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NASA NTRS1975

The isostatic state of Martian topography

As is evidenced by the gravity data, the regional topography of Mars falls into two disctinct age groups. The older group is isostatically compensated at relatively shallow depth. All of our analyses indicate that the younger group is only partly compensated and that the depth of partial compensation is also shallow. The young topography is composed primarily of the Tharsis plateau and the adjacent low areas of Chryse and Amazonis. They appear to have all undergone the same amount of partial compensation, suggesting a comtemporaneous origin. All of the topography is consistent with a model of viscous relaxation in an environment of approximate thermal steady state. The minimum viscosity necessary to explain the partial compensation is 10 to the 27th power P, a value typical of a number of lunar studies. Alternatively, the strength required to support the uncompensated fraction of the topography is similar to strengths determined for the earth and moon.

Phillips, R. J.↗

NASA NTRS1976

Aircraft digital control design methods

Variations in design methods for aircraft digital flight control are evaluated and compared. The methods fall into two categories; those where the design is done in the continuous domain (or s plane) and those where the design is done in the discrete domain (or z plane). Design method fidelity is evaluated by examining closed loop root movement and the frequency response of the discretely controlled continuous aircraft. It was found that all methods provided acceptable performance for sample rates greater than 10 cps except the uncompensated s plane design method which was acceptable above 20 cps. A design procedure based on optimal control methods was proposed that provided the best fidelity at very slow sample rates and required no design iterations for changing sample rates.

Powell, J. D.↗

NASA NTRS1976

Use of calibration maneuvers for improved performance of strapdown attitude reference systems

Conventional strapdown configurations require precise knowledge of the orientation of the gyro input axes as well as a moderately large, fast computer to provide inertial attitude. This paper presents the mechanization and discusses the operation and performance of an omnidirectional, strapdown pointing control system called All Sky Pointer which does not require precise gyro alignment or a sophisticated computer. Errors caused by gyro-optical sensor misalignment, gyro-integrator bias, and scale factor error are compensated for by the use of calibration maneuvers. Control and computation are provided by an electronics package utilizing technology similar to that found in hand-held calculators. Simulation results indicate that sub arc-minute pointing performance is possible and pointing errors are reduced by as much as an order of magnitude compared with uncompensated systems.

Lorell, K. R.↗

NASA NTRS1976

A comparison of digital flight control design methods

Many variations in design methods for aircraft digital flight control have been proposed in the literature. In general, the methods fall into two categories: those where the design is done in the continuous domain (or s-plane), and those where the design is done in the discrete domain (or z-plane). This paper evaluates several variations of each category and compares them for various flight control modes of the Langley TCV Boeing 737 aircraft. Design method fidelity is evaluated by examining closed loop root movement and the frequency response of the discretely controlled continuous aircraft. It was found that all methods provided acceptable performance for sample rates greater than 10 cps except the 'uncompensated s-plane design' method which was acceptable above 20 cps. A design procedure based on optimal control methods was proposed that provided the best fidelity at very slow sample rates and required no design iterations for changing sample rates.

Powell, J. D.↗

NASA NTRS1976

Development of doped-germanium photoconductors for astronomical observations at wavelengths from 30 to 120 micrometers

Technology was developed for production of doped-germanium detectors which have optimized performance in the 30- to 120-micrometer wavelength range and are capable of achieving the objectives of the Infrared Astronomy Satellite space mission. The work of this phase was divided into the following major tasks: (1) growth of Ge:Ga crystals from high-purity starting material with Ga concentrations different from that previously produced, and development of a zone leveling method to produce a uniform Ga doping concentration; (2) growth of uncompensated Ge:Be crystals from high-purity starting material with a range of Be concentrations between 10 to the 14th power and 10 to the 16th power atoms/cubic cm; (3) evaluation of crystals by means of Hall effect and resistance measurements as a function of temperature; (4) fabrication and test of detectors made from both Ge:Be and Ge:Ga crystals to determine the relative performance between different crystals. Correlation of detector test data with material evaluation data and analysis of how to further optimize detector performance.

Bratt, P. R.↗

NASA NTRS1978

The isostatic state of the lunar Apennines and regional surroundings

High-resolution gravity and topography data taken over the Apennine Mountains have been used to compute their isostatic state. Results show that the Apennines are uncompensated; thus this state implies that the lunar crust and upper mantle have been strong enough over 3.9 b.y. to support the load exerted by this topographic excess. The Apennines produce a maximum shear stress of 60 bars at a depth of 60 km. A lower bound on the lunar crustal viscosity of 10 to the 27th power P is calculated on the basis of the assumption of a 10% relaxation over 3.9 b.y. Studies of a broad negative regional anomaly located between Maria Serenitatis and Imbrium necessitate a locally thicker crust to satisfy the observed data. This anomaly may have been produced by a lateral transport of crustal material from beneath the giant impact basins as a result of rebound at the crust-mantle interface.

Ferrari, A. J.↗

NASA NTRS1979

Development and analysis of a twelfth degree and order gravity model for Mars

Satellite geodesy techniques previously applied to artificial earth satellites have been extended to obtain a high-resolution gravity field for Mars. Two-way Doppler data collected by 10 Deep Space Network (DSN) stations during Mariner 9 and Viking 1 and 2 missions have been processed to obtain a twelfth degree and order spherical harmonic model for the martian gravitational potential. The quality of this model was evaluated by examining the rms residuals within the fit and the ability of the model to predict the spacecraft state beyond the fit. Both indicators show that more data and higher degree and order harmonics will be required to further refine our knowledge of the martian gravity field. The model presented shows much promise, since it resolves local gravity features which correlate highly with the martian topography. An isostatic analysis based on this model, as well as an error analysis, shows rather complete compensation on a global (long wavelength) scale. Though further model refinements are necessary to be certain, local (short wavelength) features such as the shield volcanos in Tharsis appear to be uncompensated. These are interpreted to place some bounds on the internal structure of Mars.

Christensen, E. J.↗

NASA NTRS1981

Venus gravity - A high-resolution map

The Doppler data from the radio tracking of the Pioneer Venus Orbiter (PVO) have been used in a two-stage analysis to develop a high-resolution map of the gravitational potential of Venus, represented by a central mass and a surface mass density. The two-stage procedure invokes a Kalman filter-smoother to determine the orbit of the spacecraft, and a stabilized linear inverter to estimate the surface mass density. The resultant gravity map is highly correlated with the topographic map derived from the PVO radar altimeter data. However, the magnitudes of the gravity variations are smaller than would be expected if the topography were uncompensated, indicating that at least partial compensation has taken place.

Reasenberg, R. D.↗

NASA NTRS1981

GPS aiding of ocean current determination

The navigational accuracy of an oceangoing vessel using conventional GPS p-code data is examined. The GPS signal is transmitted over two carrier frequencies in the L-band at 1575.42 and 1227.6 MHz. Achievable navigational uncertainties of differenced positional estimates are presented as a function of the parameters of the problem, with particular attention given to the effect of sea-state, user equivalent range error, uncompensated antenna motion, varying delay intervals, and reduced data rate examined in the unaided mode. The unmodeled errors resulting from satellite ephemeris uncertainties are shown to be negligible for the GPS-NDS (Navigation Development) satellites. Requirements are met in relatively calm seas, but accuracy degradation by a factor of at least 2 must be anticipated in heavier sea states. The aided mode of operation is examined, and it is shown that requirements can be met by using an inertial measurement unit (IMU) to aid the GPS receiver operation. Since the use of an IMU would mean higher costs, direct Doppler from the GPS satellites is presented as a viable alternative.

Mohan, S. N.↗

NASA NTRS1981

Susceptibility of materials processing experiments to low-level accelerations

The types of material processing experiments being considered for shuttle can be grouped into four categories: (1) contained solidification experiment; (2) quasicontainerless experiments; (3) containerless experiments; and (4) fluids experiments. Low level steady acceleration, compensated and uncompensated transient accelerations, and rotation induced flow factors that must be considered in the acceleration environment of a space vehicle whose importance depends on the type of experiment being performed. Some control of these factors may be exercised by the location and orientation of the experiment relative to shuttle and by the orbit vehicle attitude chosen for mission. The effects of the various residual accelerations can have serious consequence to the control of the experiment and must be factored into the design and operation of the apparatus.

Naumann, R. J.↗

NASA NTRS1981

Information theory lateral density distribution for Earth inferred from global gravity field

Information Theory Inference, better known as the Maximum Entropy Method, was used to infer the lateral density distribution inside the Earth. The approach assumed that the Earth consists of indistinguishable Maxwell-Boltzmann particles populating infinitesimal volume elements, and followed the standard methods of statistical mechanics (maximizing the entropy function). The GEM 10B spherical harmonic gravity field coefficients, complete to degree and order 36, were used as constraints on the lateral density distribution. The spherically symmetric part of the density distribution was assumed to be known. The lateral density variation was assumed to be small compared to the spherically symmetric part. The resulting information theory density distribution for the cases of no crust removed, 30 km of compensated crust removed, and 30 km of uncompensated crust removed all gave broad density anomalies extending deep into the mantle, but with the density contrasts being the greatest towards the surface (typically + or 0.004 g cm 3 in the first two cases and + or - 0.04 g cm 3 in the third). None of the density distributions resemble classical organized convection cells. The information theory approach may have use in choosing Standard Earth Models, but, the inclusion of seismic data into the approach appears difficult.

Rubincam, D. P.↗

NASA NTRS1982

Support of topographic and other loads on the moon and on the terrestrial planets

The existence of mascons on the moon indicates that the lunar elastic lithosphere can support substantial loads for about three billion years. Lunar topography also appears to be uncompensated. Observations of gravity on Mars show that the Tharsis uplift is only partially compensated. A number of authors have attributed this support to lithospheric flexure. In this paper it is shown that membrane stresses play an important role in the support of loads on the moon, Mars, and Mercury. For loads that have been expressed in terms of spherical harmonics analytical expressions for the degree of compensation are obtained as a function of the degree of the load. The results are compared with the observed dependence of the ratio of gravitational potential to topography on degree. It is also concluded that membrane stresses can support a significant ellipticity for a tidally despun planetary body.

Willemann, R. J.↗

NASA NTRS1982

Venus - Comparison of gravity and topography in the vicinity of Beta Regio

The Doppler tracking data obtained from the Pioneer Venus Orbiter when it passed near Beta Regio yielded a peak vertical anomaly of 150 mGal when analyzed by our two stage procedure. A comparison of maps of the gravity and topography at comparable resolution shows a striking correlation. A scatter plot shows that the observed gravity anomaly is approximately 0.4 of that expected from uncompensated topography of half the mean density of Venus. However, the spectral admittance shows that the gravity anomalies can not be explained either by Airy compensation at fixed depth or by a model comprising an elastic plate atop an inviscid fluid. The gravity and topography variations may signify deep compensation or dynamic support for Beta Regio and more shallow compensation for other features.

Reasenberg, R. D.↗

NASA NTRS1982

Degree variances of the earth's potential, topography and its isostatic compensation

A spherical harmonic expansion of the earth's gravitational potential and equivalent rock topography to degree and order 180 is described. The potential implied by the topography considered as uncompensated and with isostatic compensation has been computed. Good agreement with the observed potential field is found when the depth of compensation in the Airy theory is assumed to be 50 km. At the higher degrees the correlation coefficient between the potential expansion and the equivalent rock topography is about 0.5. The Lachapelle equations for the topographic isostatic potential were tested using 1 x 1 deg equivalent rock topography. The degree variances agree at the lower degrees but at degree 36 the Lachapelle results using 5 deg data underestimate the potential degree variances by about one-third.

Rapp, R. H.↗

NASA NTRS1983

Dynamic gas temperature measurement system, volume 1

A gas temperature measurement system with compensated frequency response of 1 kHz and capability to operate in the exhaust of a gas turbine engine combustor was developed. A review of available technologies which could attain this objective was done. The most promising method was identified as a two wire thermocouple, with a compensation method based on the responses of the two different diameter thermocouples to the fluctuating gas temperature field. In a detailed design of the probe, transient conduction effects were identified as significant. A compensation scheme was derived to include the effects of gas convection and wire conduction. The two wire thermocouple concept was tested in a laboratory burner exhaust to temperatures of about 3000 F and in a gas turbine engine to combustor exhaust temperatures of about 2400 F. Uncompensated and compensated waveforms and compensation spectra are presented.

Elmore, D. L.↗

NASA NTRS1984

Fault-tolerant system considerations for a redundant strapdown inertial measurement unit

The development and evaluation of a fault-tolerant system for the Redundant Strapdown Inertial Measurement Unit (RSDIMU) being developed and evaluated by the NASA Langley Research Center was continued. The RSDIMU consists of four two-degree-of-freedom gyros and accelerometers mounted on the faces of a semi-octahedron which can be separated into two halves for damage protection. Compensated and uncompensated fault-tolerant system failure decision algorithms were compared. An algorithm to compensate for sensor noise effects in the fault-tolerant system thresholds was evaluated via simulation. The effects of sensor location and magnitude of the vehicle structural modes on system performance were assessed. A threshold generation algorithm, which incorporates noise compensation and filtered parity equation residuals for structural mode compensation, was evaluated. The effects of the fault-tolerant system on navigational accuracy were also considered. A sensor error parametric study was performed in an attempt to improve the soft failure detection capability without obtaining false alarms. Also examined was an FDI system strategy based on the pairwise comparison of sensor measurements. This strategy has the specific advantage of, in many instances, successfully detecting and isolating up to two simultaneously occurring failures.

Motyka, P.↗

NASA NTRS1985

Venus gravity west of Beta Regio

Doppler tracking data from the Pioneer Venus Orbiter (PVO) have been used to estimate the anomalous gravity field in the region of Venus west of Beta Regio. The analysis invokes a Kalman filter-smoother to solve the nonlinear spacecraft state estimation problem and a linear Bayesian estimator to perform the geophysical inversion. The topographic map for this region, derived from the PVO radar, has been filtered to have the same distortions and degree of smoothing as the gravity map. The undulations of the gravity are about 0.2 times as large as expected from the topography, on the assumption that the latter is uncompensated. A comparison of the gravity and topography by means of the spectral admittance is consistent with Airy compensation at a depth of 50 km, if the surface material has a density of 2.6 g/cu cm. However, this is not a unique interpretation.

Goldberg, Z. M.↗

NASA NTRS1987

Filter distortion effects on telemetry signal-to-noise ratio

The effect of filtering on the Signal-to-Noise Ratio (SNR) of a coherently demodulated band-limited signal is determined in the presence of worse-case amplitude ripple. The problem is formulated mathematically as an optimization problem in the L2-Hilbert space. The form of the worst-cast amplitude ripple is specified, and the degradation in the SNR is derived in a closed form expression. It is shown that when the maximum passband amplitude ripple is 2 delta (peak to peak), the SNR is degraded by at most (1 - delta squared), even when the ripple is unknown or uncompensated. For example, an SNR loss of less than 0.01 dB due to amplitude ripple can be assured by keeping the amplitude ripple to under 0.42 dB.

Sadr, R.↗