1.19. Tacheometry

In tacheometry, horizontal and vertical distances are determined by angular observations with a tacheometer. Tacheometry is more accurate than the chaining/taping, and more rapid in rough and difficult terrain where levelling is tedious and measuring distance by chaining/taping is not only inaccurate but slow and laborious. It is a best suited method when taking observations for steep and undulating/broken ground, river, water or swampy areas. Tacheometry is preferably used for traversing, but it is also used for contouring.

Tacheometry is a surveying method used to measure distances using angles and an instrument known as a tacheometer. It’s more accurate than traditional methods like chaining or taping, especially in challenging environments like steep hills or marshy areas where measuring distances can be difficult and time-consuming. This method is particularly useful for mapping and traversing landscapes that are uneven or difficult to walk on.

Imagine you are hiking in a mountainous area where the ground is uneven. If you tried to measure distances by walking with a tape, it would take a lot of time and effort. Instead, using a tacheometer allows you to quickly and accurately measure how far away different points are without needing to walk to them directly, much like using a pair of binoculars to look at landmarks in the distance.

The main instruments used in tacheometry are a tacheometer and a levelling rod. A tacheometer is a transit theodolite where the telescope is fitted with a special diaphragm, called stadia hairs, i.e., a diaphragm fitted with three horizontal hairs; one at the top, another in the middle and the third at the bottom of the diaphragm. These horizontal hairs are equidistant from the central one. The types of stadia diaphragm commonly used in tacheometers are shown in Figure 1.46. The term tacheometer is restricted to a transit theodolite which is provided with an anallactic lens in the telescope. The essential characteristics of a tacheometer are that the value of the multiplying constant (K= f / I) should be 100 and additive constant (C= f + d) should be zero. Levelling rod used is similar to those used in levelling work. To make the value of the additive constant zero, an additional convex lens, known as anallatic lens, is provided in the telescope. By having K=100 and C=0, the calculation work is considerably reduced.

Two main instruments are used in tacheometry: the tacheometer and the levelling rod. The tacheometer has a special setup that includes a telescope with stadia hairs to assist in measuring distances. The apparatus is designed to ensure that the calculations for distances are simplified through two constants: K (which is generally set to 100) and C (which should ideally be zero) to make calculations quicker and more efficient. The levelling rod helps to determine the height differences.

Think of the tacheometer as a high-tech camera for surveyors. Just like a camera lens has different parts to focus on and capture sharp images, the tacheometer has stadia hairs and anallatic lenses that help surveyors focus on measuring distances with precision. The levelling rod is like a ruler that gives the surveyor the height reference needed to understand elevation.

The principle used in tacheometry is that the horizontal distance between an instrument station and a point where the levelling rod is kept can be determined with the staff intercept (difference of top reading and bottom reading). For determining the horizontal distance between two points, a tacheometer is kept at one point and levelling staff is kept at another, and stadia readings on the levelling staff are read.

The main method in tacheometry involves measuring the difference in readings on the staff at two points – the top reading and the bottom reading – which provides what is called the staff intercept. When this intercept is multiplied by the multiplying constant (K) and then adjusted by any additive constant (C), the horizontal distance between the tacheometer and the levelling rod can be calculated. This allows surveyors to determine measurements without having to travel the horizontal distance directly.

Picture a game of tennis. Instead of running back and forth to measure how far you've hit the ball (which would take time and energy), you can stand at one spot and observe where your ball lands through a special pair of glasses that measure the distance without making you move. This observation lets you quickly gather important information about how far you've played.

In a simplified form, the above equation for horizontal distance (D) can be written as D = K S + C, where K is the multiplying constant (usually 100), S is the staff intercept and C is the additive constant (usually zero). There could be situations when the ground is undulating and the levelling staff is either above or below the line of sight. In such cases, a vertical angle subtended by the point at instrument station is also measured, in addition to stadia readings, to determine the horizontal distance using trigonometrical relationships.

When the line of sight is perfectly horizontal, the calculation to find the horizontal distance relies simply on the values of K, S, and C. Most often used K equals 100, while C is typically zero, making calculations easier. In situations where the land is uneven, however, surveyors must take additional measurements for vertical angles to adjust their calculations for the real horizontal distance.

Imagine you’re using a ruler to measure the length of a book on a flat table. It’s straightforward because the ground is level and you just line up the ruler. But if the table were wobbly or tilted, you’d have to find different ways to make sure you’re still measuring the true length of the book accurately. Similarly, tacheometry adjusts measurements to account for uneven surfaces.

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 staff is held vertically.

When the terrain does not allow for a horizontal line of sight, the tacheometric readings can still be obtained by taking measurements with the staff either held vertically or at a normal angle to the line of sight. This simpler setup generally allows for easier calculations compared to other methods, emphasizing the practical adaptability of tacheometry.

Consider trying to take a photograph of a mountain from below. Sometimes, you may need to tilt your camera upward at an angle to capture the full height. Adjusting the angle of the camera (analogous to holding the staff differently) allows you to still get a clear, accurate image even if you cannot see it straight on.

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