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FORTRAN digital computer program for axial distribution of aerodynamic normal force characteristics for axisymmetric, multistage launch vehicles in linear angle of attack ranges
Specific magnitudes of crosswinds may exist that could be constraints to the success of an aircraft mission such as the landing of the proposed space shuttle. A method is required to determine the orientation or azimuth of the proposed runway which will minimize the probability of certain critical crosswinds. Two procedures for obtaining the optimum runway orientation relative to minimizing a specified crosswind speed are described and illustrated with examples. The empirical procedure requires only hand calculations on an ordinary wind rose. The theoretical method utilizes wind statistics computed after the bivariate normal elliptical distribution is applied to a data sample of component winds. This method requires only the assumption that the wind components are bivariate normally distributed. This assumption seems to be reasonable. Studies are currently in progress for testing wind components for bivariate normality for various stations. The close agreement between the theoretical and empirical results for the example chosen substantiates the bivariate normal assumption.
Modern engineering design practices are tending more toward the treatment of design parameters as random variables as opposed to fixed, or deterministic, values. The probabilistic design approach attempts to account for the uncertainty in design parameters by representing them as a distribution of values rather than as a single value. The motivations for this effort include preventing excessive overdesign as well as assessing and assuring reliability, both of which are important for aerospace applications. However, the determination of the probability distribution is a fundamental problem in reliability analysis. A random variable is often defined by the parameters of the theoretical distribution function that gives the best fit to experimental data. In many cases the distribution must be assumed from very limited information or data. Often the types of information that are available or reasonably estimated are the minimum, maximum, and most likely values of the design parameter. For these situations the beta distribution model is very convenient because the parameters that define the distribution can be easily determined from these three pieces of information. Widely used in the field of operations research, the beta model is very flexible and is also useful for estimating the mean and standard deviation of a random variable given only the aforementioned three values. However, an assumption is required to determine the four parameters of the beta distribution from only these three pieces of information (some of the more common distributions, like the normal, lognormal, gamma, and Weibull distributions, have two or three parameters). The conventional method assumes that the standard deviation is a certain fraction of the range. The beta parameters are then determined by solving a set of equations simultaneously. A new method developed in-house at the NASA Glenn Research Center assumes a value for one of the beta shape parameters based on an analogy with the normal distribution (ref.1). This new approach allows for a very simple and direct algebraic solution without restricting the standard deviation. The beta parameters obtained by the new method are comparable to the conventional method (and identical when the distribution is symmetrical). However, the proposed method generally produces a less peaked distribution with a slightly larger standard deviation (up to 7 percent) than the conventional method in cases where the distribution is asymmetric or skewed. The beta distribution model has now been implemented into the Fast Probability Integration (FPI) module used in the NESSUS computer code for probabilistic analyses of structures (ref. 2).
A method is presented for the rapid calculation of the incremental chordwise normal-force distribution over an airfoil section due to the deflection of a plain flap or tab, a split flap, or a serially hinged flap. This report is intended as a supplement to NACA Report no. 631, wherein a method is presented for the calculation of the chordwise normal-force distribution over an airfoil without a flap or, as it may be considered, an airfoil with flap (or flaps) neutral. The method enables the determination of the form and magnitude of the incremental normal-force distribution to be made for an airfoil-flap combination for which the section characteristics have been determined. A method is included for the calculation of the flap normal-force and hinge-moment coefficients without necessitating a determination of the normal-force distribution.
Solar energetic particles can be used as probes for the turbulence level in the interplanetary medium. It is of general interest to compare the LOCAL scattering properties near an observer with GLOBAL properties which characterize the average scattering along the magnetic field. We discuss various methods by which the scattering conditions can be determined: (1) overall fits of observed particle intensities and anisotropies to a transport model; (2) evaluation of the steady-state pitch angle distribution; and (3) suitably normalized angular distributions during the intensity maximum of a particle event. Energetic particle data from HELIOS 1/2 are analyzed, and the mean free paths obtained with the different methods are compared with each other. As a result one can state: (1) for a number of solar particle events the radial mean free path is essentially constant between the Sun and Helios; and (2) large variations in the degree of scattering exist from one event to the other. These results indicate the existence of 'regimes' where the amount of particle scattering is relatively constant over extended regions in radius and azimuth, but with marked differences from one regime to the other.
The mechanical properties of a symmetrical, eight-step, titanium-boron-epoxy joint are discussed. A study of the effect of adhesive and matrix stiffnesses on the axial, normal, and shear stress distributions was made using the finite element method. The NASA Structural Analysis Program (NASTRAN) was used for the analysis. The elastic modulus of the adhesive was varied from 345 MPa to 3100 MPa with the nominal value of 1030 MPa as a standard. The nominal values were used to analyze the stability of the joint. The elastic moduli were varied to determine their effect on the stresses in the joint.
Normalized double-differential cross sections for top quark pair ( $\mathrm{t}\overline{\mathrm{t}}$ ) production are measured in pp collisions at a centre-of-mass energy of 8 $\,\text {TeV}$ with the CMS experiment at the LHC. The analyzed data correspond to an integrated luminosity of 19.7 $\,\text {fb}^{-1}$ . The measurement is performed in the dilepton $\mathrm {e}^{\pm }\mu ^{\mp }$ final state. The $\mathrm{t}\overline{\mathrm{t}}$ cross section is determined as a function of various pairs of observables characterizing the kinematics of the top quark and $\mathrm{t}\overline{\mathrm{t}}$ system. The data are compared to calculations using perturbative quantum chromodynamics at next-to-leading and approximate next-to-next-to-leading orders. They are also compared to predictions of Monte Carlo event generators that complement fixed-order computations with parton showers, hadronization, and multiple-parton interactions. Overall agreement is observed with the predictions, which is improved when the latest global sets of proton parton distribution functions are used. The inclusion of the measured $\mathrm{t}\overline{\mathrm{t}}$ cross sections in a fit of parametrized parton distribution functions is shown to have significant impact on the gluon distribution.
The local structure of the pseudo-cubic solid solution 0.6BaTiO{sub 3}-0.4BiScO{sub 3}, which exhibits reentrant dipole-glass behavior, has been determined using the Reverse Monte Carlo method to simultaneously fit (1) neutron and X-ray total scattering data (including the corresponding real-space pair-distribution functions), (2) Bi and Sc extended X-ray absorption fine structure, and (3) patterns of diffuse scattering in electron diffraction. These structural refinements revealed the multi-site probability density distributions for both Bi (14-sites) and Ti (8 sites), whereas Ba and Sc featured normal unimodal distributions. Bi atoms are displaced along both the 〈111〉 and 〈100〉 directions, while Ti atoms are shifted along 〈111〉. Correlated dynamic hopping of Bi and Ti over their corresponding split sites combined with chemical disorder is proposed as the origin of the strong frequency dispersion observed in dielectric measurements. The existence of split sites also explains the reentrant dipole-glass behavior reported for this system.
The reattachment of a fully turbulent, two-dimentional shear layer downstream of a backward-facing step has been studied experimentally. The work examines the effect of variations in inlet conditions on the process of reattachment. A series of experiments was conducted in a low-speed wind tunnel using specialized instrumentation suited to the highly turbulent reversing flow near reattachment. Accurate characterization of the time-mean features of the reattaching flows was possible. Assuming linear scaling normalized on distance from reattachment, distributions of normalized pressure coefficient and forward flow fraction, and time-averaged skin friction coefficient appear universal for two-dimensional reattachment, independent of initial conditions and step height, for given duct geometry (area ratio) and for high step-height Reyolds numbers with thin separating boundary layers. The results suggest universal flow structure in the reattachment zone.
The effect of laminate thickness on the interlaminar stresses in rectangular quasi-isotropic laminates under uniform axial strain was studied. Laminates from 8-ply to infinitely thick were analyzed. Thick laminates were synthesized by stacking (45/0/-45/90) ply groups, rather than grouping like plies. Laminates with and without delaminations were studied. In laminates without delaminations, the free-edge interlaminar normal stress distribution in the outer ply groups was insensitive to total laminate thickness. The interlaminar normal stress distribution for the interior ply groups was nearly the same as for an infinitely thick laminate. In contrast, the free-edge inter-laminar shear stress distribution was nearly the same for inner and outer ply groups and was insensitive to laminate thickness. In laminates with delaminations those delaminations near the top and bottom surfaces of a thick laminate have much larger total strain-energy-release rates (G sub t) and mode I-to-total (G sub t/G sub t) ratios than delaminations deep in the interior. Therefore, delaminations can be expected to grow more easily near the surfaces of a laminate than in the interior.
The effect of laminate thickness on the interlaminar stresses in rectangular quasi-isotropic laminates under uniform axial strain was studied. Laminates from 8-ply to infinitely thick were analyzed. Thick laminates were synthesized by stacking (45/0/-45/90) ply groups, rather than grouping like plies. Laminates with and without delaminations were studied. In laminates without delaminations, the free-edge interlaminar normal stress distribution in the outer ply groups was insensitive to total laminate thickness. The interlaminar normal stress distribution for the interior ply groups was nearly the same as for an infinitely thick laminate. In contrast, the free-edge inter-laminar shear stress distribution was nearly the same for inner and outer ply groups and was insensitive to laminate thickness. In laminates with delaminations those delaminations near the top and bottom surfaces of a thick laminate have much larger total strain-energy-release rates (G sub t) and mode I-to-total (G sub t/G sub t) ratios than delaminations deep in the interior. Therefore, delaminations can be expected to grow more easily near the surfaces of a laminate than in the interior.
Bending moments and other associated parameters were measured on a Scout vehicle during a launch through high velocity horizontal winds. Comparison of the measured data with predictions revealed some unexplained discrepancies. Possible sources of error in the experimental data and predictions were considered; one of which is the predicted aerodynamic characteristics. A wind tunnel investigation was initiated, including supersonic force and pressure tests, to better define the aerodynamics. In addition to basic aerodynamic coefficients from the force test, detailed pressure and load distributions along the body were established from the pressure test. Pressure coefficients were integrated to determine normal load distributions, total normal force, and total pitching moment of the body. Comparison of the normal forces from pressure and force tests resulted in agreement within 15%. Comparison of pitching moment data from the two tests resulted in larger differences.
For over a century, vibrational spectroscopy has enhanced the study of materials. Yet, assignment of particular molecular motions to vibrational excitations has relied on indirect methods. Here, we demonstrate that applying group theoretical methods to the dynamic pair distribution function analysis of neutron scattering data provides direct access to the individual atomic displacements responsible for these excitations. Applied to the molecule-based frustrated magnet with a potential magnetic valence-bond state, LiZn{sub 2}Mo{sub 3}O{sub 8}, this approach allows direct assignment of the constrained rotational mode of Mo{sub 3}O{sub 13} clusters and internal modes of MoO{sub 6} polyhedra. We anticipate that coupling this well known data analysis technique with dynamic pair distribution function analysis will have broad application in connecting structural dynamics to physical properties in a wide range of molecular and solid state systems.
Ths Special Sensor Microwave/Imager radiometer on board the DMSP satellite measured microwave radiation at 19.35, 22.235, 37.0, and 85.5 GHz with a swath width of 1400 km, providing an opportunity to study global precipitation distributions. A monthly averaged rainfall index was derived using only the 19.35 GHz data. It covers the + or - 50 deg portion of the world with a 5 deg x 5 deg grid. The brightness temperature histogram is analyzed to derive the rainfall distribution. Estimates of the freezing level heights and the water vapor contents are utilized to understand the rainfall distribution better. Log normal and gamma distribution functions are fitted to the data and the derived monthly rainfall index compares favorably with historical precipitation patterns.
The Reynolds-stress and triple product Lag models were created with a normal stress distribution which was defined by the accepted 4:3:2 distribution of streamwise, spanwise and wall normal stresses, and a ratio of τ(sub w) = 0.3k in the log layer region of high Reynolds number flat plate flow, which implies R11(+) = 4/(9/2)∗.3 ≈ 2.96. More recent measurements show a more complex picture of the log layer region at high Reynolds numbers. The first cut at improving these models along with the direction for future refinements is described. Comparison with recent high Reynolds number data shows areas where further work is needed, but also shows inclusion of the modeled turbulent transport terms improve the prediction where they influence the solution. Additional work is needed to develop a model that better matches experiments, but there is significant improvement in many of the details of the log layer behavior.
The Reynolds-stress and triple product Lag models were created with a normal stress distribution which was defined by the accepted 4:3:2 distribution of streamwise, spanwise and wall normal stresses, and a ratio of τ(sub w) = 0.3k in the log layer region of high Reynolds number flat plate flow, which implies R11(+) = 4/(9/2)∗.3 ≈ 2.96. More recent measurements show a more complex picture of the log layer region at high Reynolds numbers. The first cut at improving these models along with the direction for future refinements is described. Comparison with recent high Reynolds number data shows areas where further work is needed, but also shows inclusion of the modeled turbulent transport terms improve the prediction where they influence the solution. Additional work is needed to develop a model that better matches experiments, but there is significant improvement in many of the details of the log layer behavior.
Characteristics of the raindrop size distribution in seven tropical cyclones have been studied through impact-type disdrometer measurements at three different sites during the 2004-06 Atlantic hurricane seasons. One of the cyclones has been observed at two different sites. High concentrations of small and/or midsize drops were observed in the presence or absence of large drops. Even in the presence of large drops, the maximum drop diameter rarely exceeded 4 mm. These characteristics of raindrop size distribution were observed in all stages of tropical cyclones, unless the storm was in the extratropical stage where the tropical cyclone and a midlatitude frontal system had merged. The presence of relatively high concentrations of large drops in extratropical cyclones resembled the size distribution in continental thunderstorms. The integral rain parameters of drop concentration, liquid water content, and rain rate at fixed reflectivity were therefore lower in extratropical cyclones than in tropical cyclones. In tropical cyclones, at a disdrometercalculated reflectivity of 40 dBZ, the number concentration was 700 plus or minus 100 drops m(sup -3), while the liquid water content and rain rate were 0.90 plus or minus 0.05 g m(sup -3) and 18.5 plus or minus 0.5 mm h(sup -1), respectively. The mean mass diameter, on the other hand, was 1.67 plus or minus 0.3 mm. The comparison of raindrop size distributions between Atlantic tropical cyclones and storms that occurred in the central tropical Pacific island of Roi-Namur revealed that the number density is slightly shifted toward smaller drops, resulting in higher-integral rain parameters and lower mean mass and maximum drop diameters at the latter site. Considering parameterization of the raindrop size distribution in tropical cyclones, characteristics of the normalized gamma distribution parameters were examined with respect to reflectivity. The mean mass diameter increased rapidly with reflectivity, while the normalized intercept parameter had an increasing trend with reflectivity. The shape parameter, on the other hand, decreased in a reflectivity range from 10 to 20 dBZ and remained steady at higher reflectivities. Considering the repeatability of the characteristics of the raindrop size distribution, a second impact disdrometer that was located 5.3 km away from the primary site in Wallops Island, Virginia, had similar size spectra in selected tropical cyclones.
The effects of El Chichon's April 1982 eruption on stratospheric aerosol dynamics are presently discussed in terms of log-normal size distributions over 15-20 km sample altitudes between 30 and 45 deg N over the contiguous U.S. After collection, samples were studied by SEM, and log-normal size distributions were fitted to the data-points obtained. It is found that stratospheric aerosol behavior is explainable by the laws of aerosol mechanics more easily than has been the case for tropospheric aerosol, for which the source-sink relationship is much more complex.