---
title: "Define relative misclosure ratio"
subject: "Surveying I"
chapter: 4
key: "semester_3/surveying_i:define-relative-misclosure-ratio"
source: https://www.bctengineer.com/q/semester_3/surveying_i/define-relative-misclosure-ratio
site: BCT Engineering
---

# Define relative misclosure ratio

Surveying I · Chapter 4: The Compass

- Asked in: 2081 Baisakh, 1 marks
- Video: [Traverse Calculations // Surveying](https://www.youtube.com/watch?v=mMDcODSe_ic) — engiNERDing
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/define-relative-misclosure-ratio
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-4

## Question

Define relative misclosure ratio.

## Short answer

Relative misclosure (precision) ratio is the ratio of the linear closing error √((ΣL)²+(ΣD)²) to the total perimeter length, expressed as 1/N. It indicates survey accuracy; a larger N means higher precision.

## Answer

The **relative misclosure (precision) ratio** is the linear closing error of a traverse divided by the total length (perimeter) of the traverse, written as 1 in N:

$$
\text{Relative misclosure} = \frac{\sqrt{(\Sigma L)^2 + (\Sigma D)^2}}{\text{Perimeter}} = \frac{1}{N}
$$

where $\Sigma L$ and $\Sigma D$ are the sums of latitudes and departures. It measures the accuracy of the traverse; a larger N means a better survey.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Relative misclosure is:
   A. Angular error divided by number of angles
   B. Sum of latitudes divided by sum of departures
   C. Linear closing error divided by the perimeter
   D. Perimeter divided by closing error squared
   Answer: C. It equals closing error / perimeter, written as 1 in N. (Key point: Definition)

2. The linear closing error is computed as:
   A. ΣL + ΣD
   B. ΣL x ΣD
   C. (ΣL + ΣD)/2
   D. sqrt((ΣL)^2 + (ΣD)^2)
   Answer: D. It is the resultant of the sum of latitudes and sum of departures. (Key point: Closing error formula)

3. A larger N in 1 in N means:
   A. A more accurate traverse
   B. A less accurate traverse
   C. A longer traverse only
   D. A larger angular error
   Answer: A. A bigger N means the error is a smaller fraction of the perimeter. (Key point: Meaning of N)

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