Search NASA⌕ Search

SEARCH · Search NASA

Results for “ellipses”

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 217 records · Page 12

Three-dimensional crack problems

Methods for solving three dimensional crack problems are discussed. The stress intensity factor for the case of uniform pressure on the surface crack is analysis. An analysis of concentrated forces acting on the crack faces parallel to the crack front of a half-plane crack was made. Two dimensional calculations were made using the exact solution for the stress field around an elliptical hole in a uniformly stretched plate. The strain energy density was computed in the neighborhood of the ends of narrow, but sharp, ellipses.

Hartranft, R. J.↗

The physical librations of the moon, including higher harmonic effects

The equations of the physical libration of the moon are developed using a representation of the earth-moon orbit as a Kepler ellipse referred to the lunar equator and expanding the lunar potential in terms of these Kepler elements. The Improved Lunar Ephemeris is used to calculate solar perturbations, and a linear integration of all effects arising from lunar gravitational harmonics through the fourth degree is performed. Aside from unobservable constant offsets of the principal axes, the main effects of the higher harmonics on longitude are: 10-sec six-yearly (argument omega), 1.2-sec three-yearly, 0.5-sec annual, and 0.1-sec monthly; on pole direction they are on the order of 0.5-sec six-yearly and 1.0-sec monthly. The higher harmonics must hence be taken into account in analyzing ranging data of 10 cm accuracy.

Kaula, W. M.↗

Optimal high- and low-thrust geocentric transfer

A computer code which rapidly calculates time optimal combined high- and low-thrust transfers between two geocentric orbits in the presence of a strong gravitational field has been developed as a mission analysis tool. The low-thrust portion of the transfer can be between any two arbitrary ellipses. There is an option for including the effect of two initial high-thrust impulses which would raise the spacecraft from a low, initially circular orbit to the initial orbit for the low-thrust portion of the transfer. In addition, the effect of a single final impulse after the low-thrust portion of the transfer may be included. The total Delta V for the initial two impulses must be specified as well as the Delta V for the final impulse. Either solar electric or nuclear electric propulsion can be assumed for the low-thrust phase of the transfer.

Sackett, L. L.↗

Angiocardiographic methods for determination of left ventricular geometry and volume

Methods are described for calculating left ventricular (LV) dimensions and chamber volumes from radiographic films. The use of biplane films for the calculation of LV volume and volume change is based on the assumption of an ellipsoidal geometry. Calculation of LV volumes from biplane films usually overestimated known volumes in postmortem hearts regardless of the methods used for volume calculation. The reasons for this are probably best explained by the fact that a smooth-surface ellipse is used to represent the irregular cavity of the LV chamber. LV volume calculated from data in a single plane compared favorably and closely with volumes calculated from biplane films. A table of normal values of ventricular volume established by angiographic studies is presented.

Sandler, H.↗

Trimetric Scale for Drafting Machines

Device allows three basic projections to be drawn from a single scale zero setting. Ellipse proportions are included for convenience. Axonometric projections can also be determined.

Ryan, J. C.↗

On the cost of approximating and recognizing a noise perturbed straight line or a quadratic curve segment in the plane

Approximation of noisy data in the plane by straight lines or elliptic or single-branch hyperbolic curve segments arises in pattern recognition, data compaction, and other problems. The efficient search for and approximation of data by such curves were examined. Recursive least-squares linear curve-fitting was used, and ellipses and hyperbolas are parameterized as quadratic functions in x and y. The error minimized by the algorithm is interpreted, and central processing unit (CPU) times for estimating parameters for fitting straight lines and quadratic curves were determined and compared. CPU time for data search was also determined for the case of straight line fitting. Quadratic curve fitting is shown to require about six times as much CPU time as does straight line fitting, and curves relating CPU time and fitting error were determined for straight line fitting. Results are derived on early sequential determination of whether or not the underlying curve is a straight line.

Cooper, D. B.↗

A boundary-layer analysis of atmospheric motion over a semi-elliptical surface obstruction

Flow over surface obstructions can produce adverse flying conditions for helicopters, V/STOL vehicles, etc. The disturbed boundary-layer concept is applied in approximating the localized flow field induced around a surface obstruction (modeled by a two-dimensional cylinder with elliptical cross section) by an impinging wind. The analysis concludes that: (1) localized wind-speed maxima occur at the top of a surface obstruction, which are expected in physically real flows; (2) increased elliptical aspect ratio decreases with speed within the boundary layer at the top of the ellipse; (3) increased surface roughness decreases velocity in the boundary layer; (4) Reynolds number has a negligible effect on the overall flow for the Re range considered; (5) decreased elliptical aspect ratio and increased surface roughness cause larger separation regions.

Frost, W.↗

Self-precession and frequency shift for electromagnetic waves in homogeneous plasmas

The nonlinear propagation of an arbitrarily polarized electromagnetic wave in a uniform plasma is studied. It is shown that nonlinear effects cause precession of the polarization ellipse as the wave propagates. The ellipticity remains constant, but the orientation of the principal axes is rotated relative to its initial value. A relativistic Vlasov model is used to study nonlinear frequency shifts as well as self-precession, in a plasma of arbitrary temperature. Even when the electron temperature is much greater than the product of the electron mass times the square of the velocity of light, the qualitative nature of these two processes remains unchanged, although their dependence on the plasma density is altered in significant ways. Implications of these effects for plasma instabilities driven by strong electromagnetic waves are briefly discussed.

Arons, J.↗

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.↗

Micropulsations in the morning sector. II - Satellite observations of 10to 45-s waves at synchronous orbit, ATS 1

A study of 13 wave events having 10- to 45-s periods and observed by ATS 1 in the morning sector reveals that these events, which have been called band-limited pulsations and are thought to be related to Pi 1, appear actually to be Pc 3. Digital power-spectral and coherency analysis was used to determine the characteristics of the wave activity. The average peak frequency of the events (about 0.04 Hz) and their generally narrow-band nature correspond closely with the characteristics of Pc 3. The local-time distribution of the events (peaking at 0900 LT) and their less than complete association with substorms also correspond more closely with Pc 3 characteristics. The orientation of the major axis of the polarization ellipse for these events was predominantly azimuthal, which agrees more closely with the east-west polarization of Pi 1 observed on the ground. However, some examples of radial orientation were observed in the satellite data.

Arthur, C. W.↗

The occultation of Kappa Geminorum by Eros

The paper discusses predictions and observations of the occultation of Kappa Gem by (433) Eros on January 24, 1975. Several positive and negative observations made in western New England are described. Local circumstances for the occultation are reconstructed, and the size and shape of Eros are determined analytically as well as graphically. The calculations yield two extremes for the cross section: a circle 23 km in diameter or a somewhat irregular figure 20 km by 6 or 7 km. Arguments based on the expected albedo of the asteroid suggest that the circle should be warped into an ellipse 21 by 13 km or that the irregular figure might be one component of a dumbbell-like profile.

Oleary, B.↗

Inlets for high angles of attack

Different inlet designs for high angle of attack STOL and VTOL applications were tested in a subsonic wind tunnel. Three removable entry lips having contraction ratios of 1.30, 1.34 and 1.38 were tested with a single diffuser. The internal contour of each entry lip was an ellipse with a major to minor axis of 2.0. Each lip and diffuser assembly was tested to determine its tolerance to angle of attack, first with a conventional centerbody and then with an extended centerbody. Results indicate that a large improvement in separation angle (determined as a function of lip contraction ratio and inlet flow) was obtained for the extended centerbody for all contraction ratios. Improved inlet tolerance to angle of attack was obtained by reducing the adverse pressure gradient downstream of the throat.

Miller, B. A.↗

Mercury's rotation axis and period

Recent measurements made from high-resolution Mariner 10 photography of the planet Mercury yield a rotation period of 58.6461 + or 0.005 days, in excellent agreement with the period required for a precise 2/3 resonance with its orbital period (58.6462 days). The axis of rotation of the planet was calculated to be offset about 2 deg from the perpendicular to its orbital plane within a 50% probability error ellipse of + or - 2.6 deg by + or - 6.5 deg. Dynamical considerations make it most likely that the true displacement from the orbit normal is less than 1 deg.

Klaasen, K. P.↗

Additional studies of forest classification accuracy as influenced by multispectral scanner spatial resolution

First, an analysis of forest feature signatures was used to help explain the large variation in classification accuracy that can occur among individual forest features for any one case of spatial resolution and the inconsistent changes in classification accuracy that were demonstrated among features as spatial resolution was degraded. Second, the classification rejection threshold was varied in an effort to reduce the large proportion of unclassified resolution elements that previously appeared in the processing of coarse resolution data when a constant rejection threshold was used for all cases of spatial resolution. For the signature analysis, two-channel ellipse plots showing the feature signature distributions for several cases of spatial resolution indicated that the capability of signatures to correctly identify their respective features is dependent on the amount of statistical overlap among signatures. Reductions in signature variance that occur in data of degraded spatial resolution may not necessarily decrease the amount of statistical overlap among signatures having large variance and small mean separations. Features classified by such signatures may thus continue to have similar amounts of misclassified elements in coarser resolution data, and thus, not necessarily improve in classification accuracy.

Sadowski, F. E.↗

A generalized orthogonal coordinate system for describing families of axisymmetric and two-dimensional bodies

A generalized curvilinear orthogonal coordinate system is presented which can be used for approximating various axisymmetric and two-dimensional body shapes of interest to aerodynamicists. Such body shapes include spheres, ellipses, spherically capped cones, flat-faced cylinders with rounded corners, circular disks, and planetary probe vehicles. A set of transformation equations is also developed whereby a uniform velocity field approaching a body at any angle of attack can be resolved in the transformed coordinate system. The Navier-Stokes equations are written in terms of a generalized orthogonal coordinate system to show the resultant complexity of the governing equations.

Gnoffo, P. A.↗

Stress intensity factors for long, deep surface flaws in plates under extensional fields

Using a singular solution for a part circular crack by Smith, a Taylor Series Correction Method (TSCM) was verified for extracting stress intensity factors (SIFs) from photoelastic data. Photoelastic experiments were then conducted on plates with part circular and flat bottomed cracks for flaw depth to thickness ratios of 0.25, 0.50, and 0.75 and for equivalent flaw depth to equivalent ellipse length values ranging from 0.066 to 0.319. Experimental results agreed well with the Smith theory but indicated that the use of the 'equivalent' semi-elliptical flaw for correlating the part circular flaw results with semi-elliptical flaw results was not valid for a/2c much less than 0.20. Best overall agreement for the moderate (a/t about 0.5) to deep flaws (a/t about 0.75) and a/2c greater than 0.15 was found with a semi-empirical theory due to Newman when compared on the basis of equivalent flaw depth and area. The Smith theory, when correlated on the basis of flaw depth and area, appears to yield reasonable estimates (within 10%) of the SIF for flat bottomed flaws for the geometries studied here.

Harms, A. E.↗

Analysis of vector wind change with respect to time for Cape Kennedy, Florida

Multivariate analysis was used to determine the joint distribution of the four variables represented by the components of the wind vector at an initial time and after a specified elapsed time is hypothesized to be quadravariate normal; the fourteen statistics of this distribution, calculated from 15 years of twice-daily rawinsonde data are presented by monthly reference periods for each month from 0 to 27 km. The hypotheses that the wind component changes with respect to time is univariate normal, that the joint distribution of wind component change with respect to time is univariate normal, that the joint distribution of wind component changes is bivariate normal, and that the modulus of vector wind change is Rayleigh are tested by comparison with observed distributions. Statistics of the conditional bivariate normal distributions of vector wind at a future time given the vector wind at an initial time are derived. Wind changes over time periods from 1 to 5 hours, calculated from Jimsphere data, are presented. Extension of the theoretical prediction (based on rawinsonde data) of wind component change standard deviation to time periods of 1 to 5 hours falls (with a few exceptions) within the 95 percentile confidence band of the population estimate obtained from the Jimsphere sample data. The joint distributions of wind change components, conditional wind components, and 1 km vector wind shear change components are illustrated by probability ellipses at the 95 percentile level.

Adelfang, S. I.↗