Survey Plan and Area Calculation: A Cursory Look

Saji Koduvath, Advocate, Kottayam.

Introduction

A survey plan shows the shape and size of a property. It helps in calculating the area of the land.

In survey plans, two types of lines are commonly seen—continuous lines and broken (or dashed) lines. Alongside the survey plan, we also find the field book (or ladder).

Continuous and Broken Lines

Continuous lines show the periphery of the property.

Broken (dashed) lines that represent the internal diagonals are drawn from one bend or a corner of the plot to an opposite bend or corner.

  • The purpose of fixing the diagonal is to facilitate the measurement of perpendicular distances (offsets) from the diagonal to the boundary bends on either side.
  • In surveying practice, these internal diagonals are fixed first.  
  • In the case of a large field, there may be more than one internal diagonal.

The number and placement of diagonals are determined with a view that the entire plot can be divided into imaginary triangles without overlap.

Station Points

Station points are the starting and ending points of a diagonal line.

Calculation of Area

For calculating the area of the plot, it is divided into (imaginary) triangles. Each triangle is shaped in the following manner: the required portion of the diagonal will be one side, the offset measurement as the second side, and the outer boundary as the third side. The area is calculated using the rectangle-triangle method. A rectangle-triangle is a triangle having one angle of 90 degrees.

The formula applied for calculating its area is:

  • Area = ½ base × altitude

The area of certain parts may have to be calculated with the side measurements of the triangle. The formula applied in that case (Heron’s formula) with side measurements of the triangle a, b, c, is the following:

  • A = √[s(s-a)(s-b)(s-c)]
  • ‘s’ is the semi-perimeter of the triangle given by s = (a + b + c)/2.

Method Adopted by the Surveyor

In surveying, the cross-staff is used by the surveyor while measuring the (perpendicular) distance from the diagonal to the boundary bends. The cross staff is used to ensure the 90 degrees angle. This measurement from the diagonal to the outer bend is called offset.

The surveyor follows these steps:

  • A rough sketch (draft) of the plot is prepared.
  • One or more diagonals are fixed and drawn. The beginning and end points of each diagonal are assigned letters (A–B; if there are multiple diagonals, they are placed as C–D, E–F, and so on).
  • To measure offset length – between the diagonal and the outer bend (which are marked L, M, N, O, P, etc.) – the cross-staff is used. The surveyor aligns the cross-staff along the diagonal by sighting (i) the two station points through the slit and (ii) the required outer bend through the opposite cross-slit.
  • After fixing the cross staff as stated above, the distance (i) from a station point to the position of the cross staff and (ii) the distance from the outer bend to the diagonal (position of the cross staff) are measured and duly entered in the diagram.
  • In that way, all the distances from the bends to the diagonal (or diagonals) are taken and recorded in the sketch.

Field Book or Ladder

The field book is usually recorded in the following form:

               B  
M2070  
  2515L
  A  

It is prepared in the following manner:

  • At the bottom, the starting station point (denoted by alphabet A) is entered.
  • Above it, the distance from station point A to the first offset point on the diagonal (say, 25 metres) is recorded.
  • If the first offset (first bend) is towards the right, the offset distance (say, 15 metres) is entered in the right-hand column, and the corresponding boundary bend (L) is noted in the further right column.
  • If the second offset is towards the left, the offset distance (say, 20 metres) is entered in the left-hand column, and the corresponding boundary bend (M) is recorded on the next left column.

Area calculation

  • Areas of all the triangles are calculated adopting the aforesaid formulas.
  • Finally, the areas of all triangles are added together to get the total extent of the property.

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1 Comment

  1. sensationallyllamaa53656cf3d's avatar sensationallyllamaa53656cf3d says:

    such a useful information Mr. Saji. great thankyou

    Like

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