Cartography and Map Projections
Cartography questions test whether you can pick a projection for a purpose and quantify the distortion it introduces.
Projection families
- Conformal projections (Mercator, Transverse Mercator, Lambert Conformal Conic) preserve angles and local shape and distort area away from the line of zero distortion.
- Equal-area projections (Albers, Mollweide) preserve area and distort shape.
- Equidistant projections preserve distance only along specific lines - never everywhere.
- UTM has 60 zones of 6° longitude using Transverse Mercator with central-meridian scale factor k₀ = 0.9996, false easting 500 000 m, and false northing 0 in the northern hemisphere or 10 000 000 m in the southern.
Scale factor and convergence
Point scale factor rises with distance from the central meridian: k ≈ k₀[1 + x²/(2R²)], where x is the distance from the central meridian. Grid distance = ground distance × k, so observations must be reduced to the projection before comparison with grid coordinates. Grid convergence is the angle between grid north and true north.
Worked example: a point 100 km from the central meridian, with R = 6371 km. x²/(2R²) = 10 000 000 000 / (2 × 6 371 000²) = 1.232 × 10⁻⁴. k = 0.9996 × 1.0001232 = 0.999723. A ground distance of 1000.000 m therefore appears as 999.723 m on the grid; converting back, ground = grid / k.
Design and generalisation
Generalisation operators are selection, simplification, smoothing, aggregation, displacement and exaggeration. The classification method (equal interval, quantile, natural breaks) changes the map's message more than the projection does.
Traps
- Applying the scale factor to areas as k rather than k².
- Ignoring the systematic 0.9996 factor: over 1 km that is about 0.4 m, a real blunder in engineering work.
- Using Web Mercator for area or distance measurement; it is conformal but grossly distorts area at high latitude.