For example, on a map with R = 1 the values of y = 0, 1, 2, 3 correspond to latitudes of φ = 0°, 50°, 75°, 84° and therefore the successive intervals of 1 cm on the map correspond to latitude intervals on the globe of 50°, 25°, 9° and distances of 5,560 km, 2,780 km, and 1,000 km on the Earth. The interpretation of such bar scales is non-trivial. It is particularly useful for navigation, though the scale… The Mercator map projection was invented by Gerardus Mercator (1512-1594). It became the standard map projection for navigation because it is unique in representing north as up and south as down everywhere while preserving local directions and shapes. Note: I’m no cartographer. Only accurate Mercator projections of regions near the equator will necessitate the ellipsoidal corrections. La projection de Mercator ou projection Mercator est une projection cartographique de la Terre, dite «cylindrique», tangente à l' équateur du globe terrestre sur une carte plane formalisée par le géographe flamand Gerardus Mercator, en 1569. One measure of a map's accuracy is a comparison of the length of corresponding line elements on the map and globe. The transformation equations and scale factor for the non-secant version are. "A World Map on a Regular Icosahedron by Gnomonic Projection.". English-Estonian dictionary. If there is no such scale then the ruler distances between the end points and the equator, y1 and y2, give the result via an inverse formula: These formulæ give rhumb distances on the sphere which may differ greatly from true distances whose determination requires more sophisticated calculations. He even quantifies his statement: "When the great circle distances which are to be measured in the vicinity of the equator do not exceed 20 degrees of a great circle, or 15 degrees near Spain and France, or 8 and even 10 degrees in northern parts it is convenient to use rhumb line distances". For Australia, taking 25° as a median latitude, hk = 1.2. Below is what it looked like: Universitat de Barcelona Promotor: Institut Cartogràfic de Catalunya, 2013. sinònims complementaris: projecció cilíndrica conforme de Mercator, projecció conforme de Mercator, planisferi de Mercator, mapa de Mercator cs proyección de Mercator; fr projection cylindrique; it proiezione cilindrica; en cylindrical projection; de zylindrische Abbildung When the Earth is modelled by a spheroid (ellipsoid of revolution) the Mercator projection must be modified if it is to remain conformal. Scale is unity on the equator (for a non-secant projection). When α = 0 or π it corresponds to a meridian great circle (if continued around the Earth). Any of the inverse transformation formulae may be used to calculate the corresponding latitudes: The figure comparing the infinitesimal elements on globe and projection shows that when α=β the triangles PQM and P′Q′M′ are similar so that the scale factor in an arbitrary direction is the same as the parallel and meridian scale factors: This result holds for an arbitrary direction: the definition of isotropy of the point scale factor. This projection is widely used for navigation charts, because any straight line on a Mercator projection map is a line of constant true bearing that enables a navigator to plot a straight-line course. For cylindrical projections, the axes of the ellipse are aligned to the meridians and parallels. The Mercator projection is a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator in 1569. A straight line on the Mercator map at angle α to the meridians is a rhumb line. Updates? 1989. At a latitude of ±25° the value of sec φ is about 1.1 and therefore the projection may be deemed accurate to within 10% in a strip of width 50° centred on the equator. [e] For the Mercator projection, h = k, so the ellipses degenerate into circles with radius proportional to the value of the scale factor for that latitude. Projection Pro*jec tion, n. [L. projectio: cf. In a secant (in the sense of cutting) Mercator projection the globe is projected to a cylinder which cuts the sphere at two parallels with latitudes ±φ1. English: The Mercator projection is a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator in 1569. English-German geography dictionary . It became the standard map projection for nautical purposes because of its ability to represent lines of constant course, known as rhumb lines or loxodromes, as straight segments. For two points, A and B, separated by 10° of longitude on the parallel at 60° the distance along the parallel is approximately 0.5 km greater than the great circle distance. (The value of e2 is about 0.006 for all reference ellipsoids.) Autor: Dr. Josep Maria Rabella. Elles correspondent donc à une projection cylindrique équidistante. So my first recommendation is: Verify if you reallyneed a rectangular map or if a different shape might fit the purpose of the map better. On any other parallel the scale factor is sec φ so that. Mercator projection, type of map projection introduced in 1569 by Gerardus Mercator. Often, it is innocent of the crimes it is accused of, and I want to address this as well as what it actually is guilty of. The scale factor is unity on the equator, as it must be since the cylinder is tangential to the ellipsoid at the equator. For a ruler measurement of a short line, with midpoint at latitude φ, where the scale factor is k = sec φ = 1/cos φ: With radius and great circle circumference equal to 6,371 km and 40,030 km respectively an RF of 1/300M, for which R = 2.12 cm and W = 13.34 cm, implies that a ruler measurement of 3 mm. It is a cylindrical map projection that is a product of its time. On peut obtenir ainsi trois types de projections : cylindrique, conique ou azimutale ... Mercator Projection - Duration: 3:12. La projection cartographique est un ensemble de techniques permettant de représenter la surface de la Terre dans son ensemble ou en partie sur la surface plane d'une carte. See the discussion on distance formulae below. Our editors will review what you’ve submitted and determine whether to revise the article. English-Chinese geology dictionary (英汉地质大词典). 3:12. This chord subtends an angle at the centre equal to 2arcsin(cos φ sin λ/2) and the great circle distance between A and B is 2a arcsin(cos φ sin λ/2).) The projection of Mercator is a cylindrical cartographic projection that represents the whole terrestrial surface. The scale on the equator is 0.99; the scale is k = 1 at a latitude of approximately ±8° (the value of φ1); the scale is k = 1.01 at a latitude of approximately ±11.4°. Today, the use of the Mercator projection is not justified except by specific interests. The result is that deviation of the scale from unity is reduced over a wider range of latitudes. Calling the ruler distances of the end points on the map meridian as measured from the equator y1 and y2, the true distance between these points on the sphere is given by using any one of the inverse Mercator formulæ: where R may be calculated from the width W of the map by R = W/2π. In this case the maximum latitude attained must correspond to y = ±W/2, or equivalently y/R = π. The area scale factor is the product of the parallel and meridian scales hk = sec2φ. [1913 Webster] 2. More general example of Tissot's indicatrix: the, Fisher, Irving (1943). The northern inflation acutely distorts Russia's shape as well, making it appear much taller north-to-south and greatly stretching its arctic regions compared to its mid latitudes. For Great Britain, taking 55° as a median latitude, hk = 3.04. Originally, this and other map projections were achieved by a systematic method of drawing… American Cartographer. Over long distances the rhumb lines…, …the result was the now-familiar Mercator map shown in the photograph.…. The corresponding distances for latitudes 20°, 40°, 60° and 80° are 846 km, 689 km, 450 km and 156 km respectively. Corrections? (See Legend 12 on the 1569 map.) The Mercator projection was developed in 1569 by Gerardus Mercator as a navigational tool. 16(3): 222–223. A jutting out; also, a part jutting out, as of a building; an extension beyond something else. Converting ruler distance on the Mercator map into true (great circle) distance on the sphere is straightforward along the equator but nowhere else. a map projection of the earth onto a cylinder; areas appear greater the farther they are from the equator cylindrical projection. This article was most recently revised and updated by, https://www.britannica.com/science/Mercator-projection. (The distance AB along the parallel is (a cos φ) λ. Therefore, by construction, the Mercator projection is perfectly accurate, k = 1, along the equator and nowhere else. Nicolas Tissot noted that the scale factors at a point on a map projection, specified by the numbers h and k, define an ellipse at that point. The Mercator map was designed as an aid to navigators with straight lines, loxodromes or rhumb lines—representing lines of constant compass bearing—that are perfect for "true" direction. For all other values it is a spiral from pole to pole on the globe intersecting all meridians at the same angle, and is thus not a great circle. Cartography of Belgium (history of surveying and creation of maps of, Cartography of the Low Countries (history of surveying and creation of maps of the, This page was last edited on 8 December 2020, at 06:18. The ellipsoidal correction of the scale factor increases with latitude but it is never greater than e2, a correction of less than 1%. Najboljši sosed: prodajna mesta, akcije, ugodnosti, novice, dogodki, recepti in mnogo več. This is much smaller than the scale inaccuracy, except very close to the equator. [f], Map projection for navigational use that distorts areas far from the equator. [1913 Webster] 1. Oh yes, I did. This need not be done symmetrically. projection cylindrique oblique. Les coordonnées des contours résultent d'une simple conversion sur un plan des coordonnées géodésiques. One problem is the variation of scale with latitude, and another is that straight lines on the map (rhumb lines), other than the meridians or the equator, do not correspond to great circles. By signing up for this email, you are agreeing to news, offers, and information from Encyclopaedia Britannica. Did I mention that I’m not a big fan of cylindric projections? Some numerical values are listed below. These circles are rendered on the projected map with extreme variation in size, indicative of Mercator's scale variations. The Mercator projection has been used extensively for world maps im which the distortion towards the polar regions grows rather large, thus incorrectly Map Projections Geradus Mercator invented his famous projection in 1569 as an aid to navigators. cylindrical projection 圆柱投影. Even more extreme truncations have been used: a Finnish school atlas was truncated at approximately 76°N and 56°S, an aspect ratio of 1.97. The ordinate y of the Mercator projection becomes infinite at the poles and the map must be truncated at some latitude less than ninety degrees. Abigail Alkire 48,509 views. Omissions? Let us know if you have suggestions to improve this article (requires login). The property of the Mercator projection map that made it useful to navigators is that it preserves angles. , There are many alternative expressions for y(φ), all derived by elementary manipulations. On the other hand, the geodesic between these points is a great circle arc through the pole subtending an angle of 60° at the center: the length of this arc is one sixth of the great circle circumference, about 6,672 km. The classic way of showing the distortion inherent in a projection is to use Tissot's indicatrix. [1913… He stressed that the rhumb line distance is an acceptable approximation for true great circle distance for courses of short or moderate distance, particularly at lower latitudes. In fact, the Mercator projection was the first projection regularly identified in atlases. projection.] His name is a latinized version of Gerhard Kramer. Much Web-based mapping uses a zoomable version of the Mercator projection with an aspect ratio of one. When α = π/2 or 3π/2 the rhumb corresponds to one of the parallels; only one, the equator, is a great circle. Scegli tra immagini premium su Mercator Projection della migliore qualità. For the above model 1 cm corresponds to 1,500 km at a latitude of 60°. Mercator projection, type of map projection introduced in 1569 by Gerardus Mercator.It is often described as a cylindrical projection, but it must be derived mathematically.The meridians are equally spaced parallel vertical lines, and the parallels of latitude are parallel horizontal straight lines that are spaced farther and farther apart as their distance from the Equator increases. The Mercator projection (/ m ər ˈ k eɪ t ər /) is a cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. A generator of a cylinder is a straight line on the surface parallel to the axis of the cylinder. A meridian of the map is a great circle on the globe but the continuous scale variation means ruler measurement alone cannot yield the true distance between distant points on the meridian. The recommendations below are made by a complete layman! Since ruler measurements can furnish the map ordinate y and also the width W of the map then y/R = 2πy/W and the scale factor is determined using one of the alternative forms for the forms of the inverse transformation: The variation with latitude is sometimes indicated by multiple bar scales as shown below and, for example, on a Finnish school atlas. It was developed by Gerardus Mercator in the sixteenth century, in the year 1569. in any direction from a point on the equator corresponds to approximately 900 km. Map Projections. It is less practical for world maps, however, because the scale is distorted; areas farther away from the Equator appear disproportionately large. Specified in [square brackets]: Actual size of the projection (minus the black or white background). If the latitudes of the end points cannot be determined with confidence then they can be found instead by calculation on the ruler distance. This is a standard technique of extending the region over which a map projection has a given accuracy. Since α is constant on the rhumb this expression can be integrated to give, for finite rhumb lines on the Earth: Once again, if Δφ may be read directly from an accurate latitude scale on the map, then the rhumb distance between map points with latitudes φ1 and φ2 is given by the above. The graph shows the variation of the scale factor with latitude. Therefore, the projection has an accuracy of 1%, over a wider strip of 22° compared with the 16° of the normal (tangent) projection. Born in what is now the German region, Mercator was a keen cartographer and even coined the term ‘atlas’ to describe a collection of maps. Image of: Mercator. Working from the projected map requires the scale factor in terms of the Mercator ordinate y (unless the map is provided with an explicit latitude scale). Be on the lookout for your Britannica newsletter to get trusted stories delivered right to your inbox. In 1569 he created the Mercartor map projection. Mercator's\ projection Mercatori projektsioon. If α is neither 0 nor π then the above figure of the infinitesimal elements shows that the length of an infinitesimal rhumb line on the sphere between latitudes φ; and φ + δφ is a sec α δφ. So in case you really need a cylindric map – let’s see how Patterson works out for different kinds of maps… Mercator projection translation in English-French dictionary. La projection de Mercator est une représentation plane de la Terre de type cylindrique. For example, the basic transformation equations become. Scopri le migliori foto stock e immagini editoriali di attualità di Mercator Projection su Getty Images. English-Spanish dictionary of Geography . It is often described as a cylindrical projection, but it must be derived mathematically. In the extreme case where the longitudinal separation is 180°, the distance along the parallel is one half of the circumference of that parallel; i.e., 10,007.5 km. It was the standard map projection for nautical purposes because of its ability to represent cruise lines, known as rhumb lines as segments that maintain constant angles with the meridians. When the Portuguese, under the leadership of Prince Henry the Navigator, ventured farther south along the west coast of Africa, they encountered navigational difficulties by assuming that the charts used in the Mediterranean could simply be extended. assurée par un modèle mathématique appelé système de projection. This is his famous world map of 1569. The aspect ratio of his map is 198/120 = 1.65. geography in cartography, any of numerous map projections of the terrestrial sphere on the surface of a cylinder that is then unrolled as a plane. Mercator's original map is truncated at 80°N and 66°S with the result that European countries were moved towards the centre of the map. The map is thereby conformal. magnetic directions, instead of geographical directions, Universal Transverse Mercator coordinate system, "Mercator Projection vs. Peters Projection, part 2", "Mercator Projection vs. Peters Projection, part 1", Table of examples and properties of all common projections, An interactive Java Applet to study the metric deformations of the Mercator Projection, Web Mercator: Non-Conformal, Non-Mercator (Noel Zinn, Hydrometronics LLC), Mercator's Projection at University of British Columbia, Map projection of the tri-axial ellipsoid, Early modern Netherlandish cartography, geography and cosmography, Dutch celestial cartography in the Age of Discovery, Dutch celestial and lunar cartography in the Age of Exploration, Dutch systematic mapping of the far southern sky, c. 1595–1599, Dutch commercial cartography in the Age of Discovery, Dutch corporate cartography in the Age of Discovery, Dutch maritime/nautical cartography in the Age of Discovery, Golden Age of Dutch exploration and discovery, Constellations created and listed by Dutch celestial cartographers, Dutch discovery, exploration and mapping of Svalbard, Dutch discovery, exploration and mapping of Jan Mayen, European exploration and mapping of Southern Africa, Great Southern Land/Great Unknown South Land, European maritime exploration of Australia, Dutch discovery, exploration and mapping of Australasia, Dutch discovery, exploration and mapping of Nova Hollandia, Dutch discovery, exploration and mapping of Tasmania/Van Diemen's Land, Dutch discovery, exploration and mapping of the Australian continent, Dutch discovery, exploration and mapping of the Australian mainland, Dutch discovery, exploration and mapping of Nova Zeelandia, Dutch exploration and mapping of Formosa/Taiwan, Dutch exploration and mapping of the East Indies, Dutch exploration and mapping of Southern Africa, Dutch exploration and mapping of South Africa, Dutch exploration and mapping of the Americas, Dutch exploration and mapping of the Pacific, Dutch discovery and exploration of Easter Island, Science and technology in the Dutch Republic, Golden Age of Dutch science and technology, Early modern Iberian (Spanish and Portuguese) cartography, First undisputed non-Indigenous discovery, exploration and mapping of Australasia, First published systematic uses of the triangulation method in modern surveying and mapmaking, First published use of the Mercator projection for maritime navigation, First printed nautical atlas in the modern sense, History of selenography / lunar cartography, First published scientific map of the Moon with a topographical nomenclature, History of uranography / celestial cartography, https://en.wikipedia.org/w/index.php?title=Mercator_projection&oldid=992995821, Short description is different from Wikidata, Articles with unsourced statements from July 2020, Articles with unsourced statements from February 2017, Wikipedia articles with SUDOC identifiers, Creative Commons Attribution-ShareAlike License, Greenland's real area is comparable to the, Africa appears to be roughly the same size as. Similarly sec 2.56° = 1.001, so a strip of width 5.12° (centred on the equator) is accurate to within 0.1% or 1 part in 1,000.