1.19.2. Methods of tacheometry

The principle used in tacheometry is that the horizontal distance between an instrument-station and a point where levelling rod is kept can be determined with the staff intercept (difference of top reading and bottom reading).

Tacheometry allows surveyors to quickly calculate horizontal distances between points using a tacheometer. By focusing on a levelling rod (staff) placed at a survey point, the instrument measures the distance based on the difference between its top and bottom readings, known as the staff intercept. This principle makes it easier to gather data without having to measure distances directly, which can be cumbersome, especially in challenging terrains.

Imagine trying to survey a steep mountain. Instead of trekking down to measure distance, you can position your tacheometer at a spot and read the height difference from the bottom to the top of a rod held at the mountain base. This allows for a swift distance calculation without making a long trek.

The staff intercept reading is multiplied by the instrument constant (K) and added with an additive constant (C) to get the horizontal distance between tacheometer and levelling staff. The horizontal distance (D) is computed as;

D = K S + C (1.16) Where K is the multiplying constant (usually 100), S is the staff intercept and C is the additive constant (usually zero).

In this scenario, when the line of sight is horizontal, surveyors simply read the staff intercept and apply the known constants: the multiplying constant (K) and the additive constant (C). Typically, K is set to 100, which means that the distance calculated from the intercept is straightforward: you just multiply the reading from the staff intercept by 100, and with C as zero, you get the direct horizontal distance. This method simplifies calculating the horizontal distance, making it efficient and reliable.

Consider a rectangular swimming pool. If you are positioned at one end and want to find out how far it is to the opposite end, using a measuring tape would be laborious. In this case, if you can read the height difference on a stick held at the opposite end, string it together with the known distance your eyes are from the water's surface and apply some simple math, you could easily find out how far it stretches without diving in.

In case the ground is undulating and horizontal sights are not possible, inclined sights are taken. In this case, the staff may be held either vertical or normal to the line of sight. In general, most commonly adopted method is when the staff is held vertical as it is simpler in calculation.

When the terrain is not flat, using a horizontal line of sight may not be feasible. Hence, tacheometry allows the surveyor to take measurements with an inclined sight. This means the staff can be positioned either upright or angled relative to the tacheometer. Holding the staff vertically is preferred since it reduces calculation complexity while accurately gathering data no matter the slope's steepness. Measurement might include both the distance and vertical angles to get accurate results.

Picture trying to measure the height of a tree on a hill. If you can't measure straight across to the base from your vantage point because of jagged terrain, you can position the measuring stick vertical next to it. As you read the angle between your eyes and the top of the stick, you can compute not just its height but also the distance to the tree without having to traverse all the uneven ground.

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