Gnomonic projection
Definition
A gnomonic projection is a specific type of azimuthal map projection created by projecting points from the center of the Earth onto a plane that is tangent to the Earth's surface at a single point; its most critical and defining property is that all great circles (the shortest paths between two points on a sphere) are represented as straight lines on the map, making it uniquely valuable for navigation, as it allows navigators to plot a direct great-circle route simply by drawing a straight line between the origin and destination, although this useful property comes at the extreme cost of extreme scale, area, and shape distortion that increases rapidly with distance from the center of projection, limiting its practical use to a relatively small area around the tangent point.
Application
The quintessential practical application of the Gnomonic projection is in long-range air and sea navigation for plotting the shortest path. A navigator can place a Gnomonic chart with its tangent point centered on their port of departure, plot their destination, and draw a straight line between them�this line represents the great-circle route, the true shortest distance over the Earth's curvature. While this straight line cannot be followed as a constant compass bearing, its coordinates are then transferred to a Mercator chart for actual sailing or flying, as the Mercator represents constant bearing (rhumb lines) as straight lines. This two-step process, using the Gnomonic to find the optimal path and the Mercator to navigate it, is fundamental for efficient global routing.
FAQ
What is the unique, most useful property of the Gnomonic projection?
Its unique and most critical property is that all great circles appear as straight lines on the map. A great circle is the shortest path between any two points on a sphere. This makes the Gnomonic projection the only projection where you can find the absolute shortest route between two points simply by drawing a straight line between them on the chart.
If it shows the shortest route as a straight line, why can't I just sail or fly along that line using this map?
While the great-circle route is straight on the Gnomonic map, it corresponds to a constantly changing compass bearing (azimuth) in reality. You cannot steer a constant course to follow it directly from this chart. Instead, the Gnomonic is used as a planning tool: you plot the straight-line great-circle route on it, determine a series of intermediate points (waypoints) along that line, and then plot those coordinates on a Mercator chart, where you can navigate by following constant bearings (rhumb lines) between each waypoint.
Why is the distortion on a Gnomonic map so extreme?
The extreme distortion is a direct mathematical consequence of its construction. Points are projected from the center of the Earth onto a tangent plane. This causes scale to increase infinitely as you move away from the center point; a hemisphere would theoretically project to an infinitely large plane. Therefore, it can only show less than one hemisphere and is unusable beyond about 60-70 degrees from the center. Area and shape become wildly distorted even within its usable range.
What are its main practical uses besides navigation planning?
Beyond its primary role in great-circle route finding, the Gnomonic projection is used in seismology to plot the epicenters of earthquakes, as seismic waves often travel along great-circle paths. It is also used in some forms of photogrammetry and for certain astronomical charts, where representing great circles as straight lines simplifies analysis. Its use is always specialized due to its severe limitations.
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