Methods Generally Used or Indirect Method of Contouring, Arithmetical Method of Interpolation of Contour

In this method, the RLs of different points (spot levels) are taken at regular intervals along a series of lines net up on the ground. The positions of these points are plotted on a sheet to any suitable scale. The spot levels are noted at the respective points. Then the points of contour lines are found out by interpolation, after which they are joined to get the required contour lines. Although very quick, this method gives only the approximate positions of the contour lines.
This method can be adopted in two ways: (a) cross-sections, and (b) squares.
(a) Using Cross Sections
In this method, a bottom line , center line or profile line is taken into account . Cross sections are taken perpendicular to the present line at regular intervals (say 50 m. 100 m, etc.). After this, points are marked along the cross sections at a daily intervals (say, 5 m. 10 m, etc). A temporary bench-mark is about up near the location . Staff readings are taken along the bottom line and therefore the cross sections. The readings are entered within the level book: the bottom line and therefore the cross sections should even be mentioned. The RL of each points calculated. Then the bottom line and cross sections are plotted to an appropriate scale. Subsequently, the RLs of the respective points are noted on the map, after which the specified contour is drawn by interpolation.
This method is suitable for route survey, when cross sections are taken transverse to the longitudinal section.

(b) Using Squares
In this method, the area is divided into a number of squares. The size of those squares depends upon the character and extent of the bottom . Generally, they have a sides varying from 5 to 20 m. The corners of the squares are numbered serially, as 1, 2, 3….. A temporary bench-mark is set up near the site, and the level is set up at a suitable position. The staff readings on the corners of the squares are taken and noted within the level book maintaining the sequence of the serial numbers of the corners. The RLs of all the corners are calculated. The skeletons of the squares are plotted to an appropriate scale. The respective RLs are noted on the corners, after which the contour lines are drawn by interpolation.

Arithmetical  Method of Interpolation of Contour

The process of locating the contours proportionately between the plotted points is termed interpolation.  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 10 m.

                              Horizontal distance between A and B = 10 m

                              Vertical difference between A and B = 100.75 – 98.75 = 2 m

Let a contour of 99.00 m be required. Then,

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

Now, distance of 99.00 m contour line from A = (10/2) x 0.25 = 1.25 m

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.