The effects of series truncation on estimates and the transformation of errors Semiannual status report, 1 Mar. - 30 Aug. 1970
Series truncation in parametric estimation and error transformation
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Theoretical and experimental vibration and buckling results for blunt truncated conical shells with ring-supported edges
Theoretical and experimental vibration and buckling results for blunt truncated conical shells with ring supported edges
Dixon, S. C.↗
Pumping characteristics of a rotating truncated cone
Pumping characteristics of rotating truncated cone
Gorland, S. H.↗
Vibration and flutter tests of a pressurized thin-walled truncated conical shell
Vibration and flutter tests of pressurized thin walled truncated conical shell
Dixon, S. C.↗
Supersonic asymmetric flutter and divergence of truncated conical shells with ring supported edges
Supersonic asymmetric flutter and divergence characteristics of truncated conical shells with ring-supported edges under three types of flow-induced instabilities
Dixon, S. C.↗
Use of the negative binomial-truncated Poisson distribution in thunderstorm prediction
A probability model is presented for the distribution of thunderstorms over a small area given that thunderstorm events (1 or more thunderstorms) are occurring over a larger area. The model incorporates the negative binomial and truncated Poisson distributions. Probability tables for Cape Kennedy for spring, summer, and fall months and seasons are presented. The computer program used to compute these probabilities is appended.
Cohen, A. C.↗
A digital computer study of the buckling of shallow spherical caps and truncated hemispheres
A study of the buckling of thin shells was conducted using a digital computer program for the geometrically nonlinear analysis of arbitrarily loaded shells of revolution. The objective was an evaluation of the program's applicability to bifurcation buckling and imperfection sensitivity analysis. Clamped spherical caps under pressure loading and clamped truncated hemispheres under axial tension were investigated. Buckling loads were determined for axisymmetric and nearly axisymmetric loads and are compared with previously published analytical results based on geometric imperfections.
Stilwell, W. C.↗
Annular truncated plug nozzle flowfield and base pressure characteristics.
The flowfield and base pressure characteristics of an internal-external expansion, truncated plug nozzle are described over the pressure ratio range from 'open' wake to 'closed' wake conditions. The effect of plug length on these characteristics, including the process of wake 'closure' is also presented. An existing method for calculating the flowfield and base pressure, for 'closed' wake operation, is modified to include the internal shock wave generated near the shroud exit. The supersonic portion of the flow is calculated using rotational axisymmetric method of characteristics. The technique of Hartree is employed so that the downstream characteristic point locations can be chosen to fit the developing flowfield. An overexpansion technique is used to detect the internal shock wave in the vicinity of the shroud exit so that its effect on the plug base pressure could be determined. Good agreement between the analytical results and experimental data is obtained for 'closed' wake operations.
Sule, W. P.↗
Laminar film condensation on the inside of slender, rotating truncated cones.
A solution for film condensation on the inside of slender rotating truncated cones is established in the region where the half cone angle phi is close to zero and where the equation of Dhir and Lienhard (1971) is no longer valid. All the familiar assumptions used in Nusselt's theory of laminar film condensation are assumed valid, including negligible sub-cooling and momentum changes in the condensate film, no interfacial shear between the condensate and the vapor, and pure conduction within the condensate film. A Runge-Kutta numerical integration method using a digital computer was used. Results for a specific geometry are given for water condensing at 212 F on a condenser wall maintained at 70 F.
Marto, P. J.↗
Comparative evaluation of predicted and measured performance of a 68-cubic meter truncated reverberant noise chamber
The performance of a medium size, truncated reverberation chamber is evaluated in detail. Chamber performance parameters are predicted, using classical acoustic theory, and are compared to results from actual chamber measurements. Discrepancies are discussed in relation to several available empirical corrections developed by other researchers. Of more practical interest is the confirmation of a recent theory stating that the present guide for the ratio of specimen volume to test chamber volume, approximately 10 percent, is overly conservative, and can be increased by a factor of at least 2 and possibly 3. Results and theoretical justification of these findings are presented.
Cyphers, H. D.↗
Power conservation for reflector antennas with truncated feed patterns
Reflector-antenna calculations using idealised truncated feed patterns can lead to incorrect values of total secondary radiated power. It is demonstrated that this discrepancy is due to the presence of higher-order spherical modes incident on the reflector. When a proper spherical-wave expansion of the incident field is used, in conjunction with the physical-optics technique, to determine the scattered field, the total power of the scattered field will equal the power radiated by the feed.
Rush, W. V. T.↗
Cylindrical diffuser performance using a truncated plug nozzle
Cylindrical diffuser performance for a truncated plug nozzle without external flow was tested in a blowdown wind tunnel. The nozzle was designed for an exit Mach number of 1.9 and the plug was conical in shape from the throat and converged to the axis of symmetry at an angle of 10 degrees. The diffuser section was fashioned into two 13.97 cm lengths to facilitate boring of the duct diameter and to allow for testing of two different duct lengths. A slotted hypotube was installed in the base of the diffuser to measure pressure distribution down the centerline of the diffuser. The data obtained included: the typical centerline and sidewall pressure ratio variation along the diffuser, cell pressure ratio vs overall pressure ratio for long and short diffusers and a comparison of minimum experimental cell pressure ratio vs area ratio.
Galanga, F. L.↗
High-latitude truncation errors of box-type primitive equation models
The 'box-type' finite-difference method includes a weighted average of the pressure gradient with weights proportional to the surface of the grid walls. It is shown that this averaging introduces first-order truncation errors near the poles. An example is shown in which the relative error is of zero order and the scheme produces large distortions in the solution at high latitudes.
Kalnay-Rivas, E.↗
Solar concentrating properties of truncated hexagonal, pyramidal and circular cones
The solar concentrating properties of specularly reflecting truncated pyramidal, hexagonal, and circular cones are evaluated. Pyramidal and hexagonal configurations are discussed with reference to the concentration factor as a function of half apex angle and the length of the side over the width, and to the irradiance distribution. Expressions are derived for the concentration factor and the irradiance at the base of a circular cone when the sunlight is incident normal to the aperture and for oblique incidence.
Burkhard, D. G.↗
Effects of truncation of a predominantly compression load spectrum on the life of a notched graphite/epoxy laminate
Constant amplitude and transport wing spectrum compressive loading tests were used to explore the fatigue behavior of a notched, graphite/epoxy T300/5208 laminate specimen. Results indicate that (1) the amount of buckling near the notch allowed in the tests significantly affected fatigue life; (2) load spectrum truncation at either high or low ends produced lives greater than those obtained for the baseline complete-spectrum test, but with greater impact at the high-load end; and (3) the predictions of the Palmgren-Miner cumulative damage theory were found to always be far longer than those obtained in the spectrum loading tests.
Phillips, E. P.↗
Stable and unstable near-resonant states in multilevel, severely truncated, quasi-geostrophic models
Multilevel, severely truncated, quasi-geostrophic models with damping that extend from the surface to 100 km, are used to study the stationary-wave response to orography and the concomitant feedbacks on the zonal flow. For a typical winter zonal-wind profile, it is shown that large amplitude or resonant planetary waves of intermediate zonal wavenumbers of about 4 or 5 occur with an equivalent barotropic structure. It is also shown that wave-zonal flow interaction with a mountain torque and temperature transport is stable to small perturbations on the low side of resonance and unstable on the high side of resonance. Resonant zonal wavenumbers of lower wave wavenumber also occur for the same zonal profile and have a node in the vertical with a small amplitude maximum near the surface and a larger amplitude maximum in the stratosphere. Instability depends on the presence of the orography and the basic asymmetric state as Newtonian damping and surface friction are sufficient to damp the baroclinic instability associated with a linear inviscid model.
Roads, J. O.↗
Evaluation of truncation error and adaptive grid generation for the transonic full potential flow calculations
The effects of truncation error on the numerical solution of transonic flows using the full potential equation are studied. The effects of adapting grid point distributions to various solution aspects including shock waves is also discussed. A conclusion is that a rapid change of grid spacing is damaging to the accuracy of the flow solution. Therefore, in a solution adaptive grid application an optimal grid is obtained as a tradeoff between the amount of grid refinement and the rate of grid stretching.
Nakamura, S.↗
Nonlinear truncation error analysis of finite difference schemes for the Euler equations
It is pointed out that, in general, dissipative finite difference integration schemes have been found to be quite robust when applied to the Euler equations of gas dynamics. The present investigation considers a modified equation analysis of both implicit and explicit finite difference techniques as applied to the Euler equations. The analysis is used to identify those error terms which contribute most to the observed solution errors. A technique for analytically removing the dominant error terms is demonstrated, resulting in a greatly improved solution for the explicit Lax-Wendroff schemes. It is shown that the nonlinear truncation errors are quite large and distributed quite differently for each of the three conservation equations as applied to a one-dimensional shock tube problem.
Klopfer, G. H.↗