While carrying out a traverse survey ABCDA' using a theodolite with the originating station A, the departures and latitudes of the lines, as obtained, are shown in the following figure (not drawn to scale). It is seen that, due to the observational errors, the originating station A and its computed station A' are not the same. For this survey, the 'closing error' in m is 
The closing error in a traverse survey represents the distance between the starting point \(A\) and the final calculated point \(A'\). It occurs due to observational errors in measurements. To find it, we first determine the algebraic sum of the latitudes and departures for each leg of the traverse based on the provided figure.
1. Tabulating Latitudes and Departures
In surveying, Latitude refers to the north-south component (positive for North, negative for South), and Departure refers to the east-west component (positive for East, negative for West).
- Line AB:
- Latitude (\(L_1\)) = \(+2 \text{ m}\) (Upward)
- Departure (\(D_1\)) = \(+9 \text{ m}\) (Rightward)
- Line BC:
- Latitude (\(L_2\)) = \(-12 \text{ m}\) (Downward)
- Departure (\(D_2\)) = \(+6 \text{ m}\) (Rightward)
- Line CD:
- Latitude (\(L_3\)) = \(-7 \text{ m}\) (Downward)
- Departure (\(D_3\)) = \(-10 \text{ m}\) (Leftward)
- Line DA':
- Latitude (\(L_4\)) = \(+10 \text{ m}\) (Upward)
- Departure (\(D_4\)) = \(-8 \text{ m}\) (Leftward)
2. Calculating Total Error Components
Now, we find the algebraic sum of latitudes (\(\sum L\)) and departures (\(\sum D\)):
$$\sum L = (+2) + (-12) + (-7) + (+10) = -7 \text{ m}$$
$$\sum D = (+9) + (+6) + (-10) + (-8) = -3 \text{ m}$$
3. Determining the Closing Error
The total closing error (\(e\)) is the resultant of the total errors in latitude and departure, calculated using the Pythagorean theorem:
$$e = \sqrt{(\sum L)^2 + (\sum D)^2}$$
Substituting the values:
$$e = \sqrt{(-7)^2 + (-3)^2}$$
$$e = \sqrt{49 + 9} = \sqrt{58}$$
$$e \approx 7.61577 \text{ m}$$
Rounding to two decimal places, we get:
$$e \approx 7.62 \text{ m}$$
Conclusion
The 'closing error' for the survey is 7.62 m.
Important Questions from Traversing
- The forebearing of four sides of a closed quadrilateral ABCDA are
AB = 60°, BC = 149.87°, CD = 269.5°, DA = 20.17°.
The calculated value of interior angle D is _____° (Answer in decimal degrees and rounded off to two decimal values). The angular misclosure of the closed-loop traverse shown in the figure is _____________ ° (Answer in decimal degrees and rounded off to three decimal places)
- It is needed to establish the coordinates of a station A. Two stations B and C are available whose coordinates are given in the table.
Length of line CA = 1212.38 m; ∠BCA = 64°.
The Easting of station A is _______ m (Rounded off to two decimal places).
Assume station A lies to the west of the traverse line BC.Station Easting (m) Northing (m) B 11054.09 9484.37 C 10827.62 10112.15 - If the departure and latitude of a line are 70 m and -130 m, respectively, then the whole circle bearing of the line in degrees is
Figure below shows an open traverse PQRS, where P is the starting point of traverse and S is the end point of traverse. Which one of the following is correct?
