Numerical Examples for Errors in Chain Surveying

A practical Example for Calculation of the True Area of the field | Errors in Chain Surveying

In my previous article, we studied how to measure true distance considering the Errors occurring in Surveying.

Correction formulas to be kept in mind (for incorrect length of Chain)

True distance = L’/L*measured distance

True area = (L’/L)2*measured area

True Volume = (L’/L)3 * measured volume

Where, L’ = incorrect length of chain

L = correct length of chain

The chain was tested before starting the surveying and was found to be 20m. At the end of surveying, it was tested again and was found to be 20.12m. The area of the plan of the field drawn to a scale 1cm = 6m was 50.4sqm. Find the true area of the field in sqcm.

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Chaining on Sloping Ground | Guide to Surveying and Levelling

Chaining on Sloping Ground | Surveying and Levelling

There are two methods for determining horizontal distance on sloping ground.

  1. Direct Method
  2. Indirect Method

Direct Method of Chain Surveying

This method is also known as “Stepping Method”.

The horizontal distances are directly measured by the process of stepping.

Procedure

A path of chain or tape is stretched out from ‘P’.

The path length of chain or tape depends on the steepness of the ground.

The follower holds the zero end of the chain at ‘P’ and directs the leader at P1 to be in the line of PQ and stretch the chain or tape above the ground in horizontal line.

Direct Method | Chain Surveying
Direct Method | Chain Surveying

The leader then transfers the point ‘P1’ to P2 on the ground by means of plumb bob or dropping a pebble or an arrow,

Now the followers take the new position ‘P2’ and directs the leader to move forward and stretch the tape or chain in a line of PQ.

Now the followers take the new position ‘P2’ and directs the leader to move forward and stretch the tape or chain in a line of PQ and the new position is P3.

Again the leader transfers the point P3 to P4 on the ground as done earlier.

This process is repeated till the point Q is reached.

Horizontal distance PQ = S1 + S2 + S3 + S4 + S5

Read moreChaining on Sloping Ground | Guide to Surveying and Levelling

Numerical Examples for Chain Surveying | Errors in Surveying

Numerical Examples for Errors in Chain Surveying

We will now move on with different numerical problems on the concept of Errors in Chain Surveying. Going through these numericals will actually give you an idea as to how the calculations are done inspite of errors occurring in the Chain Surveying.

Correction due to incorrect length of chain

This is like a formula list which is to be kept in mind while making Calculations:

True distance = L’/L*measured distance

True area = (L’/L)2*measured area

True Volume = (L’/L)3 * measured volume

Where, L’ = incorrect length of chain

L = correct length of chain

The length of a line measured with 20m chain was found to be 500m. It was subsequently found that the chain was 0.04m too long. What is the length of line?

Correct length of chain, L’ = 20 + 0.04 = 20.04m

Length, L = 20m

Read moreNumerical Examples for Chain Surveying | Errors in Surveying

Errors in Chaining | Guide to Surveying and Levelling

Types of Errors occurring in Chain Surveying

There are two types of Errors that are commonly seen to occur in Chain Surveying. For students studying the concept of Chain Surveying, study of the occurrence of different types of Errors in Chain Surveying is important. In this article, we will briefly discuss different types of Errors in Chain Surveying and the situations in which they occur.

Types of Errors:

  1. Cumulative error
  2. Compensative error

Cumulative error

These errors always accumulate in one direction and are serious in nature. They affect the survey work considerably.

They make measurements too long or too short.

These errors are of two types and are known as systematic errors.

They are classified as follows:

  1. Positive error
  2. Negative error

Positive error

These errors make the measured length more than the actual length which results into wrong calculations by the Surveyor.

Read moreErrors in Chaining | Guide to Surveying and Levelling