Tape Corrections in chain surveying is very important. The chain surveying performed by tape is expected to have some errors because of incorrect tape measurements. In an ordinary chaining survey, the errors are neglected. But for crucial and precise survey works in construction, accurate tape corrections are provided.
In this article, various corrections provided for tape measurement while conducting chain survey are explained. If the incorrect length is to be increased then the correction is positive and if the incorrect length is to be decreased then the correction is negative.
Table of Contents
Tape Corrections in Chain Surveying
The corrections performed for seven basic mistakes in linear measurements by tape are:
- Correction for absolute length
- Correction for pull or tension
- Correction for temperature
- Correction for Sag
- Correction for Slope
- Correction for Alignment
- Reduction for the sea level
We will learn these 7 types of tape corrections in chain surveying.
1. Correction for absolute length
If Ca is the correction for absolute length or the actual length, then it is calculated by the formula:
Ca = Lc/l
Where, L = Measured length of the line; c = Correction per tape length; l= designated length of the tape or the nominal length of the tap.
Two different cases for absolute lengths are:
(A) Absolute length > Designated length, means Measured distance is short, hence the correction is additive.
(B) Absolute length < Designated length, means Measured distance is long, hence the correction is subtractive.
The sign of correction Ca be the same as that of ‘c’.
2. Correction for Temperature
The correction for temperature Ct is calculated by the formula:
Tm is the mean temperature in the field during measurement; Tα is the temperature during the standardization of the tape; L = Measured length
Here, are two cases of possible.
(A) If The temperature of the field is greater than the temperature at which the tape is standardized; Tm > To. This results in an increase in the tape length, making the measured length shorter. Thus, the correction is additive.
(B) If The temperature of the field is lesser than the standardized temperature, i.e. Tm<To, then the tape length decreases. This results in an increase in the measured length than the original. Thus, the correction is subtractive.
3. Correction for Pull or Tension
The correction for pull or tension is calculated by the given formula:
Where, P = Pull applied during the measurement; Po= Standard Pull; Both P and Po are measured in Newtons; L = measured length; A =Area of cross-section measured in cm2; E = Young’s modulus measured in N/cm2.
Here, two cases are possible:
(A) If Pull applied during the measurement is greater than the pull at which the tape is standardized i.e. P > Po. This results in an increase in the length of tape which makes the measured length shorter. Thus the correction is additive.
(B) If Pull applied during the measurement is lesser than the pull at which the tape is standardized i.e. P < Po. This results in a decrease in the length of tape which makes the measured length longer. Thus the correction is subtractive.
The pull applied in the field should be less than 20 times the weight of the tape used for measurement.
4. Correction for Sag
Stretching the tape between two supports makes the tape make a horizontal catenary. Thus, the horizontal distance becomes more than the distance along the curve.
Hence,
Sag Correction = Horizontal distance – length along the horizontal catenary
As shown in the figure below, the curve is expected as a parabola to facilitate the calculation of correction for sag.
Tape correction per length is given by,
Cs = lW2 /24n2P2
Where, Cs = Tape Correction per Tape length; l=Total length of the tape; W= total weight of the tape; n= number of equal spans; P= Pull applied;
5. Correction for Slope or Vertical Alignment
The slope correction or correction due to vertical alignment is given by the formula:
Cv = 2L sin2(x/2)
Or
Where, h = The difference in elevation between the ends; x = slope measured;
The distance that is measured along the slope is always more than the horizontal distance. That is why the correction is subtractive.
6. Correction for Horizontal Alignment
There are three possibilities that can occur for Horizontal Alignment
(I) Bad Ranging or Misalignment Error
Extending the tape out of line results in a greater distance value. The correction is hence negative. As shown in the following figure, AB is the measured length and AC is the correct alignment. Hence, the correction is calculated by:
Ch = d2/2L
(II) Deformation of the Tape in Horizontal Plane
If the tape is not pulled straight, the length L1 of the tape stands out of the line by an amount ‘d’. Then the correction is calculated by the formula
Ch = (d2/2L2) + (d2/2L2)
(III) Broken Base
Due to some obstacles, it won’t be possible to set out the base in a single continuous line. Such a base is known as a broken base.
If the two sections of the broken base are AB and BC, with an outdoor angle beta, then the rectification is given by:
Ch = (a +c)-b
It will be subtractive.
Which is calculated as;
7. Reduction to Mean Sea Level
The horizontal distance measured must be decreased to the distance at sea level. This distance is known as geodetic distance.
Given, L = Measured Horizontal Distance; D = Geodetic MSL; h= mean the equivalent of the baseline above the mean sea level. R = Radius of the earth; An angle is subtended at the center of the earth.
Then the correction is calculated as,
Sum Up
These are the 7 types of tape corrections in chain surveying. A surveyor must have knowledge these corrections to avoid any error in chain surveying.