What is said about that traverse when total latitude and departure are zero ?

Question

Examoogle · Accepted Answer

Option D: Both A and B

Explanation & Concepts:
When the sum of all latitudes ($\sum L$) and the sum of all departures ($\sum D$) are both equal to zero, it signifies that the survey starts and ends at the exact same point, defining a closed traverse. Furthermore, this condition means there is no closing error, and the traverse is perfectly balanced mathematically.

Working Principle: In surveying, latitude is the north-south component ($L = L \cos 	heta$) and departure is the east-west component ($D = L \sin 	heta$) of a line. For a closed loop traverse, the algebraic sum of latitudes must equal zero (total northing equals total southing) and the algebraic sum of departures must equal zero (total easting equals total westing). When these conditions are satisfied, the total displacement is zero, confirming both a closed traverse and complete balancing.

Key Formulas: $\sum L = 0$ — Sum of latitudes for a balanced closed traverse; $\sum D = 0$ — Sum of departures for a balanced closed traverse; $e = \sqrt{(\sum L)^2 + (\sum D)^2}$ — Closing error magnitude

Key Points: Latitude ($L$) is the projection of a traverse line on the north-south meridian ($L = l \cos 	heta$).; Departure ($D$) is the projection of a traverse line on the east-west reference line ($D = l \sin 	heta$).; When $\sum L = 0$ and $\sum D = 0$, the closing error $e = 0$, representing a perfectly balanced closed traverse.

Advantages: Ensures geometric consistency and closure in field surveying control networks.; Eliminates linear misclosure, allowing precise boundary mapping and area computation.

Disadvantages: Does not guarantee the total absence of systematic or compensating operational errors that cancel each other out.; Requires high precision in both angular and linear measurements to achieve zero closing error naturally.

Applications: Establishment of horizontal control networks for major civil engineering projects.; Cadastral survey, land boundary determination, and topographic mapping.

Additional Info: Option A is correct because when total latitude and departure are zero, the traverse requires no further corrections and is considered balanced.. Option B is correct because a closed traverse forms a closed loop returning to the origin where total latitude and departure algebraically sum to zero.. Option C is incorrect because closing error exists when $\sum L 
eq 0$ or $\sum D 
eq 0$.

Answer: D is correct — Total latitude and departure being zero defined a perfectly closed traverse with zero closing error, representing a fully balanced condition.

Exam Tip: In exam problems, if $\sum L 
eq 0$ or $\sum D 
eq 0$, the direction (bearing) of the closing error is given by $	an 	heta = \frac{\sum D}{\sum L}$.

Examoogle · Answer

Option A: Balancing of the traverse

Examoogle · Answer

Option B: Closed traverse

Examoogle · Answer

Option C: Closing error

Correct Answer

Discussion (0)

Correct Answer

Related Questions

Discussion (0)