Search NASA⌕ Search

SEARCH · Search NASA

Results for “Analytic derivatives”

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 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Analytical modeling of under-the-wing externally blown flap powered-lift noise

The sound field produced by the interaction of a subsonic jet with a large-scale model of the under the wing externally blown flap in an approach attitude was analyzed. The analysis was performed to obtain a better understanding of the dominant noise sources and the mechanisms governing the peak sound pressure level frequencies of the broadband spectra. An analytical expression is derived which incorporates two available theories and experimental data; the expression predicts the sound field along a circular arc of approximately 120 deg measured from the upstream jet axis in the fly-over plane. The analysis compares favorably with test results obtained from two large-scale models, one using cold air from a conical nozzle and the other using hot gas from a TF-34 turbofan engine having a conical exhaust nozzle with a 12 lobe internal forced mixer. The frequency at which the peak sound pressure level occurs appears to be governed by a phenomenon which produces periodic formation and shedding of large-scale turbulence structures from the nozzle lip.

Mckinzie, D. J., Jr.↗
NASA NTRS1978

Galactic civilizations: Population dynamics and interstellar diffusion

The interstellar diffusion of galactic civilizations is reexamined by potential theory; both numerical and analytical solutions are derived for the nonlinear partial differential equations which specify a range of relevant models, drawn from blast wave physics, soil science, and, especially, population biology. An essential feature of these models is that, for all civilizations, population growth must be limited by the carrying capacity of the environment. Dispersal is fundamentally a diffusion process; a density-dependent diffusivity describes interstellar emigration. Two models are considered: the first describing zero population growth (ZPG), and the second which also includes local growth and saturation of a planetary population, and for which an asymptotic traveling wave solution is found.

Newman, W. I.↗
NASA NTRS1978

Tidal friction in the solid earth

The earth's imperfectly elastic response to body and loading tidal forces is discussed using complex Love numbers and complex mass loading coefficients. Exact analytical expressions were derived relating the energy dissipation within an inhomogeneous, compressible solid earth to the surface values of these complex characteristic numbers, thus relating the global dissipation function Q to the phase shifts in the potential, gravity, tilt, strain and displacement tides. Integration of a global ocean tidal model shows that energy dissipated in the solid earth due to ocean loading is at least 10% of that dissipated in the body tides.

Zschau, J.↗
NASA NTRS1979

Interaction between a normal shock wave and a turbulent boundary layer at high transonic speeds. Part 1: Pressure distribution

Analytical solutions are derived which incorporate additional physical effects as higher order terms for the case when the sonic line is very close to the wall. The functional form used for the undisturbed velocity profile is described to indicate how various parameters will be calculated for later comparison with experiment. The basic solutions for the pressure distribution are derived. Corrections are added for flow along a wall having longitudinal curvature and for flow in a circular pipe, and comparisons with available experimental data are shown.

Messiter, A. F.↗
NASA NTRS1979

Cardiovascular regulatory response to lower body negative pressure following blood volume loss

An attempt is made to explain the cardiovascular regulatory responses to lower body negative pressure (LBNP) stress, both in the absence of and following blood or plasma volume loss, the latter being factors regularly observed with short- or long-term recumbency or weightlessness and associated with resulting cardiovascular deconditioning. Analytical expressions are derived for the responses of mean venous pressure and blood volume pooled in the lower body due to LBNP. An analysis is presented for determining the HR change due to LBNP stress following blood volume loss. It is concluded that the reduced orthostatic tolerance following long-term space flight or recumbency can be mainly attributed to blood volume loss, and that the associated cardiovascular responses characterizing this orthostatic intolerance is elicited by the associated central venous pressure response.

Shimizu, M.↗
NASA NTRS1979

Input filter design for switching regulators

A small signal average model is derived to study analytically the complex interaction among input filter, output filter and control loop, which frequently causes degradation of switch regulator performance. Analytically based design guidelines are formulated, and key design parameters are identified. It is shown that minimization of the forward transfer characteristics and the output impedance of the input filter at filter resonance are key to designing an input filter for a switching regulator with given output filter parameters and specified line and load conditions.

Lee, F. C.↗
NASA NTRS1979

Pre-Voyager velocities, accelerations and shrinkage rates of Jovian cloud features

Voyager I data provide detailed information on the latitudinal dependence of velocities in the Jovian atmosphere. In the present paper, pre-Voyager velocity data are summarized, and gross differences with the Voyager I results are revealed. Analytical expressions are derived for the shrinkage rates and acceleration of the Great Red Spot and white ovals (located at -23 degrees and -34 degrees latitude, respectively) for the period from 1943 to 1979.

Beebe, R. F.↗
NASA NTRS1979

Effect of streamwise vortices on Tollmien-Schlichting waves

The method of multiple scales is used to determine a first order uniform expansion for the effect of counter rotating steady streamwise vortices in growing boundary layers on Tollmien-Schlichting waves. The results show that such vortices have a strong tendency to amplify three dimensional Tollmien-Schlichting waves having a spanwise wavelength that is twice the wavelength of the vortices. An analytical expression is derived for the growth rates of these waves. These growth rates increase linearly with increasing amplitudes of the vortices.

Nayfeh, A. H.↗
NASA NTRS1980

Analysis and design of a uniform-clearance, pumping-ring rod seal for the Stirling engine

A uniform clearance pumping ring, as opposed to the conventional taper clearance one, is described. The uniform clearance concept eliminates complex elastohydrodynamic problems and enables a simple analytical treatment to be made. An analytical expression is derived for the pumping rate showing the effect of various design parameters on the pumping ring's performance. An optimum clearance is found by which the pumping rate is maximized and a numerical example is presented to demonstrate the potential of the uniform clearance design.

Etsion, I.↗
NASA NTRS1979

Surface temperature variations as measured by the Heat Capacity Mapping Mission

The AEM-1 satellite, the Heat Capacity Mapping Mission, has acquired high-quality thermal infrared data at times of day especially suited for studying the earth's surface and the exchange of heat and moisture with the atmosphere. Selected imagery illustrates the considerable variability of surface temperature in and around cities, in the dry southwestern United States, in the Appalachian Mountains, and in agricultural areas. Through simplifying assumptions, an analytic experience is derived that relates day/night temperature differences to the near-surface layer (thermal inertia) and to meteorological factors. Analysis of the result suggests that, in arid regions, estimates of relative thermal inertia may be inferred, whereas, in agricultural areas, a hydrologic interpretation is possible.

Price, J. C.↗
NASA NTRS1980

Thermal bremsstrahlung from high-temperature plasmas

Analytic expressions are derived for the total bremsstrahlung energy-loss rate per unit volume and the spectral emission rate of a very hot (10 million K to 1 billion K) plasma. At these temperatures the principal contribution to emission can be computed from the nonrelativistic limit of electron-ion bremsstrahlung in the Born approximation. Modifications to this rate are evaluated from (1) relativistic corrections to the thermal-electron velocity distribution function, (2) relativistic and spin corrections to the nonrelativistic electron-ion bremsstrahlung cross section, (3) electron-electron bremsstrahlung, and (4) first-order Born approximation corrections to electron-ion bremsstrahlung.

Gould, R. J.↗
NASA NTRS1980

Spacecraft momentum management procedures

Techniques appropriate for implementation onboard the space telescope and other spacecraft to manage the accumulation of momentum in reaction wheel control systems using magnetic torquing coils are described. Generalized analytical equations are derived for momentum control laws that command the magnetic torquers. These control laws naturally fall into two main categories according to the methods used for updating the magnetic dipole command: closed loop, in which the update is based on current measurements to achieve a desired torque instantaneously, and open-loop, in which the update is based on predicted information to achieve a desired momentum at the end of a period of time. Physical interpretations of control laws in general and of the Space Telescope cross product and minimum energy control laws in particular are presented, and their merits and drawbacks are discussed. A technique for retaining the advantages of both the open-loop and the closed-loop control laws is introduced. Simulation results are presented to compare the performance of these control laws in the Space Telescope environment.

Chen, L. C.↗
NASA NTRS1981

Effect of streamwise vortices on Tollmien-Schlichting waves

The method of multiple scales is used to determine a first-order uniform expansion for the effect of counter-rotating steady streamwise vortices in growing boundary layers on oblique Tollmien-Schlichting waves. The results show that such vortices have a strong tendency to amplify oblique Tollmien-Schlichting waves having a spanwise wavelength that is twice the wavelength of the vortices. An analytical expression is derived for the growth rates of these waves. These exponential growth rates increase linearly with increasing amplitudes of the vortices. Numerical results are presented. They suggest that this mechanism may dominate the instability.

Nayfeh, A. H.↗
NASA NTRS1981

Eikonal approximation for charge transfer from a multielectron atom to fast projectiles

The eikonal approach developed previously for calculating electron-capture cross sections for bare projectiles colliding with hydrogenic targets is extended here to allow for multielectron targets. Both the impact and wave pictures are employed and their equivalence is discussed. As a first approximation, each atomic orbital is specified by the three hydrogenic quantum numbers, an effective nuclear charge Z sub t, and an energy eigenvalue in the impact picture, or ionization potential in the wave picture. The Z sub t prime appearing in the eikonal phase factor is left undetermined because of incomplete information on the many-body target. However, analytic expressions are derived for the theoretical cross sections, and numerical values are calculated for simple choices of Z sub t prime. Those results are compared with existing experimental data for C, Ne, Ar, N2, O2, and He targets.

Ho, T. S.↗
NASA NTRS1983

Sound diffraction at wall impedance discontinuities in a circular cylinder, investigated using Wiener-Hopf technique

Rigorous solutions are presented for sound diffraction in a circular cylinder with axial discontinuities of the wall admittance (or impedance). Analytical expressions are derived for the reflection and the transmission coefficients for duct modes. The results are discussed quantitatively in the limits of small admittance shifts (delta) and of low frequencies (ka). One of the results is the low frequency behavior of the reflection coefficient R(o) sub 00 of the fundamental mode. For the mode of a hardwall duct reflected from the junction with a softwall duct, (R(o) sub oo yields - (1-square root of (ka) square root of (2/i delta)); this result is in contrast to the frequency dependence of the reflection from the open end of a hardwall duct, for which R(o) sub oo yields - 1-(ka) squared/2 .

Cho, Y. C.↗
NASA NTRS1982

On the statistical uncertainties associated with line profile fitting

The paper considers the statistical uncertainties in the best-fit parameters associated with the fitting of observational data by model line profiles of specific form. The parameters involved are amplitude, center, and width. A general procedure is described for any profile type of parametric form. The case of Gaussian profiles is treated in detail, and numerical solutions are presented for equally spaced data of equal weight. Approximate analytical solutions are derived that give good general agreement with the numerical solutions over the whole range of interest. Approximate solutions are also obtained for the case of Lorentzian profiles. It is shown that the Lorentzian results can be used in conjunction with the Gaussian results to estimate the corresponding parameter uncertainties in the case of the general Voigt profile.

Landman, D. A.↗
NASA NTRS1982

Climatic influence of background and volcanic stratosphere aerosol models

A simple modelization of the earth atmosphere system including tropospheric and stratospheric aerosols has been derived and tested. Analytical expressions are obtained for the albedo variation due to a thin stratospheric aerosol layer. Also outlined are the physical procedures and the respective influence of the main parameters: aerosol optical thickness, single scattering albedo and asymmetry factor, and sublayer albedo. The method is applied to compute the variation of the zonal and planetary albedos due to a stratospheric layer of background H2SO4 particles and of volcanic ash.

Deschamps, P. Y.↗
NASA NTRS1983

Thick plate flexure

Analytical expressions are derived for the displacements and stresses due to loading of a floating, uniform, elastic plate of arbitrary thickness by a plane or axisymmetric harmonic load. The solution is exact except for assumptions of small strains and linear boundary conditions, and gravitation within the plate is neglected. For typical earth parameters its predictions are comparable to those of the usual thin plate theory frequently assumed in studies of lithospheric flexure, gravity and regional isostasy. Even for a very thick lithosphere, which may exist in some regions of Mars, the thin plate theory is a better approximation to the thick plate solution than the elastic half-space limit, except for short-wavelength loads.

Comer, R. P.↗