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Some of the simpler mathematical equations which may be used in Loran-C navigation calculations were examined. A technique is presented to allow Loran-C time differences to be predicted at a location. This is useful for receiver performance work, and a tool for more complex calculations, such as position fixing.
An unsteady finite difference procedure was used to calculate the steady inviscid flow over an 11% thickness ratio NASA supercritical profile of LWP 505 at M sub infinity = 0.80 and alpha = 0. An attempt is made to include the viscous effects using a modified form of Head's entrainment method to calculate the turbulent boundary layer. The attempt to predict the viscous effects using the compressible form of Head's integral method with a modified auxiliary equation for the form factors was unsatisfactory. Though a reasonably separation bubble was established on the lower surface, a grossly exaggerated displacement effect resulted downstream of the shock on the upper surface. There clearly is substantial further effort required to evolve a satisfactory boundary layer procedure, which must then be coupled in a still unproven manner with the inviscid procedure.
A discussion of various theoretical and experimental techniques for the calculation of long range interaction between two atomic systems at moderate separation is presented. Some applications of these techniques for obtaining gaseous properties are described. The forces between neutral molecules and metallic surfaces are also discussed and numerical values of heats of adsorption for a number of systems are calculated.
Calculations of the fan tone acoustic power and modal structure generated by complex distortions in axial inflow velocity are presented. The model used treats the motor as a rotating three-dimensional cascade and calculates the acoustic field from the distortion-produced dipole distribution on the blades including noncompact source effects. Radial and circumferential distortion shapes are synthesized from Fourier-Bessel components representing individual distortion modes. The relation between individual distortion modes and the generated acoustic modes is examined for particular distortion cases. Comparisons between theoretical and experimental results for distortions produced by wakes from upstream radial rods show that the analysis is a good predictor of acoustic power dependence on disturbance strength.
Calculation procedures for non-reacting compressible two- and three-dimensional turbulent boundary layers were reviewed. Integral, transformation and correlation methods, as well as finite difference solutions of the complete boundary layer equations summarized. Alternative numerical solution procedures were examined, and both mean field and mean turbulence field closure models were considered. Physics and related calculation problems peculiar to compressible turbulent boundary layers are described. A catalog of available solution procedures of the finite difference, finite element, and method of weighted residuals genre is included. Influence of compressibility, low Reynolds number, wall blowing, and pressure gradient upon mean field closure constants are reported.
A comparison is made between remote sensing data measured over water at altitudes ranging from 30 m to 15.2 km and data calculated for corresponding altitudes using surface measurements and an atmospheric radiative transfer model. Data were acquired on June 22, 1978 in Lake Erie, a cloudless, calm, near haze free day. Suspended solids and chlorophyll concentrations were 0.59 + or - 0.02 mg/1 and 2.42 + or - 0.03 micrograms/1 respectively throughout the duration of the experiment. Remote sensor data were acquired by two multispectral scanners each having 10 bands between 410 nm and 1040 nm. Calculated and measured nadir radiances for altitudes of 152 m and 12.5 km agree to within 16% and 14% respectively. The variation in measured radiance with look angle was poorly simulated by the model. It was concluded that an accurate assessment of the source of error will require the inclusion in the analysis of the contributions made by the sea state and specular sky reflectance.
A study was performed to determine the effects of the number and position of total pressure probes on the calculation of five compressor face distortion descriptors. This study used three sets of 320 steady state total pressure measurements that were obtained with a special rotating rake apparatus in wind tunnel tests of a mixed-compression inlet. The inlet was a one third scale model of the inlet on a YF-12 airplane, and it was tested in the wind tunnel at representative flight conditions at Mach numbers above 2.0. The study shows that large errors resulted in the calculation of the distortion descriptors even with a number of probes that were considered adequate in the past. There were errors as large as 30 and -50 percent in several distortion descriptors for a configuration consisting of eight rakes with five equal-area-weighted probes on each rake.
A simple charge balance model based on the work of DeForest was adapted for the calculation of spacecraft potentials. The model was calibrated with ATS 5 plasma data. Once calibrated, the model was used to calculate the time-varying potential that was observed as a spacecraft passes in and out of eclipse. Errors on the order of + or - 800 volts were observed over a range of 0 to -10,000 volts. Possible applications of the model to large space structures are discussed.
The impact of oxygen enrichment of the combustion air on the generator and overall plant performance was studied for the ECAS-scale MHD/steam plants. A channel optimization technique is described and the results of generator performance calculations using this technique are presented. Performance maps were generated to assess the impact of various generator parameters. Directly and separately preheated plant performance with varying O2 enrichment was calculated. The optimal level of enrichment was a function of plant type and preheat temperature. The sensitivity of overall plant performance to critical channel assumptions and oxygen plant performance characteristics was also examined.
This method uses a so-called panel method to calculate incompressible flow about arbitrary three-dimensional inlets with or without centerbodies for four fundamental flow conditions: unit onset flows parallel to each of the coordinate axes plus static operation. The computing time is scarcely longer than for a single solution. A linear superposition of these solutions quite rigorously gives incompressible flow about the inlet for any angle of attack, angle of yaw, and mass flow rate. Compressibility is accounted for by applying a well-proven correction to the incompressible flow. Since the computing times for the combination and the compressibility correction are small, flows at a large number of inlet operating conditions are obtained very cheaply. A number of graphical output features are provided to aid the user, including streamline tracing and automatic generation of curves of constant pressure, Mach number, and flow inclination at selected inlet cross sections. This paper describes the method in some detail and presents calculated results.
Calculations of the fan tone acoustic power and modal structure generated by complex distortions in axial inflow velocity are presented. The model used treats the rotor as a rotating three-dimensional cascade and calculates the acoustic field from the distortion-produced dipole distribution on the blades including noncompact source effects. Radial and circumferential distortion shapes are synthesized from Fourier-Bessel components representing individual distortion modes. The relation between individual distortion modes and the generated acoustic modes is examined for particular distortion cases. Comparisons between theoretical and experimental results for distortions produced by wakes from upstream radial rods show that the analysis is a good predictor of acoustic power dependence on disturbance strength.
The general reaction theory of Feshbach is applied to the calculation of resonant effects in near-threshold electron-positive-ion excitation. The theory divides configuration space into open- and closed-channel parts, resonance effects being described by the closed-channel part. The open-channel part is handled in a distorted-wave approximation to the set of open-channel coupled equations. Various methods are suggested for handling the closed-channel part. However, an 'attached-excited-target approximation' is used explicitly, which is further approximated by a set of uncoupled closed-channel equations. As an example, the 1 1S-2 1P excitation cross section of O VII below the 3 3S threshold is calculated. Various distorted-wave approximations are investigated and results from most of them are quite similar. Resonant effects arising from the attachment of the colliding electron with the 3 3S state are found to be small, but other close-lying n = 3 states have not yet been included.
Results of an atomistic calculation supporting two-dimensional diffusion of a Pt atom on a Pt(110) surface are presented. The calculations for diffusion energies indicate that interchannel diffusion by the replacement of a channel-wall atom by the adatom is energetically favorable.
A previously published numerical method to calculate the radiation properties of parabolic reflectors has been modified to also include very large spherical reflectors. The method has been verified by comparing the calculated and the measured results for a 120-wavelength spherical reflector.
Progress in the application of finite-volume methods to the calculation of transonic potential flows past general wing-body combinations is reviewed. Two different methods of generating boundary-conforming grids are investigated, and the results compared to provide an estimate of solution sensitivity to grid geometry. Both conservative and quasi-conservative difference schemes are used in one of the coordinate systems. Results show that the error introduced by the quasi-conservative formulation seems to be small, although a one-dimensional analysis suggests that schemes of this type do not necessarily produce mass-conserving shocks. Comparison of calculated results with experimental data for realistic fuselage geometries clearly shows the importance of modelling the effect of fuselage geometry upon the wing pressure distribution.
A computer program called NEQRAP is described that calculates the radiative properties of nonequilibrium ionized hydrogen. From the given electron temperature, electron density, and atom density values (which do not necessarily satisfy the equilibrium relationship) and intensities of incident radiation, the non-Boltzmann populations of electronic states are computed by solving the equation of quasi-steady-state population distribution. Emission and absorption coefficients are determined as functions of wavelength by invoking the principle of detailed balance between the upper and lower states of each radiative transition. Radiative transport through the medium is computed assuming a one-dimensional uniform slab. The rate of ionic reaction is also computed. When used on a sample case, the program shows that there is a large difference between the calculated intensities of radiation emitted by a bulk of equilibrium and nonequilibrium hydrogen. The accuracy of the program is estimated to be better than 10%.
A new technique to improve Woodward's (1968) unified subsonic and supersonic panel method is described. The pressure prediction is improved based on a new two-dimensional theory. The method used by Lan (1977) is then used to calculate the leading-edge and side-edge suction forces by direct use of the predicted pressure distribution. The method is applicable to both subsonic and supersonic flow. It is shown that the improved Woodward panel method is capable of accurately predicting leading-edge and side-edge suction forces in subsonic and supersonic flow. Therefore, the method can be used not only to predict the vortex lift of complex planforms through the method of suction analogy, but also to calculate some lateral-directional stability derivatives.
The present paper compares remote sensing data measured over water at altitudes ranging from 30 m to 15.2 km to data calculated for corresponding altitudes using surface measurements and an atmospheric radiative transfer model. The data were acquired on June 22, 1978 in Lake Erie and it was found that suspended solids and chlorophyll concentrations were 0.59 + or - 0.02 mg/liter and 2.42 + or - 0.03 micro gram/liter respectively throughout the duration of the experiment. Calculated and measured nadir radiances for altitudes of 152 m and 12.5 km agree to within 16% and 14% respectively. It is noted that the model offered a poor simulation of the variation in measured radiance with look angle. Finally, it is concluded that an accurate assessment of the source of error will require the inclusion in the analysis of the contributions made by the sea state and specular sky reflectance