Drag Error Research Articles

A variable fidelity approach for predicting aerodynamic wall quantities of hypersonic vehicles using the ConvNeXt encoder-decoder framework

Computational fluid dynamics (CFD) simulations for obtaining three-dimensional hypersonic vehicle aerodynamic characteristics are resource-intensive. Deep learning offers a promising alternative for predicting aerodynamic wall quantities but typically requires a large dataset, which conflicts with the intention to reduce CFD costs. To address this, we propose a novel prediction model leveraging variable fidelity data to alleviate computational demands. The model utilizes an encoder-decoder architecture with ConvNeXt blocks as operators, processing variable fidelity data as inputs and outputs. We also developed a U-Net with residual blocks (ResUNet) for performance comparison. Transformation and topology patching techniques were applied to tackle the challenges posed by large grid volumes and complex topologies in three-dimensional vehicles. Results demonstrate that the ConvNeXt Encoder-Decoder predicts peak regions more accurately than ResUNet and aligns closely with CFD in low-value areas. The ConvNeXt Encoder-Decoder maintains maximum heat flux errors below 1 % and viscous drag errors below 3.81 % across varying angles of attack. It exhibits superior fitting performance with minimal deviation from CFD compared to ResUNet. Prediction accuracy decreases under multiple inflow changes compared to the angle of attack variations alone. Heat flux predictions show high consistency with CFD, with relative errors below 6.38 %, whereas friction predictions exhibit higher errors with 10.28 % maximum error and 0.28 % minimum error. The model accurately predicts friction variation trends in peak regions at the blunt edge's central plane but performs poorly in low-value areas. In summary, the ConvNeXt Encoder-Decoder accurately predicts the wall quantities under varying multiple inflow conditions.

Some effects of domain size and boundary conditions on the accuracy of airfoil simulations

This paper investigates a specific case of one of the most popular fluid dynamic simulations, the incompressible flow around an airfoil (NACA 0012 here) at a high Reynolds number (6×106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$6 \ imes 10^6$$\\end{document}). OpenFOAM software was used to study the effect of domain size and four common choices of boundary conditions on airfoil lift, drag, surface friction, and pressure. We also examine the relation between boundary conditions and the velocity, pressure, and vorticity distributions throughout the domain. In addition to the common boundary conditions, we implement the “point vortex” boundary condition that was introduced many years ago but is now rarely used. We also applied the point vortex condition for the outlet pressure instead of using the traditional Neumann condition. With the airfoil generating significant lift at incidence angles of 5∘,10∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$5^\\circ , 10^\\circ$$\\end{document}, and 14∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$14^\\circ$$\\end{document}, we confirm a previous finding that the boundary conditions combine with domain size to produce an induced (pressure) drag. The change in the pressure drag with domain size is significant for the commonly-used boundary conditions but is much smaller for the point vortex alternative. The point vortex boundary condition increases the execution time, but this is more than offset by the reduction in domain size needed to achieve a specified accuracy in the lift and drag. This study also estimates the error in total drag and lift due to domain size and shows it can be almost eliminated using the point vortex boundary condition. We also used the impulse form of the momentum equations to study the relation between drag and lift and spurious vorticity, which is generated as a result of using non-exact boundary conditions. These equations reveal that the spurious vorticity throughout the domain is associated with cancelling circulation around the domain boundaries.

A method for quantifying the resistances of light and heavy-duty vehicles under in-use conditions

Tyre rolling resistance and air drag significantly affect road-vehicle fuel and energy consumption. Their importance is recognised in vehicle certification regulations and standards worldwide. Detailed methodologies for their determination exist that require testing in dedicated proving grounds or specialised test facilities outside of actual driving conditions. As countries strive to improve vehicle efficiency, in-use verification of vehicle resistances will become essential for research and vehicle homologation. Multiple factors may limit such activities such as cost, lack of dedicated test infrastructure and equipment, and incompatibility with other vehicle-related tests that already take place. This study proposes a new method for determining vehicle resistances during on-road measurements based on wheel torque data. The method allows less expensive, more versatile test procedures that could be applied to a wide sample of vehicles across the fleet. The method was evaluated experimentally with nine vehicles (3 light-duty, 6 heavy-duty). Repeatability tests showed that the air drag error standard deviation ranged from 1 to 5.5 % for light-duties, and the pooled error standard deviation was 5.8 % among all heavy-duty vehicles. The results showed a divergence from the target cycle energy demand of <5 % during the on-road tests, a limit indicating the highest expected test discrepancy due to test uncertainties. Vehicle fuel consumption was simulated with both the measured and official resistance coefficients as a secondary validation. The on-road calculated coefficients led to accurate estimates of real-world consumption. The study discusses the impact of the wind vector during the test on the air drag and resistances’ influence on consumption.

Dimensionality reduction for regularization of sparse data-driven RANS simulations

Data assimilation can reduce the model-form errors of RANS simulations. A spatially distributed corrective parameter field can be introduced into the closure model, whose optimal values can be efficiently found by an adjoint method and gradient-based optimization. When assimilating experimental data, which in most cases are sparsely distributed or based on a low-resolution grid, the inverse problem is highly underdetermined and thus ambiguous. Therefore, to reduce the ambiguity, regularization is required. Established regularization approaches such as total variation and Sobolev gradient methods can produce smooth and physically meaningful velocity fields in many cases. However, if the measurements are located close to walls, spiky and unphysical wall shear stress profiles can occur. A new regularization strategy based on a piecewise linear approximation of the corrective field is proposed. This method is shown to lead to a very accurate free stream velocity field and smooth wall shear stress profiles. The resulting skin friction drag error for the case of flow over periodic hills was around 1.38% which is seven times lower than the error obtained with the Sobolev gradient and two orders of magnitude lower than that obtained with the other two methods.

On Improved Understanding of Airfoil Performance Evaluation Methods at Low Reynolds Numbers

Airfoil performance for the Eppler 387 airfoil at low Reynolds number ( to 460,000) is studied numerically and compared to existing experimental data. Two- and three-dimensional unsteady laminar Navier–Stokes simulations are performed to evaluate the large-scale dynamics of the flow. All cases show laminar separation of the boundary layer followed by the shedding of large coherent vortices resulting in reattachment only observed in the mean flow, referred to as bubble flapping. Integrated aerodynamic coefficients, pressure distributions, and separation–reattachment locations are presented and compared to experimental data. Absolute averaged section lift and drag errors in the range to 300,000 are 5 and 7%, respectively, and good agreement of the pressure distributions is obtained. Laminar separation locations are predicted within 2%-chord, and turbulent reattachment is on average predicted within 5%-chord of the experimental values, which is improved to 3%-chord when updated experimental data are used. The work illustrates that bubble flapping, and the resulting mean airfoil performance, can be analyzed using laminar unsteady Navier–Stokes simulations, and that it does not necessitate external disturbances or three-dimensional instabilities. The shear layer transition over airfoils is found to be dominated by two-dimensional vortex shedding resulting in unsteady reattachment.

Influence of atmospheric density and area-to-mass errors on orbit prediction accuracy

Abstract Due to the fact that the space is becoming increasingly congested, there is a high requirement for the orbit prediction accuracy of space targets to support collision warning tasks. This is especially true for space debris with high area-to-mass ratio and low orbit altitude. This paper focuses on the along-track position error caused by the atmospheric density error and area-to-mass ratio error for targets with near-circular orbit in the orbit prediction. We derive a semi-analytical expression to describe the along-track position error, and the expression’s validity is evaluated by a goodness-of-fit index compared with the simulated “true” along-track position error. The simulation is based on Encke’s special perturbation method, in which the drag error is treated as a perturbation. The drag error is modeled by the difference between the JB2008 and MISIS density model and the sinusoidal oscillation error model concerning the inexact area-to-mass ratio. Furthermore, targets with various orbit altitudes ranging from 300km to 800km are selected to investigate whether the along-track position error can meet the collision warning requirements.

Comparing Multi-Element Airfoil Flow Solutions Using Multiple Solvers with Output-Based Adapted Meshes

In this work, Reynolds-averaged Navier–Stokes (RANS) solutions for a multi-element airfoil computed with Massachusetts Institute of Technology Solution Adaptive Numerical Simulator (SANS), United States Department of Defense High Performance Computing Modernization Program CREATETM-AV Kestrel component Conservative Field Finite Elements (COFFE), and SU2 using output-based adapted meshes are compared with RANS solutions computed using manually generated meshes adhering to “best practices.” The adapted meshes are generated using the process implemented in SANS, which seeks to find a mesh that minimizes the error estimate of a given output functional. The manually generated meshes are the result of a systematic study of the influence of a range of meshing parameters on solution accuracy. Using the adapted meshes generally leads to a reduction of more than one order of magnitude in lift and drag error relative to the manually generated meshes of a comparable node count for all of the computational fluid dynamics solvers. Alternatively, the node counts of the adapted meshes are more than an order of magnitude smaller than the manually generated meshes for a given lift and drag error level. The improved accuracy in lift and drag computed with the adapted meshes can partially be attributed increased resolution around the stagnation points and trailing edges of the airfoil elements relative to the manually generated meshes. Notably, the adapted meshes provide accurate results despite having values generally significantly larger than one.

Drag computation for incompressible flows with a Nitsche’s type stabilization method

We study the drag error for the Navier–Stokes equations approximated by conforming low-order finite elements. The numerical scheme uses a SUPG stabilization and a new Nitche’s type stabilization on the whole boundary. We introduce a definition of the discrete drag which contains additional terms resulting from the discrete formulat. We prove O(h2) convergence for the drag error and illustrate the theoretical results by numerical tests. The extension to other finite element methods is also discussed.

Behavior of numerical error in pore-scale lattice Boltzmann simulations with simple bounce-back rule: Analysis and highly accurate extrapolation

We perform the viscosity-independent Stokes flow simulations in regular sphere packings using the two-relaxation-times (TRT) lattice Boltzmann method (LBM) with the simple bounce-back (BB) rule. Our special discretization procedure reduces the scatter in integral quantities, such as drag force, and quantifies the solution convergence error. We assume transition to linear (−1) convergence rate for different sets of TRT parameters and use this assumption to provide a simple extrapolation scheme. After establishing the accurate reference values of drag for a wide range of porosities, 0.26–0.78, we show a ten-fold decrease in the drag error using the suggested extrapolations. This error decrease allows the simple LBM/BB scheme to reach an accuracy of the high-order interpolated boundary schemes. The suggested extrapolation approach is straightforward to apply in porous media, whose pore space can be discretized at several resolutions.

Contribution of uncertainty in estimation of active drag using assisted towing method in front crawl swimming

ABSTRACTActive drag force in swimming can be calculated from a function of five different variables: swim velocity, tow velocity, belt force, power output and exponent of velocity. The accuracy of the drag force value is dependent on the accuracy of each variable, and on the contribution of each variable to drag estimation. To calculate uncertainty in drag value, first the derivatives of the active drag equation with respect to each variable were obtained. Second, these were multiplied by the uncertainty of that variable. Twelve national age and open level swimmers were recruited to complete four free swimming and five active drag trials. The uncertainties for the free and the tow swim velocities, and for the belt force, contributed approximately 5–6% and 2–3% error, respectively, in calculation of drag. The result of the uncertainty of the velocity exponent (1.8–2.6) indicated a contribution of about 6% error in active drag. The contribution of unequal power output showed that if a power changed 7.5% between conditions, it would lead to about 30% error in calculated drag. Consequently, if a swimmer did not maintain constant power output between conditions, there would be substantial errors in the calculation of active drag.

Entropy-Based Drag-Error Estimation and Mesh Adaptation in Two Dimensions

This paper presents a method for estimating the drag error in two-dimensional computational fluid dynamics simulations using a method that does not require auxiliary adjoint solutions. The error of interest is that caused by the numerical discretization, including effects of finite mesh size and approximation order. The target output is a drag calculation based on a farfield integration of the entropy. The error estimate is motivated by an interpretation of entropy variables as adjoint solutions to an entropy balance output. As entropy variables are obtained by a direct transformation of the state, no separate adjoint solution is required. The method is shown to be applicable not only to inviscid and laminar flows, but also to turbulent Reynolds-averaged Navier-Stokes flows, for which entropy variables generally lose their symmetrization property. Since the proposed drag error estimate is based on an integral of a weighted residual over the computational domain, it can be localized to provide an adaptive indicator over each element. Adaptive results for several flows of aerodynamic interest show that the error estimate is effective and that the method performs on par with adjoint-based methods. ∗Assistant Professor, AIAA Senior Member †Graduate Research Assistant ‡Professor, AIAA Fellow

Thermospheric density model biases at the 23rd sunspot maximum

Uncertainties in the neutral density estimation are the major source of aerodynamic drag errors and one of the main limiting factors in the accuracy of the orbit prediction and determination process at low altitudes. Massive efforts have been made over the years to constantly improve the existing operational density models, or to create even more precise and sophisticated tools. Special attention has also been paid to research more appropriate solar and geomagnetic indices. However, the operational models still suffer from weakness. Even if a number of studies have been carried out in the last few years to define the performance improvements, further critical assessments are necessary to evaluate and compare the models at different altitudes and solar activity conditions.Taking advantage of the results of a previous study, an investigation of thermospheric density model biases during the last sunspot maximum (October 1999—December 2002) was carried out by analyzing the semi-major axis decay of four satellites: Cosmos 2265, Cosmos 2332, SNOE and Clementine. Six thermospheric density models, widely used in spacecraft operations, were analyzed: JR-71, MSISE-90, NRLMSISE-00, GOST-2004, JB2006 and JB2008. During the time span considered, for each satellite and atmospheric density model, a fitted drag coefficient was solved for and then compared with the calculated physical drag coefficient. It was therefore possible to derive the average density biases of the thermospheric models during the maximum of the 23rd solar cycle.Below 500km, all the models overestimated the average atmospheric density by amounts varying between +7% and +20%. This was an inevitable consequence of constructing thermospheric models from density data obtained by assuming a fixed drag coefficient, independent of altitude. Because the uncertainty affecting the drag coefficient measurements was about 3% at both 200km and 480km of altitude, the calculated air density biases below 500km were statistically significant. The minimum average biases were obtained with JB2008, NRLMSISE-00 and GOST-2004.Above 500km, where only one satellite was analyzed (at 630km), and errors tend to increase with altitude, it cannot be asserted that the calculated biases are significant. Nevertheless, they are presented to show how the various models diverge at higher altitudes. Around 630km, NRLMSISE-00 had a negligible average bias, while the other models underestimated (GOST-2004) or overestimated the average density, by amounts varying between 6% and 16%. However, in terms of semi-major axis root mean square residuals, JB2006 and JB2008 were the best in any case.Below 500km, the short-term behavior of the models was also investigated by fitting the semi-major axis decay over 30-day arcs. The resulting fitted drag coefficients displayed a significant variability, probably associated with mismodeled density variations, but JB2008, followed by JB2006, provided the smallest semi-major axis residuals and a reduced short-term variability of the density bias at just a few frequencies, having been probably successful in removing a significant fraction of the mismodeling sources.

Drag Coefficient Estimation in Orbit Determination

Drag modeling is the greatest uncertainty in the dynamics of low Earth satellite orbits where ballistic coefficient and density errors dominate drag errors. This paper examines fitted drag coefficients found as part of a precision orbit determination process for Stella, Starlette, and the GEOSAT Follow-On satellites from 2000 to 2005. The drag coefficients for the spherical Stella and Starlette satellites are assumed to be highly correlated with density model error. The results using MSIS-86, NRLMSISE-00, and NRLMSISE-00 with dynamic calibration of the atmosphere (DCA) density corrections are compared. The DCA corrections were formulated for altitudes of 200–600 km and are found to be inappropriate when applied at 800 km. The yearly mean fitted drag coefficients are calculated for each satellite for each year studied. The yearly mean drag coefficients are higher for Starlette than Stella, where Starlette is at a higher altitude. The yearly mean fitted drag coefficients for all three satellites decrease as solar activity decreases after solar maximum.

Measurement of drag and its cancellation

The design of drag cancellation missions of the future will take advantage of the technology experience of the past. The importance of data for modeling of the atmosphere led to at least six types of measurement: (a) balloon flights, (b) missile-launched falling spheres, (c) the ‘cannonball’ satellites of Ken Champion with accelerometers for low-altitude drag measurement (late 1960s and early 1970s), (d) the Agena flight of LOGACS (1967), a Bell MESA accelerometer mounted on a rotating platform to spectrally shift low-frequency errors in the accelerometer, (e) a series of French low-level accelerometers (e.g. CACTUS, 1975), and (f) correction of differential accelerations for drag errors in measuring gravity gradient on a pair of satellites (GRACE, 2002). The independent invention of the drag-free satellite concept by Pugh and Lange (1964) to cancel external disturbance added implementation opportunities. Its first flight application was for ephemeris prediction improvement with the DISCOS flight (1972)—still the only extended free test mass flight. Then successful flights for reduced disturbance environment for science measurement with gyros on GP-B (2004) and for improved accuracy in geodesy and ocean studies (GOCE, 2009) each using accelerometer measurements to control the drag-canceling thrust. LISA, DECIGO, BBO and other gravity wave-measuring satellite systems will push the cancellation of drag to new levels.

논문 : 외란 관측기를 이용한 대기권 재진입 궤적 추종성능 향상

In the re-entry comtrol system, errors apt to induce because the time deriviative of drag acceleration is analytically estimated. Still more, the difficulty of estimation of th exact drag coefficient in hypersonic velocity and the non-reality of the scale height cause a steady-state drag errer. In the Space-Shuttle, a steady-state drag error is reduced by the addition of the integral term of drag acceleation error into the control system. This method, however, induces a difficulties in respect to the modern controller composition due to the multi-poles in a closed-loop system. Thus, this paper proposes the additional method of the disturbance observer. This reduces the steady-state drag error according to the following by the analytic calculation, and then creates the new drag acceleration time derivative using the estimated error. The performance of the re-entry control system is verified about 32 refernce trajectories.

Spacecraft orbit determination using GPS navigation solutions

The orbit determination using the GPS navigation solutions for the KOMPSAT-1 spacecraft has been studied. The Cowell method of special perturbation theories was employed to develop a precision orbit propagation, and the perturbations due to geopotential, the gravity of the Sun and the Moon, solid Earth tides, ocean tides, the Earth's dynamic polar motion, solar radiation pressure, and atmospheric drag were modeled. Specifically, the satellite box-wing macro model was applied to minimize the drag errors at low altitude. The estimation scheme consisted of an extended Kalman filter and Bayesian least square method. To investigate the applicability of the method to the KOMPSAT-1 spacecraft, the orbit determination was accomplished using the GPS navigation solutions for the TOPEX/POSEIDON and TAOS satellites. The orbit determination results were compared with NASA POE generated by global laser tracking. The position and velocity accuracy was estimated about 16∼7 m and 0.0157∼0.0074 m·s −1 RMS, respectively, for the two satellites in the presence of SA. These results verify that an orbit determination scheme using GPS navigation solutions can provide the static orbit information and reduce conspicuously the position and velocity errors of navigation solutions. It can be suggested that the sequential and batch orbit determination using the GPS navigation solutions be the most appropriate method in the KOMPSAT-1 type mission.

Precision Low Earth Orbit Determination Using Atmospheric Density Calibration

Atmospheric drag is the largest uncertainty in determining orbits of low altitude satellites. Deficiencies in operational satellite drag models persist due to empirical model limitations as well as inadequacies of proxy indices used as model drivers. Satellite drag errors result in degraded accuracy, requirements for frequent updates and inadequate predictions of true positions for accurate catalog maintenance, collision avoidance and re-entry operations. Time-dependent global corrections to operational drag models have been derived based on assimilation of satellite tracking data. These corrected drag values circumvent the persisting deficiencies of current drag models and provide significant improvements in precision orbit determination and prediction for low-earth orbit satellites.

Convergence of lift and drag predictions by a Morino panel method (VSAERO)

CONVERGENCE results from both two-dimensional and three-dimensional versions of a Morino-type code are presented an analyzed. In both two and three dimensions it is found that reasonably accurate lift and moment predictions are obtained using modest numbers of nominally uniform-sized panels, but induced drag predictions are seriously inaccurate and converge at best very slowly with increasing density. Two ways are found to improve accuracy and convergence of drag predictions: 1) use cosine spacing for chordwise distribution of panels on foil sections, or 2) deduce lift and drag from the far-field wake by a classical Trefftzplane analysis. Of the two methods, the far-field has superior accuracy and convergence properties and, indeed, produces highly accurate and stable drag predictions even from quite coarse panelizations. It is also shown that large benefits in accuracy and/or savings in computational effort are possible by use of Richardson extrapolation applied to results from two or more relatively coarse (but systematically related) panelizations. Contents Although methods have been extensively employed and validated for aerodynamic lift and moment calculations, they have a reputation for being inaccurate or unreliable with respect to drag. The work reported here was stimulated by attempts to apply the code VSAERO to calculate the lift and induced drag of complex wing-body configurations representing sailboat hull, keel, and rudder geometries,1 for which induced drag (effective span) is the characteristic that most strongly impacts performance. (Note that there exist various versions of VSAERO. The three-dimensional code used in this study, a public-domain version obtained directly from NASA in 1984 and currently distributed by COSMIC, may differ from commercial versions.) Conventional VSAERO drag predictions were found to be highly sensitive to details and density of panelization and in poor agreement with experiments. These studies, undertaken to discover the sources and magnitude of the errors, led eventually to usably accurate drag predictions by two methods that are believed to be applicable to most three-dimensional codes. Any code is a discrete approximation to a continuous flow: a mostly smooth body surface is approximated by an assemblage of triangular or quadrilateral panels, and continuous flow quantities (e.g., singularity strengths and pressure) are approximated by simple distributions over each panel. As the subdivision of the body is made successively finer, the discretized model approximates the true body geometry and the continuous flow more closely and so, presumably, computed flow quantities such as lift and drag will converge toward the exact continuous solution. The rate of convergence is of considerable practical interest because the computational effort of a method increases rapidly with the number TV of panels. Using a finer panelization than necessary is, therefore, very expensive in terms of time and computer resources. Also, if reliable rates of convergence can be established for some systematic way of subdividing the panels, a projection to infinite density is possible from two or more relatively coarse panelizations using Richardson extrapolation. VSAERO2'3 is a low-order three-dimensional subsonic code for general configurations. In common with many current production codes, for its potential-flow calculations it adopts the Morino formulation4 with constant known source and unknown doublet panels. In the solution phase, a Morino code sets up and solves a large system of linear equations for the unknown doublet densities on the panels. In the phase, surface velocities, hence pressures, are obtained by local differencing of the doublet densities; these pressures are multiplied by areas and normals and summed to obtain total forces. This near-field force calculation is referred to in the sequel as panel pressure analysis (PPA). A principal tool for investigating the sources of drag error was VSA2D, a two-dimensiona l incompressible code based on the same singularity model, the same integral equation, and the same pressure, force, and moment calculations as VSAERO. VSA2D alternatively evaluates lift and drag from a far-field (FFA), which is extremely simple in two dimensions. Numerical results are given for two airfoils for which exact analytic results are available for comparison: a biconvex section and a Joukowsky section. Some lift and drag results are plotted in Fig.l against I/TV, for both uniform and cosine spacings on the 10% biconvex section, with TV ranging from 6 to 80.

Determination of high frequency variations in earth's rotation from Doppler satellite observations

The determination of high frequency variations in UT-1 and a component of pole position from a single pass of Doppler observations of a Navy Navigation Satellite is affected by instrument errors and uncertainties in the gravity field and atmospheric drag forces used in computing the satellite orbit. For elevation angles above20°, instrument errors contribute about2 msec to the determination of UT-1 and “.03 to the determination of pole position. Gravity and drag errors contribute about 0“.03 of correlated error. But gravity errors may be inferred by statistical analysis of residuuls after drag errors are reduced by drag-compensating devices aboard future Navy Navigation Satellites. Since20 Doppler stations nominally acquire about100 passes each day, daily observations of UT-1 and pole position could achieve precisions of0.2 msec and “.005, respectively, assuming half the passes contribute to the determination of each component of pole position. The current accuracy of Doppler results for two day solutions is about50 cm for pole position and1 msec for high frequency variations in UT-1.

Practical Realization of a Reference System for Earth Dynamics by Satellite Methods

AbstractObservations of artificial earth satellites provide a means of establishing an.origin, orientation, scale and control points for a coordinate system. Neither existing data nor future data are likely to provide significant information on the .001 angle between the axis of angular momentum and axis of rotation. Existing data have provided data to about .01 accuracy on the pole position and to possibly a meter on the origin of the system and for control points. The longitude origin is essentially arbitrary. While these accuracies permit acquisition of useful data on tides and polar motion through dynamio analyses, they are inadequate for determination of crustal motion or significant improvement in polar motion. The limitations arise from gravity, drag and radiation forces on the satellites as well as from instrument errors. Improvements in laser equipment and the launch of the dense LAGEOS satellite in an orbit high enough to suppress significant gravity and drag errors will permit determination of crustal motion and more accurate, higher frequency, polar motion. However, the reference frame for the results is likely to be an average reference frame defined by the observing stations, resulting in significant corrections to be determined for effects of changes in station configuration and data losses.