# Tape Corrections in Chain Surveying

The chain surveying performed by a tape is expected to have some errors due to incorrect tape measurements. In ordinary chaining works, the errors are neglected. But for important and precise survey works in construction, accurate tape corrections are provided.

Also Read: Errors in Chain Survey

Different corrections provided for tape measurements while conducting chain surveying are explained in the article. The correction is positive if the erroneous length is to be increased and the correction is negative if the erroneous length must be decreased.

Also Read: Types of Tapes used in Surveying

## Tape Corrections

The corrections performed for seven common errors 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

### 1. Correction for Absolute Length

If Ca is the correction for absolute length or the actual length, then it is given by:

#### 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.

Different cases are:

- Absolute length > Designated length means Measured distance is short, hence the correction is additive.
- Absolute length < Designated length means, Measured distance is long, hence the correction is subtractive.

The sign of correction Ca is the same as that of ‘c’.

### 2. Correction for Temperature

The correction for temperature Ct is given by the formula:

Tm is the mean temperature in the field during measurement; To is the temperature during the standardization of the tape; L = Measured length;

There are two cases possible:

1. The temperature of the field is greater than the temperature at which the tape is standardised; Tm > To. This results in an increase in the tape length, making the measured length shorter. Hence the correction is additive.

2. The temperature of the field is lesser than the standardised temperature, i.e. Tm<To, then the tape length decreases. This results in an increase the measured length than the original. Hence the correction is subtractive.

### 3. Correction for Pull or Tension

The correction for pull or tension is given by the 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 in cm^{2}; E = Young’s modulus in N/cm^{2}.

Two cases are possible:

1. Pull applied during the measurement is greater than 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. Hence the correction is additive.

2. Pull applied during the measurement is lesser than pull at which the tape is standardized i.e. P < Po. This results in a decrease in length of tape which makes the measured length longer. Hence the correction is subtractive.

The pull applied in the field must be less than 20 times the weight of the tape used for measurement.

### 4. Correction for Sag

Stretching the tape between two supports make the tape to form a horizontal catenary. Hence, the horizontal distance becomes greater 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 assumed as a parabola to facilitate the calculation of correction for sag.

Tape correction per length is given by,

**Cs = lW**^{2} /24n^{2}P^{2}

^{2}/24n

^{2}P

^{2}

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 relation:

**Cv = 2L sin**^{2}(x/2)

^{2}(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 greater than the horizontal distance. This makes the correction to be subtractive.

### 6. Correction for Horizontal Alignment

There are three possibilities under this:

#### a. Bad Ranging or Misalignment Error

Stretching the tape out of line results in greater distance value. The correction is therefore negative. As shown in figure below, AB is the measured length and AC is the correct alignment. Hence, the correction is given by:

#### Ch = d^{2}/2L

#### b. Deformation of the Tape in Horizontal Plane

When 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 given by,

#### Ch = (d^{2}/2L_{2}) + (d^{2}/2L_{2})

#### c. Broken Base

Due to some obstructions, it won’t be possible to set out the base in a single continuous line. Such a base is called a broken base.

If the two sections of the broken base are AB and BC, with an exterior angle beta, then the correction is given by:

Ch = (a +c)-b which is subtractive

Which is given by,

### 7. Reduction to Mean Sea Level

The horizontal distance measured must be reduced to the distance at sea level. This distance is called 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 given by:

Also Read: Incorrect Chain in Surveying