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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Wavefront error sensing for LDR

Wavefront sensing is a significant aspect of the LDR control problem and requires attention at an early stage of the control system definition and design. A combination of a Hartmann test for wavefront slope measurement and an interference test for piston errors of the segments was examined and is presented as a point of departure for further discussion. The assumption is made that the wavefront sensor will be used for initial alignment and periodic alignment checks but that it will not be used during scientific observations. The Hartmann test and the interferometric test are briefly examined.

Tubbs, Eldred F.↗
NASA NTRS1981

Daylight imagery of ocean surface waves for wave spectra

A simple second-order model is developed to describe the transformation between surface wave slope and radiance incident on an optical sensor. The model includes azimuth as well as elevation variations in the sky-radiance distribution and their effects on the imaging of wave slopes approaching the sensor azimuth from various directions. The model also includes upwelling radiance. Comparison between the exact transformation from wave slope to radiance and the second-order model suggests that they yield quantitatively similar results. The model is used in physical interpretations of how wave slopes are imaged and in indicating a way of optimizing the linearity and contrast of the transfer function relating wave slope to radiance for various sensor geometries, thereby minimizing sources of error. One-dimensional numerical simulations of the imaging of an analytically generated wave-slope profile demonstrate the utility of this technique in obtaining slope spectra.

Monaldo, F. M.↗
NASA NTRS1986

Crystal/liquid partitioning of REE in basaltic systems Extreme fractionation of REE in olivine

The calculation of partial coefficients for Nd, Sm, Gd, and Yb between olivine and synthetic basaltic melts using the percent level doping technique and microprobe analytical techniques is examined. The experimental and analytical procedures are described. The relationship between rare earth elements (REEs) concentrations and crystal margins caused by Rees X-rays from surrounding glass is discussed. Average olivine/liquid distribution coefficients for Nd, Sm, Gd, and Yb for mare and highlands basaltic melts are presented. The data reveal that the distribution coefficients for light REEs are lower than those obtained in previous studies, and the slope of the olivine/liquid distribution coefficient pattern is steeper; potential sources of error in the previous and present studies which could explain the differences in distribution coefficients and slope are investigated.

Mckay, G. A.↗
NASA NTRS1998

Laser pointing determination for the geoscience laser altimeter system

The Geoscience Laser Altimeter System (GLAS) is a space-based lidar being developed to monitor changes in the mass balance of the Earth's polar ice sheets (Thomas et al. 1985). GLAS is part of NASA's Earth Observing System (Schutz 1995), and is being designed to launch into a 600 km circular polar orbit in the year 2001, for continuous operation over 3 to 5 years. The orbit's 94 degree inclination has been selected to allow good coverage and profile patterns over the ice sheets of Greenland and Antarctica. The GLAS mission uses a small dedicated spacecraft provided by Ball Aerospace, which is required to have a very stable nadir and zenith pointing platform which points to within approximately 100 urad (20 arcseconds) of Nadir. Accurate knowledge of the laser beam's pointing angle (in the far field) is critical since pointing the laser beam away from nadir biases the altimetry measurements (Gardner 1992, Bufton et al. 1991). This error is a function of the distance of the laser centroid off nadir multiplied by the orbit altitude and the tangent of the slope angle of the terrain. Most of the ice sheet surface slopes are less than 1? resulting in pointing knowledge bias of only 7.6 cm with 7.3 urad accuracy, and overall single shot height accuracy of approximately 15 cm. However, over a 3 deg surface slope pointing knowledge to approximately 7.3 urad is the largest error source (23 cm) in achieving 26 cm height accuracy. The GLAS design incorporates a stellar reference system (SRS) to relate the laser beam pointing angle to the star field to an accuracy of 7.3 urad. The stellar reference system combines an attitude determination system (ADS) operating from 4 to 10 Hz coupled to a 40 Hz laser reference system (LRS) to perform this task.

Miller, Pamela S.↗
NASA NTRS1999

The Geoscience Laser Altimeter System (GLAS) for the ICESAT Mission

Accurate measurements of surface heights and atmospheric backscatter have been demonstrated with the SLA, MOLA and LITE space lidar. Recent MOLA measurements of the Mars surface have 40 cm resolution and have reduced the global uncertainty in Mars topography from a few km to approx. 10 m. GLAS is a next generation lidar being developed as part of NASA's Icesat Mission for Earth orbit . The GLAS design combines a 10 cm precision surface lidar with a sensitive dual wavelength cloud and aerosol lidar. GLAS will precisely measure the heights of the Earth's polar ice sheets, determine the height profiles of the Earth's land topography, and profile the vertical backscatter of clouds and aerosols on a global scale. GLAS will fly on a small dedicated spacecraft in a polar orbit at 598 km altitude with an inclination of 94 degrees. GLAS is scheduled to launch in summer 2001 and to operate continuously for a minimum of 3 years with a goal of 5 years. The primary mission for GLAS is to measure the seasonal and annual changes in the heights of the Greenland and Antarctic ice sheets. GLAS will measure the vertical distance to the ice sheet from orbit with 1064 nm pulses from a Nd:Yag laser at 40 Hz. Each 5 nsec wide laser pulse is used for a single range measurement. When over land GLAS will profile the heights of the topography and vegetation. The GLAS receiver uses a I m diameter telescope and a Si APD detector. The detector signal is sampled by an all digital receiver which records each surface echo waveform with I nsec resolution and a stored echo record lengths of either 200, 400, or 600 samples. Analysis of the echo waveforms within the instrument permits discrimination between cloud and surface echoes. Ground based echo analysis permits precise ranging, determining the roughness or slopes of the surface as well as the vertical distributions of vegetation illuminated by the laser, Errors in knowledge of the laser beam pointing angle can bias height measurements of sloped surfaces. For surfaces with 2 deg. slopes, knowledge of pointing angle of the beam centroid to about 8 urad is required to achieve 10 cm height accuracy. GLAS uses a stellar reference system (SRS) to determine the pointing angle of each laser firing relative to inertial space. The SRS uses a high precision star camera oriented toward local zenith whose measurements are combined with a gyroscope to determine the inertial orientation of the SRS optical bench. The far field pattern of each laser pulse is measured with a laser reference system (LRS). Optically measuring each laser far field pattern relative to the star camera and gyroscope permits the angular offsets of each laser pulse to be determined. GLAS will also determine the vertical distributions of clouds and aerosols by measuring atmospheric backscatter profiles at both 1064 and 532 nm. The 1064 nm measurements use an analog detector and profile the height and vertical structure of thicker clouds. Measurements at 532 nm use new highly sensitive photon counting detectors, and measure the height distributions of very thin clouds and aerosol layers. With averaging these can be used to determine the height of the planetary boundary layer. The instrument design and expected performance will be discussed.

Abshire, James B.↗
NASA NTRS1989

Basic properties of developed wind waves and their influence on microwave remote sensing signatures

Error trends in wind speed measurements by satellite scatterometer altimeter and microwave radiometer are shown to be correlated with the degree of wave development. These errors are analyzed theoretically by studying the rms wave slope which, directly or indirectly, affects all microwave signatures. For equilibrium sea state, the influence of spectrum parameters on the wave slope is reviewed. In well-developed seas, the dominant wavelength is shown to have no effect on the slope. Temporal-spatial rates of steep and breaking waves are derived and compared with field observations. The inner scale that determines a rapid falloff of spectral density function at high frequencies is estimated. The dependence of the spectral parameters on wind speed and sea maturity is studied using NOAA buoy observations. It is concluded that the removal of environmental error trends from satellite measurements can be best accomplished by a joint processing of microwave returns from several independent instruments.

Glazman, Roman E.↗
NASA NTRS1975

Soft X-ray spectroscopy of three extragalactic sources

Soft X-ray spectra (0.5 to 5 KeV) acquired with a rocket-borne argon-methane proportional counter are reported for M87, 3C 273, and NGC 4151. The counter sensitivity range allowed derivation of simultaneous information on the magnitude of soft X-ray absorption and the slope of the hard X-ray spectrum. Error estimation techniques for the free parameters of X-ray spectra are analyzed, and the results are applied to the spectra previously reported for these sources. It is shown that the technique used to analyze the previous spectra can drastically underestimate the magnitude of errors, and it is concluded that the proposed division of extragalactic X-ray sources into two groups according to the magnitude of absorption in their spectra is premature.

Margon, B.↗
NASA NTRS2010

Mini-TES Observations of Comanche Carbonate and Its Distribution

The discovery by the Spirit rover of outcrops rich in Mg-Fe carbonate [Morris et al., 2010] represents another manifestation of a diverse aqueous history in Gusev crater. In 2005, observations by the Moessbauer spectrometer (MB) on outcrops dubbed Comanche provided initial indication of Fe-Mg carbonate that was subsequently supported by analysis of elemental data from the Alpha Particle X-ray Spectrometer (APXS). The recognition of a carbonate component in thermal infrared spectra measured by the Miniature Thermal Emission Spectrometer (Mini-TES) was significantly delayed due to dust contamination of the instrument's optics. With the implementation of a viable dust correction, the Comanche spectra were revisited and presented clear and compelling evidence for a Mg-Fe carbonate component that could be as much as a third of the total mineral abundance. The data from all three instruments in combination are best matched by Mg-Fe carbonate with an abundance of 16-34 wt%. Mini-TES spectra were acquired for 12 targets at various locations on the Comanche (4-5 m long) and Comanche Spur (1-2 m long) outcrops, the latter being the location of the MB and APXS measurements. The two outcrops are spectrally comparable and share similar morphology and texture based on color images from the Panoramic Camera (Pancam). The highest quality Mini-TES spectrum comes from the larger Comanche outcrop on a target named Saupitty. Linear least squares modeling of the Saupitty spectrum employed a library of laboratory spectra tailored for consistency with the APXS and MB data and included spectra representing Martian dust, a slope spectrum to account for any temperature determination errors, and a blackbody spectrum to account for differences in spectral contrast between the laboratory and Mini-TES spectrum. Successful modeling of the Comanche Saupitty spectrum required one or more carbonate phases to obtain a good fit. Excluding all carbonates from the full starting library more than doubled the root-mean-squared error of the model fit (0.147% vs. 0.299%). Because Mg-Fe carbonate and Ca-Mg carbonate (dolomite) are so spectrally similar over the range used for modeling, both provide a comparable fit. However, Carich carbonates like dolomite are precluded based on APXS data and are inconsistent with MB results. The Comanche carbonate rocks are stratigraphically above a set of olivine-rich volcaniclastic rocks known as Algonquin class that mantle the Haskin Ridge feature of the Columbia Hills. Based on ~50 Mini-TES observations, the Comanche outcrops are the only rocks that host abundant carbonate. However, a target at the base of the larger Comanche outcrop appears spectrally transitional between the carbonate and olivine units. This transitional spectral character applies to additional outcrops a few 10s of meters away from Comanche that also appear stratigraphically transitional. Additional work will attempt to establish whether we are seeing an alteration horizon or depositional unit associated with the emplacement Comanche carbonate.

Ruff, Steven W.↗
NASA NTRS2015

Static Aeroelastic Modeling of a Sub-Scale Wind Tunnel Model with Novel Flap Concept

This paper examines the static aeroelastic modeling of a flexible wind tunnel model equipped with a novel control effector known as the Variable Camber Continuous Trailing Edge Flap (VCCTEF) system. The wind tunnel model is an approximately 10 percent sub-scale version of a wing designed to be equipped on a commerical transport aircraft such as the full-scale NASA Generic Transport Model (GTM). The structure of the model is made highly flexible such that a 10 percent of semi-span wing tip deflection is expected at a design lift condition, and a representation of the VCCTEF concept is incorporated on the model. Static aeroelastic modeling is conducted by using a representative single beam structural finite-element model coupled to a vortex-lattice aerodynamic model. The resulting aeroelastic model of the flexible wind tunnel model is compared against experimental wind tunnel test results from the actual model tested at the University of Washington Aeronautical Laboratory (UWAL). Comparison cases are made using reference and VICON measurements of VCCTEF flap deflections from the wind tunnel test data, and percent errors between the lift curve parameters are presented. The results show up to a maximum percent of error of <10% with regards to lift curve slope values between the aeroelastic model and the UWAL test data. The agreement of lift curve slope values from the aeroelastic model and experimental test results serves as validation for the coupled vortex-lattice finite-element static aeroelastic model.

Aeroelasticity↗
NASA NTRS2010

Scaled CMOS Technology Reliability Users Guide

The desire to assess the reliability of emerging scaled microelectronics technologies through faster reliability trials and more accurate acceleration models is the precursor for further research and experimentation in this relevant field. The effect of semiconductor scaling on microelectronics product reliability is an important aspect to the high reliability application user. From the perspective of a customer or user, who in many cases must deal with very limited, if any, manufacturer's reliability data to assess the product for a highly-reliable application, product-level testing is critical in the characterization and reliability assessment of advanced nanometer semiconductor scaling effects on microelectronics reliability. A methodology on how to accomplish this and techniques for deriving the expected product-level reliability on commercial memory products are provided.Competing mechanism theory and the multiple failure mechanism model are applied to the experimental results of scaled SDRAM products. Accelerated stress testing at multiple conditions is applied at the product level of several scaled memory products to assess the performance degradation and product reliability. Acceleration models are derived for each case. For several scaled SDRAM products, retention time degradation is studied and two distinct soft error populations are observed with each technology generation: early breakdown, characterized by randomly distributed weak bits with Weibull slope (beta)=1, and a main population breakdown with an increasing failure rate. Retention time soft error rates are calculated and a multiple failure mechanism acceleration model with parameters is derived for each technology. Defect densities are calculated and reflect a decreasing trend in the percentage of random defective bits for each successive product generation. A normalized soft error failure rate of the memory data retention time in FIT/Gb and FIT/cm2 for several scaled SDRAM generations is presented revealing a power relationship. General models describing the soft error rates across scaled product generations are presented. The analysis methodology may be applied to other scaled microelectronic products and their key parameters.

Microelectronics Reliability↗
NASA NTRS2023

Shape from spectra

We introduce a new unified atmospheric–topographic correction approach that estimates surface geometry directly from the radiance measurement. Surface topography influences the at-sensor radiance measurement, making precise topography modeling critical in applications like vegetation or snow studies in mountainous terrain. Currently, elevation maps are used to derive topographic variables such as the slope and sky-view factor. This process is error-prone since static global digital elevation models do not generally achieve the accuracy required, and even minor mismatches in spatial resolution can introduce significant artifacts in downstream processing. Here we demonstrate that it is possible to estimate topographic parameters directly from spectral data, ensuring perfect physical consistency, temporal coincidence, and spatial alignment. We present experiments estimating topographic slope in two scenes in Southern California, with data from NASA’s Next Generation Airborne Visible/Near Infrared Imaging Spectrometer (AVIRIS-NG). We compared our radiance-based estimates against high-resolution lidar datasets. Our initial validation result showed a correlation of R 2 = 0.864 (n = 160) over the homogeneous surface of Beckman Auditorium’s cone-shaped roof on the Caltech campus in Pasadena, California. We then validate the model over a larger study site near Santa Clarita, California, finding R 2 = 0.923 (n = 40,000) in a 350 x 350m area. The accuracy of our model estimates, combined with its systematic advantages over the alternative, show the potential of the approach for use in both airborne campaigns and orbital missions.

Nimrod Carmon↗
NASA NTRS2022

Above-Aircraft Cirrus Cloud and Aerosol Optical Depth From Hyperspectral Irradiances Measured By a Total-Diffuse Radiometer

This study develops the use of spectral total and diffuse irradiance measurements, made from a prototype hyperspectral total-diffuse sunshine pyranometer (SPN-S), to retrieve layer fine-mode aerosol (τ aer ) and total optical depths from airborne platforms. Additionally, we use spectral analysis in an attempt to partition the total optical depth into its τ aer and cirrus cloud optical depth (τ cld ) components in the absence of coarse-mode aerosols. Two retrieval methods are developed: one leveraging information in the diffuse irradiance and the other using spectral characteristics of the transmitted direct beam, with each approach best suited for specific cloud and aerosol conditions. The SPN-S has advantages over traditional sun photometer systems, including no moving parts and a low cost. However, a significant drawback of the instrument is that it is unable to measure the direct-beam irradiance as accurately as sun photometers. To compensate for the greater measurement uncertainty in the radiometric irradiances, these retrieval techniques employ ratioed inputs or spectral information to reduce output uncertainty. This analysis uses irradiance measurements from the SPN-S and the solar spectral flux radiometer (SSFR) aboard the National Aeronautics and Space Administration’s (NASA) P-3 aircraft during the 2018 deployment of the ObseRvations of Aerosols above CLouds and their intEractionS (ORACLES) campaign and the 2019 Cloud, Aerosol and Monsoon Processes Philippines Experiment (CAMP 2 Ex) mission to quantify above-aircraft cirrus τ cld and derive vertical profiles of layer τ aer . Validation of the τ aer retrieval is accomplished by comparison with co-located measurements of direct solar irradiance made by the Sky-Scanning Sun-Tracking Atmospheric Research (4STAR) and in situ measurements of aerosol optical depth. For the aggregated 2018 ORACLES results, regression between the SPN-S-based method and sun photometer τ aer values yields a slope of 0.96 with an R 2 of 0.96, while the root mean square error (RMSE) is 3.0 x 10 -2 . When comparing the retrieved τ aer to profiles of integrated in situ measurements of optical extinction, the slope, R 2 , and RMSE values for ORACLES are 0.90, 0.96, and 3.4 x 10 -2 , and for CAMP 2 Ex they are 0.94, 0.97, and 3.4 x 10 -2 , respectively. This paper is a demonstration of methods for deriving cloud and aerosol optical properties in environments where both atmospheric constituents may be present. With improvements to the low-cost SPN-S radiometer instrument, it may be possible to extend these methods to a broader set of sampling applications, such as ground-based settings.

spectral instrument (SPN-S)↗
NASA NTRS1974

Estimation of structural parameters from dynamic test data

Parameters for a lumped linear model approximating a distributed elastic structure are determined from dynamic test data comprised of several mode shapes and frequencies. Measurement errors, nonlinear response, and nonmeasurable quantities such as mode slope components are accommodated. Some mass and stiffness parameters may be known accurately, whereas the remainder are to be estimated. The method entails minimizing a quadratic function of the difference between corresponding modes and frequencies of the theoretical model and the test specimen. This technique was applied to some actual vibration test data, and the special techniques that are required to overcome convergence problems are described.

Hall, B. M.↗
NASA NTRS2016

Mapping the Gas Turbulence in the Coma Cluster: Predictions for Astro-H

Astro-H will be able for the first time to map gas velocities and detect turbulence in galaxy clusters. One of the best targets for turbulence studies is the Coma cluster, due to its proximity, absence of a cool core, and lack of a central active galactic nucleus. To determine what constraints Astro-H will be able to place on the Coma velocity field, we construct simulated maps of the projected gas velocity and compute the second-order structure function, an analog of the velocity power spectrum. We vary the injection scale, dissipation scale, slope, and normalization of the turbulent power spectrum, and apply measurement errors and finite sampling to the velocity field. We find that even with sparse coverage of the cluster, Astro-H will be able to measure the Mach number and the injection scale of the turbulent power spectrum-the quantities determining the energy flux down the turbulent cascade and the diffusion rate for everything that is advected by the gas (metals, cosmic rays, etc.). Astro-H will not be sensitive to the dissipation scale or the slope of the power spectrum in its inertial range, unless they are outside physically motivated intervals. We give the expected confidence intervals for the injection scale and the normalization of the power spectrum for a number of possible pointing configurations, combining the structure function and velocity dispersion data. Importantly, we also determine that measurement errors on the line shift will bias the velocity structure function upward, and show how to correct this bias.

clusters: intracluster medium↗
NASA NTRS2004

Planetary Transmission Diagnostics

This report presents a methodology for detecting and diagnosing gear faults in the planetary stage of a helicopter transmission. This diagnostic technique is based on the constrained adaptive lifting algorithm. The lifting scheme, developed by Wim Sweldens of Bell Labs, is a time domain, prediction-error realization of the wavelet transform that allows for greater flexibility in the construction of wavelet bases. Classic lifting analyzes a given signal using wavelets derived from a single fundamental basis function. A number of researchers have proposed techniques for adding adaptivity to the lifting scheme, allowing the transform to choose from a set of fundamental bases the basis that best fits the signal. This characteristic is desirable for gear diagnostics as it allows the technique to tailor itself to a specific transmission by selecting a set of wavelets that best represent vibration signals obtained while the gearbox is operating under healthy-state conditions. However, constraints on certain basis characteristics are necessary to enhance the detection of local wave-form changes caused by certain types of gear damage. The proposed methodology analyzes individual tooth-mesh waveforms from a healthy-state gearbox vibration signal that was generated using the vibration separation (synchronous signal-averaging) algorithm. Each waveform is separated into analysis domains using zeros of its slope and curvature. The bases selected in each analysis domain are chosen to minimize the prediction error, and constrained to have the same-sign local slope and curvature as the original signal. The resulting set of bases is used to analyze future-state vibration signals and the lifting prediction error is inspected. The constraints allow the transform to effectively adapt to global amplitude changes, yielding small prediction errors. However, local wave-form changes associated with certain types of gear damage are poorly adapted, causing a significant change in the prediction error. The constrained adaptive lifting diagnostic algorithm is validated using data collected from the University of Maryland Transmission Test Rig and the results are discussed.

Lewicki, David G.↗
NASA NTRS1971

Sun compass error model

An error model is described for the Apollo 15 sun compass, a contingency navigational device. Field test data are presented along with significant results of the test. The errors reported include a random error resulting from tilt in leveling the sun compass, a random error because of observer sighting inaccuracies, a bias error because of mean tilt in compass leveling, a bias error in the sun compass itself, and a bias error because the device is leveled to the local terrain slope.

Blucker, T. J.↗
NASA NTRS1993

Geostatistical evaluation of satellite radar altimetry for high-resolution mapping of Lambert Glacier, Antarctica

The potential of satellite radar altimetry for high-resolution mapping of Antarctic ice streams is evaluated, using retracked and slope-corrected data from the Lambert Glacier and Amery Ice Shelf area, East Antarctica, acquired by Geosat during the Exact Repeat Mission (ERM), 1986-89. The map area includes lower Lambert Glacier north of 72.18 deg S, the southern Amery Ice Shelf, and the grounded inland ice sheet on both sides. The Geosat ERM altimetry is found to provide substantially more complete coverage than the 1978 Seasat altimetry, due to improved tracking. Variogram methods are used to estimate the noise levels in the data as a function of position throughout the map area. The spatial structure in the data is quantified by constructing experimental variograms using altimetry from the area of the grounding zone of Lambert Glacier, which is the area chiefly of interest in this topographically complex region. Kriging is employed to invert the along-track height measurements onto a fine-scale 3 km grid. The unsmoothed along-track Geosat ERM altimetry yields spatially continuous maps showing the main topographic features of lower Lambert Glacier, upper Amery Ice Shelf and the adjacent inland ice sheet. The probable position of the grounding line of Lambert Glacier is identified from a break in slope at the grounded ice/floating ice transition. The approximate standard error of the kriged map is inferred from the data noise levels.

Herzfeld, Ute C.↗
NASA NTRS1989

Long range geoid control through the European GPS traverse: Final results

The European north-south Global Positioning System (GPS)-traverse proposed by IAG SSG 3.88, should control and improve the European geoid. This traverse follows first order leveling lines, included in the United European Leveling Network. From May to August 1986 and in July 1987, the central and northern part of this traverse (approx. 3000 km) was observed using up to four TI 4100 receivers, covering Austria, Federal Republic of Germany, Denmark, Sweden and Norway. Both traverse parts contain 71 stations with distances of about 50 km. In addition, 8 stations have been occupied for overlapping connections, and traverse links were established for connecting the fundamental stations Wettzell (VLBI and SLR) and Onsala (VLBI). Final results show a GPS observation precision of a few cm for loops of some 100 km circumference. After transformation of the GPS results to geoid heights using the leveled heights, comparisons with different existing gravimetric geoid determinations including geopotential models were performed. In addition, new geopotential models complete to degree and order 360 tailored to gravity data in Europe, and gravimetric geoid solutions using 6 x 10' mean gravity anomalies were investigated. The comparison with GPS and leveling yields rms discrepancies of + or - 0.1...0.2 m over 1000 km traverse sections for the best solutions, but a strong slope is existing in Sweden and southern Norway in almost all solutions, which is probably caused by systematic errors in the available gravity data for Scandinavia. This is confirmed by a new geoid computation at the Danish Geodetic Institute where the slope has disappeared. If this new solution is taken for the northern traverse section and the best solution for the central part, the rms discrepancy reduces to approximately + or - 0.2 m over 3000 km. Thus, a + or - 10 (exp 7) relative height accuracy seems to be achievable over long distances with the GPS/leveling and the gravimetric geoid calculation techniques, applied in this experiment.

Torge, W.↗