Recently, the increase of geo-stationary satellites in orbit makes it desirable to develop a more simplifed satellite control system which does not need a large scale computer, and yet reduces man-power. Such a system may be realized by making an orbit computation program compact enough to be able to run on a machine like a mini-computer. In this paper, a simplifed method for computing geo-stationary satellite orbit which meets the above requirements, is discussed. This method uses the analogy and the extension of the general perturbation method-Namely, it describes the osculating orbital elements by the series expansion of time variable t and trigonometry whose arguments are products of Wi's and the time t's which is measured from some fixed epoch. Here, Wi's are frequencies that are linear combinations of the earth's angular rate of rotation, the lunar mean motion, the solar mean motion, etc. It is shown that geo-stationary orbit can be computed by the proposed method with sufficient accuracy to control the satellites. And the effectiveness of the orbit determination program based on this method is proved by the results of orbit determination experiments of CS (Medium Capacity Communications Satellite for Experimental Purposes). The size of the program is reduced to one-tenth of the conventional one using the special perturbation method, and the program can be operated on a mini-computer.
A method of applying the statistical regression analysis to thermal network correction is investigated. The reciprocal relations imposed on the parameters in the network model are taken into account by use of the Lagrange multipliers. Then a simple form of the normal equation of the parameters is obtained. An equation for the multipliers is derived and shown to be easily solved. So that the method is applicable to actual and large scale problems. The stepwise procedure of Efroymson is used for the regression analysis of the temperature data. Numerical study on a sample network showed effectiveness of the F-test in the procedure for examining the statistical importance of each parameter. It is found that there exists an optimum value for the critical F. When the only parameters contained in the original model are given as unknowns, the optimum value is about one, however, when all the possible parameters are given as unknowns, the value is about two. This result agrees with the conclusion of a general theory of optimum model estimation.
To examine whether the performance of optimum hydrofoils in the case of supercavitating flow is efficient under partialcavitating flow, optimum hydrofoils which have minimum drag coefficient under partialcavitating flow are determined by using calculus of variation, and are compared with optimum hydrofoils in the case of supercavitating flow. The results obtained in this paper are summerized as follows; (1) It is found that the relation between the lift coefficient and the cavitation number which is obtained by using Double spiral vortex model expresses the experimental data better than that obtained by using Closed, Semi-closed or Open model. (2) The lift-drag ratio of the optimum hydrofoil in the case of partialcavitating flow increases with the cavitation number, and it is seen that three is a certain value of the lift coefficient at which the lift-drag ratio becomes maximum. (3) The lift-drag ratio of the four-term optimum hydrofoils is greater than that of the twoterm hydrofoils. (4) The profiles of the two-term hydrofoils in the case of partialcavitating flow are similar to those in the case of supercavitating flow. Taking the conclusion of optimum supercavitating hydrofoils, in which the lift-drag ratio makes little difference between the two-term and four-term hydrofoils, into account, it may be analogized that optimum hydrofoils in the case of supercavitating flow have also the good performance under partialcavitating condition.
A numerical solution of equations of motion of an aircraft which represents the process from a stall state to a flat-spin state, has been obtained as a first step in evaluating the possibility of spin entry. Typical time histories of the attitude angles were assumed, and the deflection angles of control surfaces were determined by a numerical technique.