Polygonometry

The polygonometry, in this case, is a method of equalizing of theodolitic courses with several nodes.

The polygonometry can be created in the form of several courses (chain centroids).

Chain centroid is the part of a network concluded between:

- base stations and node (the node is station ОП3 (BS3));

- two nodes (nodes are stations ОП2(BS2) and ОП3(BS3));

- node and base stations (the node is a base station ОП2(BS2)).

On the point (station), being a node, must be chosen a binding direction for which the direction onto one of reference points usually is accepted. This direction should be identical in all chain centroids for the given node. If the reference point of a binding direction is a point of a course the station with the measured angle between a point of a course and a reference point equal to zero is entered in addition. This rule operates in case the node is in the beginning of a chain centroid and in case the node is in the end of a chain centroid.

At calculation the absence of data on this point (coordinates and a direction angle of a binding direction) is an attribute of a node.

The type of a theodolitic course is desirable to set "unlock" since other type of a course can be calculated, but not participate in equalizing.

Upon termination of data input the calculation and equalizing of a polygonometry is carried out - menu item: Measurements\Calculate\Calculate a polygonometry.

At the specifying a name of a point it is necessary to be cautious. Problems with names of points: -letters can be typed on different registers (Russian and English), and some letters are visually identical, but have the different coding for the computer.

The equilibration of theodolitic courses with several nodes is carried out by method of successive approximations.

Balancing by method of successive approximations.

Balancing is carried out in such order. Find the approximate values of nodal direction angles, having calculated them as the average value received from all adjacent base stations and nodes, or, as a last resort, having passed them from a base station.

Find the second approximation for each nodal direction angle as the weighted mean from all received values and from adjacent base stations and nodal for the last accept the values found from first approximations or from second approximations, if they have been already received.

For the weight of a nodal direction angle accept size, inversely to number of angles of a course on which value of this direction angle is received.

Then for all nodal direction angles find consistently the third, the fourth, etc. approximation and, having convinced, that the subsequent approximations do not bring changes of greater, than accuracy of calculations, stop calculations.

Adjusted direction angles of binding directions are accepted as initial and direction angles of lines by each course separately are adjusted.

By adjusted direction angles the increments of coordinates are calculated and their sums by courses are counted.

Further, having counted the sums of increments of coordinates for each course, calculate the most probable values of an abscissas and ordinates of nodes to similarly how it was made for direction angles. Having final values of coordinates, counterbalance each course.

It is necessary to note, that weights of the counterbalanced elements at this method can be received only by the approached formulas. The given method is applied in case a network rigid enough, i.e. the relation of number of arising conditions or numbers of the ranges, closed and basing onto firm points, to number of unsteady nodes will be more than 1,5~2.

(n-k)/k >= 1.5~2;

where n - number of all courses;

k - number of nodes.