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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.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Conic state extrapolation

The Conic State Extrapolation Routine provides the capability to conically extrapolate any spacecraft inertial state vector either backwards or forwards as a function of time or as a function of transfer angle. It is merely the coded form of two versions of the solution of the two-body differential equations of motion of the spacecraft center of mass. Because of its relatively fast computation speed and moderate accuracy, it serves as a preliminary navigation tool and as a method of obtaining quick solutions for targeting and guidance functions. More accurate (but slower) results are provided by the Precision State Extrapolation Routine.

Shepperd, S. W.↗
NASA NTRS1980

Wind-tunnel/flight correlation study of aerodynamic characteristics of a large flexible supersonic cruise airplane (XB-701) 2: Extrapolation of wind-tunnel data to full-scale conditions

The results of calculations necessary to extrapolate performance data on an XB-70-1 wind tunnel model to full scale at Mach numbers from 0.76 to 2.53 are presented. The extrapolation was part of a joint program to evaluate performance prediction techniques for large flexible supersonic airplanes similar to a supersonic transport. The extrapolation procedure included: interpolation of the wind tunnel data at the specific conditions of the flight test points; determination of the drag increments to be applied to the wind tunnel data, such as spillage drag, boundary layer trip drag, and skin friction increments; and estimates of the drag items not represented on the wind tunnel model, such as bypass doors, roughness, protuberances, and leakage drag. In addition, estimates of the effects of flexibility of the airplane were determined.

Peterson, J. B., Jr.↗
NASA NTRS1987

Extrapolation methods for vector sequences

This paper derives, describes, and compares five extrapolation methods for accelerating convergence of vector sequences or transforming divergent vector sequences to convergent ones. These methods are the scalar epsilon algorithm (SEA), vector epsilon algorithm (VEA), topological epsilon algorithm (TEA), minimal polynomial extrapolation (MPE), and reduced rank extrapolation (RRE). MPE and RRE are first derived and proven to give the exact solution for the right 'essential degree' k. Then, Brezinski's (1975) generalization of the Shanks-Schmidt transform is presented; the generalized form leads from systems of equations to TEA. The necessary connections are then made with SEA and VEA. The algorithms are extended to the nonlinear case by cycling, the error analysis for MPE and VEA is sketched, and the theoretical support for quadratic convergence is discussed. Strategies for practical implementation of the methods are considered.

Smith, David A.↗
NASA NTRS1987

An algorithm for a generalization of the Richardson extrapolation process

The paper presents a recursive method, designated the W exp (m)-algorithm, for implementing a generalization of the Richardson extrapolation process. Compared to the direct solution of the linear sytems of equations defining the extrapolation procedure, this method requires a small number of arithmetic operations and very little storage. The technique is also applied to solve recursively the coefficient problem associated with the rational approximations obtained by applying a d-transformation to power series. In the course of development a new recursive algorithm for implementing a very general extrapolation procedure is introduced, for solving the same problem. A FORTRAN program for the W exp (m)-algorithm is also appended.

Ford, William F.↗
NASA NTRS1988

Recursive algorithms for vector extrapolation methods

Three classes of recursion relations are devised for implementing some extrapolation methods for vector sequences. One class of recursion relations can be used to implement methods like the modified minimal polynomial extrapolation and the topological epsilon algorithm; another allows implementation of methods like minimal polynomial and reduced rank extrapolation; while the remaining class can be employed in the implementation of the vector E-algorithm. Operation counts and storage requirements for these methods are also discussed, and some related techniques for special applications are also presented. Included are methods for the rapid evaluations of the vector E-algorithm.

Ford, William F.↗
NASA NTRS1990

Concerning the extrapolation of solar nonlinear force-free magnetic fields

This paper contains a review and discussion of the mathematical basis of the extrapolation techniques involved in using photospheric vector magnetograms to obtain the coronal field above the surface. The two basic techniques employing the Cauchy initial value problem and the variational techniques are reviewed in terms of the mathematical and practical applications. A short review is presented of the current research on numerical modeling techniques in the area of extrapolating vector magnetograms; specifically, algorithms to extrapolate nonlinear force-free magnetic fields from the photosphere are considered.

Gary, G. Allen↗
NASA NTRS2012

3D Drop Size Distribution Extrapolation Algorithm Using a Single Disdrometer

Determining the Z-R relationship (where Z is the radar reflectivity factor and R is rainfall rate) from disdrometer data has been and is a common goal of cloud physicists and radar meteorology researchers. The usefulness of this quantity has traditionally been limited since radar represents a volume measurement, while a disdrometer corresponds to a point measurement. To solve that problem, a 3D-DSD (drop-size distribution) method of determining an equivalent 3D Z-R was developed at the University of Central Florida and tested at the Kennedy Space Center, FL. Unfortunately, that method required a minimum of three disdrometers clustered together within a microscale network (.1-km separation). Since most commercial disdrometers used by the radar meteorology/cloud physics community are high-cost instruments, three disdrometers located within a microscale area is generally not a practical strategy due to the limitations of these kinds of research budgets. A relatively simple modification to the 3D-DSD algorithm provides an estimate of the 3D-DSD and therefore, a 3D Z-R measurement using a single disdrometer. The basis of the horizontal extrapolation is mass conservation of a drop size increment, employing the mass conservation equation. For vertical extrapolation, convolution of a drop size increment using raindrop terminal velocity is used. Together, these two independent extrapolation techniques provide a complete 3DDSD estimate in a volume around and above a single disdrometer. The estimation error is lowest along a vertical plane intersecting the disdrometer position in the direction of wind advection. This work demonstrates that multiple sensors are not required for successful implementation of the 3D interpolation/extrapolation algorithm. This is a great benefit since it is seldom that multiple sensors in the required spatial arrangement are available for this type of analysis. The original software (developed at the University of Central Florida, 1998.- 2000) has also been modified to read standardized disdrometer data format (Joss-Waldvogel format). Other modifications to the software involve accounting for vertical ambient wind motion, as well as evaporation of the raindrop during its flight time.

Lane, John↗
DOE OSTI2026

Compact representation and long-time extrapolation of real-time data for quantum systems using the ESPRIT algorithm

Representing real-time data as a sum of complex exponentials provides a compact form that enables both denoising and extrapolation. As a fully data-driven method, the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm is agnostic to the underlying physical equations, making it broadly applicable to various observables and experimental or numerical setups. In this work, we consider applications of the ESPRIT algorithm primarily to extend real-time dynamical data from simulations of quantum systems. We evaluate ESPRIT's performance in the presence of noise and compare it to other extrapolation methods. We demonstrate its ability to extract information from short-time dynamics to reliably predict long-time behavior and determine the minimum time interval required for accurate results. We discuss how this insight can be leveraged in numerical methods that propagate quantum systems in time, and we show how ESPRIT can predict infinite-time values of dynamical observables, offering a purely data-driven approach to characterizing quantum phases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Mass of 101 Sn and Bayesian extrapolations to the proton drip line

The favorable energy configurations of nuclei at magic numbers of 𝑁 neutrons and 𝑍 protons are fundamental for understanding the evolution of nuclear structure. The 𝑍 = 50 (tin) isotopic chain is a frontier for such studies, with particular interest at and around the doubly magic 100 Sn isotope, for which the mass is a topic of debate. Precise mass values for neutron-deficient isotopes provide necessary anchor points for mass models to test extrapolations near the proton drip line, where experimental studies remain out of reach. In this work, we report a Penning trap mass measurement of 101 Sn . The determined mass excess of −59889.89⁢(96) keV for 101 Sn represents a factor-of-300 improvement over the current precision and indicates that 101 Sn is less bound than previously thought. Mass predictions from a recently developed Bayesian model combination framework employing statistical machine learning and nuclear masses computed within seven global models based on nuclear density functional theory agree within 1⁢𝜎 with experimental masses from the 48 ≤ 𝑍 ≤ 52 isotopic chains. The framework's resilience to new mass data gave confidence in the extrapolation of tin masses down to 𝑁 = 46. Our calculations suggest that 96 Sn is a two-proton drip line nucleus and predict a mass excess of −58090⁢(800) keV for 100 Sn , showing a preference within 1⁢𝜎 for the mass of 100 Sn derived from the 𝛽-delayed 𝑄 value measured at GSI.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Wind Turbine Sound Setbacks and Supply Curves: Ordinances and Extrapolated Trends, 110 Hub Height, 130 Rotor Diameter

This dataset provides a comprehensive set of wind turbine sound setbacks from every residential structure in the contiguous United States (CONUS). A sound setback is defined as the minimum required distance between a residential structure and a hypothetical turbine installation site to ensure that modeled sound levels received at the residence do not exceed local sound ordinances, which are commonly expressed in A-weighted decibels (dBA). Therefore, sound setbacks are a local spatial assessment combining multiple factors, including the sound pressure curve as a function of the observer location (distance and direction) relative to the turbine, local sound regulations, and the geographical distribution of residential structures. The dataset is organized into multiple scenario-based products, detailed as follows: 1. Existing and extrapolated sound setbacks. An existing scenario characterizes sound setbacks only in states or counties that have implemented sound regulations as of 2022. The extrapolated scenarios extend a constant sound threshold to counties that lack explicit sound regulations, with thresholds ranging from 35 to 60 dBA, in 5-dBA increments reflecting the variation observed in current sound ordinances. 2. Sound setbacks in directional and worst scenarios. The directional scenario accounts for the distance and orientation of residential structures relative to a hypothetical turbine location, utilizing the turbine's sound emissions in that specific direction. In contrast, the worst scenario takes loudest sound level at each distance step from the turbine, irrespective of directional considerations, which aligns with current industry practice. 3. Supply curves for Open and Reference Access scenarios. This dataset includes supply curves generated by the reV model, which integrates each of the above sound setbacks into both Open and Reference siting scenarios. In addition, two Open and Reference baselines scenarios were included which do not consider sound setbacks for comparative analysis. All sound setback data are stored in TIF files, with partial maps of the data provided in PNG format. The values in the sound setback raster range from 0 to 1, representing the fraction of developable land within a 90 meter by 90 meter pixel due to sound ordinances. A value of 0 indicates areas where wind energy development is prohibited, while a value of 1 signifies areas fully permissible. The wind turbine parameters used in the sound modeling are based on the land-based turbine from International Energy Agency (IEA), featuring a rated electrical power of 3.4 MW, a rotor diameter of 130 meters, and a hub height of 110 meters. The atmospheric conditions, including wind speed/direction, turbulence, air temperature, relative humidity, and air pressure, that drive the sound generation are obtained from the WIND Toolkit dataset.

Array↗
DOE OSTI2025

Diagenesis is key to unlocking outcrop fracture data suitable for quantitative extrapolation to geothermal targets

Exceptionally large, well-exposed sandstone outcrops in New York provide insights into folds, deformation bands, and fractures that could influence permeability, heat exchange, and stimulation outcomes of geothermal reservoir targets. Cambrian Potsdam Sandstone with <5% porosity contains decimeter-scale open, angular-limbed monoclines <0.5 km apart with associated low-porosity mm-wide cataclastic deformation bands. Crossing and abutting relationships among sub-vertical opening-mode fractures show four chronological Sets A–D, striking NNW, NE, NW, and ENE, respectively. Fracture lengths and heights range from millimeters to tens of meters. Sets A and C macro-fractures, and possibly B and D, contain quartz deposits. All sets have abundant associated quartz cemented microfractures that also record set orientations and crosscutting relations. Quartz cement deposits—evidence of diagenesis—are the key to identifying attributes of outcrop fractures suitable for extrapolation to geothermal targets in sandstones because they show which fractures formed in the subsurface. Set A fluid inclusion homogenization temperatures (120°C–129°C) are compatible with fracture at >3 km depth. Fractures are stiff and those ≥0.05 mm (Set C) and ≥0.1 mm (Set A) are open and potentially conducive to flow. Sets A and D are abundant in outcrops with close fracture spacing—0.18 m and 0.68 m, respectively—and define a rectangular connectivity network dominated by crossing and abutting X and Y nodes. Set A aperture distributions follow a power law with slope –0.8 up to 0.15 mm; other sets have lognormal distributions. Set A and D microfractures are weakly clustered, while macro-fractures commonly have 1D anticlustered (regular or periodic) arrangements at shorter length scales (<0.2 m). Sub-horizontal fractures are barren and may have formed near the surface. Fracture heights, lengths, and spatial arrangements show good trace connectivity but low open connectivity. For geothermal applications, outcrop results predict low initial well-test permeabilities owing to quartz disconnecting open fractures, but stimulation of closely spaced microfractures and partly open macro-fractures could yield high surface area for heat exchange. Quantitative extrapolation of key fracture attributes like abundance, orientation, spatial arrangement, length, and open fracture connectivity is possible from outcrops to fractured reservoirs if differing thermal histories and diagenesis are accounted for.

02 PETROLEUM↗
NASA NTRS1973

Specification of mesospheric density, pressure, and temperature by extrapolation

A procedure is presented which employs an extrapolation technique to obtain estimates of density, pressure, and temperature up to 90 km from 52 km data. The resulting errors are investigated. The procedure is combined with a special temperature interpolation method around the stratopause to produce such estimates at eight levels between 36 km and 90 km from North American sectional chart data at 5, 2, and 0.4 mb. Fifth charts were processed to obtain mean values and standard deviations at grid points for midseasonal months from 1964 to 1966. The mean values were compared with Groves' model, and internal consistency tests were performed upon the statistics. Through application of the extrapolation procedure, the atmospheric structure of a stratospheric warming event is studied.

Graves, M. E.↗
NASA NTRS1972

Precision state and filter weighting matrix extrapolation, revision 3

The matrix extrapolation routine presented is a coded algorithm for the numerical solution of modified forms of the basic differential equations which are satisfied by the geocentric state vector of a spacecraft's center of mass and by the filter-weighting matrix. The equations are described in detail and the various input and output variables designated. The capability is thus established to extrapolate any spacecraft's geocentric state vector, either backwards or forwards in time, through a force field consisting of the earth's primary central-force gravitational attraction, and a superimposed perturbing acceleration.

Robertson, W. M.↗
NASA NTRS1976

Comparison of the San Marco 3 Nace neutral composition data with the extrapolated Ogo 6 empirical model

An investigation is conducted concerning the feasibility to extrapolate the data of the Ogo 6 empirical composition model to altitudes which are lower than 450 km. Extrapolated Ogo 6 model densities are, therefore, compared with data obtained in the Neutral Atmospheric Composition Experiment (Nace) carried out during the time from April to November 1971. The results of the investigation support the conclusions of an earlier comparison of Ogo 6 and Nace data conducted by Newton et al. (1973).

Kasprzak, W. T.↗
NASA NTRS1982

Radar prediction of absolute rain fade distributions for earth-satellite paths and general methods for extrapolation of fade statistics to other locations

The first absolute rain fade distribution method described establishes absolute fade statistics at a given site by means of a sampled radar data base. The second method extrapolates absolute fade statistics from one location to another, given simultaneously measured fade and rain rate statistics at the former. Both methods employ similar conditional fade statistic concepts and long term rain rate distributions. Probability deviations in the 2-19% range, with an 11% average, were obtained upon comparison of measured and predicted levels at given attenuations. The extrapolation of fade distributions to other locations at 28 GHz showed very good agreement with measured data at three sites located in the continental temperate region.

Goldhirsh, J.↗
NASA NTRS1983

Extrapolation of optimum design based on sensitivity derivatives

In many applications, it is useful to have information regarding the effect of the perturbations of the design problem constants (parameters) on the optimum solution of the problem. Sobieszczanski-Sobieski et al. (1981) have, therefore, proposed to utilize an optimum sensitivity analysis as a structural design tool to assess the parameter perturbation effects by extrapolations based on optimum sensitivity derivatives. The present investigation is concerned with an example of optimum sensitivity analysis involving a composite panel. The case was selected in connection with the nonlinearity of the constraints and, the tendency for a set of active constraints to change when the parameters are disturbed. Under these adverse conditions, sensitivity derivatives are used in linear extrapolations to extend optimization information over a limited range of variation for a typical parameter.

Barthelemy, J.-F. M.↗
NASA NTRS1987

Extrapolation of velocity for inviscid solid boundary conditions

The present examination of an extrapolation of velocity along an arbitrary direction in the case of inviscid solid boundary conditions demonstrates the error associated with the arbitrary direction and establishes that the most appropriate procedure lies in the extrapolation of the velocity components that are tangential to the body surface. It is noted that, in a typical calculation, mesh lines generally cluster together and are therefore parallel or nearly parallel to the body surface.

Hung, Ching-Mao↗
NASA NTRS1990

Efficient Implementation of Minimal Polynomial and Reduced Rank Extrapolation Methods

The minimal polynomial extrapolation (MPE) and reduced rank extrapolation (RRE) are two effective techniques that have been used in accelerating the convergence of vector sequences, such as those that are obtained from iterative solution of linear and nonlinear systems of equation. Their definitions involve some linear least squares problems, and this causes difficulties in their numerical implementation. Timewise efficient and numerically stable implementations for MPE and RRE are developed. A computer program written in FORTRAN 77 is also appended and applied to some model problems.

Sidi, Avram↗