Computation of Areas and Volume

The computation of area and volume surveying is one of the primary goals of surveying. Because the land is irregularly shaped, surveying is necessary for proper project management and planning. In this article, we will learn more about the surface areas and volume and their computation in surveying. 

Computation of Area and Volume in Surveying 

Channel excavation, trenching for installing underground pipes, the building of bunds, earthen embankments, farm ponds digging, and land levelling and smoothing all require earthwork computation.

The cross-sectional areas are calculated first in most computations at different intervals along the length of the channels and embankments, and the prismoidal volume, which is obtained from successive cross-sections using either a trapezoidal or a prismoidal formula. 

In most cases, the cross-sectional areas at various intervals along the length are computed first, and the volume of the prismoidal is determined between subsequent cross-sections using either the trapezoidal or prismoidal formula.

The method for computing area is determined by the geometry of the tract’s boundary and the level of precision required. The area of a piece of land is calculated using its plan, which can be defined by straight, irregular, or a combination of straight and irregular boundaries. Subdividing the plan into simple geometrical figures determines the area when the boundaries are straight.

Short straight borders are used to replace uneven boundaries, and the area is calculated using approximate methods or a planimeter as necessary for irregular boundaries.

Surface Area and Volume Formulas:

The surface area and volume formulas are as follows:

• Area

 In surveying, the term area refers to the size of a tract of land projected on a horizontal plane, not the actual area. For normal polygons such as triangles, rectangles, and squares, formulas are readily available; however, for irregular polygons, various methods are employed.

The area of the land can be expressed in square meters, hectares, square feet, and acres.

The area is calculated using one of the methods listed below-

1. Graphical method
2. Co-ordinate method 
3. Planimeter 

The co-ordinate method is the most often used in land surveying for determining catchment area, drainage area, cross-sections of rivers, and channels, among other things.

This method divides a given area into two halves, with a basic line running through the middle.

There are two key rules to remember for calculating surface area and volume formulas:

• Trapezoidal Rule

Boundaries of the ordinates are presumed to be straight. Therefore the area between the lines is considered to be a trapezoid.

A=[ common distance between ordinate [{first ordinate + last ordinate} + 2{sum of other ordinates}] ]/2

This rule can be used for any number of ordinates, and hence it has no drawbacks or limitations.

• Simpson’s Rule:

An arc is assumed to be present between the boundaries of the ordinates. Therefore it is also known as the parabolic rule. 

Area= [Common distance[(First ordinate + last ordinate) + 4(Sum of even ordinates) + 2(Sum of odd ordinates)]]/3

The only limitation to this rule is that it can only be used when the number of ordinates is odd.

Simpson’s rule gives a more accurate result.

After the calculation of the cross-sectional areas, volume is also needed to be calculated to determine the capacity.

• Volume

In the design and planning of many engineering projects, volume calculations of various quantities using field measurements are required.

For proper alignment of road works, canal and sewer lines, soil and water conservation works, farm pond, and percolation pond consent, a large amount of earthwork is required.

Calculating the number of various materials such as coal, gravel, and other materials are required to verify stock files, as well as to estimate the capacities of bins, tanks, and other containers.

Cross-sections are obtained at right angles to a fixed-line that runs continuously through the earthwork to estimate the volume of the earthwork. The spacing of the cross-sections will be determined by the level of precision required.

Volume in surface area and volume formulas can be calculated by:

• The Trapezoidal Rule:

It is also known as the average end area rule, it is used when the number of sections is even, and the end section is taken separately. 

Volume= [Common distance [Area of first section + Area of last section + 2 (Sum of areas of other sections)]]/2

• The Prismoidal Rule:

This rule is applicable for the odd number of sections. 

Volume= {Common distance [Area of first section + Area of last section + 4 (Sum of areas of even section) + 2(Sum of Area of odd sections)]}/3

The results obtained from both the rules are added to get the total volume. 

Computation of Area and Volume in Building

Computation of area and volume in buildings can be measured by architectural engineers by analysing the surface area to volume ratio and helps in conducting building surveys.

Conclusion

Computation of area and volume in surveying provides an accurate measurement of buildings, land, soil, and others for proper management of the resources. The main application of computational surveys is to make topographical maps and graphs. Surface area and volume formulas are used to determine the computation surveying of any complex structure.