Coordinates & Traversing

Every point in a mine has coordinates (Easting, Northing, Elevation/RL). Learn mine grids and datums, bearings and distances, latitudes and departures (ΔN, ΔE), the join (inverse) calculation, traverses, misclosure and precision, and the Bowditch adjustment.

Surveyors are the eyes of a mine: they set out drill holes, blast patterns, drives and pit limits, and measure what has actually been mined. All this relies on a consistent coordinate system tied from surface to underground.

An analogy

Traversing is like giving walking directions — 'go 125 m on bearing 63°, then 90 m on bearing 150°' — and checking you arrive back where you started.

Mine grids

Mines use a local grid or a national projection (UTM). A mine grid often rotates to align with the orebody strike and uses a false origin so all coordinates are positive. Elevation is the reduced level (RL), often with + 1000 m or + 5000 m added to avoid negative values underground.

Traverses

A traverse is a series of connected survey lines. Closed traverses start and finish on known points, so errors can be detected and distributed. Underground, traverses are the backbone of control, extended as development advances.

Errors and adjustment

Angular misclosure is checked against (n − 2) × 180° for polygons. Linear misclosure is expressed as a ratio (e.g. 1:10 000). Bowditch (compass rule) distributes corrections proportional to line length; least squares is the rigorous method.

Geodesy in mining

Scale factors between ground and grid distances, geoid models for RL from GNSS, and datum transformations must be applied consistently — errors of metres have caused drives to miss their targets.

Formulas

• Departure and latitude: ΔE = L sin θ, ΔN = L cos θ
• Join (inverse): L = √(ΔE² + ΔN²), θ = atan2(ΔE, ΔN)
• Misclosure: e = √(ΣΔE² + ΣΔN²) for a closed loop
• Precision: 1 : (perimeter / e)
• Bowditch correction: δE_i = −ΣΔE × L_i / ΣL

Worked example: Departure and latitude

Given: Line 125.40 m on bearing 63°15′

Find: ΔE, ΔN.

• ΔE = 125.40 × sin 63.25° = 111.98 m
• ΔN = 125.40 × cos 63.25° = 56.44 m

Answer: ΔE +111.98, ΔN +56.44

Worked example: Traverse precision

Given: Closed traverse perimeter 1450 m; ΣΔE = +0.12 m, ΣΔN = −0.09 m

Find: Misclosure and precision.

• e = √(0.12² + 0.09²) = 0.15 m
• Precision = 1 : 1450/0.15 = 1 : 9667

Answer: ≈ 1 : 9700

Common mistakes

• Wrong: Using atan(ΔE/ΔN) without quadrant check. — Right: Use atan2 or check signs of ΔE and ΔN.
• Wrong: Mixing mine grid and UTM coordinates. — Right: Document and transform consistently.

Applications

• Setting out: Drill holes, blast patterns, drive centrelines.
• Survey control: Traverses extending into new development.
• Mine plans: Statutory plans of workings and boundaries.

Key takeaways

• ΔE = L sin θ, ΔN = L cos θ.
• Join with atan2 for correct quadrant.
• Check misclosure and precision.
• Keep one consistent mine grid.

Going further

• Least-squares adjustment: Rigorous network adjustment with error ellipses.
• Grid scale factors: Correcting ground distances to projection.
• Geoid models: Converting GNSS ellipsoidal heights to RL.