List the different tape corrections Explain and give expressions for tape corrections JuneJuly 2013

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## List the different tape corrections. Explain and give expressions for tape corrections. ( June/July 2013)

CORRECTION FOR SLOPE

CORRECTION FOR ABSOLUTE LENGTH

CORRECTION FOR TEMPERATURE

CORRECTION FOR TEMPERATURE

CORRECTION OF SAG

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. Correction for absolute length
2. Correction for slope
3. Correction for temperature
4. Correction for pull, and
5. Correction for sag
CORRECTION FOR ABSOLUTE LENGTH
Let, l = designated length of tape
la = absolute length of the tape
Then correction per chain length
c = la – l
Hence, if the total length measured is L, the correction is
Ca = L c/l
If absolute length of tape la is greater, correction is +ve and if negative, the correction is also
negative. Thus correct length L’ is given by
L'=L+Ca
If A is the measured area with incorrect tape, the correct area is given by
A'=A(1+2c)
CORRECTION FOR SLOPE
If length measured ‘L’ and the difference in the levels of first and last point ‘h’ are given then
correction for slope is,
Csl=h2
/2L
If θ and L are given, Csl=L(1-cosθ )
This correction is always subtractive.
CORRECTION FOR TEMPERATURE
Let α- Coefficient of thermal expansion of the material of tape
Tm – Mean temperature during measurement
To - Temperature at which tape is standardized, and
L – Measured length
Then temperature correction Ct is given by Ct=Lα(Tm-To)
CORRECTION FOR PULL
Let, E – Young’s modulus of the material of tape
A – Cross – sectional area of the tape
P – Pull applied during measurement
P0 - Standard pull, and
L – Measured length of chain
Then, the correction for pull Cp is given by Cp=(P-P0)L/AE
The above expression takes care of signs of the correction also.
CORRECTION OF SAG
While taking reading, if the tape is suspended between two supports, the tape sags under its own
weight as shown in Fig. 3.18. The shape of tape is a catenary. Hence, measured length is more than
the actual length. Hence, this correction is subtractive. This correction is given by
Cs=1/24(W/P)L
Where, W – the weight of the tape per span length
P – the pull applied during the measurement
L – Measured length.
If pull is larger than standard pull, the correction is +ve and , correction for sag is always negative.
The pull for which these two corrections neutralize each other is called Normal tension.

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