Principles of Surveying

Surveying is the science and art of determining the relative positions of points on the surface of the earth or beneath its surface or in space. It involves making measurements of distances, directions, and elevations, and then using these measurements to plot the positions of points and features on a map or plan. The fundamental principles of surveying are crucial for accurate and reliable results.

Fundamental Principles of Surveying

There are two fundamental principles that guide all surveying operations. Adherence to these principles ensures that errors are minimized and that the survey work is accurate and complete.

Principle 1: Working from the Whole to the Part

This is the most important principle in surveying. It means that the survey should be started by establishing a framework of control points over the entire area to be mapped. These control points are established with the highest possible accuracy. Once the main framework is established, the details within this framework are then surveyed and plotted. This method has several advantages:

• It prevents the accumulation of errors. If surveying is done from parts to the whole, small errors in each part can accumulate and lead to a large overall error, making the final map inaccurate and unusable.
• It localizes errors. If any error occurs, it is confined to a small area and can be easily detected and corrected.
• It provides a check on the accuracy of the work. The positions of the detail points can be checked by taking additional measurements from different control points.

For example, when surveying a large piece of land, a surveyor would first establish a few primary control points (like triangulation stations) with precise instruments. Then, secondary control points would be established within the main framework. Finally, individual features like boundaries, buildings, or roads within these secondary control areas would be surveyed and plotted relative to these control points.

Principle 2: Establishing the Position of a Point by at Least Two Independent Measurements

To fix the position of any unknown point, at least two independent measurements must be made from known points. These measurements can be of various types:

• Distance and Distance (D-D): By measuring the distance from two known points to the unknown point. This is similar to triangulation.
• Distance and Direction (D-θ): By measuring the distance from one known point and the direction (angle) from that same known point to the unknown point.
• Direction and Direction (θ-θ): By measuring the direction (angle) from two known points to the unknown point. This is the principle of resection.

The independence of measurements is key. For instance, measuring the distance from point A to point P and then measuring the distance from point A to point P again using the same method is not two independent measurements. However, measuring the distance from A to P and then measuring the distance from B to P (where A and B are known points) provides two independent measurements that can locate P.

These two fundamental principles, when applied correctly, ensure that survey data is accurate, reliable, and that the final representation of the area is a true reflection of its physical features.

Measurement of Distance

Measuring distances is a fundamental operation in surveying. The accuracy of distance measurements directly impacts the overall accuracy of the survey. Distances can be measured directly on the ground or indirectly using instruments and calculations. The method chosen depends on the required accuracy, the terrain, and the available equipment.

Direct Methods of Distance Measurement

These methods involve physically measuring the distance along the ground surface.

1. Pacing

Pacing is the simplest method of measuring distance, where the surveyor counts the number of steps taken to cover the distance. While it is quick and requires no equipment, it is also the least accurate method. It is generally used for rough estimations or for traversing small areas where high precision is not required.

• Procedure: The surveyor walks along the line to be measured, counting each step. The average length of a pace is determined beforehand by walking a known distance and dividing it by the number of paces taken.
• Accuracy: Accuracy can be improved by walking at a natural, consistent pace and by having an experienced surveyor. However, it is highly susceptible to variations in terrain, the surveyor's fatigue, and the slope of the ground.

2. Chaining (Chain Surveying)

Chain surveying is one of the oldest and simplest methods of surveying. It involves measuring distances directly on the ground using a chain or a measuring tape. The entire area is divided into a network of triangles, and the lengths of the sides of these triangles are measured.

Key components:

• Ranging Rods: Used to mark the ends of survey lines and to keep the chain/tape aligned.
• Arrows (or Pins): Small steel pins used to mark the end of each chain length on the ground.
• Offset Pegs: Used to mark points for taking offsets.
• Field Book: Used to record all measurements, such as chainages and offsets.

Types of Chains

Different types of chains are used depending on the purpose and required accuracy.

a. Gunter's Chain

A Gunter's chain is 66 feet (or 100 links) long. It was historically popular in land surveying because 10 square chains (1 chain x 1 chain) equals 1 acre. Each link is 0.66 feet long.

• Length: 66 feet
• Number of links: 100
• Length of one link: 0.66 feet
• Use: Primarily for land measurement, especially in the imperial system.

b. Engineer's Chain

An Engineer's chain is typically 100 feet long and is divided into 100 links. Each link is 1 foot long. This chain is more commonly used in engineering projects where measurements are in feet.

• Length: 100 feet
• Number of links: 100
• Length of one link: 1 foot
• Use: Engineering surveys, road construction, and other infrastructure projects.

c. Metric Chain

Metric chains are manufactured in standard lengths of 20 meters or 30 meters. They are divided into decimeters and centimeters, making them convenient for metric-based measurements.

• Length: 20 meters or 30 meters
• Divisions: Usually marked every meter, with smaller divisions (e.g., decimeters or centimeters) for finer measurements.
• Use: Widely used in modern surveying where metric units are standard.

Chain Surveying: Principles and Procedure

Chain surveying is a method where only distances are measured, and the area is divided into a network of triangles. The principle is to measure the lengths of the sides of these triangles accurately.

Objectives of Chain Surveying

The primary objective is to determine the horizontal distances between points on the ground.

Steps Involved in Chain Surveying

The process involves planning, reconnaissance, and execution.

1. Reconnaissance: A preliminary survey of the area is made to decide the general layout of the survey lines and to choose suitable sites for the main stations.
2. Sketching: A rough sketch of the area is prepared, showing the main features and the proposed survey lines.
3. Selection of Survey Lines: The main survey lines are chosen to cover the entire area. These lines should be as far as possible from obstructions and should form well-conditioned triangles (angles not too acute or too obtuse).
4. Marking Stations: The main stations (corners of the triangles) are marked on the ground using pegs or stones.
5. Ranging: This is the process of establishing a straight line between two points. If the distance is short, it can be done by eye. For longer distances, ranging rods are used, and for very long distances, optical instruments like the optical square or prism are used.
6. Measuring Distances: The lengths of all survey lines are measured accurately using a chain or tape.
7. Checking: Important lines are measured twice, or check lines are measured to ensure accuracy. For instance, the lengths of the sides of each triangle are measured, and then one diagonal might also be measured to check the measurements.
8. Plotting: The measured distances are plotted to scale on the drawing sheet using instruments like a protractor, compass, or graphic methods.

Field Work in Chain Surveying

The field work involves:

• Establishing stations.
• Ranging lines between stations.
• Measuring the lengths of the lines.
• Taking offsets: These are perpendicular or oblique distances from the survey lines to the details (e.g., trees, buildings, fences) that need to be located.

Types of Offsets

Offsets are short distances measured perpendicular to the chain line to locate features off the line.

• Perpendicular Offsets: Measured at right angles to the survey line. These are used when the feature is reasonably close to the survey line.
• Oblique Offsets: Measured at an angle to the survey line. These are used when it is difficult or impossible to measure a perpendicular offset, for example, when a feature is located behind a building or a large obstacle.

The length of the offset and the chainage (distance along the survey line from the starting point) are recorded in the field book.

Errors in Chain Surveying

Errors can arise from various sources:

• Instrumental Errors: The chain might be too long or too short due to temperature variations, wear and tear, or manufacturing defects.
• Natural Errors: Errors due to temperature, wind, or uneven ground.
• Personal Errors: Errors made by the surveyor due to carelessness, fatigue, or incorrect judgment (e.g., incorrect reading, faulty ranging).

Corrections in Chain Surveying

Corrections are applied to account for these errors, especially for instrumental and temperature errors.

• Correction for Temperature: Chains expand or contract with temperature changes. The correction is given by Ct = α (Tm - To) L, where α is the coefficient of thermal expansion, Tm is the mean temperature during measurement, To is the standard temperature for which the chain is calibrated, and L is the measured length.
• Correction for Sag: If the chain sags between supports, the measured distance will be shorter than the actual horizontal distance.
• Correction for Pull: If the pull applied to the chain during measurement differs from the standard pull, a correction is needed.
• Correction for Slope: If the ground is sloping, the measured distance along the slope is longer than the horizontal distance. The correction is approximately Cs = h2 / 2s, where h is the difference in elevation between the ends of the chain and s is the slope distance.

Measurement of Distance using Tapes

Measuring tapes are more commonly used than chains in modern surveying due to their convenience and accuracy for various distances.

Types of Tapes

• Cloth Tape: Lightweight, flexible, and easy to handle, but prone to stretching. Used for general purposes where high accuracy is not critical.
• Steel Tape: More accurate and less prone to stretching than cloth tapes. They are usually 30m or 50m long and are marked in meters, decimeters, and centimeters.
• Invar Tape: Made of an alloy of nickel and steel, Invar has a very low coefficient of thermal expansion. These are highly accurate and are used for precise measurements, especially in geodetic surveys and baseline measurements where temperature variations are a concern.

Procedure for Measuring Distance with a Tape

Similar to chain surveying, but with more emphasis on maintaining tension and alignment.

1. Alignment: Ensure the tape is laid straight along the line to be measured. Ranging rods are used to guide the alignment.
2. Tension: Apply a consistent tension to the tape to keep it taut and minimize sag. A standard pull is usually specified for tapes.
3. Zero Mark: Ensure the measurement starts from the zero mark of the tape.
4. Reading: Read the measurement at the far end of the line. For distances longer than the tape, intermediate points are marked using arrows or by holding a plumb bob.
5. Corrections: Apply corrections for temperature, pull, sag, and slope if necessary, depending on the required accuracy.

Indirect Methods of Distance Measurement

These methods involve using instruments to measure angles and then calculating distances using trigonometry.

1. Electronic Distance Measurement (EDM)

EDM instruments use electromagnetic waves (light or radio waves) to measure distances directly. They are very fast and accurate, especially over long distances. The instrument emits a signal, which is reflected back from a prism or reflector at the other end, and the time taken for the signal to travel is measured to calculate the distance.

2. Photogrammetry

This involves taking measurements from photographs, typically aerial photographs. Distances can be calculated using stereoscopic viewing and known scale information from the photographs.

3. Triangulation and Trilateration

These are older methods where distances are calculated from measured angles (triangulation) or from measured distances (trilateration) forming a network of triangles.