Methods for the computation of detailed geoids and their accuracy

Two methods for the computation of geoid undulations using potential coefficients and 1 deg x 1 deg terrestrial anomaly data are examined. It was found that both methods give the same final result but that one method allows a more simplified error analysis. Specific equations were considered for the effect of the mass of the atmosphere and a cap dependent zero-order undulation term was derived. Although a correction to a gravity anomaly for the effect of the atmosphere is only about -0.87 mgal, this correction causes a fairly large undulation correction that was not considered previously. The accuracy of a geoid undulation computed by these techniques was estimated considering anomaly data errors, potential coefficient errors, and truncation (only a finite set of potential coefficients being used) errors. It was found that an optimum cap size of 20 deg should be used. The geoid and its accuracy were computed in the Geos 3 calibration area using the GEM 6 potential coefficients and 1 deg x 1 deg terrestrial anomaly data. The accuracy of the computed geoid is on the order of plus or minus 2 m with respect to an unknown set of best earth parameter constants

The determination of gravity anomalies from geoid heights using the inverse Stokes' formula, Fourier transforms, and least squares collocation

A numerical method for the determination of gravity anomalies from geoid heights is described using the inverse Stokes formula. This discrete form of the inverse Stokes formula applies a numerical integration over the azimuth and an integration over a cubic interpolatory spline function which approximates the step function obtained from the numerical integration. The main disadvantage of the procedure is the lack of a reliable error measure. The method was applied on geoid heights derived from GEOS-3 altimeter measurements in the calibration area of the GEOS-3 satellite

A discussion of observation model, error sources and signal size for spaceborne gravitational gradiometry

Various space concepts were discussed during the past 20 years for a global improvement of the knowledge of the earth's gravity field. The concepts reach from high-low and low-low satellite-to-satellite tracking via tethered satellite gradiometers to sophisticated superconducting gradiometers. The purpose is to show that starting from one basic equation three criteria are sufficient to typify the various concepts and define the underlying observation model. Furthermore the different error sources, in particular, the time varying part of self-gravitation, and the expected signal size of all six gravity gradient components shall be discussed

Downward continuation of gravity information from satellite to satellite tracking or satellite gradiometry in local areas

Integral formulas in the parameter domain are used instead of a representation by spherical harmonics. The neglected regions will cause a truncation error. The application of the discrete form of the integral equations connecting the satellite observations with surface gravity anomalies is discussed in comparison with the least squares prediction method. One critical point of downward continuation is the proper choice of the boundary surface. Practical feasibilities are in conflict with theoretical considerations. The properties of different approaches for this question are analyzed

An integrative approach to space-flight physiology using systems analysis and mathematical simulation

An approach was developed to aid in the integration of many of the biomedical findings of space flight, using systems analysis. The mathematical tools used in accomplishing this task include an automated data base, a biostatistical and data analysis system, and a wide variety of mathematical simulation models of physiological systems. A keystone of this effort was the evaluation of physiological hypotheses using the simulation models and the prediction of the consequences of these hypotheses on many physiological quantities, some of which were not amenable to direct measurement. This approach led to improvements in the model, refinements of the hypotheses, a tentative integrated hypothesis for adaptation to weightlessness, and specific recommendations for new flight experiments

Study of critical defects in ablative heat shield systems for the space shuttle

Results are presented from an investigation to determine the effects of fabrication-induced defects on the performance of an ablative heat shield material in a simulated space shuttle reentry environment. Nondestructive methods for detecting the defects were investigated. The material considered is a fiber-filled, honeycomb-reinforced, low-density elastomer. Results were obtained for density variations, voids, fiber bundles, crushed honeycomb, undercut honeycomb, unbonded areas, face sheet delaminations, and cure variations. The data indicate that, within reasonable tolerances, the fabrication defects investigated are not critical in terms of reentry performance of the heat shield

The detection of tightly closed flaws by nondestructive testing (NDT) methods

Liquid penetrant, ultrasonic, eddy current and X-radiographic techniques were optimized and applied to the evaluation of 2219-T87 aluminum alloy test specimens in integrally stiffened panel, and weld panel configurations. Fatigue cracks in integrally stiffened panels, lack-of-fusion in weld panels, and fatigue cracks in weld panels were the flaw types used for evaluation. A 2319 aluminum alloy weld filler rod was used for all welding to produce the test specimens. Forty seven integrally stiffened panels containing a total of 146 fatigue cracks, ninety three lack-of-penetration (LOP) specimens containing a total of 239 LOP flaws, and one-hundred seventeen welded specimens containing a total of 293 fatigue cracks were evaluated. Nondestructive test detection reliability enhancement was evaluated during separate inspection sequences in the specimens in the 'as-machined or as-welded', post etched and post proof loaded conditions. Results of the nondestructive test evaluations were compared to the actual flaw size obtained by measurement of the fracture specimens after completing all inspection sequences. Inspection data were then analyzed to provide a statistical basis for determining the flaw detection reliability

Detection of tightly closed flaws by nondestructive testing (NDT) methods in steel and titanium

X-radiographic, liquid penetrant, ultrasonic, eddy current and magnetic particle testing techniques were optimized and applied to the evaluation of 4340 steel (180 KSI-UTS) and 6Al-4V titanium (STA) alloy specimens. Sixty steel specimens containing a total of 176 fatigue cracks and 60 titanium specimens containing a total of 135 fatigue cracks were evaluated. The cracks ranged in length from .043 cm (0.017 inch) to 1.02 cm (.400 inch) and in depth from .005 cm (.002 inch) to .239 cm (.094 inch) for steel specimens. Lengths ranged from .048 cm (0.019 inch) to 1.03 cm (.407 inch) and depths from 0.010 cm (.004 inch) to .261 cm (0.103 inch) for titanium specimens. Specimen thicknesses were nominally .152 cm (0.060 inch) and 0.635 cm (0.250 inch) and surface finishes were nominally 125 rms. Specimens were evaluated in the "as machined" surface condition, after etch surface and after proof loading in a randomized inspection sequence