After reading this article you will learn about:- 1. Definition of Contour 2. Contour Interval and Horizontal Equivalent 3. Characteristics 4. Methods 5. Interpolation 6. Drawing the Contour Lines.

#### Definition of Contour:

A contour or a contour line may be defined as the line of intersection of a level surface with the surface of ground. This means every point on a contour line has the same altitude as that of the assumed intersecting surface.

Supposing a depression is partly filled with water and R.L of the water surface is say 60 m, then the shore line of this water represents 60 m contour. And if the level of water is raised successively by 1 m, the successive shorelines represent 61, 62, 63 m contours and so on.

The process of tracing contour lines on the surface of the earth is called contouring and the maps upon which these lines are drawn are called contour maps. A contour map therefore, gives an ides of the altitudes of the surface feature as well as their relative positions in plan. Thus a contour map serves the purpose of both, a plan and a section.

#### Contour Interval and Horizontal Equivalent:

The constant vertical distance between two consecutive contours is called the Contour Interval and the horizontal distance between any two adjacent contours is termed as the horizontal equivalent. The horizontal equivalent depends upon the slope of the ground.

The contour interval depends upon the following factors:

(i) The nature of the ground:

In flat and uniformly sloping country, the contour interval is small, but in broken and mountainous region, the contour interval should be large otherwise the contours will come too close to each other.

(ii) The purpose and extent of the survey:

Contours interval is small if the area to be surveyed is small and the maps are required to be used for the design work or for determining the quantities of earth work etc., while wider interval shall have to be kept for large areas and comparatively less important works.

(iii) The scale of the map:

The contour interval should be in the inverse ratio to the scale of i.e. the smaller the scale, the greater the contour interval.

(iv) Time and expense of field and office work:

The smaller the interval, the greater is the amount of field -work and plotting-work.

The following are the common values of the contour interval adopted for various purposes:

(a) For large scale maps of flat country, for building sites for detailed design work and for calculation of quantities of earth work: 0.2 to 0.5 m.

(b) For reservoirs and town planning schemes: 0.5 to 2 m.

(c) For location surveys: 2 to 3 m.

(d) For small scale maps of broken country and General topographical work : 3 m, 5 m, 10 m or 25 m.

#### Characteristic of Contours:

1. All points in a contour line have the same elevation.

2. Flat ground is indicated where the contour are widely separated and the steep ground where they run close together.

3. A uniform slope is indicated when the contour lines are uniformly spaced and a plane surface when they are straight, parallel and equally spaced.

4. A series of closed contour lines on the map represent a hill, if the higher values are inside (Fig. 8.1).

5. A series of closed contours on the map indicate a depression, if the higher values are outside (Fig. 8.2).

6. Contour lines across ridge or valley lines at right angles. If the higher values are inside the bend or loop in the contour, it indicates a “Ridge”. (Fig. 8.3).

And if the higher values are outside the bend, it represents a “Valley” (Fig. 8.4).

7. Contour lines cannot end anywhere but close on themselves elders within or outside the limits of the map.

8. Contour lines cannot merge or cross one another on map except in the case of an overhanging cliff. (Fig. 8.5).

9. Contours never run into one another except in the case of a vertical cliff (Fig. 8.6). In this case, several contours coincide and the horizontal equivalent becomes zero.

10. Depression between summits is called a saddle. It is represented by four sets of contours as shown in Fig. 8.7. It represents a dip in a ridge or the junction of two ridges. And in the case of a mountain range, it takes the form of a pass. Line passing through the saddles and summits gives water shed line.

#### Methods of Contour:

There are mainly two methods of locating contours;

(1) Direct method, and

(2) Indirect method.

1. Direct Method:

In this method, the contours to be located are directly traced out in the field by locating and making a number of points on each contour. These points are then surveyed and plotted on plan and the contours drawn through them. This method is the most accurate but very slow and tedious as a lot of time is wasted in searching points of the same elevation for a contour. This is suitable for small areas and where great accuracy is required.

Procedure:

To start with, a temporary B.M. is established near the area to be surveyed with reference to a permanent B.M. by taking flying levels. The level is then set up in such a position so that the maximum number of points can be commanded from the instrument station. The height of instrument is determined by taking a back sight on the B.M. and adding it to the R.L of the bench mark.

The staff readings required to fix points on the various contours from the height of instrument. As an example, if the height of instrument is 72.58 m, then the staff readings required to locate the 72, 71 and 70m contours are 0.58, 1.58 and 2.58 m respectively. The staff is held on an approximate position of point and then moved up or down the slope until the desired reading is obtained.

The point is marked with a peg. Similarly various other points are marked on each contour. The line joining all these points gives the required contour. It may be noted that one contour is located at a time. Having fixed the contours within the range of the instrument, the level is shifted and set up in a new position. The new height of instrument and the required staff readings are then calculated in a similar manner and the process repeated till all the contours are located.

The position of the contour points are located suitably either simultaneously with levelling or afterwards. A theodolite or a compass or a plane table traversing is usually adopted for locating these points. The points are then plotted on the plan and the contours drawn by joining the corresponding points by dotted curved lines.

This method is suitable for small areas where a single point in the centre can command the whole area. Radial lines are laid out from the common centre by theodolite or compass and their positions are fixed up by horizontal angles and bearings. Temporary bench marks are first established at the centre and near the ends of the radial lines.

The contour points are then located and marked on these lines as explained above and their positions are determined by measuring their distances along the radial lines. They are then plotted on the plan and the contours drawn by joining all the corresponding points (Fig. 8.8.)

Indirect Method:

In this method, the points located and surveyed are not necessarily on the contour lines but the spot levels (spot level means the R.L. of a point on the surface of the ground) are taken along the series of lines laid out over the area.

The spot levels of the several representative points representing hills, depression, ridge and valley lines, and the changes in the slope all over the area to be contoured are also observed. Their positions are then plotted on the plan and the contours drawn by interpolation. This method of contouring is also known as contouring by spot levels.

This method is commonly employed in all kinds of surveys as this is cheaper, quicker and less tedious as compared with the direct method.

There are mainly three methods contouring under this head:

(i) By Squares. (Fig. 8.9):

In this method, the whole area is divided into a number of squares, the sides of which may vary from 5m to 30m depending upon the nature of the ground and the contour interval. The squares need not be of the same size throughout, the corners of the squares are pegged out and the reduced levels of these points are determined with a level.

The important points within the squares may be taken when required and located by measurements from the corners. The squares are plotted and the reduced levels of the corners are written on the plan. The contour lines are then interploted as in fig. 8.9.

(ii) By Cross-Sections (8.10):

This method is most suitable for survey of long narrow strips such as a road, railway canal etc. Cross -section ore run transverse lo the centre line of the work and representative points are marked along the lines of cross-section. The cross-section lines need not necessarily be at right angles to the centre line of the work.

This may be inclined at any angle to the centre line if necessary. The spacing of the cross -sections depends upon the topography of the country and the nature of the survey, the common value is 20 to 30m in hilly country and 100m in flat country. The levels of the points along the section line are plotted on the plan and the contour are then interpolated as usual as in fig. 8.10.

The method can be more clearly understood fig. 8.12.

(iii) By Tacheometric Method:

Tacheometer is transit theodolite having a diagram fitted with two stadia wires, one above and other below the central wire. The horizontal distance between the instrument and the staff -station may be determined by multiplying the difference of the staff readings of the upper and lower stadia wires with the stadia constant of the instrument, which is usually 100. Thus the tacheometer is used for both the vertical as well as for the horizontal measurements.

This method is most suitable in hilly areas as the number of stations which can be commanded by a tacheometer is far more than those by a level and thus the number of instrument-settings is considerably reduced.

A number of radial lines are laid out at a known angular interval and representative points are marked by pegs along these radial lines. Their elevations and distances are then calculated and plotted on the plan and the contour lines are then interpolated.

Relative Merits and Demerits of Direct and Indirect Methods of Contouring:

Direct Method:

1. The method is most accurate but is very slow and tedious.

2. It is used for small areas where great accuracy is desired.

3. It is not very useful when the around is hilly.

4. The calculation work of reducing the levels is comparatively more since the number of points in command from one set -up of the level is very less.

Indirect Method:

1. The method is not very accurate but is cheaper, quicker and less laborious.

2. It is used for large areas where great accuracy is not the main consideration.

3. Tacheometric method of contouring is mainly used for preparing, contour plans of hilly area. The indirect method by cross -sections is used in route surveys such as a railway, a canal etc.

4. Area in command from one set -up of the tacheometer is more, therefore, the calculation work is less.

#### Interpolation of Contours:

The process of spacing the contours proportionally between the plotted ground points is termed as interpolation of contours. This becomes necessary in the case of indirect contouring as only the spot levels are taken in this method. The intermediate contours may also be interpolated in direct contouring if the interval is large. While interpolation of contours the ground between any two points is assumed to be uniformly sloping.

There are three methods of interpolation viz:

(i) By estimation,

(ii) By arithmetical calculation, and

(iii) Graphical method.

(i) By Estimation:

The positions of the contour-points between ground -points are estimated roughly, and the contours are then drawn through these points. This is a rough method and is suitable for small scale maps.

(ii) By Arithmetical Calculation:

This is very but accurate method and is used for small areas where accurate results are necessary.

The contours are interpolated as under:

Suppose A and B are two points at a distance of 30m and the reduced levels A and B are 24.32m and 26.90m respectively. Taking the contour interval as 1m, 25 and 26m contours may be interpolated in between A and B. The difference of level between A and B is 2.58m. The difference of level between A and 25 and A and 26m contours is 0.68m and 1,68m respectively.

Therefore the horizontal distance between A and 25 m contour and that between A and 26 m contour

These distances are then plotted to scale on the map.

(iii) By Graphical Method:

Graphical method of interpolation are simpler as compared to arithmetical methods and also the results obtained are accurate.

Out of several graphical methods, the one in common use is explained below:

Suppose the contour interval is 5m , then on a piece of tracing cloth, a number of parallel lines spaced at 0.5 m (usually one tenth of the contour interval) are drawn, every tenth line being made thick (Fig. 8.11). Suppose it is required to interpolate contours between two points A and B of elevations 61.5 m and 72.5m respectively.

If the bottom line represent an elevation of 60m, then the successive thick lines will represent 65m, 70m and 75 m etc. Place the tracing cloth so that the point A is on the third line from the bottom. Now, move the tracing cloth until B is on the fifth line above the 70m thick line.

The intersections of the thick lines 1 and 2 representing elevations of 65m and 70m and the line AB give the position of the points on the 65m and 70m contours respectively and are pricked through on the plan with a pin.

#### Drawing the Contour Lines:

Contour lines are drawn as fine and smooth free hand curved lines. Sometimes they are represented by broken lines. They are linked in either in black or in brown colour. A drawing pen gives a better line than a writing pen, and French curves should be used as much as possible.

Every fifth contour is made thicker than the rest, the elevation of contours must be written in a uniform manner either on the higher side or in a gap left in the line. When the contour lines are very long the elevation are written at two or three places along the contour. In the case of small scale maps, it is sufficient to figure every fifth contour.

Tracing the Contour Gradient for Alignment of Roads, Railways and Canals etc.:

A contour gradient may be defined as a line joining the points on different contours along the same gradient.

Fig. 8.17 show a contour map on which the contour lines are at 2m intervals. The ground is sloping in an upward direction from A to B. Supposing it is required to trace the path of a road with a ruling gradient of 1 in 30 from the starting point A on the 80 m contour line Since the contour intervals is 2m and the gradient 1 in 30, the horizontal distance between successive points on consecutive contours is 60m (2 x 30).

With A as centre and radius equal to 60m draw an arc cutting the 82m contour at 1. With 1 as centre and the same radius, draw an arc intersecting the 84m contour at 2 and so on for successive contours. Join these points which lie on the desired gradient. It may be noted that each of the arcs described will intersect the next contour at two points viz 1 and i, 2 and ii, 3 and iii etc. at 82, 84, 86. metre contour etc. and the points following the desired route such as 1, 2, 3, etc. should be joined.

Finding Volume of Earth and Capacity of a Reservoir from Contour Lines:

The volume of earth work and capacity of a reservoir may be calculated by treatment of contour lines. This method is only approximate as in dealing with contour lines we have to assume that the surface of the ground slopes uniformly form one contour to the next and in most cases this assumption is incorrect. However sufficient accuracy can be attained if the contours are located with an interval small enough to record mirror features of the ground.

After preparation of the contoured plan of the particular site , the area enclosed by each contour line is measured by a planimeter, knowing the vertical distance between the first and the second contour lines (the contour interval) and their areas , Volume of earth work or water between them may be calculated wither by trapezoidal formula or by some other formula.

Let A1, A2, A3 etc. = The areas within successive contour in sq. metres.

d = the contour interval in metres

Then volume of the earth work or water between two adjacent contours:

Similarly cubic contents between successive contours may be found out, which when added together gives the required total cubical contents. This may be well understood by the following example.

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