atom Fractions in Hydrocarbon-Fueled Rocket Engine Plume

Free atom fractions (Beta) of nine elements are calculated in the exhaust plume of CH4- oxygen and RP-1-oxygen fueled rocket engines using free energy minimization method. The Chemical Equilibrium and Applications (CEA) computer program developed by the Glenn Research Center, NASA is used for this purpose. Data on variation of Beta in both fuels as a function of temperature (1600 K - 3100 K) and oxygen to fuel ratios (1.75 to 2.25 by weight) is presented in both tabular and graphical forms. Recommendation is made for the Beta value for a tenth element, Palladium. The CEA computer code was also run to compare with experimentally determined Beta values reported in literature for some of these elements. A reasonable agreement, within a factor of three, between the calculated and reported values is observed. Values reported in this work will be used as a first approximation for pilot rocket engine testing studies at the Stennis Space Center for at least six elements Al, Ca, Cr, Cu, Fe and Ni - until experimental values are generated. The current estimates will be improved when more complete thermodynamic data on the remaining four elements Ag, Co, Mn and Pd are added to the database. A critique of the CEA code is also included.

Verma, Satyajit↗
DOE OSTI2022

U-splines: Splines over unstructured meshes

U-splines are a novel approach to the construction of a spline basis for representing smooth objects in Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE). A spline is a piecewise-defined function that satisfies continuity constraints between adjacent cells in a mesh. U-splines differ from existing spline constructions, such as Non-Uniform Rational B-splines (NURBS), subdivision surfaces, T-splines, and hierarchical B-splines, in that they can accommodate local variation in cell size, polynomial degree, and smoothness simultaneously over more varied mesh configurations. Mixed cell types (e.g., triangle and quadrilateral cells in the same mesh) and T-junctions are also supported, although the continuity of interfaces with triangle and tetrahedral cells is limited in the present work. The U-spline algorithm introduces a new technique for using local null space solutions to construct basis functions for the global spline null space problem. The U-spline construction is presented for curves, surfaces, and volumes with higher dimensional generalizations possible. Lastly, a set of requirements are given to ensure that the U-spline basis is positive, forms a partition of unity, is complete, and is locally linearly independent.

42 ENGINEERING↗