In the previous article, we discussed briefly on the topic of “Scales in Surveying” where we came across an important term “Representative factor” which forms an important part in understanding the scales in Surveying.
In this article, we will discuss different types of scales used in Surveying…
The scales are classified into four categories:
Scale of chords
Lets go on with the discussion of types of scales briefly for our better understanding…
Plain Scale is one on which it is possible to measure two dimensions only. For example, measurements such as units and lengths, metres and decimetres etc.
Six different plain scales in metric used by engineers, Architects and Surveyors.
On diagonal scale, it is possible to measure three dimensions such as metres, decimetres and centimetres, units , tens and hundreds; yards, feet and inches etc.
A short length is divided into number of parts using the principle of similar triangle in which sides are proportional.
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:
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 1/3rd of the common distance between the ordinates which gives the required area.
Where O1, O2, O3, …. On are the lengths of the ordinates
d = common distance
n = number of divisions
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.