Tachometry

Tachometry, or tachometric surveying, is a rapid distance-measurement method used in surveying, geodesy, and photogrammetry. It employs a tachometer or tacheometer, typically a theodolite or total station with a stadia micrometer, to estimate distances to targets such as a graduated staff. The method emphasizes speed and reduces the need for separate distance measurements.

The core principle is the stadia method. The difference S between the upper and lower stadia readings on the staff held at the target is proportional to the distance along the line of sight. The instrument provides a distance factor K, calibrated for the specific instrument, so the line-of-sight distance to the staff is approximately D_line = K × S. By also measuring the vertical angle α, this can be converted to horizontal distance D_h = D_line × cos α. Elevation differences and heights can be obtained using the instrument and staff heights with standard trigonometric relations. Different tachometry variants may use fixed stadia intervals or alternative formulations, but all rely on the relation between stadia readings and distance.

In practice, surveyors set up the instrument at a point, sight a staff at the target, record the stadia readings and the vertical angle, and apply corrections for instrument height, staff height, and refraction as needed. Tachometry is particularly suited for rapid topographic surveys, road and railway alignments, construction layouts, and large-scale mapping where speed is valued over the highest possible accuracy.

Modern tachometry is commonly implemented in digital total stations, which automate distance and coordinate computations from stadia readings and angles, improving speed and consistency while maintaining the fundamental tachometric principle.