Area and contours

1. SURVEYING
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Area Computation & Contours

2. Determination of Areas
The primary object of the land surveying is to determine the area of the tract surveyed. Area is
defined as the area of a tract of land as projected upon a horizontal plane and not the actual area
of the surface of the land.
The units of area are in metric system commonly used are square meters or hectares (10000 Sq
m i.e., 100 m x 100 m)
Computation of Areas by direct field measurements
The area to be measured may not always be a regular polygon. In this case, the region is divided
into a regular polygon and the portion between the irregular boundary and regular polygon. The
area can be found by dividing the regular polygon into triangles.

3. Determination of Areas
1. By dividing the area into number of triangles
• In this method the area is divided into a number of triangles and the area of each
triangle is calculated by measuring their sides and included angles.
• Then, the total area of the land will be equal to the sum of the areas of individual
triangles.

4. Determination of Areas
2. Areas between the survey lines and boundaries
• In this method a number of offsets are
measured from the survey line to the boundary
at regular intervals.
• Then the area between the survey line and
boundary line is measured by,
a) Trapezoidal rule and,
b) Simpson’s one-third rule

5. Trapezoidal rule
a) Trapezoidal rule
• This is based on the assumptions that the figures are trapezoids.
• The baseline AB is divided into equal parts.
• The ordinates are measured and their lengths are scaled off.

6. Simpson’s one-third rule
b) Simpson’s one-third rule
• This method is based on the assumption that
the short lengths of boundary between the
ordinates are parabolic arcs.
• Survey baseline is divided into equal parts.
• Length of the ordinates are measured.
Note: this rule is applicable only if the number of ordinates is odd. If the number of ordinates is even, the area
of the last trapezoid is calculated separately and added to the result.
For eg. if number of ordinates = 8 (as in figure)
The area of first 7 ordinates (A1) can be obtained by applying Simpson’s rule and the area of the last trapezoid
(A2) is calculated separately and added to get the total area (A).
i.e. A₁ ( Area of seven ordinates) = d/3 [ (h₁ + h₇) + 2 ( h₃+h₅) + 4 ( h₂ + h₄ +h₆ ) ]
A ₂ (Area of eighth ordinate) = d/2 * ( h₇ + h₈ ).
Total Area, A = A₁ + A ₂

7. Determination of Areas
Comparison between Trapezoidal and Simpson’s rule
 The results obtained by use of Simpson’s rule are more accurate in all cases.
 The results obtained by using Simpson’s rule are greater or smaller than those obtained by
using the trapezoidal rule according as the curve of the boundary is concave of convex
towards the base line.
 In dealing with irregularly shaped figures, the degree of precision of either method can be
increased by increasing the number of ordinates.

8. Contour Survey
Contour
An imaginary line on the ground joining
the points of equal elevation above the
assumed datum is called a contour.
Contour Interval
The vertical distance between any two
consecutive contours is called contour
interval.
Horizontal equivalent
The least horizontal distance between
two consecutive contours is called
horizontal equivalent.
Slope
It is the ratio of contour interval to the
horizontal equivalent along the line
joining those two points.

9. Characteristics of Contours
1) Widely spaced contour indicates flat surfaces. [Fig. (a)]
2) Closely spaced contour indicates steep ground. [Fig. (b)]
3) Equally spaced contour indicates uniform slope. [Fig. (c)]
4) Irregular contour indicates uneven surface, [Fig. (d)]

10. 6) Approximately concentric closed contours
with decreasing values towards centre
indicates pond/lake. [Fig. (e)]
7) Concentric closed contours with increasing
values towards centre indicates hills.[Fig.
(f)].
8) Contour lines with V shape with convexity
towards higher ground indicate valley.[Fig.
(g)]
9) Contour lines with U shape with convexity
towards lower ground indicate ridge.[Fig.
(h)].
Characteristics of Contours

11. 10)Contour lines do not meet or intersect each other.
11)If contour lines cross each other in some portion , it shows existence of
vertical cliff or wall in that portion. [Fig. (i)].
Characteristics of Contours

12. 12)If contour lines cross each other, it shows existence of overhanging cliff or
a cave. [Fig. (j)].
13)Contours do not have sharp turnings
Characteristics of Contours

13. Contour maps are used in many Civil Engineering works. Some of them are
listed below.
1. To study the general topography of the country without doing any survey work.
2. For the site selection of various engineering works such as dams, canals, weirs,
roads, railways, etc.
3. The selection along any line can be drawn.
4. To determine the quantity of earthwork required for canals, roads, etc.
5. To determine the reservoir capacity.
6. To trace a contour gradient for road, canal and railway alignments.
7. To determine the indivisibility of points.
Uses of Contour Maps