Traverse Method with Compass Rule (Bowdith rule)

The Traverse Method with Compass Rule is a technique used in surveying to determine the positions of a series of points, typically used for establishing boundaries or mapping out areas. It involves measuring angles and distances to create a series of connected lines, or a traverse, which is then adjusted to correct any errors. Here’s a detailed explanation, including an example and relevant formulas:

Overview of the Traverse Method with Compass Rule

1. Setup and Measurement:

- Traverse: A series of connected lines between points (stations) where measurements are taken.

-Compass Rule: A method to adjust the traverse to correct for errors in measurements, assuming a closed loop or boundary.

2. Key Measurements:

- Distances: Measured between points.

- Angles: Measured at each point to determine direction changes.

Traverse Procedure

1. Field Measurements:

- Measure Distances: Use a tape measure or total station to measure the distances between traverse points.

- Measure Angles: Use a theodolite or a compass to measure horizontal angles at each point.

2. Data Recording:

- Record the measurements in a field book, noting the distances and angles between each pair of traverse points.

Compass Rule Adjustment

The Compass Rule is a balancing method that distributes the errors in a traverse proportionally to the lengths of the lines. It is used in the adjustment process to ensure that the traverse is as accurate as possible.

1. Calculate the Error:

If the traverse is a closed loop, compute the error by finding the difference between the starting and ending points. If the traverse is open, you need to close it by adding the missing lines.

- Closed Traverse Error Calculation:

 

2. Apply the Compass Rule:

Distribute the error proportionally to the lengths of the traverse lines.

- Correction for each line:

 

3. Adjust the Measurements:

- Distance Adjustments: Add or subtract the corrections from the measured distances.

- Angle Adjustments: Distribute the angle error proportionally along the traverse lines.

Example of a Traverse Method with Compass Rule

1. Field Measurements:

Let’s say we have a closed traverse with four points (A, B, C, and D), and the following measurements:

- AB: 100 meters

- BC: 120 meters

- CD: 110 meters

- DA: 90 meters

Angles measured at each point:

- ∠ABC: 90°

- ∠BCD: 90°

- ∠CDA: 90°

- ∠DAB: 90°

2. Calculate Closure Error:

Assuming you’ve computed coordinates and found the closure error to be 5 meters.

3. Apply Compass Rule:

Total Length:

Total Length=100+120+110+90=420 meters

Corrections:

Correction for AB=5x100/420=1.19 meters

Correction for BC=5x120/420​=1.43 meters

Correction for CD=5x110/420=1.31 meters

Correction for DA=5x90​/420=1.07 meters

Adjusted Distances:

- AB: 100 - 1.19 = 98.81 meters

- BC: 120 - 1.43 = 118.57 meters

- CD: 110 - 1.31 = 108.69 meters

- DA: 90 - 1.07 = 88.93 meters

4. Final Adjustments:

Use the corrected distances to update the traverse and adjust the angles if necessary, ensuring the traverse is balanced and as accurate as possible.

Conclusion

The Traverse Method with Compass Rule is a systematic approach to surveying that helps in creating accurate maps and layouts by compensating for measurement errors. By following these steps and applying the Compass Rule, you ensure that the final traverse is reliable and precise.