Methodology
Every number MapBench shows you has a documented recipe. This page lists them — and their honest limits.
| Calculation | Method & accuracy | Tool |
|---|---|---|
| Distance (haversine) | Great-circle distance on the WGS84 mean sphere (R = 6371.0088 km). Error vs. the ellipsoidal geodesic ≤ ~0.3%. | Open → |
| Bearing | Initial great-circle bearing via atan2(sin Δλ·cos φ₂, cos φ₁·sin φ₂ − sin φ₁·cos φ₂·cos Δλ), clockwise from true north. Back-bearing computed independently, not ±180°. | Open → |
| Midpoint | Spherical midpoint of the great-circle arc — correct across hemispheres and the date line, unlike naive coordinate averaging. | Open → |
| Polygon area | Spherical-excess integration over the boundary (equivalent to the standard geodesic area approximation). Accurate to well under 1% for real-world plots; handles high latitudes. | Open → |
| Radius circles | 128-vertex boundaries, each vertex placed by spherical destination-point projection, so circles stay true at any latitude. | Open → |
| Routing & travel time | FOSSGIS Valhalla on OpenStreetMap roads (auto/pedestrian/bicycle costing), OSRM fallback for driving. Durations are free-flow estimates — never presented as live traffic. | Open → |
| Isochrones | Valhalla's routing-engine isochrone polygons: genuinely network-derived reachable areas, not buffers. | Open → |
| Stop optimisation | Valhalla's optimize endpoint (TSP heuristic) with the first stop fixed as origin. | Open → |
| Coordinates | Full WGS84 UTM series expansions including the Norway/Svalbard zone exceptions; standard MGRS band/grid letters; Open Location Code (Plus Code) encode/decode. | Open → |
| Sun & moon | NOAA solar position algorithm (±1 min for modern decades) with the standard 90.833° sunrise zenith for refraction; lunar phase from synodic-month age. | Open → |
| Elevation | Open-Meteo elevation API on the Copernicus GLO-90 DEM (~90 m). Profiles use 60 great-circle samples; line-of-sight adds Earth bulge x(D−x)/(2R′) with refraction k = 0.13. | Open → |
| Population in radius | Sum of curated major-city populations (≈2020 vintage, municipal figures). Published as a transparent estimate with the contributing city list, never as a census count. | Open → |
Known limitations
- The haversine sphere differs from the WGS84 ellipsoid by up to ~0.3%. Survey-grade work needs ellipsoidal geodesics and a defined CRS.
- Free routing servers return free-flow travel times; congestion is not modelled.
- The 90 m elevation DEM cannot see buildings or tree cover — line-of-sight results are terrain-only.
- Curated population datasets lag behind real growth; vintages are always labelled.
If you find a case where a result disagrees with a trusted reference by more than the stated tolerance, that's a bug we want to hear about — reproduction steps (coordinates in, values out) make it fixable.