Search NASA⌕ Search

SEARCH · Search NASA

Results for “Integral solution”

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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

The classical solution of a definite integral occurring in the satellite theory in the extended phase space

A method of integrating the functions defined by Scheifele and Graf (1974), arising in the elimination of time from the arguments of satellite theory using Delaunay elements in the extended phase space, is proposed. By repeated applications of an identity of Stiefel and Scheifele (1971), neglecting certain terms, and assuming a solution in the form of a product of Bessel functions, a solution expanded in the eccentricity is obtained.

Bond, V. R.↗
NASA NTRS1972

A theoretical study of radar return and radiometric emission from the sea

The applicability of the various electromagnetic models of scattering from the ocean are reviewed. These models include the small perturbation method, the geometric optics solution, the composite model, and the exact integral equation solution. The restrictions on the electromagnetic models are discussed.

Peake, W. H.↗
NASA NTRS1975

Solutions to Kuessner's integral equation in unsteady flow using local basis functions

The computational procedure and numerical results are presented for a new method to solve Kuessner's integral equation in the case of subsonic compressible flow about harmonically oscillating planar surfaces with controls. Kuessner's equation is a linear transformation from pressure to normalwash. The unknown pressure is expanded in terms of prescribed basis functions and the unknown basis function coefficients are determined in the usual manner by satisfying the given normalwash distribution either collocationally or in the complex least squares sense. The present method of solution differs from previous ones in that the basis functions are defined in a continuous fashion over a relatively small portion of the aerodynamic surface and are zero elsewhere. This method, termed the local basis function method, combines the smoothness and accuracy of distribution methods with the simplicity and versatility of panel methods. Predictions by the local basis function method for unsteady flow are shown to be in excellent agreement with other methods. Also, potential improvements to the present method and extensions to more general classes of solutions are discussed.

Fromme, J. A.↗
NASA NTRS1980

A solution of one dimensional Fredholm integral equations of the second kind

Fredholm integral equations of the second kind of the one dimension are numerically solved. It is proven that the numerical solution converges to the exact solution of the integral equation. This is shown for periodic kernels and then extended to nonperiodic kernels. This development helps delineate a basic theory which has the potential of solving very complex problems.

Gabrielsen, R. E.↗
NASA NTRS2006

Solutions Network Formulation Report. Integration of OMI and TES Aerosol Products into the EPA Regional Planning Organizations' FASTNET Aerosol Tracking and Analysis Tool

Every year, more than 280 million visitors tour our Nation s most treasured parks and wilderness areas. Unfortunately, many visitors are unable to see the spectacular vistas they expect because of white or brown haze in the air. Most of this haze is not natural; it is air pollution, carried by the wind often hundreds of miles from its origin. Some of the pollutants have been linked to serious health problems, such as asthma and other lung disorders, and even premature death. In addition, nitrates and sulfates contribute to acid rain formation, which contaminates rivers and lakes and erodes buildings and historical monuments. The U.S. Environmental Protection Agency RPOs (Regional Planning Organizations) have been tasked with monitoring and determining the nature and origin of haze in Class I scenic areas, and finding ways to reduce haze in order to improve visibility in these areas. The RPOs have developed an Internet-based air quality DST (Decision Support Tool) called FASTNET (Fast Aerosol Sensing Tools for Natural Event Tracking). While FASTNET incorporates a few satellite datasets, most of the data utilized by this DST comes from ground-based instrument networks. The problem is that in many areas the sensors are sparsely located, with long distances between them, causing difficulties in tracking haze over the United States, determining its source, and analyzing its content. Satellite data could help to fill in the data gaps and to supplement and verify ground-recorded air quality data. Although satellite data are now being used for air quality research applications, such data are not routinely used for environmental decision support, in part because of limited resources, difficulties with interdisciplinary data interpretation, and the need for advanced inter-agency partnerships. As a result, the validation and verification of satellite data for air quality operational system applications has been limited This candidate solution evaluates the usefulness of OMI (Ozone Monitoring Instrument) and TES (Tropospheric Emission Spectrometer) air quality data for the RPOs by comparing OMI and TES data with ground-based data that are acquired during identified episodes of air pollution. The air quality data from OMI and TES are of different spectral ranges than data from satellites currently included in FASTNET, giving them potential advantages over the existing satellites. If the OMI and TES data are shown to be useful to the RPOs, they would then be integrated into the FASTNET DST for use on an operational basis.

Knowlton, Kelly↗
NASA NTRS2011

Efficient Solution of Three-Dimensional Problems of Acoustic and Electromagnetic Scattering by Open Surfaces

We present a computational methodology (a novel Nystrom approach based on use of a non-overlapping patch technique and Chebyshev discretizations) for efficient solution of problems of acoustic and electromagnetic scattering by open surfaces. Our integral equation formulations (1) Incorporate, as ansatz, the singular nature of open-surface integral-equation solutions, and (2) For the Electric Field Integral Equation (EFIE), use analytical regularizes that effectively reduce the number of iterations required by iterative linear-algebra solution based on Krylov-subspace iterative solvers.

sound-soft acoustic scattering↗
NASA NTRS1982

Atmospheric ozone determination by solar occultation using the UV spectrometer on the Solar Maximum Mission

The UV spectrometer polarimeter instrument on the Solar Maximum Mission spacecraft has been used to measure ozone in the 53-75 km altitude interval by the technique of solar occultation. A 1 x 180 arcsec entrance aperture spectrometer with 0.04-A spectral resolution was employed. Resulting high-quality data are reduced by expressing measured UV attenuation as a Volterra integral equation. Solution of the equation is accomplished by expressing the integral in terms of a series representing the sum of ozone densities contained in concentric shells through tangent points separated by specified altitude increments. Sample ozone vs altitude profiles are presented for the equatorial region. These data show reproducibility to better than 10%. The density at 60 km is 7.3 + or - 0.15 x 10 to the 9th/cu cm for 2.5 deg latitude and longitudes between 81 and 105 deg west in September 1980. Density vs altitude profile exhibits changes in slope between 50 and 75 km.

Aikin, A. C.↗
NASA NTRS1991

Transfer Functions Via Laplace- And Fourier-Borel Transforms

Approach to solution of nonlinear ordinary differential equations involves transfer functions based on recently-introduced Laplace-Borel and Fourier-Borel transforms. Main theorem gives transform of response of nonlinear system as Cauchy product of transfer function and transform of input function of system, together with memory effects. Used to determine responses of electrical circuits containing variable inductances or resistances. Also possibility of doing all noncommutative algebra on computers in such symbolic programming languages as Macsyma, Reduce, PL1, or Lisp. Process of solution organized and possibly simplified by algebraic manipulations reducing integrals in solutions to known or tabulated forms.

Can, Sumer↗
NASA NTRSDate not supplied

Integrated Control Design for A Partially Turboelectric Aircraft Propulsion System

Electrified Aircraft Propulsion (EAP) holds great potential for reducing aviation emissions and fuel burn. A variety of EAP architectures have been proposed including partially-turboelectric configurations that combine turbofan engines with motor-driven propulsors. Such architectures exhibit coupling between subsystems and thus require an integrated control solution. To address this need, this paper presents an integrated control design strategy for a commercial single-aisle partially-turboelectric aircraft concept consisting of two wing-mounted turbofan engines and an electric motor driven tailfan propulsor. Within this architecture the turbofans serve the dual purpose of generating thrust and supplying mechanical offtake power used to generate electricity for the tailfan motor. The propulsion control system is tasked with coordinating turbofan and tailfan operation under both steady-state and transient scenarios. The paper introduces a linear state-space representation of the architecture reflecting the coupling between the turbofan and tailfan subsystems along with loop transfer functions reflecting open- and closed-loop system dynamics. Also discussed is an applied strategy for scheduling the tailfan setpoint command based on the average sensed fan speed of the two turbofans. This approach ensures synchronized operation of the turbofan and tailfan subsystems while also allowing the turbofan fuel control design to be simplified. Performance of the integrated control design is assessed through a real-time hardware-in-the-loop test conducted at the NASA Electric Aircraft Testbed. During this test a scaled version of the electrical system and turbomachinery shaft dynamics were implemented in electrical machine hardware and evaluated under closed-loop control. Results from this facility test are presented to illustrate the efficacy of the applied integrated control design approach under steady-state and transient scenarios including a full-flight mission profile.

Electrified Aircraft Propulsion↗
NASA NTRSDate not supplied

Integrated Control Design for A Partially Turboelectric Aircraft Propulsion System

Electrified Aircraft Propulsion (EAP) holds great potential for reducing aviation emissions and fuel burn. A variety of EAP architectures have been proposed including partially-turboelectric configurations that combine turbofan engines with motor-driven propulsors. Such architectures exhibit coupling between subsystems and thus require an integrated control solution. To address this need, this paper presents an integrated control design strategy for a commercial single-aisle partially-turboelectric aircraft concept consisting of two wing-mounted turbofan engines and an electric motor driven tailfan propulsor. Within this architecture the turbofans serve the dual purpose of generating thrust and supplying mechanical offtake power used to generate electricity for the tailfan motor. The propulsion control system is tasked with coordinating turbofan and tailfan operation under both steady-state and transient scenarios. The paper introduces a linear state-space representation of the architecture reflecting the coupling between the turbofan and tailfan subsystems along with loop transfer functions reflecting open- and closed-loop system dynamics. Also discussed is an applied strategy for scheduling the tailfan setpoint command based on the average sensed fan speed of the two turbofans. This approach ensures synchronized operation of the turbofan and tailfan subsystems while also allowing the turbofan fuel control design to be simplified. Performance of the integrated control design is assessed through a real-time hardware-in-the-loop test conducted at the NASA Electric Aircraft Testbed. During this test a scaled version of the electrical system and turbomachinery shaft dynamics were implemented in electrical machine hardware and evaluated under closed-loop control. Results from this facility test are presented to illustrate the efficacy of the applied integrated control design approach under steady-state and transient scenarios including a full-flight mission profile.

Electrified Aircraft Propulsion↗
NASA NTRS2023

Integrated Control Design for A Partially Turboelectric Aircraft Propulsion System

Electrified Aircraft Propulsion (EAP) holds great potential for reducing aviation emissions and fuel burn. A variety of EAP architectures have been proposed including partially-turboelectric configurations that combine turbofan engines with motor-driven propulsors. Such architectures exhibit coupling between subsystems and thus require an integrated control solution. To address this need, this paper presents an integrated control design strategy for a commercial single-aisle partially-turboelectric aircraft concept consisting of two wing-mounted turbofan engines and an electric motor driven tailfan propulsor. Within this architecture the turbofans serve the dual purpose of generating thrust and supplying mechanical offtake power used to generate electricity for the tailfan motor. The propulsion control system is tasked with coordinating turbofan and tailfan operation under both steady-state and transient scenarios. The paper introduces a linear state-space representation of the architecture reflecting the coupling between the turbofan and tailfan subsystems along with loop transfer functions reflecting open- and closed-loop system dynamics. Also discussed is an applied strategy for scheduling the tailfan setpoint command based on the average sensed fan speed of the two turbofans. This approach ensures synchronized operation of the turbofan and tailfan subsystems while also allowing the turbofan fuel control design to be simplified. Performance of the integrated control design is assessed through a real-time hardware-in-the-loop test conducted at the NASA Electric Aircraft Testbed. During this test a scaled version of the electrical system and turbomachinery shaft dynamics were implemented in electrical machine hardware and evaluated under closed-loop control. Results from this facility test are presented to illustrate the efficacy of the applied integrated control design approach under steady-state and transient scenarios including a full-flight mission profile.

Electrified Aircraft Propulsion↗
NASA NTRS2017

Interconnect and Packaging Technologies for Terahertz Communication Systems

Using newly developed silicon micromachining technology that enables low-loss and highly integrated packaging solutions, we are developing vertically stacked transmitters and receivers at terahertz frequencies that can be used for communication and other terahertz systems. Although there are multiple ways to address the problem of interconnect and packaging solutions at these frequencies, such as system-on-package (SOP), multi-chip modules (MCM), substrate integrated waveguide (SIW), liquid crystal polymer (LCP) based multilayer technologies, and others, we show that deep reactive ion etching (DRIE) based silicon micromachining with vertical integration allows the most effective solutions at terahertz frequencies.

Micromachining↗
NASA NTRS2008

Development and Application of an Integrated Approach toward NASA Airspace Systems Research

The National Aeronautics and Space Administration's (NASA) Airspace Systems Program is contributing air traffic management research in support of the 2025 Next Generation Air Transportation System (NextGen). Contributions support research and development needs provided by the interagency Joint Planning and Development Office (JPDO). These needs generally call for integrated technical solutions that improve system-level performance and work effectively across multiple domains and planning time horizons. In response, the Airspace Systems Program is pursuing an integrated research approach and has adapted systems engineering best practices for application in a research environment. Systems engineering methods aim to enable researchers to methodically compare different technical approaches, consider system-level performance, and develop compatible solutions. Systems engineering activities are performed iteratively as the research matures. Products of this approach include a demand and needs analysis, system-level descriptions focusing on NASA research contributions, system assessment and design studies, and common systemlevel metrics, scenarios, and assumptions. Results from the first systems engineering iteration include a preliminary demand and needs analysis; a functional modeling tool; and initial system-level metrics, scenario characteristics, and assumptions. Demand and needs analysis results suggest that several advanced concepts can mitigate demand/capacity imbalances for NextGen, but fall short of enabling three-times current-day capacity at the nation s busiest airports and airspace. Current activities are focusing on standardizing metrics, scenarios, and assumptions, conducting system-level performance assessments of integrated research solutions, and exploring key system design interfaces.

Barhydt, Richard↗
NASA NTRS2018

Practical Orbit Determination for Aerobraking with Accumulated Accelerometer Data

Navigation during aerobraking missions has historically relied solely on radiometric Doppler data. Accelerometer data, available on all modern spacecraft, has the potential to supplement Doppler data, increasing operational tempos, filling tracking data gaps, and improving the accuracy of orbit determination solutions. However, integration of Doppler and accelerometer data into the batch filter solutions used for operational navigation has proven to be practically challenging, due to the narrow region of adequate linear approximation for acceleration incurred by drag. This work proposes to use the accumulated velocity changes derived from these values as a more compatible data type. Demonstrations of results focus on NASA’s Maven and ESA’s TGO mission, and how this technique can be used to improve operations for the upcoming Maven aerobraking phase with reduced tracking data and lighter staffing requirements.

Young, Brian↗