For a closed traverse, the sum of latitudes is 4 m and the sum of departures is 3 m. The closing error for the traverse would be.

🧭 Understanding Latitude, Departure, and Closing Error

In surveying, a traverse is broken down into its fundamental components to check for accuracy.

• Latitude: It is the projection of a survey line onto the North-South axis. It's calculated as L cos(θ), where L is the line's length and θ is its bearing. Northings are positive (+), and Southings are negative (-).
• Departure: It is the projection of a survey line onto the East-West axis. It's calculated as L sin(θ). Eastings are positive (+), and Westings are negative (-).
• Closing Error: In a perfect closed traverse, the survey should end exactly where it started. This means the sum of all latitudes (∑L) and the sum of all departures (∑D) should both be zero. Due to measurement imperfections, there's often a gap. The length of this gap is the closing error.

🔬 Step-by-Step Calculation

The closing error is calculated using the Pythagorean theorem on the sum of latitudes and departures.

Given Data:

• Sum of Latitudes (∑L) = 4 m
• Sum of Departures (∑D) = 3 m

Formula:

Closing Error (e) = √[ (∑L)² + (∑D)² ]

Calculation:

e = √[ (4)² + (3)² ]

e = √[ 16 + 9 ]

e = √[ 25 ]

e = 5 m

🗺️ Visualizing Latitude and Departure

The diagram below shows how a single survey line is projected onto the cardinal axes to find its latitude and departure components.