Method of interpolation of Contours, Surveying and Levelling | Surveying and Levelling Notes- Agricultural Engg - Agricultural Engineering PDF Download

Method of interpolation of contours:

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

1. Arithmetical calculation
2. The graphical method

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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:

1. Arithmetical calculation
2. 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.