# Types of error in Chaining | Correction for linear Measurement

While measuring the length between any two points there may be inaccurate measuring due to different types of error in chaining like environmental conditions, elongation and construction of chain in winter and summer season etc.

Hence to get accurate measurement we have to add correction in the length. Here we will discuss different types of error and their correction.

## Different Types of error in Chaining

The errors coming in chaining may be due to manual, instrumental or natural. All the above errors are classified into two groups depending on nature.

a) Cumulative errors

b) Compensating error

c) Accidental error

### a) Cumulative errors

The errors which occur in the same direction and tend to accumulate is called cumulative errors.

Cumulative errors are of two types:-

1. Positive cumulative errors
2. Negative cumulative error

The positive cumulative error is occurring due to length of the chain is shorter than its standard length. So correction for this is always -ve. The negative cumulative error is occurring due to the length of the chain/tape being longer than its standard length. So correction for this is always positive.

Cumulative errors are always proportional to the length of the line. and can be corrected by applying the required correction.

To avoid this error, we should check whether the length of the chain is correct or not before measuring the length.

### b) Compensating error

The error which occurs in either direction and tends to compensate is called compensating error. It is occurring due to incorrect holding of the chain, refinement is not made in plumbing, etc.

Compensating errors are proportional to the square root of the length of the line. The nature of the error is not known so, correction becomes impossible.

To avoid this error we should carefully hold the chain without sagging and hogging the chain. The length of land should be taken in straight as far as possible.

### c) Accidental error

Accidental errors are occurring due to careless of the staff involved in chaining. It is proportional to the square root of the number of observations taken.

## Correction for linear Measurement

For precise measurement following corrections is done:-

• Correction for standard length
• Correction for alignment
• Correction for Slope
• Correction for tension
• Correction for temprature

#### e) Correction for temprature,

(If the temperature is above then correction is +ve and if it is below normal, then correction is -ve)

#### Correction due to reduction to MSL

The difference in the length of the measured line and equivalent length at the MSL is called correction due to reduction to MSL. Its value is given by,

#### Normal-Tension

The pull or tension when applied to a tape in the air over two ends, equalizes the correction due to pulling, and the correction due to sag is known as normal tension.

Product of correct length and correct chain length = Product of the incorrect length and incorrect chain length

True Length =

The residual error is the difference between a measured quantity and the most probable value. It is also called variation.

The most probable error is defined as that error for which there is equal chance that the true value will be less than the probable value or will be more than the probable value.

The sign of correction is always opposite to that of the error.

Accidental errors are directly proportional to root N, where N is the number of observations made.

Angular errors of closures should not exceed 15 roots N.

## Numerical Example

#### For too short

Q) The distance between two points, measured with a 20 m chain, was recorded as 327 m. It was afterwards found that the chain was 3 cm too long. what was the true distance between the points?

Solution:-

Given, True length of chain, L =20 m

Error in chain, e = 3 cm = 0.03 m

L’= L+e (too long)

= 20 +0.03 = 20.03 m

Measured length = 327 m

True length of line = (L’/L) X 327

= 327.49 m

#### For too Short

Q) The distance between two points, measured with a 30 m chain, was recorded as 202 m. It was afterwards found that the chain was 5 cm too short. What was the true distance between the points?

Solution:-

Given, True length of chain, L = 30 m

Error in chain, e = 5 cm = 0.05 m

L’ = L – e = 30 -0.05 (too short) = 29.95 m

Measured length = 202 m

true length of the line = (L’/L) x 202

= 201.663 m

= True length of line = 201.663 m

Happy learning

Civil concept