Tachymetric Surveying

(or tacheometric surveying), a method of determining the horizontal distance, direction, and relative elevation of a point with respect to the instrument station by a single sighting with a tachymeter telescope on a graduated rod.

The terms “tachymetric surveying” and “tachymetry” (or “tacheometry”) are often used synonymously. In Soviet usage, however, the term “tachymetry” (takheometriia) is applied to the branch of geodesy that deals with measurement methods and the organization of measurements in the plotting of tachymetric traverses and in the carrying out of a tachymetric survey as a form of topographic survey of an area. The stadia method of surveying used in the USA is an example of a tachymetric method.

In tachymetric surveying, the telescope of the tachymeter is sighted on a rod located at the point being determined, and three coordinates of the point are obtained. These coordinates are the polar coordinates of the point—that is, its direction and its distance s—and the difference h between the elevation of the point and the elevation of the instrument station. The coordinates may be obtained directly, or, with some tachymeters, the coordinates may be computed from the measurement data obtained. In the latter case, the following equations are used:

Here, K is an instrument constant, l is the difference between the two stadia hair readings on the vertical rod, v is the angle of inclination of the line of sight, C is a constant for the given instrument, i is the height of the tachymeter above the ground, f is a correction for refraction and for the curvature of the earth, and v is the height, above the ground, of the point on the rod where the middle hair of the tachymeter cuts the rod. The calculation of s and h is simplified by the use of tachymetric tables.

The basis for horizontal and vertical measurements in tachymetric surveying is provided by points of a geodetic control network, points of heighting and leveling traverses made with a transit, and points of tachymetric traverses plotted between points of the first two types.

In carrying out detail work by tachymetric methods from instrument stations whose horizontal and vertical coordinates have been determined in advance, the numerical results of the measurements are recorded in the field book. These measurements include the directions (the vertical- and horizontal-circle readings of the transit) of the stakes marking detail points, the distances s to the stakes, and the differences h between the elevation of the instrument station and the points marked by the stakes. In addition, sketches are made at each station approximately in the scale of the survey; explanatory legends are provided for the symbols used. The sketches show the positions of the stakes, the contours of the ground, surface features of interest, and the directions in which the transit circles are oriented. In selecting the points to be marked by stakes, attention is paid primarily to the relief of the area. For each station the points are selected in such a number and positioned in such a manner that their elevations permit a correct representation of the relief and principal surface features of the area being surveyed and allow the calculation of the elevation of any point for which a measurement was not made. The data obtained at the stations are used to draw a large scale topographic map of the area surveyed. The scale of the map may range from 1:5,000 to 1:500, and the relief is shown by contour lines.

Tachymetric surveying is used in preparatory work for the construction of roads, pipelines, canals, industrial structures, and various other civil engineering structures. Land reclamation work may also involve the use of tachymetric surveying.