- Chain Surveying performed by using a tape is expected to have some errors due to incorrect tape measurement.
- These errors are neglected in ordinary chaining works
- But important and precise survey work requires accurate tape corrections.
- The corrections are as follows:
A. Correction for absolute / standard length
If Ca is the correction for absolute length or the actual length, it is given by,
\( C_{a} = \frac{L}{l} \times C \)
where, L = Measured length of line.
C = Correction per tape length.
L = designated length of tape (or the nominal length)
Different Cases:
1. Absolute length > Designated length means measured distance is short hence correction is additive
2. Absolute length < Designated length means measured distance is long, hence the correction is subtractive.
The sign of correction Ca is same as that of 'C'
B. Correction for Temperature
The correction for temperature Ct is given by the formula:
\( C_{t} = α (Tm - To) L \)
where, α = coefficient of thermal expansion
Tm = Mean temperature in field during me measurement
To = Temperature during standardization of tape
L= Measured length
Different cases:
If Tm > To, Measured length is shorter, Correction is additive
If Tm < To, Measured length is longer, Correction is subtractive
C. Correction for pull or tension
The correction for pull or tension is given by the formula,
\( C_{p} = \frac{(P-P_{o})L}{AE} \)
where,
P = Pull applied during the measurement (in N)
Po = standard pull (in N)
L= Measured length (in m)
A = Area of cross section (in cm²)
E = Young's Modulus of elasticity (in N/cm²)
Different cases
1. P>Po, Measured length shorter, Correction is additive.
2. P<Po, Measured Length longer, Correction is subtractive.
D. Correction for Sag
Stretching of tape between two supports makes the tape form a horizontal curve. This curve is called sag.
{figure}
The correction for sag is given by formula:
\( C_{sg} = \frac{W^2L}{24P^2n^2} \)
Where, W is the total weight of tape between supports
L= distance between support,
P = applied tension
Sag correction is always negative since sag always increases the measured length.
E. Slope Correction for slope
The slope correction is given by the formula
\( C_{sl} = \Sigma \frac{h^2}{2l} \)
Also,
\( C_{sl} = L - D \)
\( or, C_{sl} = L- \sqrt[]{L^2-h^2} \)
\( or, C_{sl} = 2L sin²( \frac{θ}{2} ) \)
Where, h = difference in elevation
D = horizontal distance between the points.
θ = slope of the terrain
L= length of slope
Slope correction is always positive.