## Understanding Linear Measurement in Surveying

**INTRODUCTION**

- Surveying can be defined as the method of determining the relative position of the points on, above and below the surface of the earth through direct or indirect measurement of direction, elevation & distance.
- It can also be defined as the method of establishing the points by predetermined linear or angular measurements.

**Note:** Earth is an** OBLATE SPHEROID** (Here, the spheroid is obtained by rotating an ellipse about one of the axis).

- Since the polar diameter of the earth is approx. 42.95 km smaller than equatorial diameter, it is termed as an OBLATE SPHEROID.
- Surveying is primarily classified into two categories on the basis of the curvature of the earth:

## primary classification

### plane surveying

### Geodetic Surveying

### A) plane surveying

- In this survey, the curvature of the earth is not considered, or the mean surface of the earth is assumed to be a planner.
- It is suitable to be used for a small area of work.
- It is considered suitable for an area less than 250 km?.
- The lines & triangles constructed during this survey will be considered as plane lines and plane triangles.
- In this survey, the level line is assumed as a straight line & plumb lines at two different points are assumed to be parallel to each other.

**important question**

## What is Level Line?

It is the distance between two points on the level surface that follows the earth's curvature.

## What is plumb Line?

A line represented by the freely suspended plumb bob.

### B) Geodetic surveying

- In this survey, the shape of the earth is taken into consideration.
- In this survey, the triangles are spherical triangles & the lines lying on the surface is curved lines.
- It is suitable to be used when the area of a surface is large (generally > 250 km
^{2}), and a high degree of precision is required. - To establish the control points, the geodetic survey is carried out by the Department of National Survey of India (Control points-Those points which are taken as the reference points for making other points in a plane surveying).

**Note**

- For any triangle with an area of 195.5 km
^{2}, the sum of interior angles would be just 1" (1sec) extra in the geodetic surveying. - For any line of length 12 km, it is just 1cm extra in geodetic survey.

## classification of survey:

### based upon the nature of survey:

#### A) Land Survey:

- The purpose of this survey is to determine the features of the land.
- It is further classified into:

### LAND SURVEY

#### tOPOGRAPHICAL SURVEY

This consist of horizontal and vertical locations of certain points by linear and angular measurements to determine natural features such as river, lake, pond, forest, hills, and artificial features such as roads, railways, canals, towns, villages etc.

#### CADASTRAL SURVEY

These surveys are made for fixing the property lines and calculation of land area or the transfer of land property.

#### CITY SURVEY

These surveys are made in connection with the construction of streets, water pipelines, sewers, LPG lines, optical fibre.

#### b) mARINE / HYDROGRAPHIC Survey:

- It deals with water bodies for the purpose of navigation, water supply, mean sea level, reservoir functioning waste disposal etc.
- It consists of measurement of discharge of streams, stage of water bodies and fluctuation in ocean tides.

#### c) ASTRONOMICAL Survey:

- The purpose of this survey is to determine the absolute location of any points on the surface of the earth with the help of heavenly/ spatial bodies.

Example: sun, any fixed star.

### based on an object of the survey:

#### A) engineering Survey:

- This is done to find sufficient data to be used for engineering design works likes Roads, Reservoirs, Sewers, Trench, Foundation etc.

#### B) military Survey:

- It is used for determining points of strategic importance.

#### c) geological Survey:

- It deals with determinations of the formation of the earth surface.

#### D) archaeological Survey:

- This is used to find the existence of past civilisation.

#### E) mine Survey:

- It is used carried out for exploration of new mines.

### based on the instrument used:

#### A) CHain Surveying:

- Linear measurements are carried out with the help of chain or tape & angular measurements are not carried out.

#### B) compass Surveying:

- Linear measurement is done with the help of chain or tape & horizontal angles are measured with the help of magnetic compass.

#### C) levelling:

- Here levelling instrument is used to determine the relative elevations (level) of various points in the vertical plane.

#### D) PLANE TABLE SURVEYING:

- Here map or plan is prepared in the field by observing the terrain after determining the direction of various lines and measuring the linear distance with chain/tape.

#### E) theodolite Surveying:

- For the measurement of vertical and horizontal angles, theodolite is used. Its accuracy is comparatively more than the compass surveying. It is further classified as:
**i) Traverse survey:**In this type of survey, various stations form a polygon.**il) Triangulation survey:**In this type of survey, various stations form a system of triangles.

#### F) tacheometric Surveying:

- In this survey, tacheometer is used, which is fitted with cross hairs in addition to central horizontal hairs. The horizontal distance, vertical distance & the horizontal angles are measured with the help of tacheometer.

#### G) photogrammetric Surveying:

- The process of taking measurements with the help of photographs is known as photogrammetry. It is generally used for topographic mapping of large areas and the areas which are difficult to access.

#### H) EDM SurveyING (ELECTRONIC DISTANCE MEASUREMENT):

- The linear measurement is done with the help of EDM. Here the control points forms the triangle, hence termed as triangulation survey.
- Triangulation survey in which length of all sides of triangle is measured is termed as "Trilateration".

## principles of surveying

The fundamental principles of surveying are as follows:

### A) Working from whole to part:

- Whether geodetic or plane surveying is carried out, the work is to be done from whole to part. First, the system of control points with a higher degree of accuracy is established then; by less precise methods, minor control points are established.
- In working from whole to part, the accumulation of errors is avoided, and minor errors are localised.

### B) Location of a point by measurement from two reference points:

- The two points are taken as references whose positions are already fixed. With the help of these two points, the relative position of the points to be surveyed will be located.

**A) **Measurement of distances AC & BC is carried out; plotting of another point C can be done by swinging the two arcs to the same scale to which AB has plotted. This principle is used in chain surveying.

**B)** A perpendicular CD can be dropped on the reference line AB and lengths AD and CD are measured. The point C can then be plotted using set square. This principle is used in the offset method.

**C)** The distance BC and the angle ABC can be measured, and point C is plotted either by means of a protractor or trigonometrically. This principle is used in traversing.

**D)** In this method, the distance AC and BC are not measured, but angle CAB and angle CBA are measured with an angle - measuring instrument.

Knowing the distance AB, point C is plotted either by means of a protractor or by the solution of triangle ABC. This principle is used in triangulation.

**E)** Angle CBA and distance AC are measured, and point C is plotted either by protracting an angle and swinging an arc from C or plotted trigonometrically. This principle is used in traversing.

**Note: In B), C), D) cases, the concerned point 'C' can be in vertical plane also.**

## pLAN AND MAPS

- A plan is a graphical representation to some scale of the features on, near or below the surface of the earth.
- Since the surface of earth is curved, and the paper of the plan is plane, no part of the surface can be represented on such a map without distortion.
- Hence it is suitable for plane surveying, in which the area involved is comparatively smaller.
- If the scale is large, the representation is termed as a plan, and if the scale is small, the representation is termed a as map.
- In the maps, the direction is represented with the help of contours & the vertical distance can also be represented with the horizontal distances.

**important question**

## What is distance?

It is a linear measurement of the horizontal plane.

## What is elevation?

It is a linear measurement of the vertical plane.

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