Question

For land survey using theodolite, if N is the number of sides of a closed traverse, then the angular error of closure in minutes should not exceed

• A. $\sqrt{N}$
• B. $10\sqrt{N}$
• C. $15\sqrt{N}$
• D. $30\sqrt{N}$

Hint:

The allowable error in a traverse is generally proportional to the square root of the number of measurements ($\sqrt{N}$).
This is a common principle in statistics for random errors.
For angular closure, remember the formula $e = c \sqrt{N}$. For a simple rule in minutes, $c$ is often taken as 1.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the permissible limit of the angular error of closure for a theodolite traverse, as a function of the number of sides, $N$.

Step 2: Detailed Explanation:
When measuring the angles of a closed traverse, small instrumental and observational errors will accumulate. The

angular error of closure is the difference between the measured sum of the angles and the theoretical sum (e.g., $(n-2) \times 180^\circ$ for interior angles).
To determine if a survey is accurate enough, this error is compared against a permissible limit. The permissible error depends on the precision of the instrument and the required accuracy of the survey.
For a standard theodolite traverse, a common rule for the permissible error of closure, $e$, is given by:
\[ e = c \sqrt{N} \] where $N$ is the number of angles (or sides), and $c$ is a constant that depends on the precision. The constant $c$ is often the least count of the instrument.
For a 20" theodolite, a common allowable error is $e \le 20" \sqrt{N}$.
The question asks for the error in minutes. $1' = 60"$. So, $20" = (1/3)'$.
The question seems to be based on a simplified rule or a specific standard where the constant is 1 minute. A widely cited rule for lower-order traverses is that the permissible error in minutes should not exceed $\sqrt{N}$. This is a common rule-of-thumb found in many textbooks.

Step 3: Final Answer:
A common permissible limit for the angular error of closure in minutes for a theodolite traverse is $\sqrt{N}$, where N is the number of sides.