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NASA NTRS1979

Theory of direct scattering of neutral and charged atoms

The theory for direct elastic and inelastic collisions between composite atomic systems formulated within the framework of the Glauber approximation is presented. It is shown that the phase-shift function is the sum of a point Coulomb contribution and of an expression in terms of the known electron-hydrogen-atom and proton-hydrogen-atom phase shift function. The scattering amplitude is reexpressed, the pure Coulomb scattering in the case of elastic collisions between ions is isolated, and the exact optical profile function is approximated by a first-order expansion in Glauber theory which takes into account some multiple collisions. The approximate optical profile function terms corresponding to interactions involving one and two electrons are obtained in forms of Meijer G functions and as a one-dimensional integral, and for collisions involving one or two neutral atoms, the scattering amplitude is further reduced to a simple closed-form expression.

Franco, V.↗

NASA NTRS1979

Empirical relationships between interplanetary conditions, magnetospheric flux transfer, and the AL index

Holzer and Slavin (1978) have found that the transfer of magnetic flux to and from the dayside magnetosphere as inferred from observed displacements of the magnetopause surface is correlated with both the magnitude of the auroral zone magnetic index AL and the incident flux of southward IMF. Empirical expressions specifying the rate at which magnetic flux is eroded in terms of interplanetary parameters and the rate of magnetic flux return as a function of AL have been developed. These relations are then used to predict magnetotail magnetic field enhancements from interplanetary and ground based data during an interval of substorm activity. The total magnetic flux in the tail is increased during intervals when the amount of flux transferred into its volume by dayside erosion exceeds the flux lost to the dayside by magnetospheric convection. Using Ogo-5 tail observations it is found for the sample events considered that these magnetic field enhancements can be described by empirical expressions for the magnetic flux transfer rates.

Slavin, J. A.↗

NASA NTRS1979

Analysis of the vibratory excitation of gear systems. II - Tooth error representations, approximations, and application

The second part of a theory for predicting the vibratory excitation of gear systems from fundamental descriptions of gear tooth elastic properties and deviations of tooth faces from perfect involute surfaces is presented. The first part of the theory provides expressions for the Fourier-series coefficients of the vibratory excitation, and this paper gives expressions for these Fourier-series coefficients in terms of easily interpreted gear tooth metrics that are readily evaluated from tooth-face measurements. Results are given for rectangular tooth-face contact regions using two-dimensional Legendre polynomial expansions of local tooth-pair stiffnesses and stiffness-weighted deviations of tooth faces from perfect involute surfaces. A rigorous transfer function approach is developed that permits separation of the effects of gear tooth errors and gear design parameters; the theory is applicable to helical and spur gears and is illustrated with measurements of tooth-spacing errors and tooth profiles obtained from a pair of spur gears.

Mark, W. D.↗

NASA NTRS1979

The erosion of planetary and satellite atmospheres by energetic atomic particles

Analytic expressions are presented which may be used to compute the sputter-erosion yield from any unimolecular gravitationally bound gas by any atomic charged particle of any energy. A calculation of solar wind proton and alpha particle induced erosion of the CO2 atmosphere of Mars predicts molecular sputtering yields. An expression for the emission yield of energetic molecular fragments produced in primary knock-on events is given in closed form; such fragment emission is of secondary importance for mass loss compared to the molecular yield itself. Erosion by radiation belt protons of a hypothetical thin O2 atmosphere associated with the Jovian satellite Ganymede is considered, and molecular sputtering yields for proton energies are determined.

Haff, P. K.↗

NASA NTRS1980

The influence of a voltage ramp on the measurement of I-V characteristics of a solar cell

For efficiency and convenience the voltage applied to a Si solar cell is often fairly rapidly driven from zero to the open circuit value typically at a common rate of 1 V per millisecond. During this time the values of current are determined as a function of the instantaneous voltage thus producing an I-V characteristic. The present paper shows that the customary expressions for the current as a function of cell parameters still remain valid provided that the diffusion length in the expression for the dark current is changed from its steady state value L to the effective diffusion length L1 given by L1 = L(1 + qV/kT.tau) to the -1/2, where V is the ramp rate considered constant and tau is the lifetime of minority carriers. This result is true to a very good approximation provided that low level injection prevails.

Von Roos, O.↗

NASA NTRS1980

Buckling of periodic structures

Equations are developed for the buckling of a general lattice structure that has repetitive geometry. Equilibrium at a typical node is expressed using finite element techniques, and the only assumption is that the response is periodic. By basing the stiffness matrix on the exact solution of the beam column equation, accurate results are obtained for complex buckling behavior that would require a very large system of equations using conventional techniques. The present method requires the eigenvalues of only a 6x6 determinant. The results are used to study the buckling of isogrid cylinders, three-element truss columns and polygonal rings. Details of the analysis including expressions for all terms in the governing stability determinant are given.

Anderson, M. S.↗

NASA NTRS1980

A simplified method for the calculation of diurnally averaged photodissociation rates

Expressions are given for the calculation of the diurnally averaged transmission of solar flux from a series summation involving relatively few terms and readily available mathematical functions. It is shown that these expressions can be scaled to remove much of the dependence on latitude and solar declination so that at large optical depth, they become asymptotic to a function which depends only on the optical depth at noon and displays an inverse-square-root variation. From this variation, a simple analytic form containing one adjustable parameter is proposed. The functional dependence of this parameter on latitude and solar declination is determined by numerical fitting procedures. The accuracy of the analytic approximation is better than 4.5% for all altitudes, latitudes and seasons of the year.

Boughner, R. E.↗

NASA NTRS1980

Delta V errors due to attitude correction maneuvers of a spinning spacecraft

A statistical error analysis has been performed to evaluate the change in velocity of a spin stabilized spacecraft due to thruster induced attitude correction maneuvers. Analytical expressions were developed to determine the mean and variance of the velocity in terms of the nominal values and uncertainties of key spacecraft parameters. These parameters include thrust, thruster timing, thruster alignment, plume impingement force and estimated spacecraft mass. Typical values of these parameters and their uncertainties for NASA's Galileo spacecraft were used to evaluate these expressions. The results of the analysis allow the effect of attitude correction maneuvers to be evaluated with respect to the functional requirements on nongravitational acceleration. Other results include the identification of major sources of delta V error and studies of the sensitivity of delta V to variations in the error sources.

Zipursky, H. J.↗

NASA NTRS1980

Compliance and stress intensity coefficients for short bar specimens with chevron notches

For the determination of fracture toughness especially with brittle materials, a short bar specimen with rectangular cross section and chevron notch can be used. As the crack propagates from the tip of the triangular notch, the load increases to a maximum then decreases. To obtain the relation between the fracture toughness and maximum load, calculations of Srawley and Gross for specimens with a straight-through crack were applied to the specimens with chevron notches. For the specimens with a straight-through crack, an analytical expression was obtained. This expression was used for the calculation of the fracture toughness versus maximum load relation under the assumption that the change of the compliance with crack length for the specimen with a chevron notch is the same as for a specimen with a straight-through crack.

Munz, D.↗

NASA NTRS1980

Effect of geometry and operating conditions on spur gear system power loss

The results of an analysis of the effects of spur gear size, pitch, width and ratio on total mesh power loss for a wide range of speeds, torques and oil viscosities are presented. The analysis uses simple algebraic expressions to determine gear sliding, rolling and windage losses and also incorporates an approximate ball bearing power loss expression. The analysis shows good agreement with published data. Large diameter and fine-pitched gears had higher peak efficiencies but lower part-load efficiency. Gear efficiencies were generally greater than 98 percent except at very low torque levels. Tare (no-load) losses are generally a significant percentage of the full-load loss except at low speeds.

Anderson, N. E.↗

NASA NTRS1980

A solution of the variational equations for elliptic orbits in rotating coordinates

For elliptic reference orbits, formulas are given for the perturbation state transition matrix of the two-body problem. The formulas relate perturbations expressed in a local vertical rotating coordinate system and are valid for motion in the linear neighborhood of reference orbits with e in the range of 0 to 1. The elements of the state transition matrix are expressed in terms of natural parameters (horizontal and radial velocity, radius, eccentricity, true anomaly, etc.) at the initial and final points. In addition to the general form, a simplified version, valid for small eccentricity orbits, is given.

Jones, J. B.↗

NASA NTRS1980

Asymptotic behavior of the efficiencies in Mie scattering

Consideration is given to the asymptotic behavior of the Mie scattering and extinction efficiencies for large absorbing spheres as sphere size approaches infinity. It is shown that the method used by Chylek (1975) for evaluating the infinite sums over the Mie partial wave coefficients representing these efficiencies and proving that the extinction efficiency approaches 2 is invalid, despite the correctness of the result, and that the limiting expression for the scattering efficiency obtained by this method is also incorrect. An analytical expression is then derived from geometrical optics considerations for the scattering efficiency limit which is valid when the imaginary component of the refractive index is much less than 1.

Acquista, C.↗

NASA NTRS1980

A current access, self-structured, multilayered bubble domain memory

Preliminary experimental results are reported on a self-structured, multilayer bubble memory with buried data layer. Stripe domains are used to move carrier bubbles by magnetostatic coupling. An expression is derived for that coupling as a function of thickness of the GGG separation layer. Experimental values of coupling are given as a function of bias field. An expression for stripe curvature as a function of bias field is derived. The performance of seven different current access stripe propagation circuits is reported.

Stermer, R. L., Jr.↗

NASA NTRS1980

Multi-mode horn antenna simulation

Radiation patterns were computed for a circular multimode horn antenna using waveguide electric field radiation expressions. The circular multimode horn was considered as a possible reflector feed antenna for the Large Antenna Multifrequency Microwave Radiometer (LAMMR). This horn antenna uses a summation of the TE sub 11 deg and TM sub 11 deg modes to generate far field primary radiation patterns with equal E and H plane beamwidths and low sidelobes. A computer program for the radiation field expressions using the summation of waveguide radiation modes is described. The sensitivity of the multimode horn antenna radiation patterns to phase variations between the two modes is given. Sample radiation pattern calculations for a reflector feed horn for LAMMR are shown. The multimode horn antenna provides a low noise feed suitable for radiometric applications.

Dod, L. R.↗

NASA NTRS1980

The multispecies modeling of the premixed, laminar steady-state ozone flame

Species dependent kinetic, transport and thermodynamic coefficients were employed in a one dimensional model of the premixed, laminar, steady state ozone flame. Convenient expressions for these coefficients are reported. They are based on independent measurements, no arbitrary parameters are used. The governing equations are solved using a relaxation technique and the partial differential equation package, PDECOL. Species and temperature profiles and the burning velocities are found over the range of initial ozone mole fraction of 0.25 to 1.00. The computed burning velocities are no more than 30% greater than the measurements of Streng and Grosses. Comparison with the computed results of Warnatz shows agreement within + or - 12%, even though quite different expressions for some of the kinetic coefficients were used. These differences are most obvious in the atomic oxygen and temperature profiles at an initial ozone mole fraction of unity.

Heimerl, J. M.↗

NASA NTRS1981

A sensitivity model for energy consumption in buildings. Part 1: Effect of exterior environment

A simple analytical model is developed for the simulation of seasonal heating and cooling loads of any class of buildings to complement available computerized techniques which make hourly, daily, and monthly calculations. An expression for the annual energy utilization index, which is a common measure of rating buildings having the same functional utilization, is derived to include about 30 parameters for both building interior and exterior environments. The sensitivity of a general class building to either controlled or uncontrolled weather parameters is examined. A hypothetical office type building, located at the Goldstone Space Communication Complex, Goldstone, California, is selected as an example for the numerical sensitivity evaluations. Several expressions of variations in local outside air temperature, pressure, solar radiation, and wind velocity are presented.

Lansing, F. L.↗

NASA NTRS1981

Impulsive phase of solar flares. 1: Characteristics of high energy electrons

The variation along a magnetic field line of the energy and pitch angle distribution of high energy electrons injected into a cold hydrogen plasma containing either an open or closed magnetic field structure was investigated. The problem is formulated as a time independent Fokker-Planck Equation for the electron number distribution as a function of the electron energy, electron pitch angle, and the structure of the global magnetic field. Simple analytic solution valid in the small pitch angle regime and for slowly varying magnetic field is presented. For the more general situation a numerical code for solving the Fokker-Planck Equation was used and it was found that the analytic expression agrees well with the numerical results to values of the pitch angle much larger than expected. For most practical applications, one many confidently use the analytic expression instead of having to resort to lengthy numerical computations. These results are useful in the study of the nonthermal models of the impulsive phase of solar flares.

Leach, J.↗

NASA NTRS1981

Acceleration wave breakup of liquid jets with airstreams

Characteristic mean drop diameters were determined for downstream and upstream injection into nonswirling and swirling airflows. The effects of the aerodynamic and liquid surface forces on the mean drop size were obtained with a scanning radiometer. Water jet breakup was studied primarily in the acceleration wave regime with values of WeRe 10 to the 6th power and the following empirical expression was obtained: D(o)/D(m) =C (WeRe) to the 0.4, power where D(o) and D(m) are the orifice and mean drop diameters, respectively. We and Re are the Weber and Reynolds numbers defined as repectively, We = rho(a)D(o)V(r)/sigma and Re = D(o)V(r)/nu, where V(r) and rho(a) are airstream relative velocity and density, respectively, and sigma and nu are surface tension and kinematic viscosity of the liquid, respectively. The proportionally constant C was evaluated as follows: for downstream injection, C = 0.023 with nonswirling airflow, and C = 0.027 with swirling airflow. For upstream injection, the empirical expression D(o)/D(m) = 0.0045 (WeRe) to the 0.5 power was obtained with nonswirling airflow. Experimental conditions included a water flow rate of 68 liter per hour and an airflow rate per unit area range of 4.6 to 25.2 gm/sq cm sec at 293 K and atmospheric pressure.

Ingebo, R. D.↗