Time and motion of departing aircraft, especially, of jet aircraft are observed at Tokyo International Airport by observers at the airport traffic control tower. The results show that the average taxi-speed, V(km/h), is approximately proportional to 1/2 power to the taxi-distance, D (km), and it is given by the following equation in terms of D log10V=0.51log10D+1.22±0.10 Theoretical analysis by using a simplified model of speed patterns assumed on the basis of observations was made in order to compare with the empirical results mentioned above. It shows that there are two kinds of speed pattern modes. The following equations are suitable for estimating V from a known D. forD≤Dc V=√α/2D1/2 for D≥Dc V=VmaxD/(D+Dc) where α, Vmax and Dc are the acceleration, the maximum taxi-speed and the critical distance (=Vmax2/α) respectively. In comparison with the actual data obtained, and supposing Vmax=20 knots≅37km/h, t yields Dc=1.3km, α≅33332km/hh2
Two-dimensional transonic potential flows are expressed in the form of non-linear partial differential equation in the physical plane. This equation is a mixed type as elliptic and hyperbolic. Therefore, it is almost impossible to obtain analytical solutions of the partial differential equation. Furthermore, we can not know previously the sonic-line in the physical plane. This is one of the reasons why numerical calculations become difficult. Following method is divided into two groups, calculations of subsonic flows and of supersonic flows. At first, an artifical function of the Mach number M which can be determined arbitrarily is introduced in M>1 region of the differential equation. This function of M changes the partial differential equation from the mixed type into the elliptic type, however does not show natural law of the gaseous flows. The converted partial differential equation is solved in the boundary value problem. A subsonic flow and an artifical flow which is due to the introduced artifical function of M around a given arbitrary aerofoil section can be obtained. A sonic-line is determined as boundary of the both flows. Next, under initial conditions along the sonicline, the original partial differential equation which is the hyperbolic type in M>1 region is solved in the CAUCHY problem. A supersonic flow is obtained and the aerofoil section must be changed partially. The artifical flow is been superseded by this supersonic flow. The subsonic flow and the oupersonic flow must be continuous for the sonic-line. As a result of those problems, shockless transonic flows around aerofoil sections which are partially different from a given arbitrary aerofoil section can be obtained. At least, this method could be put into practice numerically. Some numerical examples were obtained in the way described above.
When a circular cylinder is supported through both side walls of a wind tunnel, the effects of the boundary layers along the side walls on the wake of the cylinder in a uniform flow were investigated in the pure Karman-vortex range of Reynolds number. When the boundary layers are cut off from the uniform flow passing the cylinder by two small circular plates attached to each end of the cylinder, the behaviours of the vortex shedding can be classified into two modes by the Reynolds number. Namely, in the range of Re≤160, i.e., the regular mode, the regular vortex shedding takes place uniformly in the axial direction of the cylinder, and the Karman-vortex street is formed in the wake. The primary Karmanvortex street is deformed as the distance from the cylinder is increased. Farther downstream in the wake, however, it tends to rearrange itself again into a configuration of the Karman-vortex street on a larger scale than that of the primary one. In the range of Re>160, i.e., the irregular mode, the turbulent velocity fluctuations are observed in the wake. The rearrangement of vortices in the wake can not be observed. On the other hand, when that end of the cylinder which has no circular plate is immersed in the boundary layer on a wall. the vortex shedding is affected by the boundary layer so that two more transitions between the regular and irregular mode appear in the range of Re≤160, The transition Reynolds numbers depend on the distance from the wall. No rearrangement into the secondary Karman-vortex street is seen in the regular mode. The flow in the rangeof Re>160 has always the irregular mode.
Probabilistic properties of nonlinear response of a simply supported rectangular panel for both flat and buckled states to random excitation are studied by a simulation method as a theoretical analysis of the sonic fatigue problem. The main purpose of the present study is to disclose the accuracy of the one mode approximation nonlinear solution which has been obtained in the first author's previous paper by using the analytical solution of the FOKKER-PLANCK equation. Simultaneous nonlinear differential equations derived by GALERKIN's method in the three mode approximation are numerically solved by NEWMARK's β method for random excitation forces produced in computer by the MONTE-CALRO tequnique and the fast FOURIER transformation, and the probabilistic quantities including the fatigue failure time are calculated. The simulation solutions for one mode approximation are also calculated and show good agreement with the corresponding analytical solutions. The results show that the one mode approximation does not yield a satisfactory solution but a fairly good solution for the very large sound pressure level which produces the sonic fatigue.
We derive the stiffness matrix of finite element in order to estimate the stress distribution and the stiffness of thin walled curved beam with arbitrary cross section. It is well known that this type beam, which is subjected to bending moment, shows considerable high stress and reduced stiffness due to the effect of wall bending. For example, restricted cases, circular and elliptical tubes, etc., have been treated by analytical way. So, based on the axisymmetric shell theory, at first, the assumed stress "Hybrid" FEM is formulated for arbitrary shapes. It makes us easy to carry out the parametric examinations. Second, since we want to take an ordinary beam for a member of structure as well as thin walled curved one, we could consider how to describe the characteristics of the member, here. Several representative cases are computed, but we find out that the reduced stiffness is more serious under the out-plane bending than in-plane.
Failure strengths of unidirectional composites are theoretically obtained based on several basic assumptions and strengths of the constituents and the fiber-matrix interface. The following three additional assumptions are introduced. Probabilistic nature of failure phenomena is ignored. Macroscopic failure occurs when one of stress levels in composites reaches a certain semimicroscopic failure criterion. Failure strengths are averaged as for θ, which is a projection angle of the loading direction in the transverse plane. As the first step, thermal residual stress state is calculated using temperature dependent matrix properties. Next, an external loading in an arbitrary direction is resolved into basic loadings in the xyz-coordinate. After solutions for the basic loads and thermal residual stresses are superposed, macroscopic failure strengths are determined. Numerical calculations are carried out for a CFRP with four kinds of criteria in matrix. It is shown that the closest results to TSAI-WU theory for the minimum F12 is obtained based on maximum principal stress criterion in matrix. Thermal residual stresses do not have important effects on strengths if an interface normal strength is large. It is also shown that there are no significant differences between the results on the hexagonal and square models. A possibility of evaluation of strength theories by combinating these results and proper experiments is suggested.