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Report discusses several methods of performing numerical integration with computer. When data can be expressed as state vector that is dependent variable in a differential equation, self-starting integrators can be used to predict future data.
Sources of discrepancies noted between propulsion aerodynamic characteristics as predicted from wind tunnel tests and as measured in flight are discussed. The variable Reynolds capability of the National Transonic Facility will provide a tool for understanding and quantifying uncertainties involved in extrapolating the corrected wind tunnel data from tunnel conditions to full scale flight conditions.
An empirical stochastic computer model was developed with the capability of generating random thermodynamic profiles of the atmosphere below an altitude of 99 km which are characteristic of any given season, latitude, and time of day. Samples of temperature, density, and pressure profiles generated by the model are statistically similar to measured profiles in a data base of over 6000 rocket and high-altitude atmospheric soundings; that is, means and standard deviations of modeled profiles and their vertical gradients are in close agreement with data. Model-generated samples can be used for Monte Carlo simulations of aircraft or spacecraft trajectories to predict or account for the effects on a vehicle's performance of atmospheric variability. Other potential uses for the model are in simulating pollutant dispersion patterns, variations in sound propagation, and other phenomena which are dependent on atmospheric properties, and in developing data-reduction software for satellite monitoring systems.
Mars radar observations at 12.6-cm wavelength indicate that many of what were potential Viking landing sites along the planet's equator are rougher than interpretations of Mariner 9 images suggested. Root mean square surface slopes are typically 5 degrees in the region bounded by 160 and 200 degrees W, 0 and 12 degrees S. From Tharsis Montes west to 160 degrees W, radar-scattering characteristics suggest extreme roughness on small scales, perhaps exceeding 10 degrees in rms magnitude. East of Tharsis and north of Valles Marineris the surface is smooth, with values of rms slope as low as 1 degree; the elevation of this plateau was too high for a Viking landing. Study of spectral shapes indicates the Hagfors scattering law remains the best descriptor of quasi-specular surface scattering properties in an average sense; widespread variations in the surface argue against its indiscriminate use, however. Backscattering at moderate (25-40 degrees) incidence angles was studied qualitatively and was found to be significantly above the level predicted by a strictly quasi-specular (e.g., Hagfors) process; it also is variable over the surface.
The author has identified the following significant results. Yield modelling for crop production estimation derived a means of predicting the within-a-year yield and the year-to-year variability of yield over some fixed or randomly located unit of area. Preliminary studies indicated that the requirements for interpreting LANDSAT data for yield may be sufficiently similar to those of signature extension that it is feasible to investigate the automated estimation of production. The concept of an advanced yield model consisting of both spectral and meteorological components was endorsed. Rationale for using meteorological parameters originated from known between season and near harvest dynamics in crop environmental-condition-yield relationships.
Tensile fatigue tests were conducted on several laminates of boron/aluminum (6061-0). In laminates with 0 deg fibers on the outside, an analysis that identifies "shakedown" conditions predicted the stress amplitude below which no fatigue damage accumulated. A fatigue damage accumulation model which relates matrix fatigue cracking and the overall laminate properties is described. A model for the saturation damage stage development is presented, that identical laminates, tested in directions 90 deg apart (such that one layup has 90 deg outer plies and the other 0 deg), have different fatigue behaviors due to the stacking sequence. The 90 deg plies on the surface develop cracks earlier than predicted by shakedown. An attempt was made to explain this stacking sequence effect. Variable load history effects on the fatigue damage response were investigated. Tests reveal that for a given stress ratio the specimen seeks the saturation damage state for the largest stress range to which it is subjected. It was also found that little damage is generated by shifting a given stress range down, whereas significant damage may be created by shifting it upward. The laminate stresses were always tensile.
It is found from the comparisons that large longitudinal aerodynamic differences exist between wind tunnel predictions and flight measurements. Cold gas plume simulation underpredicted Shuttle base pressure. It is concluded that observed flight prediction increments are probably caused by several factors such as input error, independent variable errors, plume effects, and Reynolds number effects.
Modeling the depth of regolith on asteroids is approached from a statistical point of view. It is demonstrated that average values are not good descriptors of regolith depth on asteroids. Large deviations from the average can be expected to occur due to both large variations in depth over the surface of a body and to the fact that each asteroid has a unique regolith. The utility of the average depth is not significantly increased by excluding the parts of a surface which are occupied by large craters; a procedure adopted in existing regolith models. Although an asteroid's surface may be 'smoothed out' by movement of debris into gravitationally low spots, the regolith depth retains its variability because of variations in topography at the bottom of the regolith layer. The large variability associated with regolith depth severely limits the power of regolith models in predicting parent body size for the brecciated meteorites.
Literature survey was conducted to determine the effects of different microstructural features and different load histories on fatigue crack initiation and propagation of aluminum alloys. Comparison of microstructure and monotonic and cyclic properties between powder metallurgy (P/M) and ingot metallurgy (I/M) alloys is presented. The two alloys that are representative of each process on which the comparison is focused are X7091 and 7050. Included is a detailed description of the microstructure produced through the P/M and I/M proesses. The effect of each pertinent microstructural feature on monotonic and cyclic properties, such as yield strength, toughness, crack initiation and propagation is discussed. Also discussed are the proposed mechanisms for crack initiation and propagation, as well as the effects of aggressive environments on these cyclic properties. The effects of variable amplitude loadin on fatigue crack propagation and the various models proposed to predict load interaction effects are discussed.
A previously derived theory is applied to a microstrip antenna with a reactive load to produce a dual-band radiator. A model consisting of a rectangular patch radiator loaded with a variable length short-circuited coaxial stub was investigated experimentally. Comparisons of theoretical predictions and experimental data are made for the impedance and resonant frequencies as a function of the position of the load, the length of the stub, and the characteristic impedance of the stub.
Most models of crop growth and yield require an estimate of canopy leaf area index (LAI) or absorption of radiation. Relationships between photosynthetically active radiation (PAR) absorbed by corn canopies and the spectral reflectance of the canopies were investigated. Reflectance factor data were acquired with a Landsat MSS band radiometer. From planting to silking, the three spectrally predicted vegetation indices examined were associated with more than 95 percent of the variability in absorbed PAR. The relationships developed between absorbed PAR and the three indices were evaluated with reflectance factor data acquired from corn canopies planted in 1979 through 1982. Seasonal cumulations of measured LAI and each of the three indices were associated with greater than 50 percent of the variation in final grain yields from the test years. Seasonal cumulations of daily absorbed PAR were associated with up to 73 percent of the variation in final grain yields. Absorbed PAR, cumulated through the growing season, is a better indicator of yield than cumulated leaf area index. Absorbed PAR may be estimated reliably from spectral reflectance data of crop canopies.
Observations made with the Einstein X-ray observatory and Exosat have shown Procyon (Alpha CMi) to have a measurable X-ray flux. The flux observed is similar to the upper limits previously reported. The interpretation of the X-ray data in the context of models made previously by Brown and Jordan (1981) based on spectra obtained with the IUE satellite. The X-ray data lead to a higher electron pressure than does the UV spectrum. These results support the conclusion by Brown and Jordan that the UV data cannot be reconciled with a hot corona in a spherically symmetric uniform model. Two types of models are explored; one in which the X-ray emission originates from an isothermal corona but the UV emission is restricted to limited regions of the disk, analogous to solar supergranulation structure; the other in which hot loop structures are embedded in a cool (T(e) of about 300,000 K) corona. Monitoring of Procyon to search for variability is urgently required to distinguish between these models. Some comparisons with the predictions of scaling laws are made. This hot isothermal coronal model agrees quite well with the predictions of Hearn's (1977) minimum flux model.
Development of the advanced turboprop has led to concerns about en route noise. Advanced turboprops generate low-frequency, periodic noise signatures at relatively high levels. As demonstrated in a flight test of NASA Lewis Research Center's Propfan Test Assessment (PTA) airplane in Alabama in October 1987, the noise of an advanced turboprop operating at cruise altitudes can be audible on the ground. The assessment of the en route noise issue is difficult due to the variability in received noise levels caused by atmospheric propagation and the uncertainty in predicting community response to the relatively low-level en route noise, as compared to noise associated with airport operations. The En Route Noise Test was designed to address the atmospheric propagation of advanced turboprop noise from cruise altitudes and consisted of measuring the noise of an advance turboprop at cruise in close proximity to the turboprop and on the ground. Measured and predicted ground noise levels are presented.
Radar studies of Mars have provided measurements of surface texture on scales of centimeters to hundreds of meters and measurements of surface material properties. Texture (rms surface tilts and estimates of small-scale roughness) may be inferred from dispersion and/or polarization of the radar echo; material properties (reflectivity of dielectric constant) are derived from echo strength. Mars is a diverse target; depending on location, rms surface tilts have been found to vary over the range 0.25 to 10 deg while reflectivity covers at least 3 to 13 percent. Plains units are the most variable, having both the smoothest and roughest surfaces, cratered terrain can be considered predictable and 'average' by comparison. Recent data identify scattering by small structures (perhaps rocks on or near the surface) as playing a more important role than previously recognized. Scattering by the residual ice cap near Mars' south pole is particularly unusual. The present state of radar surface studies is summarized.
Traditional design approaches for composite materials have employed deterministic criteria for failure analysis. New approaches are required to predict the reliability of composite structures since strengths and stresses may be random variables. This report will examine and compare methods used to evaluate the reliability of composite laminae. The two types of methods that will be evaluated are fast probability integration (FPI) methods and Monte Carlo methods. In these methods, reliability is formulated as the probability that an explicit function of random variables is less than a given constant. Using failure criteria developed for composite materials, a function of design variables can be generated which defines a 'failure surface' in probability space. A number of methods are available to evaluate the integration over the probability space bounded by this surface; this integration delivers the required reliability. The methods which will be evaluated are: the first order, second moment FPI methods; second order, second moment FPI methods; the simple Monte Carlo; and an advanced Monte Carlo technique which utilizes importance sampling. The methods are compared for accuracy, efficiency, and for the conservativism of the reliability estimation. The methodology involved in determining the sensitivity of the reliability estimate to the design variables (strength distributions) and importance factors is also presented.
The x-ray phenomena of the binary system SMC X-1/Sk 160, observed with the Ginga and ROSAT x-ray observatories, are compared with computed phenomena derived from a three dimensional hydrodynamical model of the stellar wind perturbed by x-ray heating and ionization which is described in the accompanying paper. In the model the BOI primary star has a line-driven stellar wind in the region of the x-ray shadow and a thermal wind in the region heated by x-rays. We find general agreement between the observed and predicted x-ray spectra throughout the binary orbit cycle, including the extended, variable, and asymmetric eclipse transitions and the period of deep eclipse.
The X-ray phenomena of the binary system SMC X-1/Sk 160, observed with the Ginga and ROSAT X-ray observatories, are compared with computed phenomena derived from a three-dimensional hydrodynamical model of the stellar wind perturbed by X-ray heating and ionization which is described in the accompanying paper (Blondin & Woo 1995). In the model the B0 I primary star has a line-driven stellar wind in the region of the X-ray shadow and a thermal wind in the region heated by X-rays. We find general agreement between the observed and predicted X-ray spectrum throughout the binary orbit cycle, including the extended, variable, and asymmetric eclipse transitions and the period of deep eclipse.
An estimate of the probability density function of a random vector is obtained by maximizing the mutual information between the input and the output of a feedforward network of sigmoidal units with respect to the input weights. Classification problems can be solved by selecting the class associated with the maximal estimated density. Newton's s method, applied to an estimated density, yields a recursive maximum likelihood estimator, consisting of a single internal layer of sigmoids, for a random variable or a random sequence. Applications to the diamond classification and to the prediction of a sun-spot process are demonstrated.