Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Expression”

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 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Isothermal elastohydrodynamic lubrication of point contacts. 4: Starvation results

The influence of lubricant starvation on minimum film thickness was investigated by moving the inlet boundary closer to the contact center. The following expression was derived for the dimensionless inlet distance at the boundary between the fully flooded and starved conditions: m* = 1 + 3.06 ((R/b)(R/b)H) to the power 0.58, where R is the effective radius of curvature, b is the semiminor axis of the contact ellipse, and H is the central film thickness for fully flooded conditions. A corresponding expression was also given based on the minimum film thickness for fully flooded conditions. Therefore, for m m*, starvation occurs and, for m m*, a fully flooded condition exists. Two other expressions were also derived for the central and minimum film thicknesses for a starved condition. Contour plots of the pressure and the film thickness in and around the contact are shown for the fully flooded and starved lubricating conditions, from which the film thickness was observed to decrease substantially as starvation increases.

Hamrock, B. J.↗
NASA NTRS1976

On the physical interpretation of the cosmic-ray transport equations

It is pointed out that an earlier paper (Jokipii and Parker, 1967) had discussed in detail the question of the interpretation of the energy-change terms in the general equation for cosmic-ray transport in the solar wind, so that no need exists to reassess the physical interpretation, as urged by Gleeson and Webb (1974). The question concerns the expression for the adiabatic deceleration, which is 'replaced' by an expression for the mean rate of change of momentum of fast particles. It is pointed out that these two expressions represent two essentially different quantities. The adiabatic deceleration refers to the mean rate loss of kinetic energy of an individual particle as a result of the expansion of the gas and magnetic field of the wind. This parameter can in no way depend on the gradient of the fast particle density, as does the mean rate of change of momentum of the fast particles.

Jokipii, J. R.↗
NASA NTRS1976

Dynamic ductile fracture of a central crack

A central crack, symmetrically growing at a constant speed in a two dimensional ductile material subject to uniform tension at infinity, is investigated using the integral transform methods. The crack is assumed to be the Dugdale crack, and the finite stress condition at the crack tip is satisfied during the propagation of the crack. Exact expressions of solution are obtained for the finite stress condition at the crack tip, the crack shape, the crack opening displacement, and the energy release rate. All those expressions are written as the product of explicit dimensional quantities and a nondimensional dynamic correction function. The expressions reduce to the associated static results when the crack speed tends to zero, and the nondimensional dynamic correction functions were calculated for various values of the parameter involved.

Tsai, Y. M.↗
NASA NTRS1977

Computer transformation of partial differential equations into any coordinate system

The use of tensors to provide a compact way of writing partial differential equations in a form valid in all coordinate systems is discussed. In order to find solutions to the equations with their boundary conditions they must be expressed in terms of the coordinate system under consideration. The process of arriving at these expressions from the tensor formulation was automated by a software system, TENSR. An allied system that analyzes the resulting expressions term by term and drops those that are negligible is also described.

Sullivan, R. D.↗
NASA NTRS1977

Theory of motion of Jupiter's Galilean satellites

Final results are presented for a theory enabling one to calculate the positions of the Galilean satellites and their partial derivatives. Extensive use of algebraic manipulation software on a digital computer is made to generate the final expressions. The theory is, in effect, a revitalization of Sampson's (1921) theory. Algebraic and mathematical errors existing in Sampson's work are removed, some neglected effects due to solar interactions and the 3-7 commensurability are introduced, allowance is made for nonzero amplitude and phase of the free libration, and the final results are expressed as analytic functions of variations in 49 arbitrary constants of integration and physical parameters. The theory is constructed in a manner which readily allows for future revision, and analytic expressions are provided for the partial derivatives with respect to the 49 parameters.

Lieske, J. H.↗
NASA NTRS1976

Construction of analytically solvable models for interacting species

The basic form of a model representation for systems of n interacting biological species is a set of essentially nonlinear autonomous ordinary differential equations. A generic canonical expression for the rate functions in the equations is reported which permits the analytical general solution to be obtained by elementary computation. It is shown that a general analytical solution is directly obtainable for models where the rate functions are prescribed by the generic canonical expression from the outset. Some illustrative examples are given which demonstrate that the generic canonical expression can be used to construct analytically solvable models for two interacting species with limit-cycle dynamics as well as for a three-species interdependence.

Rosen, G.↗
NASA NTRS1977

Effects of growth, diving history, and high altitude on blood oxygen capacity in harbor seals

Blood volume and body composition for diving and nondiving harbor seals were measured at six-week intervals during a 10-month period of captitivity. Whole body hematocrit, red cell volume per kg of lean body mass, and total circulating hemoglobin per kg lean body mass were significantly higher in the diving group, but relatively large blood volumes expressed in terms of body weight (11-12%) were found in both groups. A pair of harbor seals exposed to high altitude for about three months registered significant increases in red cell volume, blood hemoglobin levels, and blood volume expressed in terms of body weight; results of alveolar gas analyses indicate that hyperventilation also occurred. These typical mammalian responses to hypoxia suggest that the harbor seal's large blood volume and high hemoglobin content are an expression of phylogenetic control, and that in spite of its adaptability to apnea during its diving life, the animal cannot be considered preacclimatized to high altitude.

Kodama, A. M.↗
NASA NTRS1977

Multimodal far-field acoustic radiation pattern - An approximate equation

The far-field sound radiation theory for a circular duct was studied for both single mode and multimodal inputs. The investigation was intended to develop a method to determine the acoustic power produced by turbofans as a function of mode cut-off ratio. This information is essential for the design of acoustic suppressors in engine ducts. With reasonable simplifying assumptions the single mode radiation pattern was shown to be reducible to a function of mode cut-off ratio only (modal indices removed). With modal cut-off ratio as the dominant variable, multimodal radiation patterns can be reduced to a simple explicit expression. This approximate expression provides excellent agreement with an exact calculation of the sound radiation pattern using equal acoustic power per mode. Radiation patterns for cases other than equal modal power are presented using the approximate radiation equation. An approximate expression for the duct termination losses as a function of cut-off ratio is also included.

Rice, E. J.↗
NASA NTRS1978

Determination of bulk diffusion lengths for angle-lapped semiconductor material via the scanning electron microscope: A theoretical analysis

A standard procedure for the determination of the minority carrier diffusion length by means of a scanning electron microscope (SEM) consists in scanning across an angle-lapped surface of a P-N junction and measuring the resultant short circuit current I sub sc as a function of beam position. A detailed analysis of the I sub sc originating from this configuration is presented. It is found that, for a point source excitation, the I sub sc depends very simply on x, the variable distance between the surface and the junction edge. The expression for the I sub sc of a planar junction device is well known. If d, the constant distance between the plane of the surface of the semiconductor and the junction edge in the expression for the I of a planar junction is merely replaced by x, the variable distance of the corresponding angle-lapped junction, an expression results which is correct to within a small fraction of a percent as long as the angle between the surfaces, 2 theta sub 1, is smaller than 10 deg.

Vonroos, O.↗
NASA NTRS1977

Estimating surface temperature in forced convection nucleate boiling - A simplified method

A simplified expression to estimate surface temperatures in forced convection boiling was developed using a liquid nitrogen data base. Using the principal of corresponding states and the Kutateladze relation for maximum pool boiling heat flux, the expression was normalized for use with other fluids. The expression was applied also to neon and water. For the neon data base, the agreement was acceptable with the exclusion of one set suspected to be in the transition boiling regime. For the water data base at reduced pressure greater than 0.05 the agreement is generally good. At lower reduced pressures, the water data scatter and the calculated temperature becomes a function of flow rate.

Hendricks, R. C.↗
NASA NTRS1977

Radiation pressure and Poynting-Robertson drag for small spherical particles

Robertson's expression for the velocity-dependent effect of solar radiation on the motion of small particles is difficult because of its dependence on relativistic considerations, and it is also deficient in that it assumes perfectly absorbing particles. The present paper gives a heuristic derivation of the Poynting-Robertson effect. Robertson's expression for perfectly absorbing particles is obtained but on a much simpler physical basis, and an expression is also obtained for a particle that in general scatters, transmits, and absorbs light. Some numerical results on the solar radiation forces felt by small particles of cosmochemically important compositions are given.

Soter, S.↗
NASA NTRS1977

Annoyance by aircraft noise and fear of overflying aircraft in relation to attitudes toward the environment and community

It has been suggested that expressions of annoyance attributable to aircraft noise may reflect in part fear of aircraft overflights and possible crashes. If this is true, then residents of areas where crashes have occurred should express more annoyance. To test this hypothesis, 50 residents of an Albany, New York area where an aircraft crash producing fatalities recently occurred and 50 residents of a comparable nearby area without such a history, were asked to respond to a 'Quality of Life Questionnaire.' Among the items were some designed to test annoyance by noise and fear of aircraft overflights. It was predicted that those in the crash area would express more fear and would more often identify aircraft as a noise source. These hypotheses were sustained. A near-replication was carried out in Louisville, Kentucky; results were much the same. Analyses indicated that for the crash-area groups, there was associating of aircraft fear and noise annoyance responses; this was true to an apparently lesser extent for non-crash groups. The greater annoyance of crash groups by aircraft community noise apparently does not carry over to situations in which aircraft noise is assessed in the laboratory.

Loeb, M.↗
NASA NTRS1977

Derivation of the chemical-equilibrium rate coefficient using scattering theory

Scattering theory is applied to derive the equilibrium rate coefficient for a general homogeneous chemical reaction involving ideal gases. The reaction rate is expressed in terms of the product of a number of normalized momentum distribution functions, the product of the number of molecules with a given internal energy state, and the spin-averaged T-matrix elements. An expression for momentum distribution at equilibrium for an arbitrary molecule is presented, and the number of molecules with a given internal-energy state is represented by an expression which includes the partition function.

Mickens, R. E.↗
NASA NTRS1979

On the determination of diffusion lengths by means of angle-lapped p-n junctions

A standard procedure for determining the minority carrier diffusion length by means of SEM consists of scanning an angle-lapped surface of a p-n junction and measuring the resulting short circuit current as a function of beam position. The present paper points out that the usual expression linking the short circuit current induced by the electron beam to the angle between the semiconductor surface and the junction plane is incorrect. The correct expression is discussed and it is noted that, for angles less than 10 deg, the new and the old expression are practically indistinguishable.

Von Roos, O.↗
NASA NTRS1979

Approximations for proton excitation - Erratum and extension

Kastner (1977) proposed relatively simple approximations for proton excitation in coronal ions, which yield both excitation rate coefficients and excitation cross sections. An error in Kastner's expression for one of the partial excitation rate coefficients is corrected. The expression for excitation cross section is extended to higher energies, and the resulting expression for the other partial rate coefficient is given. Results obtained with the corrected and extended total excitation rate coefficient are presented for several representative transitions in Ca XIII, Ca XV, Fe X, Fe XIII, Fe XIV, Fe XVIII, and S X. The corrected and extended approximation is expected to yield excitation rates reliably within 50%.

Kastner, S. O.↗
NASA NTRS1979

Analytical method for the effects of the asteroid belt on planetary orbits

Analytic expressions are derived for the perturbation of planetary orbits due to a thick constant-density asteroid belt. The derivations include extensions and adaptations of Plakhov's (1968) analytic expressions for the perturbations in five of the orbital elements for closed orbits around Saturn's rings. The equations of Plakhov are modified to include the effect of ring thickness, and additional equations are derived for the perturbations in the sixth orbital element, the mean anomaly. The gravitational potential and orbital perturbations are derived for the asteroid belt with and without thickness, and for a hoop approximation to the belt. The procedures are also applicable to Saturn's rings and the newly discovered rings of Uranus. The effects of the asteroid belt thickness on the gravitational potential coefficients and the orbital motions are demonstrated. Comparisons between the Mars orbital perturbations obtained by using the analytic expressions and those obtained by numerical integration are discussed. The effects of the asteroid belt on earth-based ranging to Mars are also demonstrated.

Mayo, A. P.↗
NASA NTRS1979

Maximum likelihood estimation of label imperfections and its use in the identification of mislabeled patterns

The problem of estimating label imperfections and the use of the estimation in identifying mislabeled patterns is presented. Expressions for the maximum likelihood estimates of classification errors and a priori probabilities are derived from the classification of a set of labeled patterns. Expressions also are given for the asymptotic variances of probability of correct classification and proportions. Simple models are developed for imperfections in the labels and for classification errors and are used in the formulation of a maximum likelihood estimation scheme. Schemes are presented for the identification of mislabeled patterns in terms of threshold on the discriminant functions for both two-class and multiclass cases. Expressions are derived for the probability that the imperfect label identification scheme will result in a wrong decision and are used in computing thresholds. The results of practical applications of these techniques in the processing of remotely sensed multispectral data are presented.

Chittineni, C. B.↗
NASA NTRS1980

Calculation of skin-friction coefficients for low Reynolds number turbulent boundary layer flows

An analysis is presented of the reliability of various generally accepted empirical expressions for the prediction of the skin-friction coefficient C/sub f/ of turbulent boundary layers at low Reynolds numbers in zero-pressure-gradient flows on a smooth flat plate. The skin-friction coefficients predicted from these expressions were compared to the skin-friction coefficients of experimental profiles that were determined from a graphical method formulated from the law of the wall. These expressions are found to predict values that are consistently different than those obtained from the graphical method over the range 600 Re/sub theta 2000. A curve-fitted empirical relationship was developed from the present data and yields a better estimated value of C/sub f/ in this range. The data, covering the range 200 Re/sub theta 7000, provide insight into the nature of transitional flows. They show that fully developed turbulent boundary layers occur at Reynolds numbers Re/sub theta/ down to 425. Below this level there appears to be a well-ordered evolutionary process from the laminar to the turbulent profiles. These profiles clearly display the development of the turbulent core region and the shrinking of the laminar sublayer with increasing values of Re/sub theta/.

Barr, P. K.↗