Search NASA⌕ Search

SEARCH · Search NASA

Results for “FORMULAS - PROPELLERS”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1962

Thermodynamic and Transport Property Correlation Formulas for Equilibrium Air from 1,000 Degrees Kelvin to 15,000 Degrees Kelvin

The thermodynamic properties, density and temperature, as well as transport property parameters involving viscosity, Prandtl number (including diffusion effects), and gaseous radiation absorption coefficients have been correlated as a function of enthalpy at four pressure levels (10 (sup -1), 10 (sup 0), 10, and 10 (sup 2) atmospheres). The correlation formulas are written in a generalized form for which coefficients for a particular property and pressure level are tabulated. The correlation formulas are useful in digital computer programs for non-adiabatic viscous flow problems.

AIR↗
NASA NTRS1972

Field dependence of gaseous ion mobility: Test of approximate formulas

The accuracies of three approximate formulas were tested by comparison with special cases for which accurate results could be found. The Wannier free flight theory was found to be superior, and can be extended to yield a formula without further adjustable constants that gives an exact result at low electric fields and good results at medium and high fields. It is applicable for any ion neutral force law and mass ratio.

Hahn, H.↗
NASA NTRS1972

Simplified formula for mean cycle-slip time of phase-locked loops with steady-state phase error.

Previous work shows that the mean time from lock to a slipped cycle of a phase-locked loop is given by a certain double integral. Accurate numerical evaluation of this formula for the second-order loop is extremely vexing because the difference between exponentially large quantities is involved. The presented article demonstrates a method in which a much-reduced precision program can be used to obtain the mean first-cycle slip time for a loop of arbitrary degree tracking at a specified SNR and steady-state phase error. It also presents a simple approximate formula that is asymptotically tight at higher loop SNR.

Tausworthe, R. C.↗
NASA NTRS1972

A precompiler for the formula manipulation system TRIGMAN.

Discussion of a translator designed to simplify the programming of problems involving the TRIGMAN formula manipulation system. The translator allows for the introduction of a new data type, SERIES, into a FORTRAN program and translates a user's program into legal FORTRAN. The translator is adaptable to other formula manipulation systems presently used in celestial mechanics.

Jefferys, W. H.↗
NASA NTRS1972

The ATA-67 Formula for Direct Operating Cost

The ATA formulas for direct operating cost were developed for the purpose of comparing different aircraft, existing or not, on the same route or the same aircraft on different routes. Such characteristics of the airline as crew pay, maintenance procedures, and depreciation schedules are kept constant. In air transportation systems analysis the 1967 ATA formula is usually used with appropriate exceptions or modifications, such as: different maintenance labor rate, total maintenance multiplied by a factor, maintenance burden deleted, different depreciation schedule, or different spares percentages.

Faulkner, H. B.↗
NASA NTRS1973

Recursive formulas for the partial fraction expansion of a rational function with multiple poles.

The coefficients in the partial fraction expansion considered are given by Heaviside's formula. The evaluation of the coefficients involves the differential of a quotient of two polynomials. A simplified approach for the evaluation of the coefficients is discussed. Leibniz rule is applied and a recurrence formula is derived. A coefficient can also be determined from a system of simultaneous equations. Practical methods for the performance of the computational operations involved in both approaches are considered.

Chang, F.-C.↗
NASA NTRS1973

Elastohydrodynamic film thickness formula based on X-ray measurements with a synthetic paraffinic oil

An empirical elastohydrodynamic film thickness formula for heavily loaded contacts based upon X-ray film thickness measurements made with a synthetic paraffinic oil is presented. The deduced relation was found to adequately reflect the high load dependence exhibited by the measured minimum film thickness data at high Hertizian contact stresses, that is, above 1.04 x 10 to the ninth N/sq m (150,000 psi). Comparisons were made with the numerical results from a theoretical isothermal film thickness formula. The effects of changes in contact geometry, material, and lubricant properties on the form of the empirical model are also discussed.

Loewenthal, S. H.↗
NASA NTRS1973

Gyrosynchrotron radiation formulae

The wave-normal emissivity and the ray emissivity formulas for an electron moving along a helical path in a magnetoactive medium are presented. Simplified formulas for the case of an isotropic plasma are also given. Because of the helical motion of the electron, a difference exists between the radiated power per unit solid angle and the received power per unit solid angle. The relation between these two quantities in a magnetoactive medium is shown. Results are compared with those obtained by others, and the sources of discrepancies are pointed out.

Ko, H. C.↗
NASA NTRS1974

Derivation of formulas for root-mean-square errors in location, orientation, and shape in triangulation solution of an elongated object in space

Formulas are derived for the root-mean-square (rms) displacement, slope, and curvature errors in an azimuth-elevation image trace of an elongated object in space, as functions of the number and spacing of the input data points and the rms elevation error in the individual input data points from a single observation station. Also, formulas are derived for the total rms displacement, slope, and curvature error vectors in the triangulation solution of an elongated object in space due to the rms displacement, slope, and curvature errors, respectively, in the azimuth-elevation image traces from different observation stations. The total rms displacement, slope, and curvature error vectors provide useful measure numbers for determining the relative merits of two or more different triangulation procedures applicable to elongated objects in space.

Long, S. A. T.↗
NASA NTRS1974

Derivation of transformation formulas between geocentric and geodetic coordinates for nonzero altitudes

Four formulas, for the nonzero altitude transformation from geodetic coordinates (geodetic latitude and altitude) to geocentric coordinates (geocentric latitude and geocentric distance) and vice versa, are derived. The set of four formulas is expressed in each of the three useful forms: series expansion in powers of the earth's flattening; series expansion in powers of the earth's eccentricity; and Fourier series expansion in terms of the geodetic latitude or the geocentric latitude. The error incurred in these series expansions is of the order of one part in 3 x 10 to the 7th power.

Long, S. A. T.↗
NASA NTRS1975

A prefiltering version of the Kalman filter with new numerical integration formulas for Riccati equations

A prefiltering version of the Kalman filter is derived for both discrete and continuous measurements. The derivation consists of determining a single discrete measurement that is equivalent to either a time segment of continuous measurements or a set of discrete measurements. This prefiltering version of the Kalman filter easily handles numerical problems associated with rapid transients and ill-conditioned Riccati matrices. Therefore, the derived technique for extrapolating the Riccati matrix from one time to the next constitutes a new set of integration formulas which alleviate ill-conditioning problems associated with continuous Riccati equations. Furthermore, since a time segment of continuous measurements is converted into a single discrete measurement, Potter's square root formulas can be used to update the state estimate and its error covariance matrix. Therefore, if having the state estimate and its error covariance matrix at discrete times is acceptable, the prefilter extends square root filtering with all its advantages, to continuous measurement problems.

Womble, M. E.↗
NASA NTRS1977

Timing formulas for dissection algorithms on vector computers

The use of the finite element and finite difference methods often leads to the problem of solving large, sparse, positive definite systems of linear equations. MACSYMA plays a major role in the generation of formulas representing the time required for execution of the dissection algorithms. The use of MACSYMA in the generation of those formulas is described.

Poole, W. G., Jr.↗
NASA NTRS1978

The determination of gravity anomalies from geoid heights using the inverse Stokes' formula, Fourier transforms, and least squares collocation

A numerical method for the determination of gravity anomalies from geoid heights is described using the inverse Stokes formula. This discrete form of the inverse Stokes formula applies a numerical integration over the azimuth and an integration over a cubic interpolatory spline function which approximates the step function obtained from the numerical integration. The main disadvantage of the procedure is the lack of a reliable error measure. The method was applied on geoid heights derived from GEOS-3 altimeter measurements in the calibration area of the GEOS-3 satellite.

Rummel, R.↗