Which of the following are the total linear errors of closure in the compass traverse?
1 in 600
Understanding Total Linear Error of Closure in Compass Traverse
In surveying, a traverse is a series of connected lines whose lengths and directions are measured. When a traverse closes back to the starting point or connects two known points, the sum of the latitudes and the sum of the departures should theoretically be zero (for a closed loop) or equal to the difference in coordinates between the start and end points (for an open traverse connecting known points).
However, due to errors in measurement (both linear and angular), the traverse will not perfectly close. The discrepancy between the theoretical closure point and the actual closure point is called the error of closure.
What is Total Linear Error of Closure?
The total linear error of closure (\(E\)) is the straight-line distance between the starting point and the closing point of a closed traverse after calculating the latitudes and departures of all lines. It can be calculated using the Pythagorean theorem:
$$E = \sqrt{(\sum \text{Lat})^2 + (\sum \text{Dep})^2}$$
Where:
- \(\sum \text{Lat}\) is the sum of the latitude errors (algebraic sum of latitudes).
- \(\sum \text{Dep}\) is the sum of the departure errors (algebraic sum of departures).
Precision of a Traverse
The precision of a traverse indicates the accuracy relative to its size. It is often expressed as a ratio of the total linear error of closure to the total length of the traverse (\(L\)).
$$ \text{Precision Ratio} = \frac{E}{L} = \frac{1}{\text{something}} $$
A smaller ratio (meaning a larger number in the denominator) indicates higher precision.
Typical Precision for Different Traverse Types
The achievable precision depends largely on the instruments and methods used for measuring angles and distances. Here are some typical ranges:
- Compass Traverse: Angles are measured using a magnetic compass. This method is less precise due to variations in magnetic declination and difficulty in reading angles precisely. Typical precision is often in the range of 1 in 300 to 1 in 600, or sometimes up to 1 in 1000.
- Transit Traverse: Angles are measured with a transit or theodolite, which is more precise than a compass. Distances are typically measured with a tape or chain. Typical precision is often in the range of 1 in 1,000 to 1 in 5,000.
- EDM Traverse: Angles are measured with a theodolite, and distances with an Electronic Distance Measurement (EDM) device. This method offers high precision. Typical precision can range from 1 in 5,000 to 1 in 25,000 or even higher for precise work.
Analyzing the Options
We are asked about the total linear errors of closure for a compass traverse. Let's look at the options:
- 1 in 600: This ratio falls within the typical range for a compass traverse precision.
- 1 in 5000: This ratio indicates a much higher precision, usually achieved with transit or EDM.
- 1 in 10000: This ratio indicates high precision, typical of EDM traverses or precise transit work.
- 1 in 25000: This ratio indicates very high precision, common in high-order surveys using EDM and precise angular measurements.
Comparing the options to the typical precision ranges, 1 in 600 is the ratio that aligns with the expected precision of a compass traverse.
| Traverse Type | Typical Precision Range |
|---|---|
| Compass Traverse | 1 in 300 to 1 in 1,000 (often around 1 in 600) |
| Transit Traverse | 1 in 1,000 to 1 in 5,000 |
| EDM Traverse | 1 in 5,000 to 1 in 25,000+ |
Therefore, among the given options, 1 in 600 represents a realistic total linear error of closure precision for a compass traverse.
Revision Table: Key Surveying Traverse Concepts
| Concept | Description |
|---|---|
| Traverse | A series of connected survey lines. |
| Closed Traverse | Starts and ends at the same point, or starts and ends at points with known coordinates. |
| Open Traverse | Starts at a known point but does not close on itself or a point with known coordinates. Not typically used for control surveys as error checks are limited. |
| Error of Closure | The discrepancy between the computed position and the actual position of the closing point. |
| Precision | The degree of consistency between multiple measurements. Expressed as a ratio of error to total length. |
Additional Information: Sources of Error in Traversing
Errors in traversing can arise from various sources, affecting the total linear error of closure:
- Angular Measurement Errors:
- Inaccurate instrument centering or leveling.
- Improper pointing to targets.
- Reading errors on the instrument circle.
- Magnetic variations affecting compass readings.
- Linear Measurement Errors:
- Incorrect tension or sag in tapes.
- Poor alignment of the tape.
- Incorrect plumbing or horizontal measurement over sloping ground.
- Temperature or standardization errors in tapes.
- Atmospheric conditions affecting EDM measurements.
- Target Centering Errors:
- Target (e.g., prism pole) not centered directly over the station marker.
Minimizing these errors through careful field procedures and instrument calibration is crucial for achieving better traverse precision.
Important Questions from Traverse Surveying
The included angles of a theodolite traverse are generally measured as
If the perimeter of traverse is 2000 m and the amount of closing error is 10 m, then the relative closing error would be:
There are certain checks adopted for traversing the angular work. In this regard, the sum of all the exterior angles of a closed traverse having six sides is equal to
Generally, in chain triangulation, well-conditioned triangles are used for surveying. A triangle is said to be well-conditioned when no angle in it is
If the reduced bearing of a line AB is N60° W and the length is 100 m, then the latitude and departure of the line AB will be,
