Adjusted Latitude: m
Adjusted Departure: m
The Compass Rule Adjustment Calculator is a surveying tool used to distribute errors in measured traverse coordinates (latitude and departure) proportionally among all traverse lines. This adjustment method ensures that the traverse closes accurately, maintaining the geometric and positional integrity of the survey. It is a fundamental part of land surveying, construction projects, and geographic analysis.
Formula of Compass Rule Adjustment Calculator
The Compass Rule adjustment calculates corrections in latitude and departure for each traverse line using these formulas:
1. Adjustment in Latitude
Correction in Latitude (C_lat) = (Total Error in Latitude × Line Length) / Traverse Perimeter
2. Adjustment in Departure
Correction in Departure (C_dep) = (Total Error in Departure × Line Length) / Traverse Perimeter
3. Adjusted Latitude and Departure
- Adjusted Latitude = Observed Latitude ± C_lat
- Adjusted Departure = Observed Departure ± C_dep
Variables:
- C_lat: Adjustment in latitude for a specific line.
- C_dep: Adjustment in departure for a specific line.
- Total Error in Latitude: ∑ Observed Latitudes – ∑ True Latitudes (closing error in latitude).
- Total Error in Departure: ∑ Observed Departures – ∑ True Departures (closing error in departure).
- Line Length: Length of the specific line being adjusted.
- Traverse Perimeter: Sum of the lengths of all traverse lines.
Steps for Calculation:
- Compute Total Errors:
Calculate the total error in latitude and departure using observed and true coordinates. - Determine Traverse Perimeter:
Sum up the lengths of all traverse lines to get the total perimeter. - Apply Corrections:
Use the formulas to distribute the errors proportionally based on line lengths. - Adjust Coordinates:
Apply corrections to the observed latitudes and departures for all traverse lines.
Useful Conversion Table
| Term | Description | Example Values/Notes |
|---|---|---|
| Total Error in Latitude | Difference between observed and true latitudes | E.g., 0.05 m |
| Total Error in Departure | Difference between observed and true departures | E.g., 0.03 m |
| Line Length | Length of a specific traverse line | E.g., 100 m |
| Traverse Perimeter | Total length of all traverse lines | E.g., 500 m |
| Adjusted Latitude | Latitude after applying correction | Depends on the calculation |
| Adjusted Departure | Departure after applying correction | Depends on the calculation |
Example of Compass Rule Adjustment Calculator
Scenario:
A traverse has three lines with the following lengths and observed coordinates:
| Line | Length (m) | Observed Latitude (m) | Observed Departure (m) |
|---|---|---|---|
| 1 | 100 | 50.2 | 30.1 |
| 2 | 200 | 80.4 | 50.3 |
| 3 | 150 | 60.6 | 40.5 |
- Total Errors:
- Total Error in Latitude = 0.05 m
- Total Error in Departure = 0.03 m
- Traverse Perimeter:
100 + 200 + 150 = 450 m
Step 1: Calculate Corrections for Each Line
- For Line 1:
C_lat = (0.05 × 100) / 450 = 0.0111 m
C_dep = (0.03 × 100) / 450 = 0.0067 m - For Line 2:
C_lat = (0.05 × 200) / 450 = 0.0222 m
C_dep = (0.03 × 200) / 450 = 0.0133 m - For Line 3:
C_lat = (0.05 × 150) / 450 = 0.0167 m
C_dep = (0.03 × 150) / 450 = 0.0100 m
Step 2: Adjust Coordinates
- For Line 1:
Adjusted Latitude = 50.2 ± 0.0111 = 50.189
Adjusted Departure = 30.1 ± 0.0067 = 30.093 - Repeat similar calculations for Lines 2 and 3.
Most Common FAQs
The Compass Rule ensures that the traverse is mathematically closed by proportionally distributing measurement errors, which improves accuracy and reliability in land surveys.
The Compass Rule works best for small, systematic errors. Significant measurement errors may require additional analysis or re-measurements.
The traverse perimeter is the sum of the lengths of all traverse lines in the survey, providing a basis for proportional error distribution.