Theodolite

Description

A theodolite is a supplemented instrument of Géodésie of a instrument optical, measuring angles in the two horizontal and vertical planes in order to determine a direction. It is used to carry out measurements of a Triangulation: measure angles of a triangle.

It is a Lunette assembled on the two axes Vertical and Horizontal. Each axis is equipped with a graduated dial allowing the readings with the angles.

The theodolite is posed on a support and must be fixed on the horizontal level; it is often placed on a tripod, and at the exact vertical of a point known in Coordonnée S, using a plumbline and of a spherical spirit level, and its base must be perfectly horizontal (use of a toric bubble, as well as spherical bubble). The whole of this phase of use names " the setting in station".

The Théodolite belongs to the family of the measuring instruments of angles.

In Astronomy, the theodolite is used to determine the Azimut compared to the celestial pole, or the Déclinaison where the height connects of a celestial body compared to the horizon.

In Geodesy, it is used to determine the angles formed by 3 tops of mountain for example.

In Topography, it is used in measurements of a survey of the territory (topographic Levé).

In Archeology, at the time of Excavation S, it is used like measuring instrument of specific points of the relief, used then in the reconstitution of the site in three dimensions.

The instruments being used only for measurements of the horizontal angles are Goniomètre S , those being used only for measurement of the vertical angles are eclimeter S and those allowing at the same time the measurement of the horizontal angles and the vertical angles are theodolites .

The theodolite can be associated with various instruments allowing for example measurement with the distances, one speaks then about Tachéomètre , or the automatic seizure of measurements, one then speaks about total Station .

Use of the theodolite in topography

The theodolite is wholesale an improved rapporteur, who allows to raise the angle between two points. One makes use of it for work of topography. In fact, which one measures is not directly the angle between two visible reference marks (signals on a mountain, bell-tower…), but between the vertical of these signals, i.e. one makes abstraction the height to which the reference marks are visible, to retain only the Gisement of it (the vertical ones of the visible signals). One thus fixes the theodolite with the horizontal one, and the angles are measured only in the horizontal plane, with a small sight tube which can swivel vertically, to aim in height.

To improve the precision of the statements in a triangle ABC, one measures in fact the three angles in has, B, and C. These measurements are redundant, the sum of the angles having to be 180°. In fact, one always finds a small difference in measurement: it is considered that this difference comes from random errors, and one corrects the statements by withdrawing 1/3 of the difference from each value. For the statements at small distance, the geometry is practically plane, but at long distance and with a statement from precision which the theodolite allows, the curve of the ground is felt: the sum of the angles of a triangle does not make any more 180°, but also depends on the surface of the registered triangle. In work of triangulation to long distance, for example to measure the terrestrial meridian line, one is thus obliged to take account of this correction (calculation in spherical trigonometry) before correcting the statements, which if not would be systematically distorted.

The conditions of good visibility and the relief make it possible in France to work on aimings from 40 to 50 kilometers in plain, a little more on isolated high points. The angles are read, with the best theodolites, a precision about the décimilligrade; one makes the observations and calculations with a figure moreover not to degrade the precision with rounding errors. The spherical excess of a polygon is approximately of 1,6 dmgr for 100 km ² of surface. For a triangle of 40 side km, it can reach 14dmgr: it is far from being negligible. A décimilligrade is the angle under which, to 40 km, one would see an object of approximately 6 centimetres.

External bonds

theodolite

Zh-yue: 經緯儀

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