Calculation of Areas in Surveying | Simpson’s
Rule
In one of my previous articles, I discussed
Midpoint Ordinate Rule and Average Ordinate
Rule in detail with an example and listed out
various important methods used for the
calculation of areas in Surveying. In this article,
we will deal with the next important method
(rule) i.e. Simpson’s Rule along with a numerical
example used for the calculation of areas in the
field of Surveying.
Here are the five important rules (Methods) used
for the calculation of areas in Surveying:
1. Midpoint ordinate rule
2. Average ordinate rule
3. Simpson’s rule
4. Trapezoidal rule
5. Graphical rule
Simpson’s Rule
Statement
It states that, sum of first and last ordinates has
to be done. Add twice the sum of remaining odd
ordinates and four times the sum of remaining
even ordinates. Multiply to this total sum by 1/3 rd
of the common distance between the ordinates
which gives the required area.
Where O1, O2, O3, …. O n are the lengths of the
ordinates
d = common distance
n = number of divisions
Note:
This rule is applicable only if ordinates are odd,
i.e. even number of divisions.
If the number of ordinates are even, the area of
last division maybe calculated separated and
added to the result obtained by applying
Simpson’s rule to two remaining ordinates.
Even if first or last ordinate happens to be zero,
they are not to be omitted from Simpson’s rule.
The following offsets are taken from a chain line
to an irregular boundary towards right side of the
chain line.
Chainage 0 25 50 75 100 125 150
Offset ‘m’ 3.6 5.0 6.5 5.5 7.3 6.0 4.0
Common distance, d = 25m
Area = d/3[(O 1+O 7) + 2 (O 3+O 5)+4(O 2+O4+O 6)]
= 25/3[(3.6+4)+2(6.5+7.3)+4(5+5.5+6)]
Area = 843.33sqm
