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NASA NTRS1995

Efficient implementation of weighted ENO schemes

In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially non-oscillatory) finite difference schemes of Liu, Osher and Chan. It was shown by Liu et al. that WENO schemes constructed from the r-th order (in L1 norm) ENO schemes are (r+1)-th order accurate. We propose a new way of measuring the smoothness of a numerical solution, emulating the idea of minimizing the total variation of the approximation, which results in a 5-th order WENO scheme for the case r = 3, instead of the 4-th order with the original smoothness measurement by Liu et al. This 5-th order WENO scheme is as fast as the 4-th order WENO scheme of Liu et al., and both schemes are about twice as fast as the 4-th order ENO schemes on vector supercomputers and as fast on serial and parallel computers. For Euler systems of gas dynamics, we suggest computing the weights from pressure and entropy instead of the characteristic values to simplify the costly characteristic procedure. The resulting WENO schemes are about twice as fast as the WENO schemes using the characteristic decompositions to compute weights, and work well for problems which do not contain strong shocks or strong reflected waves. We also prove that, for conservation laws with smooth solutions, all WENO schemes are convergent. Many numerical tests, including the 1D steady state nozzle flow problem and 2D shock entropy wave interaction problem, are presented to demonstrate the remarkable capability of the WENO schemes, especially the WENO scheme using the new smoothness measurement, in resolving complicated shock and flow structures. We have also applied Yang's artificial compression method to the WENO schemes to sharpen contact discontinuities.

Jiang, Guang-Shan↗
NASA NTRS1997

Using High-Order Methods on Lower-Order Geometries

The desire to obtain acoustic information from the numerical solution of a nonlinear system of equations is a demanding proposition for a computational algorithm. High-order accuracy is required for the propagation of high-frequency, low-amplitude waves. The accuracy of an algorithm can be compromised by low-order errors that naturally occur in the solution of a particular problem. Such errors arise from two sources: the presence of discontinuities in the flow field or because the geometry on which the problem is defined is not everywhere smooth to the order of the scheme. The performance of high-order accurate essentially non-oscillatory (ENO) schemes on piecewise smooth solutions is well documented. Herein, the performance of these methods on smooth solutions defined on piecewise smooth geometries is investigated. The propagation of sound in a quasi-one-dimensional nozzle is considered as a test case. Some of the issues involved in the extension to two spatial dimensions are discussed.

Casper, Jay↗
NASA NTRS1961

Flight Tests of a 1/6-Scale Model of the Hawker P 1127 Jet VTOL Airplane

An experimental investigation has been made to determine the dynamic stability and control characteristics of a 1/6-scale flying model of the Hawker P lIP7 jet vertical-take-off-and-landing (VTOL) airplane in hovering and transition flight. The model was powered by a counter-rotating ducted fan driven by compressed-air jets at the tips of the fan blades. In hovering flight the model was controlled by jet-reaction controls which consisted of yaw and pitch jets at the extremities of the fuselage and a roll jet on each wing tip. In forward flight the model was controlled by conventional ailerons and rudder and an all-movable horizontal tail. In hovering flight the model could be flown smoothly and easily, but the roll control was considered too weak for rapid maneuvering or hovering in gusty air. Transitions from hovering to normal forward flight and back to hovering could be made smoothly and consistently and with only moderate changes in longitudinal trim. The model had a static longitudinal instability or pitch-up tendency throughout the transition range, but the rate of divergence in the pitch-up was moderate and the model could be controlled easily provided the angle of attack was not allowed to become too high. In both the transition and normal forward flight conditions the lateral motions of the model were difficult to control at high angles of attack, apparently because of low directional stability at small angles of sideslip. The longitudinal stability of the model in normal forward flight was generally satisfactory, but there was a decided pitch-up tendency for the flap-down condition at high angles of attack. In the VTOL landing approach condition, with the jets directed straight down or slightly forward, the nose-down pitch trim required was greater than in the transitions from hovering to forward flight, but the longitudinal instability was about the same. Take-offs and landings in still air could be made smoothly although there was a slight unfavorable ground effect on lift and a nose-down change in pitch trim near the ground. Short take-offs and landings could be made smoothly and consistently although the model experienced a decided nose-up change in pitching moment as it climbed out of ground effect.

Smith, Charles C., Jr.↗
NASA NTRS2003

HEASARC Software Archive

(1) Chandra Archive: SAO has maintained the interfaces through which HEASARC gains access to the Chandra Data Archive. At HEASARC's request, we have implemented an anonymous ftp copy of a major part of the public archive and we keep that archive up-to- date. SAO has participated in the ADEC interoperability working group, establishing guidelines or interoperability standards and prototyping such interfaces. We have provided an NVO-based prototype interface, intending to serve the HEASARC-led NVO demo project. HEASARC's Astrobrowse interface was maintained and updated. In addition, we have participated in design discussions surrounding HEASARC's Caldb project. We have attended the HEASARC Users Group meeting and presented CDA status and developments. (2) Chandra CALDB: SA0 has maintained and expanded the Chandra CALDB by including four new data file types, defining the corresponding CALDB keyword/identification structures. We have provided CALDB upgrades for the public (CIAO) and for Standard Data Processing. Approximately 40 new files have been added to the CALDB in these version releases. There have been in the past year ten of these CALDB upgrades, each with unique index configurations. In addition, with the inputs from software, archive, and calibration scientists, as well as CIAO/SDP software developers, we have defined a generalized expansion of the existing CALDB interface and indexing structure. The purpose of this is to make the CALDB more generally applicable and useful in new and future missions that will be supported archivally by HEASARC. The generalized interface will identify additional configurational keywords and permit more extensive calibration parameter and boundary condition specifications for unique file selection. HEASARC scientists and developers from SAO and GSFC have become involved in this work, which is expected to produce a new interface for general use within the current year. (3) DS9: One of the decisions that came from last year's HEADCC meeting was to make the ds9 image display program the primary vehicle for displaying line graphics (as well as images). The first step required to make this possible was to enhance the line graphics capabilities of ds9. SAO therefore spent considerable effort upgrading ds9 to use Tcl 8.4 so that the BLT line graphics package could be built and imported into ds9 from source code, rather than from a pre-built (and generally outdated) shared library. This task, which is nearly complete, allows us to extend BLT as needed for the HEAD community. Following HEADCC discussion concerning archiving and the display of archived data, we extended ds9 to support full access to many astronomical Web-based archives sites, including HEASARC, MAST, CHANDRA, SKYVIEW, ADS, NED, SIMBAD, IRAS, NVRO, SAO TDC, and FIRST. Using ds9's new internal Web access capabilities, these archives can be accessed via their Web page. FITS images, plots, spectra, and journal abstracts can be referenced, down-loaded, and displayed directly and easily in ds9. For more information, see: http://hea-www.harvard.edu/saord/ds9. Also after the HEADCC discussion concerning region filtering, we extended the Funtools sample implementation of region filtering as described in: http://hea-www.harvard.edu/saord/funtools/regions.html. In particular, we added several new composite regions for event and image filtering, including elliptical and box annuli. We also extended the panda (Pie AND Annulus) region support to include box pandas and elliptical pandas. These new composite regions are especially useful in programs that need to count photons in each separate region using only a single pass through the data. Support for these new regions was added to ds9. In the same vein, we developed new region support for filtering images using simple FITS image masks, i.e. 8-bit or 16-bit FITS images where the value of a pixel is the region id number for that pixel. Other important enhancements to DS9 this year, include supporor multiple world coordinate systems, three dimensional event file binning, image smoothing, region groups and tags, the ability to save images in a number of image formats (such as JPEG, TIFF, PNG, FITS), improvements in support for integrating external analysis tools, and support for the virtual observatory. In particular, a full-featured web browser has been implemented within D S 9 . This provides support for full access to HEASARC archive sites such as SKYVIEW and W3BROWSE, in addition to other astronomical archives sites such as MAST, CHANDRA, ADS, NED, SIMBAD, IRAS, NVRO, SA0 TDC, and FIRST. From within DS9, the archives can be searched, and FITS images, plots, spectra, and journal abstracts can be referenced, downloaded and displayed The web browser provides the basis for the built-in help facility. All DS9 documentation, including the reference manual, FAQ, Know Features, and contact information is now available to the user without the need for external display applications. New versions of DS9 maybe downloaded and installed using this facility. Two important features used in the analysis of high energy astronomical data have been implemented in the past year. The first is support for binning photon event data in three dimensions. By binning the third dimension in time or energy, users are easily able to detect variable x-ray sources and identify other physical properties of their data. Second, a number of fast smoothing algorithms have been implemented in DS9, which allow users to smooth their data in real time. Algorithms for boxcar, tophat, and gaussian smoothing are supported.

White, Nicholas↗
NASA NTRS2008

A Statistical Filtering Approach for Gravity Recovery and Climate Experiment (GRACE) Gravity Data

We describe and analyze a statistical filtering approach for GRACE data that uses a parametrized model for the temporal evolution of the GRACE coefficients. After least-squares adjustment, a statistical test is performed to assess the significance of the estimated parameters. If the test is passed, the parameters are used by the filter in the reconstruction of the field; otherwise they are rejected. The test is performed, and the filter is formed, separately for annual components of the model and the trend. This new approach is distinct from Gaussian smoothing since it uses the data themselves to test for specific components of the time-varying gravity field. The statistical filter appears inherently to remove most of the "stripes" present in the GRACE fields, although destriping the fields prior to filtering seems to help the trend recovery. We demonstrate that the statistical filter produces reasonable maps for the annual components and trend. We furthermore assess the statistical filter for the annual components using ground-based GPS data in South America by assuming that the annual component of the gravity signal is associated only with groundwater storage. The un-destriped, statistically filtered field has a X2 value relative to the GPS data consistent with the best result from smoothing. In the space domain, the statistical filters are qualitatively similar to Gaussian smoothing. Unlike Gaussian smoothing, however, the statistical filter has significant sidelobes, including large negative sidelobes on the north-south axis, potentially revealing information on the errors, and the correlations among the errors, for the GRACE coefficients.

Davis. J. L.↗
NASA NTRS2008

Geologic Mapping of the V-36 Thetis Regio Quadrangle: 2008 Progress Report

As a result of mapping, eleven material stratigraphic units and three structural units have been identified and mapped. The material units include (from older to younger): tessera terrain material (tt), material of densely fractured plains (pdf), material of fractured and ridged plains (pfr), material of shield plains (psh), material of plains with wrinkle ridges (pwr), material of smooth plains of intermediate brightness (psi), material of radardark smooth plains (psd), material of lineated plains (pli) material of lobate plains (plo), material of craters having no radar-dark haloes (c1), and material of craters having clear dark haloes (c2). The morphologies and probably the nature of the material units in the study area are generally similar to those observed in other regions of Venus [2]. The youngest units are lobate plains (plo) which here typically look less lobate than in other areas of the planet. Close to them in age are smooth plains which are indeed smooth and represented by two varieties mentioned above. Lineated plains (pli) are densely fractured in a geometrically regular way. Plains with wrinkle ridges, being morphologically similar to those observed in other regions, here occupy unusually small areas. Shield (psh) plains here are also not abundant. Locally they show wrinkle ridging. Fractured and ridged plains (pfr), which form in other regions, the so called ridge belts, are observed as isolated areas of clusters of ridged plains surrounded by other units. Densely fractured plains (pdf) are present in relatively small areas in association with coronae and corona-like features. Tessera terrain (tt) is dissected by structures oriented in two or more directions. Structures are so densely packed that the morphology (and thus nature) of the precursor terrain is not known. Structural units include tessera transitional terrain (ttt), fracture belts (fb) and rifted terrain (rt). Tessera transitional terrain was first identified and mapped by [4] as areas of fractured and ridged plains (pfr) and densely fractured plains (pdf) deformed by transverse faults that made it formally resemble tessera terrain (tt). The obvious difference between units tt and ttt is the recognizable morphology of precursor terrain of unit ttt. Fracture belts are probably ancient rift zones [3]. Rifted terrain (rt), as in other regions of Venus, is so saturated with faults that according to the recommendation of [1, 5] it should be mapped as a structural unit.

Basilevsky, A. T.↗
NASA NTRS2009

Laser Ablation Increases PEM/Catalyst Interfacial Area

An investigational method of improving the performance of a fuel cell that contains a polymer-electrolyte membrane (PEM) is based on the concept of roughening the surface of the PEM, prior to deposition of a thin layer of catalyst, in order to increase the PEM/catalyst interfacial area and thereby increase the degree of utilization of the catalyst. The roughening is done by means of laser ablation under carefully controlled conditions. Next, the roughened membrane surface is coated with the thin layer of catalyst (which is typically platinum), then sandwiched between two electrode/catalyst structures to form a membrane/ele c t - rode assembly. The feasibility of the roughening technique was demonstrated in experiments in which proton-conducting membranes made of a perfluorosulfonic acid-based hydrophilic, protonconducting polymer were ablated by use of femtosecond laser pulses. It was found that when proper combinations of the pulse intensity, pulse-repetition rate, and number of repetitions was chosen, the initially flat, smooth membrane surfaces became roughened to such an extent as to be converted to networks of nodules interconnected by filaments (see Figure 1). In further experiments, electrochemical impedance spectroscopy (EIS) was performed on a pristine (smooth) membrane and on two laser-roughened membranes after the membranes were coated with platinum on both sides. Some preliminary EIS data were interpreted as showing that notwithstanding the potential for laser-induced damage, the bulk conductivities of the membranes were not diminished in the roughening process. Other preliminary EIS data (see Figure 2) were interpreted as signifying that the surface areas of the laser-roughened membranes were significantly greater than those of the smooth membrane. Moreover, elemental analyses showed that the sulfur-containing molecular groups necessary for proton conduction remained intact, even near the laser-roughened surfaces. These preliminary results can be taken as indications that laser-roughened PEMs should function well in fuel cells and, in particular, should exhibit current and power densities greater than those attainable by use of smooth membranes.

Whitacre, Jay↗
NASA NTRS2004

Inlet Housing for a Partial-Admission Turbine

An inlet housing for a partial-admission turbine has been designed to cause the inlet airflow to make a smooth transition from an open circular inlet to an inlet slot. The smooth flow is required for purposes of measuring inlet flow characteristics and maximizing the efficiency of the turbine. A partial-admission turbine is a turbine in which the inlet slot occupies less than a complete circle around the rotor axis. In this case, the inlet slot occupies a 90 arc. The present special inlet-housing design is needed because the "bull nose" shape of a conventional turbine inlet housing fails to provide the required smooth transition in a partial-admission configuration and thereby gives rise to a loss of turbine efficiency and inaccuracies in inlet flow measurements. Upon entering the inlet housing through the circular opening, the flow encounters a "tongue"-shaped passageway, which serves as a ramp that diverts the flow to the first of two straight passages. This first passageway occupies a 90 arc and has a length equal to two passage heights. Instrumentation rakes for measuring the characteristics of the inlet flow are installed in this passageway. Just past the first straight passageway is the second one, which is narrower and leads to the 90 turbine inlet slot. This passageway is used to smooth the flow immediately prior to its passage through the turbine inlet slot. The length of this second passageway equals the length of the chord of a turbine vane. The inlet housing incorporates small ports for measuring static pressures at various locations of the flow, and incorporates bosses for the installation of the instrumentation rakes. The inlet housing also includes a flange at its inlet end for attachment to a circular inlet duct and a flange at its outlet end for attachment to the outer casing of the turbine.

Moye, Ralph↗
NASA NTRS2013

The Face that Launched a Thousand Slips

Helene, (approximately 17.6 kilometers mean radius) is an L4 Trojan co-orbital of Saturn's moon Dione. Its hemisphere features an unusual morphology consisting of broad depressions and a generally smooth surface patterned with streaks and grooves. The streaks appear to be oriented down-gradient, as are the grooves. This pattern suggests intensive mass-wasting as a dominant process on the leading hemisphere. Kilometer-scale impact craters are very sparse on the leading hemisphere other than the degraded kilometer-scale basins defining the overall satellite shape, and many small craters have a diffuse appearance suggesting ongoing mass wasting. Thus mass wasting must dominate surface-modifying processes at present. In fact, the mass wasting appears to have been sufficient in magnitude to narrow the divides between adjacent basins to narrow septa, similar, but in lower relief, to the honeycomb pattern of Hyperion. The prominent groves occur primarily near topographic divides and appear have cut into a broad, slightly lower albedo surface largely conforming to the present topography but elevated a few meters above the smooth surfaces undergoing mass wasting flow. Low ridges and albedo markings on the surface suggest surface flow of materials traveling up to several kilometers. Diffusive mass wasting produces smooth surfaces - such a pattern characterizes most of the low-lying surfaces. The grooves, however, imply that the transport process is advective at those locations where they occur, that is, erosion tends to concentrate along linear pathways separated by divides. In fact, in many places grooves have a fairly regular spacing of 125-160 meters, defining a characteristic erosional scale. Several questions are prompted by the unusual morphology of Helene: 1) What is the nature of the surface materials? 2) Are the transport processes gradual or catastrophic motion from one or a few events? 3) What mechanisms drive mass wasting and groove development? 4) Have the formative processes been active in the recent past? 5) Finally, is the surface accreting or eroding? The smooth character of the leading edge hemisphere of Helene and the dominance of mass wasting suggest that the surface is composed of fine-grained debris, probably dominated by dust-size to small gravel particles. The Lagrangian points of saturnian satellites are locations where planetesimals might have accreted to form co-orbital satellites such as and they may capture ejecta from their master moon. Published models suggest that Helene is a site of net accretion, but we find no extant explanation for the dominance of fine grain sizes for the surface (and probable subsurface) composition of Helene and the other Lagrangian satellites. Observation of the mass wasting tracks on Helene suggests the presence of well-defined streams of debris with low bordering levees that may be depositional features or remnants of the dissected higher surface. Some flows in grazing illumination appear to have a convex cross-section. This mass-flow morphology might be consistent with the occurrence of large-scale flow events, but which might have occurred through rapid emplacement or slow glacier-like creep. On the other hand, small craters appear to have been "softened" by creep-like processes, indicating ongoing mass wasting.

honeycomb pattern of Hyperion↗
NASA NTRS2016

Validation of High-Resolution CFD Method for Slosh Damping Extraction of Baffled Tanks

Determination of slosh damping is a very challenging task as there is no analytical solution. The damping physics involve the vorticity dissipation which requires the full solution of the nonlinear Navier-Stokes equations. As a result, previous investigations and knowledge were mainly carried out by extensive experimental studies. A Volume-Of-Fluid (VOF) based CFD program developed at NASA MSFC was applied to extract slosh damping in a baffled tank from the first principle. First, experimental data using water with subscale smooth wall tank were used as the baseline validation. CFD simulation was demonstrated to be capable of accurately predicting natural frequency and very low damping value from the smooth wall tank at different fill levels. The damping due to a ring baffle at different liquid fill levels from barrel section and into the upper dome was then investigated to understand the slosh damping physics due to the presence of a ring baffle. Based on this study, the Root-Mean-Square error of our CFD simulation in estimating slosh damping was less than 4.8%, and the maximum error was less than 8.5%. Scalability of subscale baffled tank test using water was investigated using the validated CFD tool, and it was found that unlike the smooth wall case, slosh damping with baffle is almost independent of the working fluid and it is reasonable to apply water test data to the full scale LOX tank when the damping from baffle is dominant. On the other hand, for the smooth wall, the damping value must be scaled according to the Reynolds number. Comparison of experimental data, CFD, with the classical and modified Miles equations for upper dome was made, and the limitations of these semi-empirical equations were identified.

Yang, H. Q.↗
NASA NTRS1972

Computer programs for plotting curves with various dashed-line sequences

Two FORTRAN-callable subprograms have been written to draw a smooth curve through a set of input points as a solid line or as a general sequence of long and short dashes. Subroutine LINSEQ draws conventional curves whereas subroutine CONSEQ draws smooth closed curves (contours). The subprograms are based on an approximate calculation of the arc length along the curve and spline interpolation along the arc length. Options are provided for smoothing of the input data and for offsetting the plotted curve from the input data points. The method of calculation of the arc length and the generation of the line sequence are described.Usage descriptions of the main subprograms, sample calling programs illustrating the various features of the subprograms, and sample plots are given. The subroutines should be readily adaptable to almost any computer-driven incremental plotter.

Desmarais, R. N.↗
NASA NTRS1972

Ultimate wind sensing capabilities of the jimsphere and other rising balloon systems

The error in the magnitude of the horizontal wind field as computed for balloons with linear and quadratic rise rates ascending through a light, moderate, or severe wind field is derived. The rise rate function of the Jimsphere is analyzed as a special case. Figures are presented of wind error versus altitude for each rise rate and wind field, assuming linear smoothing. The ultimate capability of rising balloon systems for measuring wind from the surface to 18 kilometers can be determined from the data and the wind accuracy can be computed by knowing only the rise rate behavior versus altitude. The radii of smooth and roughened spheres needed to achieve the desired rise rate at various altitudes are derived. The radii for smooth and roughened balloons for tow-meter-per-second to 20-meter-per-second rise rates at 10 and 14 km altitudes, and the wind-following capability for each are tabulated.

Luers, J. K.↗
NASA NTRS1973

A flight simulator for advanced aircraft - Servo design to realization.

Discussion of computer-aided design results obtained for a moving-base, three-man flight simulator. From a control viewpoint, the structure is discussed in terms of disturbance torques, damping ratios, natural frequencies, load acceleration, and smoothness. The use of inertia to achieve well-behaved structural transfer functions and smooth or high fidelity load accelerations is demonstrated. Transfer functions in the complex frequency domain, as well as time-dependent solutions to the system, are derived. The relative merits of using position and/or velocity as primary feedback, for a limited travel acceleration device, are discussed. Root locus plots, which were utilized in the control-system design, Bode plots, and time-dependent plots are drawn. In addition, the theoretical ratio of velocity to commanded input Bode plot is compared to the experimental results, and the dramatic effect on the load smoothness plot caused by selecting velocity over position as primary feedback is shown.

King, R. F.↗
NASA NTRS1975

Two-dimensional convolute integers for optical image data processing and surface fitting

An approach toward low-pass, high-pass and band-pass filtering is presented. Convolution coefficients possessing the filtering speed associated with a moving smoothing average without suffering a loss of resolution are discussed. Resolution was retained because the coefficients represented the equivalance of applying high order two-dimensional regression calculations to an image without considering the time-consuming summations associated with the usual normal equations. The smoothing (low-pass) and roughing (high-pass) aspects of the filters are a result of being derived from regression theory. The coefficients are universal integer valves completely described by filter size and surface order, and possess a number of symmetry properties. Double convolution lead to a single set of coefficients with an expanded mask which can yield band-pass filtering and the surface normal. For low order surfaces (0,1), the two-dimensional convolute integers were equivalent to a moving smoothing average.

Edwards, T. R.↗
NASA NTRS1974

Optimization of self-acting herringbone journal bearings for maximum stability

The stability of herringbone grooved journal bearings was increased by optimizing the groove depth, width, length, and angle. Optimization was performed on the basis of a small-eccentricity infinite-groove analysis in combination with a previously developed Newton-Raphson procedure for bearings with the smooth member rotating or with the grooved member rotating at low compressibility numbers. A newly-developed vector technique for bearings with the grooved member rotating at high compressibility numbers also was used in the analysis. The design curves obtained are suitable for choosing the optimum bearing for a wide range of operating conditions (compressibility numbers from 0 to 80, length to diameter ratios from 1/4 to 2, and smooth or grooved member rotating). Compared to bearings optimized for maximum load, bearings optimized for maximum stability are shown to provide a drastic increase in bearing-supported mass. Bearings with grooved member rotating are substantially more stable than bearing with smooth member rotating, particularly at high compressibility numbers.

Fleming, D. P.↗
NASA NTRS1975

The treatment of bias in the square-root information filter/smoother

The Dyer-McReynolds square-root information filter (SRIF) is rederived, using recursive least-square arguments. The result is applied to a system composed partly of biases. The filter sensitivity matrix, computed covariance, and consider covariance for this augmented system are reviewed. A new computationally attractive representation for the smoothed estimates, in terms of a smoothed sensitivity matrix and a smoothed computed covariance is presented.

Bierman, G. J.↗
NASA NTRS1976

Additional evidence of Mercurian volcanism

Evidence concerned with (1) the character and distribution of terrain surrounding fresh basins; (2) albedo, color, and temporal differences between a basin rim and smooth plains on its floor; and (3) the stratigraphic relations and local distribution of smooth plains in the hilly and lineated terrain are cited as additional evidence for an internal origin of much of the Mercurian smooth plains. Although the question of Mercurian volcanism should be kept open, this evidence together with that presented in an earlier paper suggests that volcanism occurred on Mercury early in its history.

Trask, N. J.↗
NASA NTRS1978

Experimental determination of the navigation error of the 4-D navigation, guidance, and control systems on the NASA B-737 airplane

Navigation error data from these flights are presented in a format utilizing three independent axes - horizontal, vertical, and time. The navigation position estimate error term and the autopilot flight technical error term are combined to form the total navigation error in each axis. This method of error presentation allows comparisons to be made between other 2-, 3-, or 4-D navigation systems and allows experimental or theoretical determination of the navigation error terms. Position estimate error data are presented with the navigation system position estimate based on dual DME radio updates that are smoothed with inertial velocities, dual DME radio updates that are smoothed with true airspeed and magnetic heading, and inertial velocity updates only. The normal mode of navigation with dual DME updates that are smoothed with inertial velocities resulted in a mean error of 390 m with a standard deviation of 150 m in the horizontal axis; a mean error of 1.5 m low with a standard deviation of less than 11 m in the vertical axis; and a mean error as low as 252 m with a standard deviation of 123 m in the time axis.

Knox, C. E.↗