Understanding Instruments in Plane Tabling Surveying

Plane tabling is a graphical method of surveying in which the field work and plotting are done simultaneously. It is particularly useful for small scale mapping and allows the surveyor to compare the plotted map with the actual ground features.

Several instruments are used in plane tabling, including the plane table, alidade, compass, spirit level, plumbing fork, and chain or tape. The question specifically asks about the instrument used for directly measuring horizontal and vertical distances within the context of plane tabling.

What is an Alidade?

An alidade is a crucial instrument used in plane tabling for sighting objects and drawing lines on the map sheet mounted on the plane table. There are two main types:

• Simple Alidade: This consists of a metal or wooden rule with sight vanes at both ends. One vane has a narrow slit, and the other has a wider opening with a thin horse hair or wire. It is used for sighting objects and drawing rays from the station plotted on the sheet towards the objects. It does not measure distances directly.
• Telescopic Alidade: This is a more advanced alidade equipped with a telescope. The telescope has stadia hairs (or lines) in addition to the central crosshair. These stadia hairs, along with a staff (like a leveling staff) held vertically at the object, allow for the direct measurement of horizontal and vertical distances based on the principle of tacheometry.

How Telescopic Alidade Measures Distances

The telescopic alidade, when used with a stadia staff, can determine distances directly in the field. The principle involves observing the intercept made by the stadia hairs on the staff held at a known point. Using the focal length of the telescope and the distance between the stadia hairs (known as the stadia interval factor), the horizontal distance to the staff can be calculated using the formula:

$\text{D} = k \cdot s + c$

Where:

• $\text{D}$ is the horizontal distance from the instrument station to the staff station.
• $k$ is the multiplying constant (typically 100 for most instruments).
• $s$ is the stadia intercept (the difference between the upper and lower stadia hair readings on the staff).
• $c$ is the additive constant (usually zero for internal focusing telescopes).

For inclined sights, the telescopic alidade also incorporates a vertical circle or an attachment that allows measuring the vertical angle ($\theta$). Using this angle and the observed stadia intercept, both the horizontal distance ($\text{H}$) and the vertical distance ($\text{V}$) between the instrument and the staff can be calculated:

$\text{H} = (k \cdot s + c) \cos^2 \theta$

$\text{V} = (k \cdot s + c) \sin \theta \cos \theta$ or $\text{V} = \frac{1}{2} (k \cdot s + c) \sin (2\theta)$

These calculations effectively allow the telescopic alidade to measure both horizontal and vertical distances directly from the readings obtained in the field, making it a very efficient tool for topographical surveying with a plane table.

Analysis of Other Options

• Simply alidade: Used for sighting and drawing lines, but cannot measure distances directly.
• Tachometer: A tacheometer is essentially a transit theodolite fitted with a diaphragm having stadia hairs. While it uses the same tacheometric principle as the telescopic alidade for distance measurement, the question asks about the instrument used *in plane tabling* for this purpose. The telescopic alidade is the equivalent instrument specifically designed for use with a plane table.
• Clinometer: A clinometer is used for measuring angles of slope or elevation. It measures vertical angles but does not directly measure horizontal or vertical distances like a telescopic alidade does using stadia.

Therefore, the instrument used in plane tabling specifically designed to measure horizontal and vertical distances directly using the tacheometric principle is the telescopic alidade.

Conclusion

Based on the functions of the various instruments used in surveying, particularly in plane tabling, the telescopic alidade is the instrument equipped to measure horizontal and vertical distances directly, typically using the stadia method. This makes it a versatile tool for generating detailed topographical maps in the field.

Revision Table: Plane Tabling Instruments

Additional Information on Surveying and Plane Tabling

Plane tabling is advantageous as it provides a visual check between the map and the ground features during the survey itself, reducing the chances of omissions. It is suitable for areas where detailed maps are required quickly and for surveys of small to medium extent. However, it is not suitable for surveys in rainy or windy conditions, and the accuracy can be lower than other methods like theodolite traversing or Total Station surveying, especially over long distances.

The accuracy of distance measurement with a telescopic alidade using the stadia method depends on factors like the accuracy of staff holding, the readability of staff graduations, the power of the telescope, and atmospheric conditions.