Introduction to Chain Surveying
Chain surveying is a type of surveying used to measure distances on land. It involves the use of a chain, usually made of metal, which is marked off into equal parts known as links. The chain is used to measure distances and map the area being surveyed. Chain surveying is usually used in construction projects where an accurate measurement of distances is needed.
Errors in Chain Surveying
Chain surveying can be prone to errors due to incorrect tape measurements. These errors can be caused by factors such as the curvature of the chain, misreading of the chain’s markings, and wear and tear of the chain. In ordinary chaining works, these errors are generally neglected. However, for important and precise survey works in construction, accurate tape corrections must be provided.
Types of Tape Corrections
Tape corrections are used to reduce errors in chain surveying. These corrections can be either positive or negative, depending on the erroneous length. A positive correction is applied when the erroneous length needs to be increased, while a negative correction is applied when the erroneous length needs to be decreased. Tape corrections can also be made for other factors such as curvature, misreading, and wear and tear.
Tape Corrections
Correction for Absolute Length
This correction is performed to make sure that the measurements taken using a tape measure are accurate. It involves measuring from a fixed point and then accounting for any variations due to the stretching of the tape.
Correction for Pull or Tension
In order to ensure accuracy, it is important to make sure that the tape is pulled tight when taking measurements. If the tape is too loose, the measurements will be inaccurate. This correction involves making sure that the tape is pulled tight enough for accurate measurements.
Correction for Temperature
Temperature can affect the accuracy of measurements taken with a tape measure as the tape can expand or contract based on the temperature. This correction involves accounting for any changes in the measurements due to temperature.
Correction for Sag
When taking measurements with a tape measure, it is important to make sure that the tape is not sagging. If the tape is sagging, the measurements will be inaccurate. This correction involves making sure that the tape is not sagging and correcting the measurements if necessary.
Correction for Slope
When taking measurements with a tape measure, it is important to make sure that the tape is level. If the tape is not level, the measurements will be inaccurate. This correction involves making sure that the tape is level and correcting the measurements if necessary.
Correction for Alignment
It is important to make sure that the tape is aligned properly when taking measurements. If the tape is not aligned properly, the measurements will be inaccurate. This correction involves making sure that the tape is aligned properly and correcting the measurements if necessary.
Reduction for the Sea Level
When taking measurements with a tape measure at sea level, it is important to account for the fact that the sea level is lower than the land. This correction involves reducing the measurements taken at sea level to account for the difference in altitude.
1. Correction for Absolute Length
Calculating Absolute Length Correction (Ca)
Absolute length is the length of a line, as measured with a surveyor’s tape. To calculate the correction for absolute length (Ca), we need to divide the correction per tape length (c) by the designated length of the tape or the nominal length (l):
Ca = Lc/l
Additive Correction
If the absolute length is greater than the designated length, this means that the measured distance is short. In this case, the correction is additive. The sign of the correction (Ca) is the same as that of ‘c’.
Subtractive Correction
If the absolute length is less than the designated length, this means that the measured distance is long. In this case, the correction is subtractive. The sign of the correction (Ca) is the same as that of ‘c’.
2. Correction for Temperature
# Temperature Correction Formula
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.
Temperature Correction Cases
There are two cases possible when considering temperature correction:
- Case 1: Temperature of Field is Greater than Standardized Temperature
When 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.
- Case 2: Temperature of Field is Lesser than Standardized Temperature
When the temperature of the field is lesser than the standardised temperature (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:
Case 1: Pull Applied During Measurement is Greater than Standard Pull
When the pull applied during a measurement is greater than the pull at which the tape is standardized (Po), the resulting measured length (L) of the tape will be shorter than its actual size. In this case, a correction must be made by adding to the measured length.
Case 2: Pull Applied During Measurement is Less than Standard Pull
When the pull applied during a measurement is less than the pull at which the tape is standardized (Po), the resulting measured length (L) of the tape will be longer than its actual size. In this case, a correction must be made by subtracting from the measured length.
Safety Considerations
For safety reasons, the pull applied in the field should not exceed 20 times the weight of the tape used for measurement.
4. Correction for Sag
Sag Correction Calculation
The process of stretching a measuring tape between two supports can form a horizontal catenary, which results in a greater horizontal distance than the length along the curve. To calculate the correction for sag, the curve is assumed to be a parabola. The pull applied in the field must not exceed 20 times the weight of the tape used for measurement. The correction per length is given by the formula:
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 relation:
Cv = 2L sin2(x/2)
Or
Where, h = The difference in elevation between the ends; x = slope measured;
Distance on Slope vs. Horizontal Distance
When measuring distances along a slope, the distance is always greater than it would be if the same distance was measured horizontally. This means that to accurately measure a distance on a slope, one must subtract the difference between the horizontal and sloped distance.
6. Correction for Horizontal Alignment
There are three possibilities under this:
a. Bad Ranging or Misalignment Error
What is Tape Stretching?
Tape stretching is the process of stretching a measuring tape out of its intended line of measurement. This results in a greater distance value than what is actually measured.
What is Tape Stretching Correction?
Tape stretching correction is the process of making adjustments to the measured length in order to account for the incorrect measurements that were taken due to tape stretching. The correction is typically negative, meaning that the measured length is typically shorter than what is actually measured.
How is Tape Stretching Correction Calculated?
Tape stretching correction is calculated by comparing the measured length (AB) to the correct line of alignment (AC). The correction is then determined by the difference between these two lengths. Generally speaking, the correction is negative, meaning that the measured length is shorter than what is actually measured.
b. Deformation of the Tape in Horizontal Plane
Correction of Tape Measure Length
When a tape measure is not pulled straight, the resulting length L1 of the tape stands out of the line by an amount ‘d’. In order to accurately measure the length of an object, it is necessary to correct for this deviation. The following formula can be used to correct for the deviation ‘d’ in the tape measure length:
L1 = L2 + 2d
Where L2 is the true length of the measured object, and d is the deviation of the tape measure from the line.
Calculating the Deviation ‘d’
In order to calculate the deviation ‘d’ of the tape measure, the following formula can be used:
d = (L1 – L2)/2
Where L1 is the measured length of the object, and L2 is the true length of the measured object. This formula can be used to accurately determine the deviation ‘d’ of the tape measure from the line.
Correcting for Deviation ‘d’
Once the deviation ‘d’ has been calculated, the formula for correcting for the deviation is as follows:
L1 = L2 + 2d
Where L1 is the measured length of the object, L2 is the true length of the measured object, and d is the deviation of the tape measure from the line. This formula can be used to accurately calculate the corrected length of the object, taking into account the deviation ‘d’ of the tape measure.
Ch = (d2/2L2) + (d2/2L2)
c. Broken Basec. Broken Base
What is a Broken Base?
A broken base is a base that cannot be set out in a single continuous line due to obstructions. How to Calculate Broken Base Correction? The correction for a broken base is calculated by subtracting the interior angle “b” from the sum of the exterior angles “a” and “c”, i.e. Ch = (a +c)-b.
Which is given by,
7. Reduction to Mean Sea Level
Geodetic Distance:
Geodetic distance is the horizontal distance measured at sea level. It is the distance between two points when measured along the surface of the Earth. It is calculated by taking into account the curvature of the Earth.
Calculation of Geodetic Distance:
Geodetic distance can be calculated using the following formula: D = L + (h * R * sinθ). Here, L is the measured horizontal distance, h is the equivalent of the baseline above the mean sea level, R is the radius of the earth and θ is the angle subtended at the center of the earth.
