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NASA NTRS1988

Recent advances in electronic structure theory and their influence on the accuracy of ab initio potential energy surfaces

Recent advances in electronic structure theory and the availability of high speed vector processors have substantially increased the accuracy of ab initio potential energy surfaces. The recently developed atomic natural orbital approach for basis set contraction has reduced both the basis set incompleteness and superposition errors in molecular calculations. Furthermore, full CI calculations can often be used to calibrate a CASSCF/MRCI approach that quantitatively accounts for the valence correlation energy. These computational advances also provide a vehicle for systematically improving the calculations and for estimating the residual error in the calculations. Calculations on selected diatomic and triatomic systems will be used to illustrate the accuracy that currently can be achieved for molecular systems. In particular, the F+H2 yields HF+H potential energy hypersurface is used to illustrate the impact of these computational advances on the calculation of potential energy surfaces.

Bauschlicher, Charles W., Jr.↗

NASA NTRS1989

Recent advances in electronic structure theory and their influence on the accuracy of ab initio potential energy surfaces

Recent advances in electronic structure theory and the availability of high speed vector processors have substantially increased the accuracy of ab initio potential energy surfaces. The recently developed atomic natural orbital approach for basis set contraction has reduced both the basis set incompleteness and superposition errors in molecular calculations. Furthermore, full CI calculations can often be used to calibrate a CASSCF/MRCI approach that quantitatively accounts for the valence correlation energy. These computational advances also provide a vehicle for systematically improving the calculations and for estimating the residual error in the calculations. Calculations on selected diatomic and triatomic systems will be used to illustrate the accuracy that currently can be achieved for molecular systems. In particular, the F + H2 yields HF + H potential energy hypersurface is used to illustrate the impact of these computational advances on the calculation of potential energy surfaces.

Bauschlicher, Charles W., Jr.↗

NASA NTRS2015

An Upper Bound on Orbital Debris Collision Probability When Only One Object has Position Uncertainty Information

Upper bounds on high speed satellite collision probability, P (sub c), have been investigated. Previous methods assume an individual position error covariance matrix is available for each object. The two matrices being combined into a single, relative position error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum P (sub c). If error covariance information for only one of the two objects was available, either some default shape has been used or nothing could be done. An alternative is presented that uses the known covariance information along with a critical value of the missing covariance to obtain an approximate but useful P (sub c) upper bound. There are various avenues along which an upper bound on the high speed satellite collision probability has been pursued. Typically, for the collision plane representation of the high speed collision probability problem, the predicted miss position in the collision plane is assumed fixed. Then the shape (aspect ratio of ellipse), the size (scaling of standard deviations) or the orientation (rotation of ellipse principal axes) of the combined position error ellipse is varied to obtain a maximum P (sub c). Regardless as to the exact details of the approach, previously presented methods all assume that an individual position error covariance matrix is available for each object and the two are combined into a single, relative position error covariance matrix. This combined position error covariance matrix is then modified according to the chosen scheme to arrive at a maximum P (sub c). But what if error covariance information for one of the two objects is not available? When error covariance information for one of the objects is not available the analyst has commonly defaulted to the situation in which only the relative miss position and velocity are known without any corresponding state error covariance information. The various usual methods of finding a maximum P (sub c) do no good because the analyst defaults to no knowledge of the combined, relative position error covariance matrix. It is reasonable to think, given an assumption of no covariance information, an analyst might still attempt to determine the error covariance matrix that results in an upper bound on the P (sub c). Without some guidance on limits to the shape, size and orientation of the unknown covariance matrix, the limiting case is a degenerate ellipse lying along the relative miss vector in the collision plane. Unless the miss position is exceptionally large or the at-risk object is exceptionally small, this method results in a maximum P (sub c) too large to be of practical use. For example, assuming that the miss distance is equal to the current ISS alert volume along-track (+ or -) distance of 25 kilometers and that the at-risk area has a 70 meter radius. The maximum (degenerate ellipse) P (sub c) is about 0.00136. At 40 kilometers, the maximum P (sub c) would be 0.00085 which is still almost an order of magnitude larger than the ISS maneuver threshold of 0.0001. In fact, a miss distance of almost 340 kilometers is necessary to reduce the maximum P (sub c) associated with this degenerate ellipse to the ISS maneuver threshold value. Such a result is frequently of no practical value to the analyst. Some improvement may be made with respect to this problem by realizing that while the position error covariance matrix of one of the objects (usually the debris object) may not be known the position error covariance matrix of the other object (usually the asset) is almost always available. Making use of the position error covariance information for the one object provides an improvement in finding a maximum P (sub c) which, in some cases, may offer real utility. The equations to be used are presented and their use discussed.

Frisbee, Joseph H., Jr.↗

NASA NTRS1981

Comparison of PASCAL and FORTRAN for solving problems in the physical sciences

The paper compares PASCAL and FORTRAN for problem solving in the physical sciences, due to requests NASA has received to make PASCAL available on the Numerical Aerodynamic Simulator (scheduled to be operational in 1986). PASCAL disadvantages include the lack of scientific utility procedures equivalent to the IBM scientific subroutine package or the IMSL package which are available in FORTRAN. Advantages include a well-organized, easy to read and maintain writing code, range checking to prevent errors, and a broad selection of data types. It is concluded that FORTRAN may be the better language, although ADA (patterned after PASCAL) may surpass FORTRAN due to its ability to add complex and vector math, and the specify the precision and range of variables.

Watson, V. R.↗

NASA NTRS1993

Determination of the stability and control derivatives of the NASA F/A-18 HARV using flight data

This report documents the research conducted for the NASA-Ames Cooperative Agreement No. NCC 2-759 with West Virginia University. A complete set of the stability and control derivatives for varying angles of attack from 10 deg to 60 deg were estimated from flight data of the NASA F/A-18 HARV. The data were analyzed with the use of the pEst software which implements the output-error method of parameter estimation. Discussions of the aircraft equations of motion, parameter estimation process, design of flight test maneuvers, and formulation of the mathematical model are presented. The added effects of the thrust vectoring and single surface excitation systems are also addressed. The results of the longitudinal and lateral directional derivative estimates at varying angles of attack are presented and compared to results from previous analyses. The results indicate a significant improvement due to the independent control surface deflections induced by the single surface excitation system, and at the same time, a need for additional flight data especially at higher angles of attack.

Napolitano, Marcello R.↗

NASA NTRS2012

Locating the LCROSS Impact Craters

The Lunar CRater Observations and Sensing Satellite (LCROSS) mission impacted a spent Centaur rocket stage into a permanently shadowed region near the lunar south pole. The Sheperding Spacecraft (SSC) separated approx. 9 hours before impact and performed a small braking maneuver in order to observe the Centaur impact plume, looking for evidence of water and other volatiles, before impacting itself. This paper describes the registration of imagery of the LCROSS impact region from the mid- and near-infrared cameras onboard the SSC, as well as from the Goldstone radar. We compare the Centaur impact features, positively identified in the first two, and with a consistent feature in the third, which are interpreted as a 20 m diameter crater surrounded by a 160 m diameter ejecta region. The images are registered to Lunar Reconnaisance Orbiter (LRO) topographical data which allows determination of the impact location. This location is compared with the impact location derived from ground-based tracking and propagation of the spacecraft's trajectory and with locations derived from two hybrid imagery/trajectory methods. The four methods give a weighted average Centaur impact location of −84.6796 deg, −48.7093 deg, with a 1σ uncertainty of 115 m along latitude, and 44 m along longitude, just 146 m from the target impact site. Meanwhile, the trajectory-derived SSC impact location is −84.719 deg, −49.61 deg, with a 1 alpha uncertainty of 3 m along the Earth vector and 75 m orthogonal to that, 766 m from the target location and 2.803 km south-west of the Centaur impact. We also detail the Centaur impact angle and SSC instrument pointing errors. Six high-level LCROSS mission requirements are shown to be met by wide margins. We hope that these results facilitate further analyses of the LCROSS experiment data and follow-up observations of the impact region

LCROSS↗

NASA NTRS2011

Effect of Thin Cirrus Clouds on Dust Optical Depth Retrievals From MODIS Observations

The effect of thin cirrus clouds in retrieving the dust optical depth from MODIS observations is investigated by using a simplified aerosol retrieval algorithm based on the principles of the Deep Blue aerosol property retrieval method. Specifically, the errors of the retrieved dust optical depth due to thin cirrus contamination are quantified through the comparison of two retrievals by assuming dust-only atmospheres and the counterparts with overlapping mineral dust and thin cirrus clouds. To account for the effect of the polarization state of radiation field on radiance simulation, a vector radiative transfer model is used to generate the lookup tables. In the forward radiative transfer simulations involved in generating the lookup tables, the Rayleigh scattering by atmospheric gaseous molecules and the reflection of the surface assumed to be Lambertian are fully taken into account. Additionally, the spheroid model is utilized to account for the nonsphericity of dust particles In computing their optical properties. For simplicity, the single-scattering albedo, scattering phase matrix, and optical depth are specified a priori for thin cirrus clouds assumed to consist of droxtal ice crystals. The present results indicate that the errors in the retrieved dust optical depths due to the contamination of thin cirrus clouds depend on the scattering angle, underlying surface reflectance, and dust optical depth. Under heavy dusty conditions, the absolute errors are comparable to the predescribed optical depths of thin cirrus clouds.

Feng, Qian↗

NASA NTRS2018

Wave-Front Error Measurements and Alignment of CLASP2 Telescope with a Dual-Band Pass Cold Mirror Coated Primary Mirror

"Chromospheric LAyer Spectro-Polarimeter (CLASP2)" is the next sounding rocket experiment of the "Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP)" that succeeded in observing for the first time the linear polarization spectra in the hydrogen Lyman- line (121.6 nm) and is scheduled to be launched in 2019. In CLASP2, we will carry out full Stokes-vector spectropolarimetric observations in the Mg II h & k lines near 280 nm with the spectro-polarimeter (SP), while imaging observations in the Lyman- line will be conducted with the slitjaw optics (SJ). For the wavelength selection of CLASP2, the primary mirror of the telescope uses a new dual-band pass cold mirror coating targeting both at 121.6 nm and 280 nm. Therefore, we have to perform again the alignment of the telescope after the installation of the recoated primary mirror. Before unmounting the primary mirror from the telescope structure, we measured the wave-front error (WFE) of the telescope. The measured WFE map was consistent with what we had before the CLASP flight, clearly indicating that the telescope alignment has been maintained even after the flight. After the re-coated primary mirror was installed the WFE was measured, and coma aberration was found to be larger. Finally, the secondary mirror shim adjustments were carried out based on the WFE measurements. In CLASP2 telescope, we improved a fitting method of WFE map (applying 8th terms circular Zernike polynomial tting instead of 37th terms circular Zernike fitting) and the improved method enables to achieve better performance than CLASP telescope. Indeed, WFE map obtained after the final shim adjustment indicated that the required specification (< 5:5 m RMS spot radius) that is more stringent than CLASP telescope was met.

chromosphere; polarimetry; sounding rocket↗

NASA NTRS1982

Misregistration's effects on classification and proportion estimation accuracy

The estimates of crop type and acreage are undertaken in the AgRISTARS program by registering multiple date acquisitions of small subareas of LANDSAT scenes (termed segments), and applying multispectral analysis to them. An important contribution to errors in classification and acreage estimates is misregistration between multiple acquisitions. The formula used to express this relationship is given and the operations applied are so shown in diagrams. The taking of a LANDSAT feature vector and the derivation of the brightness and greeness are illustrated. It is shown that for any given sensor IFOV geometry, typical populations of fields can be derived and histograms can be plotted of the number of fields against field size according to ground truth. As a function of the resolution element, the IFOV of the sensor can draw the proportion of pure pixels in a given crop. Because the thematic mapper has a smaller resolution, the proportion of pixels that are pure in any given area will be larger.

Juday, R. D.↗

NASA NTRS1985

An analysis of cross-coupling of a multicomponent jet engine test stand using finite element modeling techniques

A two axis thrust measuring system was analyzed by using a finite a element computer program to determine the sensitivities of the thrust vectoring nozzle system to misalignment of the load cells and applied loads, and the stiffness of the structural members. Three models were evaluated: (1) the basic measuring element and its internal calibration load cells; (2) the basic measuring element and its external load calibration equipment; and (3) the basic measuring element, external calibration load frame and the altitude facility support structure. Alignment of calibration loads was the greatest source of error for multiaxis thrust measuring systems. Uniform increases or decreases in stiffness of the members, which might be caused by the selection of the materials, have little effect on the accuracy of the measurements. It is found that the POLO-FINITE program is a viable tool for designing and analyzing multiaxis thrust measurement systems. The response of the test stand to step inputs that might be encountered with thrust vectoring tests was determined. The dynamic analysis show a potential problem for measuring the dynamic response characteristics of thrust vectoring systems because of the inherently light damping of the test stand.

Schweikhard, W. G.↗

NASA NTRS1989

A geometric comparison of video camera-captured raster data to vector-parented raster data generated by the X-Y digitizing table

The relative accuracy of a georeferenced raster data set captured by the Megavision 1024XM system using the Videk Megaplus CCD cameras is compared to a georeferenced raster data set generated from vector lines manually digitized through the ELAS software package on a Summagraphics X-Y digitizer table. The study also investigates the amount of time necessary to fully complete the rasterization of the two data sets, evaluating individual areas such as time necessary to generate raw data, time necessary to edit raw data, time necessary to georeference raw data, and accuracy of georeferencing against a norm. Preliminary results exhibit a high level of agreement between areas of the vector-parented data and areas of the captured file data where sufficient control points were chosen. Maps of 1:20,000 scale were digitized into raster files of 5 meter resolution per pixel and overall error in RMS was estimated at less than eight meters. Such approaches offer time and labor-saving advantages as well as increasing the efficiency of project scheduling and enabling the digitization of new types of data.

Swalm, C.↗

NASA NTRS2017

Testing the Accuracy of Data-Driven MHD Simulations of Active Region Evolution

Models for the evolution of the solar coronal magnetic field are vital for understanding solar activity, yet the best measurements of the magnetic field lie at the photosphere, necessitating the development of coronal models which are "data-driven" at the photosphere. We present an investigation to determine the feasibility and accuracy of such methods. Our validation framework uses a simulation of active region (AR) formation, modeling the emergence of magnetic flux from the convection zone to the corona, as a ground-truth data set, to supply both the photospheric information and to perform the validation of the data-driven method. We focus our investigation on how the accuracy of the data-driven model depends on the temporal frequency of the driving data. The Helioseismic and Magnetic Imager on NASA's Solar Dynamics Observatory produces full-disk vector magnetic field measurements at a 12-minute cadence. Using our framework we show that ARs that emerge over 25 hours can be modeled by the data-driving method with only approximately 1 percent error in the free magnetic energy, assuming the photospheric information is specified every 12 minutes. However, for rapidly evolving features, under-sampling of the dynamics at this cadence leads to a strobe effect, generating large electric currents and incorrect coronal morphology and energies. We derive a sampling condition for the driving cadence based on the evolution of these small-scale features, and show that higher-cadence driving can lead to acceptable errors. Future work will investigate the source of errors associated with deriving plasma variables from the photospheric magnetograms as well as other sources of errors, such as reduced resolution, instrument bias, and noise.

Leake, James E.↗

NASA NTRS2023

Robustness of Observing System Simulation Experiments

Observing System Simulation Experiments (OSSEs) are used to investigate the potential performance of proposed new instruments on numerical weather prediction (NWP). As OSSEs involve a framework in which the atmosphere and observations are all completely simulated, it is necessary to perform validation of the OSSE to ensure that it is sufficiently realistic to provide useful experimental results. A common issue that affects the forecast skill and observation impacts is the tendency of OSSEs to have insufficient model error compared to NWP in the real world. In this work, two versions of the National Aeronautics and Space Administration Global Modeling and Assimilation Office (NASA/GMAO) NWP OSSE framework are compared, with the newer framework having more simulated forecast model error than the older framework due to changes to the NWP system. The performance of the updated OSSE is validated against corresponding behavior of the same NWP system in the real world in terms of the simulated observations, the analysis increments, forecast error, and observation impacts. OSSE results of analysis and forecast impacts for three proposed new observation systems are also compared between the older and newer frameworks to evaluate the robustness of the OSSE experiments and the role of model error in observation impacts. These three new instruments are the Geostationary eXtended Observations (GeoXO) hyperspectral infrared sounder (GXS), the Midwave Infrared Sounding of Temperature and humidity in a Constellation for Winds (MISTiC Winds) atmospheric motion vectors, and additional Global Navigation Satellite System Radio Occultations (GNSS-RO).

Observing System Simulation Experiments↗

NASA NTRS1972

A Monte Carlo error analysis program for near-Mars, finite-burn, orbital transfer maneuvers

A computer program was developed which performs an error analysis of a minimum-fuel, finite-thrust, transfer maneuver between two Keplerian orbits in the vicinity of Mars. The method of analysis is the Monte Carlo approach where each off-nominal initial orbit is targeted to the desired final orbit. The errors in the initial orbit are described by two covariance matrices of state deviations and tracking errors. The function of the program is to relate these errors to the resulting errors in the final orbit. The equations of motion for the transfer trajectory are those of a spacecraft maneuvering with constant thrust and mass-flow rate in the neighborhood of a single body. The thrust vector is allowed to rotate in a plane with a constant pitch rate. The transfer trajectory is characterized by six control parameters and the final orbit is defined, or partially defined, by the desired target parameters. The program is applicable to the deboost maneuver (hyperbola to ellipse), orbital trim maneuver (ellipse to ellipse), fly-by maneuver (hyperbola to hyperbola), escape maneuvers (ellipse to hyperbola), and deorbit maneuver.

Green, R. N.↗

NASA NTRS1973

Classical eighth- and lower-order Runge-Kutta-Nystroem formulas with a new stepsize control procedure for special second-order differential equations

New Runge-Kutta-Nystrom formulas of the eighth, seventh, sixth, and fifth order are derived for the special second-order (vector) differential equation x = f (t,x). In contrast to Runge-Kutta-Nystrom formulas of an earlier NASA report, these formulas provide a stepsize control procedure based on the leading term of the local truncation error in x. This new procedure is more accurate than the earlier Runge-Kutta-Nystrom procedure (with stepsize control based on the leading term of the local truncation error in x) when integrating close to singularities. Two central orbits are presented as examples. For these orbits, the accuracy and speed of the formulas of this report are compared with those of Runge-Kutta-Nystrom and Runge-Kutta formulas of earlier NASA reports.

Fehlberg, E.↗

NASA NTRS1975

Interpolation in numerical optimization

The present work discusses the generation of the cubic-spline interpolator in numerical optimization methods which use a variable-step integrator with step size control based on local relative truncation error. An algorithm for generating the cubic spline with successive over-relaxation is presented which represents an improvement over that given by Ralston and Wilf (1967). Rewriting the code reduces the number of N-vectors from eight to one. The algorithm is formulated in such a way that the solution of the linear system set up yields the first derivatives at the nodal points. This method is as accurate as other schemes but requires the minimum amount of storage.

Hall, K. R.↗

NASA NTRS1993

Development of a large field-of-view KD potassium di-deuterium phosphate modulator: Center Director's Discretionary Fund

Magnetographs, which measure polarized light, allow solar astronomers to infer the magnetic field intensity on the Sun. The Marshall Space Flight Center (MSFC) Vector Magnetograph is such an imaging instrument. The instrument requires rapid modulation between polarization states to minimize seeing effects. The accuracy of those polarization measurements is dependent on stable modulators with small field-of-view errors. Although these devices are very important in ground-based telescopes, extending the field of view of electro-optical crystals such as KD*Ps (potassium di-deuterium phosphate) could encourage the development of these devices for other imaging applications. The work that was done at MSFC as part of the Center Director's Discretionary Fund (CDDF) to reduce the field-of-view errors of instruments that use KD*P modulators in their polarimeters is described.

West, E. A.↗

NASA NTRS1993

Flight-path estimation in passive low-altitude flight by visual cues

A series of experiments was conducted, in which subjects had to estimate the flight path while passively being flown in straight or in curved motion over several types of nominally flat, textured terrain. Three computer-generated terrain types were investigated: (1) a random 'pole' field, (2) a flat field consisting of random rectangular patches, and (3) a field of random parallelepipeds. Experimental parameters were the velocity-to-height (V/h) ratio, the viewing distance, and the terrain type. Furthermore, the effect of obscuring parts of the visual field was investigated. Assumptions were made about the basic visual-field information by analyzing the pattern of line-of-sight (LOS) rate vectors in the visual field. The experimental results support these assumptions and show that, for both a straight as well as a curved flight path, the estimation accuracy and estimation times improve with the V/h ratio. Error scores for the curved flight path are found to be about 3 deg in visual angle higher than for the straight flight path, and the sensitivity to the V/h ratio is found to be considerably larger. For the straight motion, the flight path could be estimated successfully from local areas in the far field. Curved flight-path estimates have to rely on the entire LOS rate pattern.

Grunwald, Arthur J.↗