Minor / Link Gale's Table Generator
| Line | Length (m) | WCB Bearing (° ' ") | Horiz. Angle (optional) Enter if WCB is unknown — auto-computes WCB |
|||||
|---|---|---|---|---|---|---|---|---|
| D° | M′ | S″ | D° | M′ | S″ | |||
Closed Traverse? Use the Major Gale's Table Generator
Minor & Link Traverse — Theory, Formulas & Checks
1. What is a Minor (Open) Traverse?
A minor traverse (open traverse) is a series of survey legs that starts at one point and ends at a different, unconnected point. It has no closure condition — it cannot form a closed polygon. No mathematical correction can be applied from the traverse data alone.
Key limitation: Any error in a measured bearing or length propagates into all subsequent station coordinates with no way to detect or correct it from the Gale's Table alone. Open traverses should always be connected to known control at both ends wherever possible.
2. What is a Link Traverse?
A link traverse connects two known control points at different locations. The start coordinates (E₀, N₀) and the end coordinates (Eend, Nend) are both known. This allows computation of a closing error and application of the Bowditch (compass rule) correction — exactly the same correction used in a closed traverse.
Best practice: Always connect an open survey to known control points at both ends, making it a link traverse. This provides a closure check and allows corrections to be applied.
3. WCB → Reduced (Quadrant) Bearing
Whole Circle Bearing (WCB) 0°–360° is converted to a quadrant bearing for lat/dep computation:
| WCB Range | Quadrant | QB Formula | Lat Sign | Dep Sign |
|---|---|---|---|---|
| 0° to 90° | NE | N θ E (θ = WCB) | +N | +E |
| 90° to 180° | SE | S θ E (θ = 180° − WCB) | −S | +E |
| 180° to 270° | SW | S θ W (θ = WCB − 180°) | −S | −W |
| 270° to 360° | NW | N θ W (θ = 360° − WCB) | +N | −W |
4. Latitude and Departure
5. Running Northing and Easting
6. Link Traverse Closing Error and Bowditch Correction
For a link traverse with known start (N₀, E₀) and known end (Nend, Eend):
Closing error: δL = Σ Lat − Theoretical ΔN δD = Σ Dep − Theoretical ΔE
Linear closing error: e = √(δL² + δD²) Precision = 1 : (ΣL / e) δL and δD are the errors to be distributed. Negative if measured sum is less than theoretical.
Corrected Latitudei = Latitudei + cL,i Corrected Departurei = Departurei + cD,i Sum of all cL = −δL exactly. Sum of all cD = −δD exactly. Corrected running coords reach known end point.
Check: After applying corrections, ΣCorrLat = Theoretical ΔN and ΣCorrDep = Theoretical ΔE. The final corrected running coordinate must exactly equal (Nend, Eend).
7. Bearing Propagation from Included Angles
If horizontal (included/interior) angles are measured at each station instead of direct WCB bearings:
WCBBC = (BackBearingAB + Included angle at B) mod 360° Included angle at B = angle measured clockwise from direction BA to direction BC.
8. Precision Standards
| Survey Type | Precision Ratio | Application |
|---|---|---|
| Rough/reconnaissance | 1 : 500 – 1 : 1000 | Preliminary surveys, sketch plans |
| Ordinary engineering | 1 : 1000 – 1 : 3000 | Road alignments, earthworks, rough setting-out |
| Good engineering | 1 : 3000 – 1 : 10,000 | Building setting-out, detailed engineering surveys |
| First-order control | > 1 : 25,000 | National control, precise boundary surveys |
Frequently Asked Questions
1. What is the difference between a minor traverse and a link traverse?
A minor (open) traverse starts at one known point and ends at an unconnected point — there is no closure condition and no way to detect or correct errors. A link traverse connects two known control points at different locations — the known end coordinates allow computation of a closing error (δL, δD) and application of Bowditch corrections, giving a quality-checked, corrected set of coordinates for all intermediate stations.
2. Why is there no Bowditch correction in a minor (open) traverse Gale's Table?
Bowditch correction requires a known closing error. For an open traverse, the theoretical ΔN and ΔE are unknown (the end station has no known coordinates). Without a theoretical sum to compare against, there is no closing error to compute and nothing to distribute. For a link traverse, the known end coordinates provide this theoretical sum, enabling Bowditch corrections.
3. How does this tool compute the Bowditch correction for a link traverse?
1) Compute all raw latitudes and departures. 2) Sum them: ΣLat, ΣDep. 3) Compute theoretical: ΔN = N_end − N_start, ΔE = E_end − E_start. 4) Closing errors: δL = ΣLat − ΔN, δD = ΣDep − ΔE. 5) Bowditch correction per leg: cL_i = −δL × (l_i / ΣL), cD_i = −δD × (l_i / ΣL). 6) Corrected lat/dep for each leg. 7) Corrected running coordinates that close exactly at the known end point.
4. What is WCB and how is it converted to a quadrant bearing?
WCB (Whole Circle Bearing) is measured clockwise from north, 0°–360°. For the Gale's Table: NE quadrant (WCB 0–90°): QB = N(WCB)E. SE quadrant (90–180°): QB = S(180−WCB)E. SW quadrant (180–270°): QB = S(WCB−180)W. NW quadrant (270–360°): QB = N(360−WCB)W. The quadrant bearing angle θ is always 0°–90° and determines the signs of latitude (cos θ) and departure (sin θ).
5. How are latitudes and departures calculated?
For each leg: Latitude = L × cos(θ_QB). Departure = L × sin(θ_QB). The sign depends on the quadrant: NE(+Lat, +Dep), SE(−Lat, +Dep), SW(−Lat, −Dep), NW(+Lat, −Dep). In the Gale's Table, positive latitudes go in the +N column and negative latitudes in the −S column. Similarly for departures.
6. How can I enter angles instead of WCB bearings?
Use the optional Horiz. Angle columns (D, M, S) in the input table. Enter the included/interior angle at each station (measured clockwise from the back-sight to the fore-sight). The tool computes WCBs automatically using: WCB_next = (BackBearing(WCB_prev) + included_angle) mod 360°. You still need the WCB of the first leg (or the starting bearing from the first station).
7. What check should I perform after generating a link traverse table?
1) ΣCorrLat must equal N_end − N_start exactly. 2) ΣCorrDep must equal E_end − E_start exactly. 3) The final corrected running Northing must equal N_end, and the final corrected running Easting must equal E_end. 4) The precision ratio (ΣL / closing error e) should meet the required standard for the project. Any discrepancy in checks 1–3 indicates an arithmetic error.