Consecutive Stations Research Articles

External Proton Beam Tune Calculations including Targets at Consecutive "Focii"

A beam transport program for the CDC-924A Zero Gradient Synchrotron (ZGS) control computer has been prepared which includes the change in phase space properties caused by multiple scattering in target material at the various consecutive experimental user stations (focii). The beam envelope, continuous across targets, can be displayed on an oscilloscope and the beam parameters can be adjusted to fit desired conditions. The phase space ellipse at any specified position in the beam can also be displayed. Average energy loss is included in the computations to update the beam momentum. Experimental tests will be made to determine the validity of the computations.

Energy-saving Automatic Optimisation Of TrainSpeed Commands Using Direct Search Techniques

This paper describes two computer tools that have been developed for the automatic optimisation of train speed commands. Given a target time for the trip between two consecutive stations, energy consumption is minimised. Two driving strategies have been considered, one based on coasting-remotor cycles and the other in space-related traction commands. Direct search techniques have been applied, using simulation processes that include detailed models of the train and the line.

Observations with the Cambridge Pendulum Apparatus in North, Central and South America in 1958

Summary Observations were made with the Cambridge pendulum apparatus in the period 1958 August-December at Teddington, Madison, Mexico City, Panama, Caracas, Quito, Lima, La Paz, Santiago (Chile), Buenos Aires and Rio de Janeiro. Stations were reoccupied on the return journey so that eight measures of the difference of gravity between consecutive stations were obtained. These values are reported in the paper.

An analytical treatment of the problem of triangulation by stereophotogrammetry

Abstract. An analytical solution for the basic problem of triangulation by stereophotogrammetry is derived. The most general case is defined as the problem of determining simultaneously the orientations of the two cameras, whereby all eighteen unknown parameters of the orientation are considered with no limitations on the camera orientations. The process of triangulation is treated as the computation of spatial coordintes as functions of the elements of orientation and the corresponding plate measurements. The least squares solution derived is based on rigorous mathematical expressions which connect the plate measurements with the unknown parameters. In contrast to the conventional approach, the separation of the orientation problem into the two phases of relative and absolute orientation is avoided. This analytical solution can be based on a few basic theorems of solid analytical geometry. Because the observation method — monocular or stereoscopic — does not influence the formulas expressing the rigorous geometry, it is possible to make use of absolute control points which are not common to the area covered by the two photographs under consideration. Thus more favorable geometry is introduced into the problem of the double-point intersection in space. The least squares solution derived is suitable for any number and any combination of absolute, partially absolute and relative control points. In addition, any one of the elements of orientation — including the base line components — may be enforced in the solution. By applying the concept of pseudo-residuals and by introducing cross-weights, it is possible to treat the least squares solution like a problem involving independent indirect measurements. Furthermore, it is shown that the normal equation system can be formed step by step. This method has merit when electronic computes are used since the number of points carried in the solution has only a slight effect on the amount of memory space needed. The introduction of rotational auxiliaries which are essentially direction cosines and the combination of these with the plate coordinates as linear auxiliaries render the coefficients of the observational equations as partial differential quotients in terms attractive for an analytical treatment. The process of triangulation is treated as a part of the process of orientation as well as an independent computational procedure. A special chapter deals with the determination of the mean errors of the observations, of the elements of orientation, and of the triangulation results. Finally, the application of the proposed analytical method to the problem of control extension is discussed in principle. It is shown that the method used on the universal plotters for a strip triangulation procedure is an approximate solution only, because it is based on incomplete conditional equations. The rigorous geometry for the problem of extension is interpreted as the condition that rays originating from three consecutive camera stations have to intersect for at least one point located in the area common to the three photographs under consideration. The corresponding conditional equations are derived and the coefficients, of the corresponding observational equations are given. It is shown that it is now possible to include in the extension models which are formed by the combination of photographs taken at every other camera position. The thus extended base line provides for a favorable base-height ratio otherwise obtainable only by convergent photography. As stated before, the final normal equation system can be formed step by step. Attention is called to the fact that the matrix of the unknown parameters is filled in the neighbourhood of the diagonal only, thus making it possible to use an iterative subroutine. The method presented for a strip triangulation is useful in a least squares treatment of a block triangulation also.

AN OBSERVATIONAL METHOD TO OVERCOME ZERO DRIFT ERROR IN FIELD INSTRUMENTS

By using a four‐step oscillating method of observation, four values are obtained for the increment in the measured value between consecutive stations. If the drift or “zero creep” of the instrument is regular, even when large, or not linear, this furnishes a means of improving the reliability of the readings and permits the detection of erratic readings. In areal surveys, a primary net of values may be established by this oscillating method and this net used as a base into which to adjust chains of observations. Intermediate values may sometimes be desirable, such values being adjusted into the primary net by the oscillating method. An example shows the application of the method to a gravimetric survey.