Topografie Proiect

SURVEYING CALCULUS

The esemble of works carried out in order to obtain the plan or the surveying map is called topographycal lifting. Depending on their contents, we distinguish: planimetrical lifting, when only the determination of the position in plane of the topographical surface is done, levelmetrical lifting, when only the determination of the vertical position of the points is done, and combined lifting, when the determination of both the position in plane and vertical position is made.

Project theme

For correcting the representation in plan of the topographical surface, it’s necessary knowing some basic surveying calculations related to determining the position of points according to a reference system.

Problem data

1. Rectangular coordinates of the points, 45 and 51 from the geodesic triangulation network of the country.

2. Elements measured on the field for determining the position in space of the point 101: horizontal point β, zenital angle Z, and the inclined distance measured directly with the steel braid, di(fig 1.1)

51 101

, , ,

β

45

Fig: 1.1. Sketch comprising the initial known elements (coordinates) and measured elements (angles and distances)

NOTE: Problem data, having the initial known elements (spatial coordinates) and elements resulted from field measurements (angles and distances) are made in table 1.1

Problem data

Table 1.1

Pct.

statie Pct.

vizat Distanta

Inclinata

Di

(m) Unghi

Zenital

Z

(g,c,cc) Unghi

Orizontal

Β

(g,c,cc) Coordonatespatiale Nr.

Pct.

X Y Z

45 51 - - 0g00c 2422.02 1833.12 231.96 51

101 133.08 94g51c 135g39c 1735.43 2351.12 164.55 45

Work will include

1. Calculus of orientation and horizontal distances, from the triangulation points coordinates, 45 and 51.

2. Calculus of orientation direction 45 – 101, through transmission.

3. Reduced distance calculation on the horizon, and the level difference, between the station point and the new point 101, , -level difference.

4. Relative plane coordinates calculus, , of the new point 101, in relation to the known point, 51, , .

5. Absolute coordinates calculus X,Y,Z of the new point , 101, , , .

Homework solving

The position of the points on the plane is defined over a rectangular system of axes. I the case of our country, according to the stereograph projection on the unique secant plane 1970, the general system of axes was obtained taking as abscisa axe, the projection in plane of the central meridian point, situated north of Fagaras, and coordinates, the perpendicular on the abscisa axes in the central point. The abscisaaxes is orientated on the south-north direction and the ordonate axe on west-east direction.

In topography the reference direction is represented in north direction. Because on the surface of globe, through every point, passes a geographic meridian, of fixed position, as well as a magnetic meridian of variable position in time, as reference direction is taken the parallel to the geographic meridian of the central point, taken in the considered point. In this way, the orientation of a direction, , is defined as being the angle by the geographic parallel meridian of the central point with the direction on the field, measured directly clockwise. The orientation may take positive values from to .

+X N N

N B