Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “determinant”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,117 records · Page 62

Determination of the hypersonic-continuum/rarefied-flow drag coefficient of the Viking lander capsule 1 aeroshell from flight data

Results of an investigation to determine the full scale drag coefficient in the high speed, low density regime of the Viking lander capsule 1 entry vehicle are presented. The principal flight data used in the study were from onboard pressure, mass spectrometer, and accelerometer instrumentation. The hypersonic continuum flow drag coefficient was unambiguously obtained from pressure and accelerometer data; the free molecule flow drag coefficient was indirectly estimated from accelerometer and mass spectrometer data; the slip flow drag coefficient variation was obtained from an appropriate scaling of existing experimental sphere data. Comparison of the flight derived drag hypersonic continuum flow regime except for Reynolds numbers from 1000 to 100,000, for which an unaccountable difference between flight and ground test data of about 8% existed. The flight derived drag coefficients in the free molecule flow regime were considerably larger than those previously calculated with classical theory. The general character of the previously determined temperature profile was not changed appreciably by the results of this investigation; however, a slightly more symmetrical temperature variation at the highest altitudes was obtained.

Blanchard, R. C.↗

Atmospheric media effects on ARIES baseline determination

Different types of media effects on ARIES baseline determination are compared. The effectiveness of simple ionospheric calibration models are studied. To perform the covariance analysis, an ARIES observation sequence needs to be assumed. For the current purposes, the observation sequence is selected to be that of experiment 80D over the JPL/Goldstone baseline (approximately 180 km). This experiment consisted of 96 observations over a period of approximately 25 hours on March 25 to 26, 1980. It is found through covariance analyses that the component most sensitive to media depends heavily upon the correlation, between the two stations, of the media effects. It is also found that relying on the cancellation of ionospheric delays between the two ray paths of VLBI observations at S band results in a large error in baseline length determination. High degree removal of ionospheric effects is possible with a crude model, providing correct diurnal peak and minimum ionospheric levels are input.

Wu, S. C.↗

A rapid perturbation procedure for determining nonlinear flow solutions: Application to transonic turbomachinery flows

Perturbation procedures and associated computational codes for determining nonlinear flow solutions were developed to establish a method for minimizing computational requirements associated with parametric studies of transonic flows in turbomachines. The procedure that was developed and evaluated was found to be capable of determining highly accurate approximations to families of strongly nonlinear solutions which are either continuous or discontinuous, and which represent variations in some arbitrary parameter. Coordinate straining is employed to account for the movement of discontinuities and maxima of high gradient regions due to the perturbation. The development and results reported are for the single parameter perturbation problem. Flows past both isolated airfoils and compressor cascades involving a wide variety of flow and geometry parameter changes are reported. Attention is focused in particular on transonic flows which are strongly supercritical and exhibit large surface shock movement over the parametric range studied; and on subsonic flows which display large pressure variations in the stagnation and peak suction pressure regions. Comparisons with the corresponding 'exact' nonlinear solutions indicate a remarkable accuracy and range of validity of such a procedure.

Stahara, S. S.↗

The geographic bias in determining average variations of total ozone from ground-based observations

The mean monthly hemispheric total ozone values as determined from between the two sets of data indicates that the mean difference between the calculated total ozone amount as determined for the entire period from all the satellite data and that derived from the satellite data restricted to location of ground based stations is 1.3 m atm cm for the Northern Hemisphere and 0.7 m atm cm for the Southern Hemisphere (0.3 and 0.2 percent respectively of the average total ozone in each hemisphere).

London, J.↗

Multispectral Resource Sampler (MRS): Proof of concept study on atmospheric corrections. Determinations of atmospheric optical parameters using the multispectral resource sampler atmospheric optical

An investigation was performed to determine which mathematical algorithms should be used in the calculation of atmospheric optical parameters using the Multispectral Resource Sampler (MRS) sensor. A simulation of the MRS sensor was performed using a radiative-transfer model. The simulation provides the spectral radiance at the satellite sensor in terms of various atmospheric parameters, such as optical thickness, solar zenith angle, nadir view angle, relative azimuth angle, bi-directional reflectance of the target, background albedo, and wavelength. Atmospheric correction algorithms were also developed for the determination of the total spectral optical thickness of the atmosphere for: (1) homogeneous (horizontal) hazy atmospheres with diffuse targets; (2) inhomogeneous (horizontal) hazy atmospheres with diffuse targets; and (3) homogeneous (horizontal) hazy atmospheres with non-diffuse targets.

Turner, R. E.↗

Determination of in vivo mechanical properties of long bones from their impedance response curves

A mathematical model consisting of a uniform, linear, visco-elastic, Euler-Bernoulli beam to represent the ulna or tibia of the vibrating forearm or leg system is developed. The skin and tissue compressed between the probe and bone is represented by a spring in series with the beam. The remaining skin and tissue surrounding the bone is represented by a visco-elastic foundation with mass. An extensive parametric study is carried out to determine the effect of each parameter of the mathematical model on its impedance response. A system identification algorithm is developed and programmed on a digital computer to determine the parametric values of the model which best simulate the data obtained from an impedance test.

Borders, S. G.↗

Apparatus and method for determining the position of a radiant energy source

The position of a terrestrial RF source is determined from a geostationary, synchronous satellite by scanning the beam of a narrow beam width antenna in first and second orthogonal directions over a region including the source. The peak level of energy transduced by the antenna in each of the scanning directions is detected and correlated with the scanning position of the beam by feeding the output of a detector responsive to the transduced signal to an indicator of an X-Y recorder. The X and Y axes of the recorder are scanned in synchronism with the beam being respectively scanned in the first and second directions to form X and Y traces on which are indicated the detected peak position in each of the scanning directions. The source position is determined from an intersection of lines drawn parallel to the X and Y axes and including the detected peak position of each trace.

Schaefer, G. J.↗

Determination of rain rate from a spaceborne radar using measurements of total attenuation

Studies shows that path-integrated rain rates can be determined by means of a direct measurement of attenuation. For ground based radars this is done by measuring the backscattering cross section of a fixed target in the presence and absence of rain along the radar beam. A ratio of the two measurements yields a factor proportional to the attenuation from which the average rain rate is deduced. The technique is extended to spaceborne radars by choosing the ground as reference target. The technique is also generalized so that both the average and range-profiled rain rates are determined. The accuracies of the resulting estimates are evaluated for a narrow beam radar located on a low earth orbiting satellite.

Meneghini, R.↗

Determination of the geopotential from satellite-to-satellite tracking data

Ground-based observation of the deviation of artificial satellite trajectories from a reference path is the classical means for determining the parameters of the global geopotential. However, for the short wavelengths (less than 10 deg), tracking coverage from ground stations of sufficient density is impossible to obtain. But one or more satellites can observe another satellite and obtain the needed global data coverage. Results are presented of error analyses of possible satellite-to-satellite tracking missions to determine the geopotential at a resolution of 1 x 1 deg. To achieve an accuracy of a few milligals at this resolution requires a satellite altitude at or near 150 km and measurements of intersatellite speed to 10 to the -6th m/s.

Douglas, B. C.↗

A rapid method for the approximate determination of nonlinear solutions Application to aerodynamic flows

A method for determining highly accurate approximations to families of strongly nonlinear solutions which are either continuous or discontinuous, and which represent variations in some arbitrary parameters, is developed and evaluated. The procedure consists of defining a unit perturbation by employing two or more nonlinear solutions which differ from one another by a nominal change in some geometric or flow parameter, and then using that unit perturbation to predict a family of related nonlinear solutions over a range of parameter variation. Coordinate straining is used in determining the unit perturbation to account for the movement of discontinuities and maxima of high-gradient regions due to the perturbation. Although the procedure is generally applicable, results are presented here for nonlinear aerodynamic applications. Attention is focused in particular on transonic flows which are strongly supercritical and exhibit large surface shock movement over the parametric range studied; and on subsonic flows which display large pressure variations in the stagnation and peak suction pressure regions. Flows past both isolated airfoils and compressor cascades involving a variety of flow and geometry parameter changes are considered. Comparisons with the corresponding 'exact' nonlinear solutions indicate a remarkable accuracy and range of validity of such a procedure. Computational time is trivial.

Stahara, S. S.↗

Are sulfur isotope ratios sufficient to determine the antiquity of sulfate reduction

Possible limitations on the use of sulfur isotope ratios in sedimentary sulfides to infer the evolution of microbial sulfate reduction are discussed. Current knowledge of the ways in which stable sulfur isotope ratios are altered by chemical and biological processes is examined, with attention given to the marine sulfur cycle involving various microbial populations, and sulfur reduction processes, and it is noted that satisfactory explanations of sulfur isotope ratios observed in live organisms and in sediments are not yet available. It is furthermore pointed out that all members of the same genus of sulfate reducing bacteria do not always fractionate sulfur to the same extent, that the extent of sulfur fractionation by many sulfate-reducing organisms has not yet been determined, and that inorganic processes can also affect sulfur isotope fractionation values. The information currently available is thus concluded to be insufficient to determine the time of initial appearance of biological sulfate reduction.

Ashendorf, D.↗

Three-axis attitude determination from vector observations

Two computationally efficient algorithms are presented for determining three-axis attitude from two or more vector observations. The first of these, the TRIAD algorithm, provides a deterministic (i.e., nonoptimal) solution for the attitude based on two vector observations. The second, the QUEST algorithm, is an optimal algorithm which determines the attitude that achieves the best weighted overlap of an arbitrary number of reference and observation vectors. Analytical expressions are given for the covariance matrices for the two algorithms using a fairly realistic model for the measurement errors. The mathematical relationship of the two algorithms and their relative merits are discussed and numerical examples are given. The advantage of computing the covariance matrix in the body frame rather than in the inertial frame (e.g., in terms of Euler angles) is emphasized. These results are valuable when a single-frame attitude must be computed frequently. They will also be useful to the mission analyst or spacecraft engineer for the evaluation of launch-window constraints or of attitude accuracies for different attitude sensor configurations.

Shuster, M. D.↗

The Seasat Precision Orbit Determination Experiment

The objectives and conclusions reached during the Seasat Precision Orbit Determination Experiment are discussed. It is noted that the activities of the experiment team included extensive software calibration and validation and an intense effort to validate and improve the dynamic models which describe the satellite's motion. Significant improvement in the gravitational model was obtained during the experiment, and it is pointed out that the current accuracy of the Seasat altitude ephemeris is 1.5 m rms. An altitude ephemeris for the Seasat spacecraft with an accuracy of 0.5 m rms is seen as possible with further improvements in the geopotential, atmospheric drag, and solar radiation pressure models. It is concluded that since altimetry missions with a 2-cm precision altimeter are contemplated, the precision orbit determination effort initiated under the Seasat Project must be continued and expanded.

Tapley, B. D.↗

Relative performance of algorithms for autonomous satellite orbit determination

Limited word size in contemporary microprocessors causes numerical problems in autonomous satellite navigation applications. Numerical error introduced in navigation computations performed on small wordlength machines can cause divergence of sequential estimation algorithms. To insure filter reliability, square root algorithms have been adopted in many applications. The optimal navigation algorithm requires a careful match of the estimation algorithm, dynamic model, and numerical integrator. In this investigation, the relationship of several square root filters and numerical integration methods is evaluated to determine their relative performance for satellite navigation applications. The numerical simulations are conducted using the Phase I GPS constellation to determine the orbit of a LANDSAT-D type satellite. The primary comparison is based on computation time and relative estimation accuracy.

Tapley, B. D.↗

Determination of the potential in a synodic system

Determination of the potential field in a fixed (inertial) system may be accomplished by the solution of a homogeneous linear partial differential equation when a family of orbits of a body moving in the field is given. This partial differential equation was presented and thoroughly analyzed earlier. The present paper discusses the same problem in a rotating system where the centrifugal and Coriolis effects render the pertinent partial differential equation in general non-homogeneous and non-linear. A linear, though non-homogeneous, partial differential equation for the determination of the synodic potential is obtained only in the special case of iso-energetic families of orbits.

Szebehely, V.↗

Inertial attitude determination for a dual-spin planetary spacecraft

Design and performance evaluations of an onboard inertial attitude determination system for a dual-spin planetary spacecraft are presented. A quaternion integration algorithm and a rate estimator sequentially determine the scan platform's inertial attitude and rate from the drift and misalignment compensated gyro outputs. A least-squares estimator algorithm processes the star transit data from a rotor-mounted star scanner, and provides periodic updates of the scan platform's attitude as a means of correcting the drift of the quaternion integration algorithm. Computer simulated algorithm performance in the presence of nutation and sensor noise are presented.

Wong, E. C.↗

Use of Faraday-rotation data from beacon satellites to determine ionospheric corrections for interplanetary spacecraft navigation

Faraday-rotation data from the linearly polarized 137-MHz beacons of the ATS-1, SIRIO, and Kiku-2 geosynchronous satellites are used to determine the ionospheric corrections to the range and Doppler data for interplanetary spacecraft navigation. The JPL operates the Deep Space Network of tracking stations for NASA; these stations monitor Faraday rotation with dual orthogonal, linearly polarized antennas, Teledyne polarization tracking receivers, analog-to-digital converter/scanners, and other support equipment. Computer software examines the Faraday data, resolves the pi ambiguities, constructs a continuous Faraday-rotation profile and converts the profile to columnar zenith total electron content at the ionospheric reference point; a second program computes the line-of-sight ionospheric correction for each pass of the spacecraft over each tracking complex. Line-of-sight ionospheric electron content using mapped Faraday-rotation data is compared with that using dispersive Doppler data from the Voyager spacecraft; a difference of about 0.4 meters, or 5 x 10 to the 16th electrons/sq m is obtained. The technique of determining the electron content of interplanetary plasma by subtraction of the ionospheric contribution is demonstrated on the plasma torus surrounding the orbit of Io.

Royden, H. N.↗

An Empirical Method Permitting Rapid Determination of the Area, Rate and Distribution of Water-Drop Impingement on an Airfoil of Arbitrary Section at Subsonic Speeds

An empirical method for the determination of the area, rate, and distribution of water-drop impingement on airfoils of arbitrary section is presented. The procedure represents an initial step toward the development of a method which is generally applicable in the design of thermal ice-prevention equipment for airplane wing and tail surfaces. Results given by the proposed empirical method are expected to be sufficiently accurate for the purpose of heated-wing design, and can be obtained from a few numerical computations once the velocity distribution over the airfoil has been determined. The empirical method presented for incompressible flow is based on results of extensive water-drop. trajectory computations for five airfoil cases which consisted of 15-percent-thick airfoils encompassing a moderate lift-coefficient range. The differential equations pertaining to the paths of the drops were solved by a differential analyzer. The method developed for incompressible flow is extended to the calculation of area and rate of impingement on straight wings in subsonic compressible flow to indicate the probable effects of compressibility for airfoils at low subsonic Mach numbers.

Bergrun, N. R.↗