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Topic 10

## Lesson 11. Contours- Introduction

The art of determining relative altitudes of points on the surface of the earth of beneath the surface of earth is called LEVELLING.

A contour is defined as an imaginary line of constant elevation on the ground surface. It can also be defined as the line of intersection of a level surface with the ground surface. For example, the line of intersection of the water surface of a still lake or pond with the surrounding ground represents a contour line.

**Definition:**

A line joining points of equal elevations is called a contour line. It facilitates depiction of the relief of terrain in a two dimensional plan or map.

**Characteristics of contour:**

The principal characteristics of contour lines which help in plotting or reading a contour map are as follows:

The variation of vertical distance between any two contour lines is assumed to be uniform.

The horizontal distance between any two contour lines indicates the amount of slope and varies inversely on the amount of slope. Thus, contours are spaced equally for uniform slope

The steepest slope of terrain at any point on a contour is represented along the normal of the contour at that point. They are perpendicular to ridge and valley lines where they cross such lines.

Contours do not pass through permanent structures such as buildings.

Contours of different elevations cannot cross each other (caves and overhanging cliffs are the exceptions).

Contours of different elevations cannot unite to form one contour (vertical cliff is an exception).

Contour lines cannot begin or end on the plan.

A contour line must close itself but need not be necessarily within the limits of the map.

A closed contour line on a map represents either depression or hill . A set of ring contours with higher values inside, depicts a hill whereas the lower value inside, depicts a depression (without an outlet).

Contours deflect uphill at valley lines and downhill at ridge lines. Contour lines in U-shape cross a ridge and in V-shape cross a valley at right angles. The concavity in contour lines is towards higher ground in the case of ridge and towards lower ground in the case of valley .

Contours do not have sharp turnings.

**Contour Interval: **

The vertical distance between any two consecutive contours is known as a contour interval. For example, if the various consecutive contours are 100m, 98m,96 m etc., then the contour interval is 2m. This interval depends upon,

The nature of the ground

The scale of the map and

The purpose of survey

Contour intervals for flat country are generally small, eg. 0.25m, 0.5m, 0.75 m etc. For a steep slope in hilly area is greater, eg. 5m, 10m, 15 m etc.

Again ,for a small-scale map, the interval may be of 1m,2m,3m etc. and for large scale map,it may be of 0.25m,0.50m,0.75m etc.

It should be remembered that the contour interval for a particular map is constant.

**Contouring:**

The process of locating these contour lines on the surface of the earth is known as contouring.

**Methods of contouring:**

The method of establishing / plotting contours in a plan or map is known as contouring. It requires planimetric position of the points and drawing of contours from elevations of the plotted points. Contouring involves providing of vertical control for location of points on the contours and horizontal control for planimetric plotting of points. Thus, contouring depends upon the instruments used (to determine the horizontal as well as vertical position of points). In general, the field methods of contouring may be divided into two classes:

Direct methods

Indirect methods

**Direct Method:**

In the direct method, the contour to be plotted is actually traced on the ground. Points which happen to fall on a desired contour are only surveyed, plotted and finally joined to obtain the particular contour. This method is slow and tedious and thus used for large scale maps, small contour interval and at high degree of precision.

**Vertical control :**** **

In this method, a benchmark is required in the project area. The level is set up on any commanding position and back sight is taken on the bench mark. Let the back sight reading on the bench mark be 1.485 m. If the reduced level of the bench mark is 100 m, the height of instrument would be 100 + 1.485 = 101.485 m.

To locate the contour of 100.5 m value, the staff man is directed to occupy the position on the ground where the staff reading is 101.485 -100.500 = 0.985 m. Mark all such positions on the ground where the staff reading would be 0.985 m by inserting pegs. Similarly locate the points where the staff reading would be 101.485 -101 = 0.485 m for 101m contour.

The contour of 101.5 m cannot be set from this setting of the instrument because the height of instrument for this setting of the instrument is only 101.485 m. Therefore, locating contours of higher value, the instrument has to be shifted to some other suitable position.

Establish a forward station on a firm ground and take fore sight on it. This point acts as a point of known elevation, for shifting the position of the instrument to another position, from where the work proceeds in the similar manner till the entire area is contoured.

**Horizontal control :**

The horizontal control is generally provided by method of plane table surveying or locating the positions of points.

**Indirect method of contouring:**

In this method, the spot levels of selected guide points are taken with a level and their levels are computed. The horizontal positions of these points are measured or computed and the points are plotted on the plan. The contours are then drawn by a process called interpolation of contours from the levels of the guide points. The following are the indirect methods are commonly used for locating contours.

Squares or Grid method

Cross section method

**Square or grid method:**

In this method, the area to be surveyed is divided into a grid or series of squares. The grid size may vary from 5 m x 5 m to 25 m x 25 m depending upon the nature of the terrain, the contour interval required and the scale of the map desired. Also, the grids may not be of the same size throughout but may vary depending upon the requirement and field conditions. The grid corners are marked on the ground and spot levels of these comers are determined by leveling. The grid is plotted to the scale of the map and the spot levels of the grid corners are entered. The contours of desired values are then located by interpolation. Special care should be taken to give the spot levels to the salient features of the ground such as hilltops, deepest points of the depressions, and their measurements from respective corners of the grids, for correct depiction of the features. The method is used for large scale mapping and at average precision.

**Cross section method:**

In these sections, a base line, centre line or profile line is considered. Cross sections are taken perpendicular to this line at regular intervals. After this points are marked along the cross sections at regular intervals. A temporary bench mark is set up near the site. Staff readings are taken along the base line and the cross sections. The readings are entered in the level book the base line and the cross sections should also be mentioned. The RL of each of the points calculated. Then the base line and cross sections are plotted to a suitable scale. Subsequently the RLs of the respective points are noted on the map, after which the required contour line is drawn by interpolation

This method is suitable for route survey, when cross sections are taken transverse to the longitudinal section.

**Method of interpolation of contours:**

The process of locating the contours proportionately between the plotted points is termed interpolation. Interpolation may be done by:

Arithmetical calculation

The graphical method

By arithmetical calculation

Let A and B be two corners of the squares. The RL of A is 98.75 m, and that of B 100.75 m. the horizontal distance between A and B is 10m.

Horizontal distance between A and B = 10m

Vertical difference A and B = 100.75-98.75=2m

Let a contour of 99.00 m be required. Then,

Difference of level between A and 99.00m contour = 99.00-98.75=0.25m

Therefore, distance of 99.00 m contour line form A= 10/2 *0.25=1.25m

This calculated distance is plotted to the same scale in which the skeleton was plotted to obtain a point of RL of 99.00 m.

Similarly, the other points can be located.

**By graphical method**

On a sheet of tracing paper, a line AB is drawn and divided into equal parts. AB is bisected at C and a perpendicular is drawn at this point. A point O is selected on this perpendicular line and then radial lines are drawn from O to the divisions on AB. After this lines 1-1, 2-2, 3-3….are drawn parallel to AB. These lines serve as guide lines. Boundary line and every fifth the line is marked with a thick or red line.

Suppose we have to interpolate a 2m contour between two points a and b of RLs 92.5 and 100.75m.

Let us consider the lowest radial line OB to represent an RL of 90.00. So, every fifth line will represent 95,100,105, etc. The tracing paper is moved over the plan until ‘a’ lies at 92.5 and ‘b’ at 100.25. Line ‘ab’ should be parallel to AB. Now the points 94, 96, 98,100 are picked through to obtain the positions of the required contours.

**Method of interpolation of contours:**

The process of locating the contours proportionately between the plotted points is termed interpolation. Interpolation may be done by:

Arithmetical calculation

The graphical method

**By arithmetical calculation**

Let A and B be two corners of the squares. The RL of A is 98.75 m, and that of B 100.75 m. the horizontal distance between A and B is 10m.

Horizontal distance between A and B = 10m

Vertical difference A and B = 100.75-98.75=2m

Let a contour of 99.00 m be required. Then,

Difference of level between A and 99.00m contour = 99.00-98.75=0.25m

Therefore, distance of 99.00 m contour line form A= 10/2 *0.25=1.25m

This calculated distance is plotted to the same scale in which the skeleton was plotted to obtain a point of RL of 99.00 m.

Similarly, the other points can be located.

**By graphical method**

On a sheet of tracing paper, a line AB is drawn and divided into equal parts. AB is bisected at C and a perpendicular is drawn at this point. A point O is selected on this perpendicular line and then radial lines are drawn from O to the divisions on AB. After this lines 1-1, 2-2, 3-3….are drawn parallel to AB. These lines serve as guide lines. Boundary line and every fifth the line is marked with a thick or red line.

Suppose we have to interpolate a 2m contour between two points a and b of RLs 92.5 and 100.75m.

Let us consider the lowest radial line OB to represent an RL of 90.00. So, every fifth line will represent 95,100,105, etc. The tracing paper is moved over the plan until ‘a’ lies at 92.5 and ‘b’ at 100.25. Line ‘ab’ should be parallel to AB. Now the points 94, 96, 98,100 are picked through to obtain the positions of the required contours.