Test: Reciprocal Levelling - Civil Engineering (CE) MCQ

When it is necessary to carry a levelling across a river ravine or any obstacle requiring a long site between two points so situated that no place for the level can be found from which the lens of foresight and backsight will be even approximately equal, special method that is reciprocal levelling must be used. It is used to obtain better accuracy.

Reciprocal levelling is adopted to accurately determine the level difference between two points which are separated by obstacles like a river, ponds, lakes, etc.
It eliminates the following errors:
i) error in instrument adjustments i.e error due to collimation
ii) the combined effect of Earth's curvature and the refraction of the atmosphere
iii) variation in the average refraction
Important Points:
Reciprocal levelling eliminates the error due to collimation and error due to curvature of Earth completely, but as the refraction depends upon the atmosphere which may change every minute;

​Reciprocal Leveling

• ​This technique of leveling work is used to find the exact height difference or to find the exact RL(Reduce level) of the point by equalizing the distance when there is a large obstruction like a river, ponds, lakes, etc. in direction of the survey.
• It eliminates the following errors:
  (i) error in instrument adjustments i.e error due to collimation
  (ii) the combined effect of Earth's curvature and the refraction of the atmosphere
  (iii) variation in the average refraction.

Important Point
Reciprocal leveling eliminates the error due to collimation and error due to curvature of Earth completely, but as the refraction depends upon the atmosphere which may change every minute.

The true difference between levels P and Q, by using the concept of reciprocal leveling, is given as:

Where a and b are readings taken when the instrument is at or near P and c and d are readings when the instrument is at or near Q.
RL of point  Q = RL of Point P – h
Calculation:
a = 1.96 and b = 1.36 m; c = 2.02 m and d = 1.52 m
On substituting the values of a, b, c, and d in the above formula, we get

h = 0.55 m
Now, the Reduced Level of point Q is calculated as:
RL of Q = 60 – 0.55 = 59.45 m

Reciprocal levelling is adopted to accurately determine the level difference between two points which are separated by obstacles like a river, ponds, lakes, etc.
It eliminates the following errors:

• error in instrument adjustments i.e error due to collimation
• the combined effect of Earth's curvature and the refraction of the atmosphere
• variation in the average refraction

Important Points

• Reciprocal levelling eliminates the error due to collimation and error due to curvature of Earth completely, but as the refraction depends upon the atmosphere which may change every minute;

When it is necessary to carry a levelling across a river ravine or any obstacle requiring a long site between two points so situated that no place for the level can be found from which the lens of foresight and backsight will be even approximately equal, special method that is reciprocal levelling must be used. It is used to obtain better accuracy.

When observations are taken from P the apparent difference in elevation between P and Q is 2.748 – 1.824 = 0.924. When observations are taken from Q the apparent difference in elevation between P and Q is 1.606 – 0.928 = 0.678. Hence true difference in elevation is (0.924 +0.678)/2 = 0.801 m. Therefore true elevation of Q is 126.386 – 0.801 = 125.585 m.

When observations are taken from P the apparent difference in elevation between P and Q is 2.748 – 1.824 = 0.924. When observations are taken from Q the apparent difference in elevation between P and Q is 1.606 – 0.928 = 0.678. Hence true difference in elevation is (0.924 +0.678)/2 = 0.801 mts. Error in observation = 0.924 – 0.801= 0.123 m. Error due to curvature and refraction is 0.069 mts. Therefore error in collimation is 0.123 – 0.069 = 0.054 m.

Combined correction for curvature and refraction is 0.06728 d² = 0.06728(1.010)² = 0.069 m.

Combined correction for curvature and refraction is 0.06728 d² = 0.06728(1.010)² = 0.069 mts.