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FITLOS is computer program which implements new curve fitting technique. Main program reads input data, calls appropriate subroutines for curve fitting, calculates statistical analysis, and writes output data. Method was devised as result of need to suppress noise in calibration of multiplier phototube capacitors.
The stresses in a sheet with an interference-fit bolt have been calculated for two sheet-bolt interface conditions: a frictionless interface and a fixed (no-slip) interface. The stress distributions were calculated for various combinations of sheet and bolt moduli. The results show that for repeated loading the local stress range is significantly smaller if an interference bolt is used instead of a loosely fitting one. This reduction in local stress range is more pronounced when the ratio of bolt modulus to sheet modulus is large. The analysis also indicates that currently used standard values of interference cause yielding in the sheet.
Time-delay experiments are analyzed within the frame of a curved space-time. Residuals from Newtonian best fits of relativistic data are used as a measure of the 'relativistic effects.' Radial transponder trajectories are considered. If the motion is towards the sun, the relativistic residuals are of the order of 100 m. If the motion is away from the sun, they are at the 10-km level and the fraction due to the second-order curvature of the metric is at the 1-km level. Those effects are significantly smaller than those calculated from the divergence of the Newtonian and relativistic predictions after exact fit of the initial measurements.
This experiment was conducted to determine what physiological effects result when highly trained subjects are confined to bed, deprived of sleep, or allowed to discontinue training. Results indicated: (1) There was a moderate increase in strength variables due to the training in this experiment but the stress which the subjects received caused a negligible change in strength variables. (2) The training program resulted in highly significant changes in specific bicycle ergometer variables indicating good increases in cardiopulmonary fitness. Five days of bed rest or fifty hours of sleep deprivation caused comparable drastic decreases in cardiopulmonary fitness. Post stress the subjects reverted to a normal daily schedule and after two weeks they had recovered about half of what they lost. (3) Cardiac output remains relatively constant at a constant work load, but stroke volume increases with conditioning and decreases with deconditioning due to stress.
Experiments that were conducted over a 52-month period showed that isometric and isotonic training on the Exer-Genie gave negligible increases in cardiorespiratory fitness whereas training on the ergometer at a programmed pulse rate increased fitness moderately.
Fundamental characterization of the constant-amplitude fatigue crack propagation is achieved by an analysis of the rate of change of crack length with change in number of applied loading cycles, defining the rate values such that they are consistent with the basic assumption of smoothness and continuity in the fatigue crack growth process. The technique used to satisfy the analytical conditions and minimize the effects of local material anomalies and experimental errors is that of fitting a smooth curve to the entire set of basic data by least square regression. This yields a well-behaved function relating the number of cycles to the crack length. By taking the first derivative of the function, the crack growth rate is obtained for each point. The class of curve fitting functions used in the analysis is the polynomial of degree n.
A curve fitting approach was developed to solve the flutter equation for the critical flutter velocity. The psi versus nu curves are approximated by cubic and quadratic equations. The curve fitting technique utilized the first and second derivatives of psi with respect to nu. The method was tested for two structures, one structure being six times the total mass of the other structure. The algorithm never showed any tendency to diverge from the solution. The average time for the computation of a flutter velocity was 3.91 seconds on an IBM Model 50 computer for an accuracy of five per cent. For values of nu close to the critical root of the flutter equation the algorithm converged on the first attempt. The maximum number of iterations for convergence to the critical flutter velocity was five with an assumed value of nu relatively distant from the actual crossover.
A fatigue analysis, based on finite-element calculations and fatigue tests, was conducted for an aluminum-alloy sheet specimen with a steel interference-fit bolt. The stress analysis of the region near the bolt hole showed that the beneficial effect of an interference-fit bolt can be interpreted as the combined result of two effects: (1) load transfer through the bolt and (2) the compressive interference stresses in the sheet. Results of the fatigue tests show that progressively higher interference levels produced longer fatigue lives. The tests also show that a high level of interference prevents fretting at the bolt-sheet interface and that interferences larger than this level produced little additional improvement in fatigue life.
The Aerodynamic Data Analysis and Integration System (ADAIS), developed as a highly interactive computer graphics program capable of manipulating large quantities of data such that addressable elements of a data base can be called up for graphic display, compared, curve fit, stored, retrieved, differenced, etc., was described. The general nature of the system is evidenced by the fact that limited usage has already occurred with data bases consisting of thermodynamic, basic loads, and flight dynamics data. Productivity using ADAIS of five times that for conventional manual methods of wind tunnel data analysis is routinely achieved. In wind tunnel data analysis, data from one or more runs of a particular test may be called up and displayed along with data from one or more runs of a different test. Curves may be faired through the data points by any of four methods, including cubic spline and least squares polynomial fit up to seventh order.
Attempts are made to generate acceptable coordinate systems for two-body configurations. The first method to be tried was to use the body-fitted coordinate system technique to obtain the best system. This technique alone did not produce very good results, so another approach was investigated. This new approach involved using a combination of the body fitted coordinate system procedure and a complex variable transformation method that was used successfully in conformal mapping.
A method for automatic generation of boundary-fitted curvilinear coordinate systems, where the transformed coordinates are solutions of an elliptic differential system in the physical plane, and where the coordinate lines are coincident with all boundaries of a general multiply-connected, two-dimensional region containing any number of arbitrarily shaped bodies, and is described along with a suitable computer code for implementing the method. Any partial differential system can be solved on the boundary-fitted coordinate system by appropriate transformations. The transformed equations are approximated by finite differences and solved numerically in the transformed plane. All computations, whether for generating coordinate system or then solving the transformed equations, can be done on a rectangular field with square mesh with no interpolation required on the boundaries. The physical boundaries may even be time-dependent.
The technique of boundary-fitted coordinate systems is based on a method of automatic numerical generation of a general curvilinear coordinate system having a coordinate line coincident with each boundary of a general multi-connected region containing any number of arbitrarily shaped bodies. Once the curvilinear coordinate system is generated, any partial differential system of interest can be solved on this coordinate system by transforming the equations and solving the resulting system in finite difference approximation on the rectangular transformed plane. This method of automatic body-fitted curvilinear coordinate generation is used to construct finite-difference solutions of the full, time dependent Navier-Stokes equations for the unsteady viscous flow about arbitrary two-dimensional airfoils, or any other two-dimensional bodies. Finally, initial results for three-dimensional applications are also presented.
A method is presented for computing orthogonal boundary fitted coordinate systems for geometries with coordinate distributions specified on all boundaries. The system which has found most extensive use in generating boundary fitted grids is made up of Poisson equations, of which the functions P and Q provide a means for controlling the spacing and density of grid lines in the coordinate system. While questions remain concerning the existence and uniqueness of orthogonal systems, the generating method presented adds to the available, useful techniques for constructing these systems.
A three dimensional body-fitted coordinate system developed for use in the calculation of inviscid flows over ablated, asymmetric reentry vehicle nosetips is described. Because of the potential geometric asymmetries, no standard coordinate system (e.g., spherical, axisymmetric reference surface-normal) is capable of being closely aligned with the nosetip surface. To generate a 3-D, body-fitted coordinate system an analytic mapping procedure is applied that is conformal within each meridional plane of the nosetip; these transformations are then coupled circumferentially to yield a three dimensional coordinate system. The mappings used are defined in terms of hinge points, which are points selected to approximate the body contours in each meridional plane. The selection of appropriate hinge points was automated to facilitate the use of the resulting nosetip flow field code.
Installation of titanium (6Al-4V) threaded fittings on 1/4 in. tubing is sensitive to workmanship and to the state of repair of the installation tooling. Tooling with very slight out-of-specification imperfections produces less than optimum swaged fittings. A significant quantity of samples were fabricated and X-rays were used to determine the depth of swage. Joint performance was assessed through static and dynamic testing.
Method using two transparent plastic sheets and polyethylene foam spacer produces flat templates from contoured surfaces. Once prepared, templates laid flat, and insulation inserted between two templates cut to shape to fit contoured surface. Sections of insulation prepared by contour-transferring technique fit contoured surfaces precisely. Procedure used for tailoring protective covers or for installation of vibrationabsorbing material over contoured surfaces.
This report demonstrates the successful application of statistical variable selection techniques to fit splines. Major emphasis is given to knot selection, but order determination is also discussed. Two FORTRAN backward elimination programs using the B-spline basis were developed, and the one for knot elimination is compared in detail with two other spline-fitting methods and several statistical software packages. An example is also given for the two-variable case using a tensor product basis, with a theoretical discussion of the difficulties of their use.
The successful application of statistical variable selection techniques to fit splines is demonstrated. Major emphasis is given to knot selection, but order determination is also discussed. Two FORTRAN backward elimination programs, using the B-spline basis, were developed. The program for knot elimination is compared in detail with two other spline-fitting methods and several statistical software packages. An example is also given for the two-variable case using a tensor product basis, with a theoretical discussion of the difficulties of their use.