About Traverse Closure & Bowditch Adjustment Calculator
The traverse closure calculator checks how well a closed-loop survey traverse closes and then balances it using the Bowditch (compass-rule) method. For each leg it resolves the measured bearing and distance into a latitude (the change in Northing) and a departure (the change in Easting). For a perfectly closed traverse the latitudes and departures each sum to zero; in practice small measurement errors leave residuals that constitute the misclosure.
The linear misclosure is the straight-line distance sqrt(sumLat² + sumDep²) between where the traverse should close and where it actually closes. Dividing the perimeter by the misclosure gives the relative precision, conventionally written 1:N. The Bowditch rule then distributes the misclosure back into each leg in proportion to its length, producing adjusted latitudes, departures, and a balanced set of station coordinates that close exactly.
How It Works
- Enter each leg of the closed traverse as a whole-circle bearing (azimuth, clockwise from North, 0–360°) and a horizontal distance; at least three legs are required.
- The calculator computes latitude = L·cos(bearing) and departure = L·sin(bearing) for every leg and sums them.
- The misclosure in latitude and departure are combined into the linear misclosure, and the relative precision is reported as perimeter ÷ misclosure (1:N).
- The Bowditch adjustment applies a correction to each leg of −sumComponent × (legLength ÷ perimeter), giving adjusted latitudes and departures that sum to zero and a closed set of coordinates.
Worked Example
A four-leg traverse runs N (0°) 100 m, E (90°) 100 m, S (180°) 100 m, and W (270°) 99 m. The latitudes are +100, 0, −100, 0 (sum = 0) and the departures are 0, +100, 0, −99 (sum = +1). The linear misclosure is sqrt(0² + 1²) = 1.000 m over a 399 m perimeter, a relative precision of 1:399. The Bowditch departure correction for the first 100 m leg is −1 × (100 ÷ 399) = −0.2506 m; once every leg is corrected in proportion to its length the adjusted departures sum to zero and the traverse closes.
Formulas
- Latitude and departure of a leg
latitude = L * cos(bearing); departure = L * sin(bearing)- Linear misclosure
e = sqrt( (sum latitudes)^2 + (sum departures)^2 )- Relative precision
precision = perimeter / e (reported as 1 : N, N = perimeter / e)- Bowditch (compass-rule) correction
latCorr_i = -(sum latitudes) * (L_i / perimeter); depCorr_i = -(sum departures) * (L_i / perimeter)
Standards & References
- Bowditch (compass) rule
- Closed-traverse balancing
- Plane / coordinate surveying
- Ghilani & Wolf, Elementary Surveying
Frequently Asked Questions
What bearing convention does the calculator use?
It uses the whole-circle bearing, also called the azimuth: an angle measured clockwise from North between 0 and 360 degrees. Latitude is L·cos(bearing) and departure is L·sin(bearing), so a bearing of 90° points due East and 180° points due South.
How is the relative precision interpreted?
Relative precision is the perimeter divided by the linear misclosure, written 1:N. A result of 1:5000 means the misclosure is one part in five thousand of the distance traversed; larger N values indicate a more accurate, tighter-closing traverse.
Why use the Bowditch rule rather than the transit rule?
The Bowditch (compass) rule distributes the misclosure in proportion to each leg’s length, which assumes angle and distance measurements are of comparable precision. It is the most widely used balancing method for ordinary traverses. The transit rule instead distributes by the magnitude of each latitude or departure and suits traverses where angles are more precise than distances.
Does the traverse have to close back to its start?
This tool is for a closed-loop traverse that begins and ends at the same station, so the latitudes and departures should each sum to zero. The residual sums are the misclosure that the Bowditch adjustment removes so the balanced coordinates close exactly.