Understanding Relative Closing Error in Traverse Surveying

In surveying, a traverse is a series of connected lines whose lengths and angles are measured. A closed traverse begins and ends at points with known positions, or it begins at a known point and ends at another known point. Due to inevitable errors in field measurements, a closed traverse will usually not perfectly close; the end point calculated from the measurements will not exactly coincide with the starting point (or known end point). This discrepancy is known as the closing error or error of closure.

What is Closing Error?

The closing error is the vector sum of the errors in the measured lengths and angles of the traverse. It represents the total error accumulated over the entire traverse. It can be broken down into errors in the easting and northing coordinates (or latitude and departure).

Calculating Relative Closing Error

While the total closing error gives a sense of the magnitude of the error, it's often more useful to express this error relative to the size of the traverse. This is where the relative closing error comes in. The relative closing error is the ratio of the closing error to the perimeter (total length) of the traverse. It is usually expressed as a fraction or ratio, often in the form of 1 in some number (e.g., 1 in 5000).

The formula for relative closing error is:

$$\text{Relative Closing Error} = \frac{\text{Closing Error}}{\text{Perimeter of Traverse}}$$

Sometimes, this ratio is inverted to show the precision as 1 part in 'X', where 'X' is the perimeter divided by the closing error. The question asks for the direct ratio.

Step-by-Step Calculation

Given the information:

• Perimeter of the traverse = 2000 m
• Amount of closing error = 10 m

Using the formula:

$$\text{Relative Closing Error} = \frac{10 \text{ m}}{2000 \text{ m}}$$

Now, perform the division:

$$\text{Relative Closing Error} = \frac{10}{2000}$$

$$\text{Relative Closing Error} = \frac{1}{200}$$

$$\text{Relative Closing Error} = 0.005$$

So, the relative closing error is 0.005. This can also be expressed as 1 part in 200 (1:200) when inverted ($$\frac{2000}{10} = 200$$).

Relating to the Options

The calculated relative closing error is 0.005, which matches one of the provided options.

Revision Table: Traverse Errors

Additional Information on Traverse Accuracy and Errors

Understanding and managing errors is crucial in surveying to ensure the accuracy and reliability of the survey results. Different types of errors can occur in traverse surveying:

• Instrumental Errors: Errors due to imperfections in the surveying equipment (e.g., a misaligned transit, incorrect tape length).
• Personal Errors: Errors caused by the surveyor's limitations or carelessness (e.g., inaccurate centering, poor sighting, reading errors).
• Natural Errors: Errors caused by natural conditions (e.g., temperature affecting tape length, wind affecting plumbing, refraction).

After calculating the closing error, if it exceeds the permissible limit for the project's standards, the traverse must be re-surveyed. If the error is within acceptable limits, it is typically distributed among the traverse legs using adjustment methods like the Bowditch method (Compass Rule) or the Transit Rule. These methods adjust the measured latitudes and departures to ensure the traverse mathematically closes.

The relative closing error provides a simple way to assess the overall quality of the survey fieldwork for that specific traverse. Different types of surveys and different project requirements will have varying standards for acceptable relative closing error (e.g., higher precision required for urban boundary surveys than for preliminary topographic surveys).