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Numerical simulations with periodic boundary conditions are widely used in cosmology. These have a multiply connected topology known as a three-torus. Such nontrivial topologies for the actual universe may have arisen in the Big Bang. A two-dimensional numerical model with a twisted topology, sometimes a Klein bottle, is shown as well as the fact that local properties of the model are not dependent on topology.
Simple, accurate methods of calculating ideal MHD instability eigenvalues for infinitely long cylindrical tubes with twist function T(r) are developed. The results show that the most rapidly growing and energetic instabilities occur in the Gold-Hoyle v = 0 field, with the instability progressively weakening with increasing v. However, the maximum force eigenvalue is always small, so that even in the Gold-Hoyle case only a small proportion of the available magnetic energy can be released in the linear phase. The results also confirm that the linear pinch is remarkably weak yet relatively resistant to line-tying. It is shown that the weakness of the force eigenvalue implies that the influence of uniform gas pressure on stability is negligible. Implications for the energy-release mechanism in solar flares are discussed.
Algorithm proposed for use with strapdown inertial sensors synthesizes gyrocompass and repeatedly refines alignment of synthetic gyrocompass to maintain accuracy until time of departure. In original application, inertial sensors located in spacecraft twisting and swaying in wind on launching pad, and time of departure is time of launch. Also possible to devise terrestrial version of algorithm for use in aircraft, ground vehicle, or vessel. Algorithm includes local-level-navigator, coarse-alignment, and fine-alignment subalgorithms.
Recent numerical simulations of magnetic buoyancy instabilities suggest a new mechanism for the variation with the solar cycle in the scale and structure of surface magnetic flux. The nonlinear evolution of a predominantly toroidal field is found to depend crucially on the distribution of the weaker poloidal ingredient. For certain field configurations large, helical magnetic fragments are produced; for others the escaping field is small-scale and untwisted. We propose that the observed structural variations in flux may be accounted for by small changes in the twist of a deep-seated field. The large fragments will appear at the surface as active regions, which dominate at solar maximum, while the small-scale field will emerge as ephemeral regions which constitute practically all of the flux at solar minimum.
A method for computing the aerodynamic induction of wings with elliptic plan form if arbitrarily twisted.
The results presented in this note show the effect of twist and sweepback on the span load distribution over two monoplane wing models. The tests were made in the Atmospheric Wind Tunnel of the Langley Memorial Aeronautical Laboratory. The data are taken from the results of an investigation dealing primarily with lateral stability. As presented, they are suitable as an aid in the structural design of certain monoplane wings.
A graphical method is described for finding the shape (camber and twist) of an airfoil having an arbitrary distribution of lift. The method consists in replacing the lifting surface and its wake with an equivalent arrangement of vortices and in finding the associated vertical velocities. By a division of the vortex pattern into circular strips concentric about the downwash point instead of into the usual rectangular strips, the lifting surface is reduced for each downwash point to an equivalent loaded line for which the induced velocity is readily computed. The ratio of the vertical velocity to the stream velocity is the slope of the surface in the free-stream direction. As an illustration, the shape of the wing consistent with the pressure distribution derived from the two-dimensional theories is found for two wings: a straight elliptical wing and one with 30 degree sweepback. Application of the method to solve the reverse problem - finding the lift distribution over a given surface - is briefly discussed.
The differential equations of motion for the lateral and torsional deformations of twisted rotating beams are developed for application to helicopter rotor and propeller blades. No assumption is made regarding the coincidence of the neutral, elastic, and mass axes, and the generality is such that previous theories involving various simplifications are contained as subcases to the theory developed and presented in this paper. Special attention is given to coupling terms not found in previous theories, and methods of solution of the equations of motion are indicated by selected examples.
An investigation of two semispan wings swept back 50 degrees 38 minutes was conducted in the Langley high-speed 7- by 10-foot tunnel over a Mach number range of 0.68 to 1.15 by use of the transonic-bump technique. This paper presents the results of the investigation of wing-alone and wing-fuselage configurations of the two wings; one was an untwisted uncambered wing and the other was the same wing but incorporated twist and camber designed to give uniform load at a lift coefficient of 0.25 at a Mach number of 1.10. The semispan wings had their quarter-chord lines swept back 50 degrees 38 minutes, aspect ratios 2.98, taper ratios 0.45, and modified NACA 64A-series airfoil sections tapered in thickness. Lift, pitching moment, drag, and bending moment were obtained for these configurations.
This report presents the results of an investigation to ascertain the lift, drag, and pitching moment of a wing-body combination having a triangular wing of aspect ratio 2 with NACA 0003-63 thickness distribution in streamwise planes and twisted and cambered for a nearly elliptical span load distribution. Results are shown for Mach numbers from 0.60 to 0.90 and from 1.30 to 1.70 at Reynolds numbers of 3.0 million and 7.5 million.
This reports presents the results of pressure distribution tests on a thick, tapered and twisted monoplane wing model. The investigation was conducted for the purpose of obtaining data on the aerodynamic characteristics of the new wing and to provide additional information suitable for use in the design of tapered cantilever wings. The tests included angles of attack up to 90 degrees. The span loading over the wing was approximately of elliptical shape, which gave rise to relatively small bending moments about the root. The angle of zero lift for all sections along the span varied only within plus or minus 0.4 degree of the angle of zero lift for the whole wing, resulting in small leading edge loads for the high-speed condition of flight. The results also add to the available information for the study of large angles of attack.
A graphical method is described for finding the shape (camber and twist) of an airfoil having an arbitrary distribution of lift. The method consists in replacing the lifting surface and its wake with an equivalent arrangement of vortices and in finding the associated vertical velocities. By division of the vortex pattern into circular strips concentric about the downwash point instead of into the usual rectangular strips, the lifting surface is reduced for each downwash point to an equivalent loaded line for which the induced velocity is readily computed. The ratio of the vertical velocity to the stream velocity is the slope of the surface in the free-stream direction.
The differential equations of motion for the lateral and torsional deformations of twisted rotating beams are developed for application to helicopter rotor and propeller blades. No assumption is made regarding the coincidence of the neutral, elastic, and mass axes, and the generality is such that previous theories involving various simplifications are contained as subcases to the theory presented in this paper. Special attention is given the terms which are not included in previous theories. These terms are largely coupling-type terms associated with the centrifugal forces. Methods of solution of the equations of motion are indicated by selected examples.
On the basis of the present investigation of the twisting of thin-walled, stiffened cylinders the following conclusions can be reached: 1) there is as yet no generally applicable formula for the buckling moment of the skin; 2) the mathematical treatment of the condition of the shell after buckling of the skin is based on the tension-field theory, wherein the strain condition is considered homogenous.
Proceeding from the basic assumptions of the Batho-Bredt theory on twisting failure of thin-walled columns, the discrepancies most frequently encountered are analyzed. A generalized approximate method is suggested for the determination of the disturbances in the stress condition of the column, induced by the constrained warping in one of the end sections.
Stress fields near the tip of a through crack in an elastic plate under bending and twisting moments are reviewed assuming both Kirchhoff and Reissner plate theories. The crack tip displacement and rotation fields based on the Reissner theory are calculated. These results are used to calculate the J-integral (energy release rate) for both Kirchhoff and Reissner plate theories. Invoking Simmonds and Duva's (1981) result that the value of the J-integral based on either theory is the same for thin plates, a universal relationship between the Kirchhoff theory stress intensity factors and the Reissner theory stress intensity factors is obtained for thin plates. Calculation of Kirchhoff theory stress intensity factors from finite elements based on energy release rate is illustrated. It is proposed that, for thin plates, fracture toughness and crack growth rates be correlated with the Kirchhoff theory stress intensity factors.
This investigation is a continuation of the experimental and theoretical evaluation of blended wing-body combinations. The basic diamond, delta, and arrow plan forms which had an aspect ratio of 2 with leading-edge sweeps of 45.00 deg., 59.04 deg., and 70.82 deg. and trailing edge of -45.00 deg., -18.43 deg., and 41.19 deg., respectively, are used herein as standards for evaluating the effects of camber and warp. The wing thickness distributions were computed by varying the section shape along with the body radii (blending process) to match the prescribed area distribution and wing plan form. The wing camber and warp were computed to try to obtain nearly elliptical spanwise and chordwise load distributions for each plan form and thus to obtain low drag due to lift for a range of Mach numbers for which the velocities normal to the wing leading edge are subsonic. Elliptical chordwise load distributions were not possible for the plan forms and design conditions selected, so these distributions were somewhat different for each plan form. The models were tested with transition fixed at Mach numbers from 0.60 to 3.50 and at Reynolds numbers, based on the mean aerodynamic chord of the wing, of roughly 4,000,000 to 9,000,000. At speeds where the velocities normal to the wing leading edges were supersonic, an increase in the experimental wave-drag coefficients due to camber and twist was evident, but this penalty decreased with increased sweep. Thus the minimum wave-drag coefficients for the cambered arrow model were almost identical with the zero-lift wave- drag coefficients for the uncambered arrow model at all test Mach numbers.
An iteration method is presented by which the detailed aerodynamic loading and twist characteristics of a flexible wing with known elastic properties may be calculated. The method is applicable at Mach numbers approaching 1.0 as well as at subsonic Mach numbers. Calculations were made for a wing-body combination; the wing was swept back 45 deg and had an aspect ratio of 4. Comparisons were made with experimental results at Mach numbers from.0.80 to 0.98.