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The scale of a map is the ratio of a distance on the map to the corresponding distance on the ground. This simple concept is complicated by the curvature of the Earth's surface, which forces scale to vary across a map. Because of this variation, the concept of scale becomes meaningful in two distinct ways.
Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude. This distance is an element in solving the second (inverse) geodetic ...
The length of the line on the linear scale is equal to the distance represented on the earth multiplied by the map or chart's scale. In most projections, scale varies with latitude, so on small scale maps, covering large areas and a wide range of latitudes, the linear scale must show the scale for the range of latitudes covered by the map. One ...
Many maps are drawn to a scale expressed as a ratio, such as 1:10,000, which means that 1 unit of measurement on the map corresponds to 10,000 of that same unit on the ground. The scale statement can be accurate when the region mapped is small enough for the curvature of the Earth to be neglected, such as a city map .
The ground-based long-distance observations cover the Earth's landscape and natural surface features (e.g. mountains, depressions, rock formations, vegetation), as well as manmade structures firmly associated with the Earth's surface (e.g. buildings, bridges, roads) that are located farther than the usual naked-eye distance from an observer.
For an observer standing on the roof of the Burj Khalifa, 828 metres (2,717 ft) from ground, and about 834 metres (2,736 ft) above sea level, the horizon is at a distance of 103 kilometres (64 mi). For an observer atop Mount Everest (8,848 metres (29,029 ft) in altitude), the horizon is at a distance of 336 kilometres (209 mi).
Each of the 60 zones uses a transverse Mercator projection that can map a region of large north-south extent with low distortion. By using narrow zones of 6° of longitude (up to 668 km) in width, and reducing the scale factor along the central meridian to 0.9996 (a reduction of 1:2500), the amount of distortion is held below 1 part in 1,000 ...
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path ...
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