Among the following corrections applied for tape measurement, identify the correction which is NOT always negative in sign.
The steel tape is used for precision works, but the measured length is likely to be subjected to the following corrections for various reasons.
Correction of slope:- While measuring on unevenly sloping ground, tapes are suspended at shorter lengths and horizontal distances are measured. This technique eliminates error due to measurement along slopes but necessitates correction for sag.
Hence, the measured length is more than the actual length. Thus the correction is -ve (negative), which is the difference between the length of catenary and true length is given by
${C_s} = \frac{{{W^2}L}}{{24{P^2}}}$
Where
W = weight of the tape of span length
P = the pull applied,
L = measured length.
Correction for Incorrect Alignment:- If the intermediate points are not in correct alignment with the ends of the line or they are not on the line to be measured, a correction, Ch is known as correction for alignment has to be subtracted from a measured distance. Hence the correction of the wrong alignment is always negative. It is given by
${C_h} = \frac{{{d^2}}}{{2L}}$
where d is the perpendicular distance by which the other end of the tape of length L is out of alignment.
Correction for sag:- When the tape sags between points of support, it takes the form of a catenary. The correction for sag Cs is always subtracted from an observed distance and is given by
${C_s} = \frac{{{W^2}L}}{{24{P^2}}}$
Where
W = weight of the tape of span length
P = the pull applied,
L = measured length
Correction for Tension (Pull):- If the pull applied to the tape during measurement is more than the standard pull at which the tape was standardized, its length increases. Hence the distance measured becomes less than the actual. The pull correction C_{p}, is given by:
\({C_p} = \frac{{(P - {P_o})L}}{{AE}}\)
where
P = standard pull
P_{o} = pull applied during measurement
A = area of cross-section of the tape
E = modulus of elasticity of tape
L = measured length (in m)
Tension correction is positive, if the applied pull is more than the standard pull, and negative, if the applied pull is less than the standard pull.
The following table shows the correction nature for different types of corrections:
Error due to |
Error |
Correction |
Standardization |
+ve or -ve |
-ve or +ve respectively |
Temperature |
+ve or -ve |
-ve or +ve respectively |
Pull |
+ve or -ve |
-ve or +ve respectively |
Slope |
Always +ve |
Always -ve |
Sagging |
Always +ve |
Always -ve |
Wrong Alignment |
Always +ve |
Always -ve |