What is the Bowditch rule in traverse adjustment?

Short Answer:

The Bowditch rule in traverse adjustment is a method used to correct small errors in a closed traverse by distributing the total error proportionally to the length of each traverse line. It is also called the compass rule and is suitable when both angle and distance measurements are equally reliable.

In this method, if there is a misclosure in calculated coordinates, the error is shared across all lines based on their lengths. This adjusted data gives more accurate positions and helps in preparing correct maps and layouts for engineering and boundary works.

Detailed Explanation:

Bowditch rule in traverse adjustment

The Bowditch rule, also known as the compass rule, is a mathematical method used to balance or adjust a closed traverse when there is a closing error. In surveying, when a closed traverse is conducted, it is expected that the sum of all movements (latitudes and departures) should bring the survey back to the starting point. However, due to slight errors in field measurements of angles and distances, a small difference (called closing error) usually remains.

The Bowditch rule is used to distribute this error proportionally among all the measured lines based on their lengths. It assumes that the errors in distance and angle are small and uniformly spread.

When to use Bowditch rule

This rule is most suitable when:

  • The survey is a closed traverse (starts and ends at a known point).
  • The measurements of angles and distances are equally precise.
  • The total error is small and due to natural or instrumental causes.

Steps to apply Bowditch rule:

  1. Measure all angles and distances in the traverse using a theodolite and tape/chain.
  2. Calculate bearings, then find latitudes and departures for each line using trigonometry:
    • Latitude = Length × cos(Bearing)
    • Departure = Length × sin(Bearing)
  3. Add all latitudes and departures separately. Ideally, their total should be zero in a perfect closed traverse. But usually, a small closing error exists.
  4. Calculate total error:
    • Error in Latitude = sum of all latitudes
    • Error in Departure = sum of all departures
  5. Apply Bowditch correction to each line:
    • Correction in Latitude = (Length of line / Total length of traverse) × Total error in Latitude
    • Correction in Departure = (Length of line / Total length of traverse) × Total error in Departure
  6. Adjust each line’s latitude and departure by subtracting or adding the corrections.
  7. Use the adjusted values to find the correct coordinates of all stations.

Importance of Bowditch rule

  • It provides a simple and reliable way to balance small errors.
  • It improves the accuracy of plotting and map preparation.
  • It allows surveyors to proceed confidently with corrected data, especially in land development, construction, and legal surveys.
  • It saves time and avoids repeating the whole survey for minor mistakes.

Surveyors prefer Bowditch rule for medium-sized traverses, such as housing plots, small town layouts, and farm mapping. For very large projects, more complex methods like the least squares method may be used.

Conclusion

The Bowditch rule is a method used to adjust a closed traverse by distributing errors in proportion to line lengths. It ensures that small errors in angles and distances are corrected, helping in accurate plotting and layout preparation. This rule is widely used in civil engineering for practical and quick error correction in traverse surveying.