架空索道の動的理論に関する研究

Abstract

There are two theories, ----the catenary and the parabolic----, for the calculation of the problems of aerial cableway. They treat the problems statically, for the load is assumed not to be running on the cableway. However, we must consider the problems on the kinetic theory in the case of a running load. In chapter 2, assuming that the locus of the running load is recognized, the problem is studied theoretically. Therefore, the auther made a study of the locus of the running load on the aerial cableway in terms of theory and experiment. Assuming that the locus of a running load is recognized, the tension of the main rope is studied theoretically as the method of the statical theory on the problems of the aerial cableway. But we cannot investigate theoretically the locus of the running load on the cableway under general conditions. However, we can theoretically clear the locus of the running load on the cableway under the special conditions. a. When the load weight is nearly zero, the curve of its locus is approximately a catenary of a parabola. b. When the load weight is alike infinite, the locus curve is an ellipse, which has two focus on the upper-and lower support, and a major axis of rope length. c. When the speed of the running load is nearly zero, its locus curve is studied by the calculating method of the statical theory. The locus under the general condition, as mentioned before is studied only by the experimental method. In this experiment, we must be sure that the load is running smoothly on the cableway. The result of experiment is as follows: The resultant force of external force ---- a running load a centrifugal force of running load, and running resistance of the carriage ---- acting as the loading point on the cable way, is nearly equal to the running load at the center of the span. The tension of the rope becomes the maximum, because the radius of curvature of the locus of the running load is very long and, as a result, the centrifugal force is very small. As the locus of the running load is nearer the ellipse than the original curve, the speed (v) of the running load is calculated from a formula v2=2g(y-μx), if the locus of the running load is given as y=f(x). here, g: the acceleration of gravity. μ: the coefficient of running resistance of carriage. "μ" is nearly constant all the time while the carriage is running on the cableway. The locus of the running load is the upper part of the calculated locus by the statical theory, because the situation of the rope is changed by the movement of the running load. When the running load exists at the center of the span, the tension of the rope become maximum, the locus of the running load agrees with the calculated locus by the statical theory, as if the weight of load were "w" (0.6 ~ 0.8) times. This "w" is called the coefficient of the adjusted load. The coefficient relates to the ratio (l/u) which compares the rope length (l) with the distance (u) between two supports of the cableway. This relation is shown by the experimental formula w=-11.43 1/u+12.26. The speed and centrifugal force of the running load is very near the calculated value from the statical locus, but we must calculate the rope tension by using the coefficient of the adjusted load.