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# Linear Measurement: Errors in Linear Measurement

In an engineering survey, the linear horizontal distance has to be measured. The measurement of this linear horizontal distance between two points on the earth's surface is known as linear measurement. The study of surveying helps us determine the relative position of points, the height of buildings without actually measuring the settlement, etc. It is generally done before the construction of buildings.

Linear and angular measurements are equally important during an engineering survey. Bearing, rotation, etc. are the angular measurements, while distance is a linear measurement.

The difference between two or more measured values of the same quantity is known as error. In linear measurement, there can be various types of errors. They are;

1. Wrong length of chain

3. Variation in temperature

4. Variation in tension

5. Sagging

Let us discuss these errors in detail.

## Wrong Length of Chain

There may be some discrepancy in manufacturing the chains. The length of the chain may not be always exact. So there may be an error due to the incorrect length every time the chain is used. To prevent this type of error we can use correction factors.

Actual length = measured length + correction factor

Actual length= Measured length + Actual chain length/ Incorrect chain length

If the actual chain length is more than the incorrect chain length, then a positive correction is applied.

If the chain is stretched out of the line, the measured distance will always be more and hence the error will be positive. For each and every stretch of the chain, the error due to bad ranging will be cumulative and the effect will be too great a result.

## Variation in Temperature

A temperature higher or lower will change the length of the tape. So this can cause errors. This can be correct by ;

Ct = α (Tm-To)L

Where,α= coefficient of thermal expansion

Tm= mean-field temperature

To= calibration temperature

L= measured length

If Tm>To, positive correction is applied

## Variation in Pull/Tension

If tension is greater than the standard then the tape will stretch. If less than standard tension is applied the tape will be shorter than standard. This is corrected by,

Cp=(P-Po)L/Aε

Where; P= applied pull

Po= standard pull

L = measured length

A = area of cross-section

ε = Young’s Modulus

If P>Po, positive correction is applied.

## Sagging

A tape not supported along its entire length will sag. By applying correct tension the sag can be reduced. This can be corrected by;

Cs=L/24(W/T)²

where; L = measured length

W = weight of the chain

T = tension/pull

If the chain is not held properly, it sags. The correction applied is negative.

Yeah, that's it for this blog. We will meet soon again in another blog. Till then show me your understanding of this topic by solving the question below. Thank You!