无定向角导线在导线测量中的应用（The application of undirected Angle wire in the measuring of wire）

1、无定向角导线在导线测量中的应用（The application of undirected Angle wire in the measuring of wire）Abstract: in this paper, the problem of traverse measurement is discussed in this paper.Keywords: no orientation, rotation, zoomingPreface:Now urban construction rapid development, especially such as Shanghai internati

2、onal metropolis, high-rise buildings to spring up, this may make the control points of the original no longer visibility, so that it did not have the necessary to calculate each conductor of azimuth orientation Angle, to traverse. This paper introduces a method to calculate the two control points.1.

3、 Closed conditions of single undirected angular conductorsThe essence of the single undirected angular conductor is that the single echo of the directional Angle is not observed at both ends, as shown in figure 1For a single with n - 1 for fixed-point astatic Angle of conductor, its necessary observ

4、ation value of 2 (n - 1), and the observed value for n + (n - 1), article n and n - 1 wires Angle, so the number of redundant observation for n + (n - 1) - 2 (n - 1) = 1. Due to the undetermined Angle of the Angle, the redundant observation condition is the length closure condition.2. Calculation id

5、easSingle no orientation Angle at the ends of the wire orientation Angle observation, but need to calculate each conductor of azimuth at least know a orientation Angle, this is a single Angle of non-directional traverse adjustment difficulties of calculation. Solve way is: will the first wire the az

6、imuth Angle of hypothesis, hypothesis azimuth as starting coordinate azimuth, using the initial azimuth and the azimuth Angle, on the edge of lead Angle observation value calculate all lead, calculated and reuse lead the coordinates of observed value calculation, on the edge of the end.Due to incorr

7、ect orientation (assumption), on the edge of starting Angle and wires and wire and the influence of observational error, will lead to the calculation of end point not consistent with the actual level, to eliminate the contradiction, can use wire fixed edge AB edges (pictured above) of known length a

8、nd azimuth respectively known as standard and orientation of the scale of the wire to wire for scaling and rotation, so that the calculation of end point is consistent with the actual point, in order to achieve the purpose of a single Angle of non-directional traverse adjustment.3. The calculation f

9、ormula of the approximate adjustment of the undirected Angle conductorAs shown in figure 1, A and B are known points, whose coordinates are xA, Ya, xB, yB, and the side length and azimuth Angle of the fixed edge AB are DAB and alpha AB; The observed value of the observed values at the wire Angle and

10、 the wire side are beta I, Di and beta I, D I; The values of the calculated values of the coordinates of the undetermined traverse points are xi, yi and xi and yi respectively.If the start edge A1 azimuth assumed to be the alpha A1, depending on the traverse Angle observation beta I can derive the c

11、alculated value of each conductor of azimuth, and then calculate the traverse side coordinates calculated value increment; On the wire coordinate calculation for the incremental and, for a quick fixed edge AB the coordinates of the incremental calculation x AB, y AB. Based on this, the calculated va

12、lue of the side length of the fixed edge is calculated by D AB and the azimuth Angle of alpha AB.If the rotation Angle and the scaling ratio of the wire are v alpha and Q, then there are:DA1 / D A1 A2 = = DA2 / D. DAB/D AB = Q (1)Alpha, aa1, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, al

13、pha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha Alpha AB - alpha AB = v alpha (2)Because = x x Ai I - xA = D cosine alpha Ai Ai; y = y Ai I - yA = D sine alpha Ai Ai; Taking into account (1) and (2) : x Ai = Q, DAi, cosine alpha (alpha Ai + v)Alpha, alpha, alpha, alp

14、ha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, Ai = y Q, DAi, sin (alpha Ai alpha + v)Alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha

15、, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha, alpha,So lets make Q1 = Q times cosine of v alpha; Q2 = Q sin v alpha, and attend to the xAi = DAi, cosine alpha Ai; yAi = DAi sine alpha Ai, there are: x Ai = Q1, xAi - Q2 yAi (3-1) y = Q1 Ai yAi + Q

16、2 xAi (3-2)As a special case of (3-1) (3-2), there are: xoAB = Q1, xAB - Q2 yAB yoAB = Q1, yAB + Q2 xABIn on type, xoAB, yoAB as known values, xAB, yAB by assuming that the starting position of alpha AB and lead Angle and lead edge observation beta I, Dij calculation and, thus can solve the Q1 and Q

17、2, namely:Q1 = ( xAB xoAB + yAB yoAB) /( xAB) + 2 ( yAB) 2) (4-1)Q2 = ( xAB yoAB + yAB xoAB) /( xAB) + 2 ( yAB) 2) (4-2)The formula for calculating the value of xi and yi in the calculated value xi and yi is calculated according to the coordinates of each undetermined traverse point, which is:X I =

18、xA + Q1 (xi-x A) -q 2 (yi - y A) (5-1)Y I = yA + Q1 (yi - y A) + Q 2 (xi-x A) (5-2)4. Application example of undirected Angle traverse is calculatedFIG. 2 shows the undirected Angle conductor for the M8 line measurement of Shanghai metro line, and the starting data of the wire is shown in the follow

19、ing table:The dotX mM YCoordinate azimuth o.Side length mT8151978.814371.917T8133842.578962.054The single undirected Angle wire adjustment calculation tablePoint nameObservation Angle value o Observation edge mSuppose the coordinate azimuth o Assumed coordinate incrementAssume that the coordinatesCo

20、ordinate adjustment x m y mX mM Ym xm yT8151978.814371.917210.82351 15 to 25131.939 161.749164.434 37.985D1141 57 322110.753 2272.502-207.483 -169.4982160.887-265.37816614957 12 13282806 175029-9.401 46237D2164 52 492555.308 2730.336-178.899 -132.6622325.637-287.67428296246 05 358163923

21、1692D306 42 1962894.259 3033.108-85.045 -83.3522586.598-397.51818103314 47 52-5.313 161319113659 -12.846D4181 24 003027.796 3189.11530306 174612766.709-416.84717069916 11 5254600 129964225794 285423D5164 30 023243.715 3373.679243255 5286782936.933-430.9181388590 41 54102739 47678147871 166103D6271 58 403476.418 3524.096676549 8426523067.311-478.95111378392 40 34169256 -450.833304485 391355D782 46 163693.352 3242.5191147.137 1538.4923102.960-370.823161830355 26 50131939 161749164434 37985D8260 57 322110.753 2272.502-207.483 -169.4983249.145-440.47523230