Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “parallel coordinates”

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 163 records · Page 9

Gigatraj: An Atmospheric Trajectory Model

Atmospheric trajectory models have a long history of success in tracking air motions in the lower stratosphere and upper troposphere over periods of up to a few days. Parcels have been traced backwards from observations to identify whatever phenomena (strong convection, volcanic eruptions, rocket launches, etc.) put their signature on them. Parcels have also been initialized at a known event and traced forward to examine their subsequent physical and chemical evolution. We describe a new trajectory model, "gigatraj," that aims to increase exibility by (a) making it straightforward to use new meteorological data sources, including those not based on regular latitude-longitude grids; (b) enabling a run-time choice of vertical coordinate system for kinematic and/or quasi-isentropic calculations; (c) allowing for the output of arbitrary meteorological products, selectable by the user and interpolated to the parcels' locations and times. The model can be run in a serial or parallel processing environment, so that large numbers of parcels can be traced in a reasonable time. Information is presented on model accuracy and performance. The former is demonstrated by runs using both test-pattern winds (comparing expected paths with actual output) and real-world winds (comparing forward and backward runs to characterize how well parcels retrace their paths). Sample cases are also shown, including a reverse domain lling (RDF) calculation illustrating a tropopause fold event. Model output can be displayed using the new Visualization And Lagrangian dynamics Immersive eXtended Reality (VALIXR) system, and an example will be shown. In addition, we describe work to incorporate a version of gigatraj into the Goddard Earth Observing System (GEOS) of NASA's Global Modeling and Assimilation O ce (GMAO) at Goddard Space Flight Center. This enables trajectory calculations to be performed within the running GEOS model at the latter's native time resolution, instead of using the winds from every few hours. It also provides access to all of GEOS's internal variables as they are calculated. This module may be useful, for example, for tracking rapid chemical changes in a Lagrangian framework.

dynamics↗

Noise generation by a finite span swept airfoil

An analysis is developed for the noise generated by a convected gust interacting with a single swept airfoil. The airfoil spans a channel with infinite parallel walls which contains a uniform subsonic mean flow. High frequency gusts, for which the noise generation is concentrated at the airfoil leading edge, are considered. The solution utilizes the Wiener-Hopf technique applied to the equations in nonorthogonal coordinates. Closed form expressions for the farfield acoustic pressure are obtained. The convected gust is assumed to be a plane wave, i.e., the lowest order spanwise mode. Because of the swept leading edge, this convected gust generates acoustic modes of all orders. At high frequencies and low Mach numbers, moderate sweep angles produce substantial noise reductions. The residual acoustic energy is carried mainly by the higher modes. The airfoil sweep also modulates the basic high frequency farfield directivity, producing lobed patterns. The angular modulation of the directivity patterns is most pronounced for the lower order modes.

Kerschen, E. J.↗

Numerical simulation of ice growth on a MS-317 swept wing geometry

An effort to develop a 3-D ice accretion modeling method was initiated. This first step towards creation of a complete aircraft icing simulation code builds on previously developed methods for calculating 3-D flow fields and particle trajectories combined with a 2-D ice accretion calculation along coordinate locations corresponding to streamlines. The types of calculations necessary to predict three-dimensional ice accretion is demonstrated. Results of calculations using 3-D method for a MS-317 swept wing geometry are projected onto a 2-D plane parallel to the free stream direction and compared to experimental results for the same geometry. It is anticipated that many modifications will be made to this approach, however, this effort will lay the groundwork for future modeling efforts. Results indicate that rime ice shapes indicate a difficulty in accurately calculating the ice shape in the runback region.

Potapczuk, M. G.↗

A Procedure for 3-D Contact Stress Analysis of Spiral Bevel Gears

Contact stress distribution of spiral bevel gears using nonlinear finite element static analysis is presented. Procedures have been developed to solve the nonlinear equations that identify the gear and pinion surface coordinates based on the kinematics of the cutting process and orientate the pinion and the gear in space to mesh with each other. Contact is simulated by connecting GAP elements along the intersection of a line from each pinion point (parallel to the normal at the contact point) with the gear surface. A three dimensional model with four gear teeth and three pinion teeth is used to determine the contact stresses at two different contact positions in a spiral bevel gearset. A summary of the elliptical contact stress distribution is given. This information will be helpful to helicopter and aircraft transmission designers who need to minimize weight of the transmission and maximize reliability.

Kumar, A.↗

Computational aeroacoustics on massively parallel computers

A computational fluid dynamics (CFD) technique is employed to solve aeroacoustics problems on massively parallel computers. The algorithm is based on a 4th order accurate central finite difference and 4th order accurate 4-stage Runge-Kutta time integration method that solves the 3-D full Navier-Stokes/Euler equations on a curvilinear coordinate system. The code has been developed to predict noise radiation from ducted fans. A specific application of this code is made here to the oscillating circular piston problem (Workshop Category 4, Problem 2) by solving the full Euler equations with nonreflecting boundary conditions in the axisymmetric mode. The features of the code that apply to this particular problem are described in this paper.

Oezyoeruek, Yusuf↗

LIS-Hydro: Authoritative Source for OCONUS Hydro-Intelligence

U.S. military forces are often tasked to participate in a variety of transboundary water-related decision-making activities, including humanitarian assistance operations through Department of State tasking, support of in-country infrastructure development activities that help develop or improve diplomatic relationships, and support of transboundary water treaty negotiations or disputes to reduce risk of conflict caused by water security issues. The U.S. intelligence communities have identified the coordination over shared water resources as an area of significant concern to U.S. national security (U.S. National Defense Strategy, 2018). Such transboundary water issues are projected to intensify in the future under increasingly complex population dynamics, political tensions due to parallel issues, and a changing climate. A 2017 joint NASA, USACE/RDC, and U.S. Air Force co-sponsored workshop revealed a lack of sufficient decision support tools and access to timely technical and contextual information needed to assess and respond to potential water-related threats around the world. The need for an integrated operational service, with the capacity to combine and synthesize hydrological modeling, assimilation, forecasting, and visualization capabilities across the U.S. Government, was highlighted as a key recommendation. In direct response, a subset of the U.S. Department of Defense, National Intelligence Community, and Oak Ridge National Laboratory are collaborating on the development of a fully integrated hydro-modeling and streamflow prediction system (i.e., LIS-Hydro). Completion of the project and sustainment of the operational capability by Air Force Weather will establish a national asset to assist federal agencies implement government-wide strategies around water resources (U.S. Global Water Strategy, 2017). The hydrological products and services will, for the very first time, establish a routinely available authoritative source of global water intelligence information supporting war-fighters, planners, and decision makers at all echelons and services of the U.S. military, Federal government, and intelligence community. A summary of the interagency scientific collaboration in addressing some of the key gaps and needs identified during the 2017 workshop will be presented.

Land Information System↗

Manufactured Porous Ambient Surface Simulants

The planetary science decadal survey for 2013-2022 (Vision and Voyages, NRC 2011) has promoted mission concepts for sample acquisition from small solar system bodies. Numerous comet-sampling tools are in development to meet this standard. Manufactured Porous Ambient Surface Simulants (MPASS) materials provide an opportunity to simulate variable features at ambient temperatures and pressures to appropriately test potential sample acquisition systems for comets, asteroids, and planetary surfaces. The original "flavor" of MPASS materials is known as Manufactured Porous Ambient Comet Simulants (MPACS), which was developed in parallel with the development of the Biblade Comet Sampling System (Backes et al., in review). The current suite of MPACS materials was developed through research of the physical and mechanical properties of comets from past comet missions results and modeling efforts, coordination with the science community at the Jet Propulsion Laboratory and testing of a wide range of materials and formulations. These simulants were required to represent the physical and mechanical properties of cometary nuclei, based on the current understanding of the science community. Working with cryogenic simulants can be tedious and costly; thus MPACS is a suite of ambient simulants that yields a brittle failure mode similar to that of cryogenic icy materials. Here we describe our suite of comet simulants known as MPACS that will be used to test and validate the Biblade Comet Sampling System (Backes et al., in review).

Carey, Elizabeth M.↗

Overview of NASA ISRU Plans, Priorites, and Activities

Introduction:The National Aeronautics andSpace Administration (NASA) of the United States ofAmerica (US) has initiated the Artemis Moon to Marsprogram to send astronauts (the first woman andperson of color) back to the lunar surface, create asustainable human lunar exploration program, andlead the first human exploration mission to the Marssurface in the 2030’s [1]. A major objective of thisprogram is to characterize the resources that exist onthe Moon and Mars, and learn how to utilize them forsustained and affordable exploration. Commonlyknown as In Situ Resource Utilization (ISRU), thesearch for, acquisition, and processing of resources inspace has the potential to greatly reduce thedependency on transporting mission consumables andinfrastructure from Earth, thereby reducing missioncosts, risks, and dependency on Earth.ISRU is Enabling: Through the extraction andprocessing of resources into mission commoditiessuch as rocket propellants, life support consumables,and fuel cell reactants, ISRU enhances and evolvesthe cis-lunar, lander, and surface transportationsystems required for human exploration; expandingand enhancing HOW humans can explore and returnfrom the Moon. Through the extraction andprocessing of resources into metals, silicon, and othermanufacturing and construction feedstock, ISRUenhances and allows for the expansion of criticalinfrastructure using in situ manufacturing andconstruction capabilities that influence WHAT humanscan do on the Moon and in cis-lunar space. Becauseof this, ISRU supports and enables commercialinvolvement beyond NASA and governmentalagencies by both lowering the cost of sustainedtransportation to/from/on the Moon as well assupporting the market required for needing thesetransportation systems. Strategic Framework:To achieve this vision,NASA’s Space Technology Mission Directorate(STMD) ensures the coordinated development ofISRU and other critical space and surfaceinfrastructure elements such as propulsion, power,manufacturing, construction, and robotics through theStrategic Technology Architecture Roundtable(STAR) process. Through STAR, an integratedframework and process has been created allowing forcapabilities and technologies to be linked andassessed, gaps to be identified, specifications andmetrics to be established, and provide a means toprioritize and implement technology development andmissions. A critical part of the STAR effort has beenthe establishment of the Strategic Framework thatorganizes all work under four major Thrusts (Go,Land, Live, and Explore) and identifies the drivingOutcomes for each of these Thrusts. From the Thrustsand Outcomes, all work can be categorized and linkedbetween Capability Areas, and Technology Gaps canbe identified and addressed (Figure 1.)Figure 1. Strategic Framework and STAR FrameworkISRU Envisioned Future: To drive thedevelopment of technologies and capabilities, theSTAR process starts with establishing a ‘grand vision’of where each Outcome and Capability is aiming tobe considered complete. For ISRU, the EnvisionedFuture is “Scalable ISRU production/utilizationcapabilities including sustainable commodities on thelunar and Mars Surface”. This involves starting with10’s of metric tons of products, but evolves into 100’sto 1000’s of metric tons of water, oxygen, propellants,construction and manufacturing feedstock, andcommodities for habitat and food production andoperations. For ISRU, the ‘Prospect to Product’philosophy starts with Destination Reconnaissance &Resource Assessment, followed by ResourceAcquisition, Isolation, and Preparation, leading intoResource Processing (which is further subdivided intomission consumables and feedstocks for constructionand manufacturing). The ISRU Envisioned Futurealso considers what resources are available andattempts to address what and when these resourceswill be evaluated and harnessed, as well asconsidering which products/commodities can beobtained for early use and which ones require moretime and/or users of refined products.It Takes an Architecture: ISRU does not existon its own. By definition, it requires customers/users SHORT TITLE HERE: A. B. Author and C. D. Authorto use the products/commodities produced by ISRUsystems. Also, for an ISRU capability to exist, itmust obtain products and services from other systemsand infrastructure. An important aspect of the STARprocess and the ISRU Envisioned Futures Prioritiesstrategy is to identify and link all of these systems andcapabilities to achieve the desired end state (Figure2).Figure 2. ISRU as Part of a Larger ArchitectureISRU Capability Drivers: The guidingprinciples for NASA’s Space TechnologyDevelopment for Artemis are to develop criticaltechnologies and capabilities that enable (i) asustainable Lunar surface presence, (ii) the future goalof sending humans to Mars, and (iii) promotingcritical technologies to enable future science andcommercial missions. It is a major goal of theArtemis campaign to establish some sort of base campat the lunar South Pole by approximately the end ofthe decade. The ISRU Envisioned Futures Prioritiesstrategy is aligned with the Artemis campaign todevelop and demonstrate ISRU capabilities in thistimeframe that could lead to sustained surfaceoperations, infrastructure growth, and commercialoperations in the next decade (Figure 3).Figure 3. ISRU Dual Path to Full Implementation and CommercializationState of the Art and Gaps: To achieve theenvisioned future, an extensive effort was performedto understand the State of the Art (SOA) for ISRUgoing back decades, and to assess the SOA against thenear and long-term goals and objectives of the ISRUStrategic Outcome objectives. While the releasedISRU Envisioned Futures Priorities only includes atop-level definition of both the SOA and Gaps, furtherinformation on these for ISRU can be found in theISRU Gap Assessment Study performed for theInternational Space Exploration Coordination Group(ISECG) [2]. To provide further guidance to industryand academia, a top level assessment was performedand provide that divides critical areas of ISRUcapabilities and technologies into 3 categories:Significant Funding, Partially Covered/MoreRequired, and Limited/No Funded Activities.Envisioned Future Priorities- Next Steps forISRU: While a significant amount of work over abroad range of technology areas has been performedover the last several years for lunar ISRU, to reach theenvisioned future for ISRU, a lot more work isrequired at the technology level leading to bothsystems and technology demonstrations in the nearfuture. To guide investments within NASA, industry,and academia, 5 specific areas of high priority wereidentified. These are:1.Complete development of the Water and Oxygen Mining Paths and close technology gaps, with emphasis on oxygen extraction from Highland regolith and parallel paths for polar water mining.2.Expand development of metal extraction and feedstock for manufacturing and construction, with emphasis on aluminum and initial/easy to obtain/make construction feedstocks leading to more refined metals and other regolith resources. Also, evaluate biologically inspired/derived technologies in bio-mining, bio-plastic, and other feedstock commodities.3.Ensure the resource assessment needed for future ISRU commercial operations is coordinated with both near/long-term science objectives as well as Artemis mission locations of interest.4.Initiate NASA and industry-led system-level analyses, integration, and testing activities for ISRU capabilities. While significant work has been performed at the technology and subsystemlevel, it is now important to understand how these technology investments can be leveraged and utilized in actual systems and applications5.Initiate lunar ISRU technology flight demonstrations leading to initial ‘Pilot Plant’ end-to-end production capability demonstrations, led by industry

ISRU↗

Application of the multigrid method to grid generation

The multigrid method (MGM), used to numerically solve the pair of nonlinear elliptic equations commonly used to generate two dimensional boundary-fitted coordinate systems is discussed. Two different geometries are considered: one involving a coordinate system fitted about a circle and the other selected for an impinging jet flow problem. Two different relaxation schemes are tried: one is successive point overrelaxation and the other is a four-color scheme vectorizeable to take advantage of a parallel processor computer for greater computational speed. Results using MGM are compared with those using SOR (doing successive overrelaxations with the corresponding relaxation scheme on the fine grid only). It is found that MGM becomes significantly more effective than SOR as more accuracy is demanded and as more corrective grids, or more grid points, are used. For the accuracy required, it is found that MGM is two to three times faster than SOR in computing time. With the four-color relaxation scheme as applied to the impinging jet problem, the advantage of MGM over SOR is not as great. This may be due to the effect of a poor initial guess on MGM for this problem.

Ohring, S.↗

Bounce-averaged Hamiltonian for charged particles in an axisymmetric but nondipolar model magnetosphere

In order to facilitate bounce-averaged guiding center simulations of geomagnetically trapped particles, we express the kinetic energy of a particle with magnetic coordinates (L,phi) as an analytic function of the first two adiabatic invariants (M,J) and the L value of the field line. The magnetic field model is axisymmetric, consisting of a dipolar vector-B field plus a uniform southward magnetic field parallel to the dipole moment mu(sub E). This model magnetosphere is surrounded by a circular equatorial neutral line whose radius b is an adjustable parameter. Our formulation provides a computationally efficient method for tracing the bounce-averaged adiabatic motion (conserving all three invariants) and nonadiabatic transport (violating the third invariant while conserving the first two invariants) of geomagnetically trapped particles in the model magnetosphere.

Schulz, Michael↗

Surface grid generation for wing-fuselage bodies

In the application of finite-difference methods to obtain numerical solutions of viscous compressible fluid flow about wing-fuselage bodies, it is advantageous to transform the governing equations to an idealized boundary-fitted coordinate system. The advantages are reduced computational complexity and added accuracy in the application of boundary conditions. The solution process requires that a grid be superimposed on the physical solution domain which corresponds to a uniform grid on a rectangular computational domain (uniform rectangular parallel-epiped). Grid generation is the determination of a one to one relationship between grid points in the physical domain and grid points in the computational domain. A technique for computing wing-fuselage surface grids using the Harris geometry and software for smooth-surface representation is described. Grid spacing control concepts which govern the relationship between the wing-fuselage surface and the computational grid are also presented.

Smith, R. E.↗

Radiation Losses Due to Tapering of a Double-Core Optical Waveguide

The theoretical model we designed parameterizes the power losses as a function of .the profile shape for a tapered, single mode, optical dielectric coupler. The focus of this project is to produce a working model that determines the power losses experienced by the fibers when light crosses a taper region. This phenomenon can be examined using coupled mode theory. The optical directional coupler consists of a parallel, dual-channel, waveguide with minimal spacing between the channels to permit energy exchange. Thus, power transfer is essentially a function of the taper profile. To find the fields in the fibers, the approach used was that of solving the Helmholtz equation in cylindrical coordinates involving Bessel and modified Bessel functions depending on the location.

Lyons, Donald R.↗

yourSky: Custom Sky-Image Mosaics via the Internet

yourSky (http://yourSky.jpl.nasa.gov) is a computer program that supplies custom astronomical image mosaics of sky regions specified by requesters using client computers connected to the Internet. [yourSky is an upgraded version of the software reported in Software for Generating Mosaics of Astronomical Images (NPO-21121), NASA Tech Briefs, Vol. 25, No. 4 (April 2001), page 16a.] A requester no longer has to engage in the tedious process of determining what subset of images is needed, nor even to know how the images are indexed in image archives. Instead, in response to a requester s specification of the size and location of the sky area, (and optionally of the desired set and type of data, resolution, coordinate system, projection, and image format), yourSky automatically retrieves the component image data from archives totaling tens of terabytes stored on computer tape and disk drives at multiple sites and assembles the component images into a mosaic image by use of a high-performance parallel code. yourSky runs on the server computer where the mosaics are assembled. Because yourSky includes a Web-interface component, no special client software is needed: ordinary Web browser software is sufficient.

Jacob, Joseph↗

Experimental Validation of Numerical Simulations for an Acoustic Liner in Grazing Flow

A coordinated experimental and numerical simulation effort is carried out to improve our understanding of the physics of acoustic liners in a grazing flow as well our computational aeroacoustics (CAA) method prediction capability. A numerical simulation code based on advanced CAA methods is developed. In a parallel effort, experiments are performed using the Grazing Flow Impedance Tube at the NASA Langley Research Center. In the experiment, a liner is installed in the upper wall of a rectangular flow duct with a 2 inch by 2.5 inch cross section. Spatial distribution of sound pressure levels and relative phases are measured on the wall opposite the liner in the presence of a Mach 0.3 grazing flow. The computer code is validated by comparing computed results with experimental measurements. Good agreements are found. The numerical simulation code is then used to investigate the physical properties of the acoustic liner. It is shown that an acoustic liner can produce self-noise in the presence of a grazing flow and that a feedback acoustic resonance mechanism is responsible for the generation of this liner self-noise. In addition, the same mechanism also creates additional liner drag. An estimate, based on numerical simulation data, indicates that for a resonant liner with a 10% open area ratio, the drag increase would be about 4% of the turbulent boundary layer drag over a flat wall.

Tam, Christopher K. W.↗

Polar exponential sensor arrays unify iconic and Hough space representation

The log-polar coordinate system, inherent in both polar exponential sensor arrays and log-polar remapped video imagery, is identical to the coordinate system of its corresponding Hough transform parameter space. The resulting unification of iconic and Hough domains simplifies computation for line recognition and eliminates the slope quantization problems inherent in the classical Cartesian Hough transform. The geometric organization of the algorithm is more amenable to massively parallel architectures than that of the Cartesian version. The neural architecture of the human visual cortex meets the geometric requirements to execute 'in-place' log-Hough algorithms of the kind described here.

Weiman, Carl F. R.↗

A Simple Tool for the Design and Analysis of Multiple-Reflector Antennas in a Multi-Disciplinary Environment

The process of designing and analyzing a multiple-reflector system has traditionally been time-intensive, requiring large amounts of both computational and human time. At many frequencies, a discrete approximation of the radiation integral may be used to model the system. The code which implements this physical optics (PO) algorithm was developed at the Jet Propulsion Laboratory. It analyzes systems of antennas in pairs, and for each pair, the analysis can be computationally time-consuming. Additionally, the antennas must be described using a local coordinate system for each antenna, which makes it difficult to integrate the design into a multi-disciplinary framework in which there is traditionally one global coordinate system, even before considering deforming the antenna as prescribed by external structural and/or thermal factors. Finally, setting up the code to correctly analyze all the antenna pairs in the system can take a fair amount of time, and introduces possible human error. The use of parallel computing to reduce the computational time required for the analysis of a given pair of antennas has been previously discussed. This paper focuses on the other problems mentioned above. It will present a methodology and examples of use of an automated tool that performs the analysis of a complete multiple-reflector system in an integrated multi-disciplinary environment (including CAD modeling, and structural and thermal analysis) at the click of a button. This tool, named MOD Tool (Millimeter-wave Optics Design Tool), has been designed and implemented as a distributed tool, with a client that runs almost identically on Unix, Mac, and Windows platforms, and a server that runs primarily on a Unix workstation and can interact with parallel supercomputers with simple instruction from the user interacting with the client.

Katz, Daniel S.↗

Lunar rovers and local positioning system

Telerobotic rovers equipped with adequate actuators and sensors are clearly necessary for extraterrestrial construction. They will be employed as substitutes for humans, to perform jobs like surveying, sensing, signaling, manipulating, and the handling of small materials. Important design criteria for these rovers include versatility and robustness. They must be easily programmed and reprogrammed to perform a wide variety of different functions, and they must be robust so that construction work will not be jeopardized by parts failures. The key qualities and functions necessary for these rovers to achieve the required versatility and robustness are modularity, redundancy, and coordination. Three robotic rovers are being built by CSC as a test bed to implement the concepts of modularity and coordination. The specific goal of the design and construction of these robots is to demonstrate the software modularity and multirobot control algorithms required for the physical manipulation of constructible elements. Each rover consists of a transporter platform, bus manager, simple manipulator, and positioning receivers. These robots will be controlled from a central control console via a radio-frequency local area network (LAN). To date, one prototype transporter platform frame was built with batteries, motors, a prototype single-motor controller, and two prototype internal LAN boards. Software modules were developed in C language for monitor functions, i/o, and parallel port usage in each computer board. Also completed are the fabrication of half of the required number of computer boards, the procurement of 19.2 Kbaud RF modems for inter-robot communications, and the simulation of processing requirements for positioning receivers. In addition to the robotic platform, the fabrication of a local positioning system based on infrared signals is nearly completed. This positioning system will make the rovers into a moving reference system capable of performing site surveys. In addition, a four degree mechanical manipulator especially suited for coordinated teleoperation was conceptually designed and is currently being analyzed. This manipulator will be integrated into the rovers as their end effector. Twenty internal LAN cards fabricated by a commercial firm are being used, a prototype manipulator and a range finder for a positioning system were built, a prototype two-motor controller was designed, and one of the robots is performing its first telerobotic motion. In addition, the robots' internal LAN's were coordinated and tested, hardware design upgrades based on fabrication and fit experience were completed, and the positioning system is running. The rover system is able to perform simple tasks such as sensing and signaling; coordination systems which allow construction tasks to begin were established, and soon coordinated teams of robots in the laboratory will be able to manipulate common objects.

Avery, James↗

Stability and transition on swept wings

This paper describes the extension and application of the Parabolized Stability Equations (PSE) to the stability and transition of the supersonic three-dimensional laminar boundary layer on a swept wing. The problem formulation uses a general coordinate transformation for arbitrary curvilinear body-fitted computational grids. Some testing using these coordinates is briefly described to help validate the software used for the investigation. The disturbance amplitude ratios as a function of chord position for supersonic (Mach 1.5) boundary layers on untapered, untwisted wings of different sweep angles are then presented and compared with those obtained from local parallel analyses.

Stuckert, Greg↗