gerardus mercator projection

Mercator projection FROM THE SIXTEENTH CENTURY TO GOOGLE MAPS. The Mercator projection is a cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. Therefore, the projection has an accuracy of 1%, over a wider strip of 22° compared with the 16° of the normal (tangent) projection. The projection is a cylindrical and conformal, with no distortion along the equator. 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. Be on the lookout for your Britannica newsletter to get trusted stories delivered right to your inbox. It is less practical for world maps, however, because the scale is distorted; areas farther away from the Equator appear disproportionately large. The scale factor is unity on the equator, as it must be since the cylinder is tangential to the ellipsoid at the equator. Mercator projection, type of map projection introduced in 1569 by Gerardus Mercator. Although accurate, these projections were difficult for navigators and explorers to use because they required that bearing constantly be recalculated as they moved (Stockton, 2013).Maps c… His Mercator projection map, invented in 1569, was the primary map … The Mercator projection was developed in 1569 by Gerardus Mercator as a navigational tool. A major navigational feature of the projection is that a line of constant azimuth is straight. 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. This need not be done symmetrically. in any direction from a point on the equator corresponds to approximately 900 km. 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. However, it has a significant flaw since it drastically distorts the … In fact, the Mercatorprojection was the first projection regularly identified in atlases. The scale is equal in all directions around any point, which keeps the angles and shapes of small objects intact. Some numerical values are listed below. Gerardus Mercator, original name Gerard De Cremer, or Kremer?, (born March 5, 1512, Rupelmonde, Flanders [now in Belgium]—died December 2, 1594, Duisburg, Duchy of Cleve [Germany]), Flemish cartographer whose most important innovation was a map, embodying what was later known as the Mercator projection, on which parallels and meridians are rendered as straight lines spaced so as … View eight larger pictures. It is a cylindrical map projection that is a product of its time. This inflation is very small near the equator but accelerates with Compare conic projection, homolosine projection, sinusoidal projection. 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. The scale is now true at these latitudes whereas parallels between these latitudes are contracted by the projection and their scale factor must be less than one. Only accurate Mercator projections of regions near the equator will necessitate the ellipsoidal corrections. Flemish cartographer Gerardus Mercator created this map in 1569. 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. The distinction between rhumb (sailing) distance and great circle (true) distance was clearly understood by Mercator. The projection is the most heavily used in our society, appearing everywhere from books to apps to Google Maps, and tends to be what most of us think of when pondering the world map. Yet it is also the bane of cartography because of the distortions it exhibits. This is a standard technique of extending the region over which a map projection has a given accuracy. On any other parallel the scale factor is sec φ so that. Like symphonies, map projections are named after their makers. It is often described as a cylindrical projection, but it must be derived mathematically. On a Mercator projection, for example, the landmass of Greenland appears to be greater than that of the continent of South America; in actual area, Greenland is smaller than the Arabian Peninsula. Gerardus Mercator (1512-1594), was a 16th century cartographer who developed one of the most dominant cartographic projections in the world, although we should rather point out: in the European world. The graph shows the variation of the scale factor with latitude. It is easy to forget it, but when you imagine a world map, when you think of the countries that arise in a trivial conversation, we all have the same imprint in our head: the Mercator projection. He is best known for a new mapping technique that bears his name, the Mercator projection. 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 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. See the discussion on distance formulae below. Over long distances the rhumb lines…, …the result was the now-familiar Mercator map shown in the photograph.…. He is most renowned for creating the 1569 world map based on a new projection which represented sailing courses of constant bearing (rhumb lines) as straight lines—an innovation that is still employed in nautical charts. When α = 0 or π it corresponds to a meridian great circle (if continued around the Earth). Gerardus Mercator’s world map dates from 1569. When α = π/2 or 3π/2 the rhumb corresponds to one of the parallels; only one, the equator, is a great circle. 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. A straight line on the Mercator map at angle α to the meridians is a rhumb line. This page was last edited on 13 March 2021, at 23:03. For Australia, taking 25° as a median latitude, hk = 1.2. This is not the shortest distance between the chosen endpoints on the parallel because a parallel is not a great circle. The result is that deviation of the scale from unity is reduced over a wider range of latitudes. The transformation equations and scale factor for the non-secant version are[21]. Flemish Geographer and Cartographer. 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. gd−1(φ). For the above model 1 cm corresponds to 1,500 km at a latitude of 60°. (See Legend 12 on the 1569 map.) Converting ruler distance on the Mercator map into true (great circle) distance on the sphere is straightforward along the equator but nowhere else. Therefore, by construction, the Mercator projection is perfectly accurate, k = 1, along the equator and nowhere else. Even if these elliptical projections were accurate, it was very difficult to use for navigators and explorers because it required recalculation as they cruised. Gerardus Mercator was a Flemish map-maker and geographer who is best known for the map projection which bears his name. The Mercator projection is a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator in 1569. The length of the chord AB is 2(a cos φ) sin λ/2. Mercator, Gerardus (1512 – 1594) A Flemish cartographer who invented a system of setting lines of latitude and longitude on charts of the spherical earth, the “ Mercator projection, ” which has become a standard for maps into modern times. The projection has become widely used, not least as Web Mercator for web mapping. It was presented by Gerardus Mercator in 1569. The difference is small for short distances but increases as λ, the longitudinal separation, increases. Therefore, interpreting ruler measurements on the equator is simple: For the above model, with RF = 1/300M, 1 cm corresponds to 3,000 km. This map projection is practical for nautical applications due to its ability to represent lines of constant course, known as rhumb lines, as straight segments that conserve the angles with the meridians. By signing up for this email, you are agreeing to news, offers, and information from Encyclopaedia Britannica. The ellipsoidal correction of the scale factor increases with latitude but it is never greater than e2, a correction of less than 1%. [18], There are many alternative expressions for y(φ), all derived by elementary manipulations. The Mercator projection is not a projection in physical terms and therefore cannot be constructed geometrically. These circles are rendered on the projected map with extreme variation in size, indicative of Mercator's scale variations. The Mercator projection was originally developed in 1569 by the Flemish cartographer Gerardus Mercator. 1989. Mercator is a conformal cylindrical map projection that was originally created to display accurate compass bearings for sea travel. (The value of e2 is about 0.006 for all reference ellipsoids.) "A World Map on a Regular Icosahedron by Gnomonic Projection.". 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. Gerardus Mercator was a 16 th Century map genius. Mercator¶ The Mercator projection takes its name from the Flemish cartographer Gheert Cremer, better known as Gerardus Mercator, who presented it in 1569. As a side effect, the Mercator projection inflates the size of objects away from the equator. The Mercator projection is a form of cylindrical projection, in which the projection is adequately distorted in the direction of the cylinder axis in order to achieve a true angular image of the earth’s surface. 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. One measure of a map's accuracy is a comparison of the length of corresponding line elements on the map and globe. A creative and skillful craftsman, he invented the map projection which bears his name and coined the term “atlas”. The map is thereby conformal. 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. Hubert Kremer worked the land and also was a cobbler, that is a shoemaker. Updated December 12, 2019 Gerardus Mercator was a Flemish cartographer, philosopher, and geographer who is best known for his creation of the Mercator map projection. Let us know if you have suggestions to improve this article (requires login). 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.[f]. In this case the maximum latitude attained must correspond to y = ±W/2, or equivalently y/R = π. In 1538 Mercator published a 14 by 21 inch (36 by 55 cm) world map, laid down on the double cordiform (double heart-shaped) projection (fig. 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. Our editors will review what you’ve submitted and determine whether to revise the article. But the Mercator Projection was never tied to racial supremacy in the first place. While every effort has been made to follow citation style rules, there may be some discrepancies. The famous 1569 map is one of the most influential in the world - but it isn't entirely accurate Scale is unity on the equator (for a non-secant projection). If the latitudes of the end points cannot be determined with confidence then they can be found instead by calculation on the ruler distance. (The distance AB along the parallel is (a cos φ) λ. 3.2) pioneered in 1531 by the French mathematician Oronce Fine (1494-1555). Gerardus Mercator (1569) Group: Conic: Cylindric: Property: Conformal: Conformal: Other Names: LCC projection — Remarks: Standard parallels set to 20° and 30° North – just because I thought that this results in a somewhat appealing world map image… The image is showing a section of the complete projection. He did many things but arguably his biggest legacy is the invention of a map projection that bears his name, the Mercator projection. 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). When the Earth is modelled by a spheroid (ellipsoid of revolution) the Mercator projection must be modified if it is to remain conformal. A generator of a cylinder is a straight line on the surface parallel to the axis of the cylinder. 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. Narrower strips are better: sec 8° = 1.01, so a strip of width 16° (centred on the equator) is accurate to within 1% or 1 part in 100. The aspect ratio of his map is 198/120 = 1.65. [17][20][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. Gerardus Mercator was a 16th-century geographer, cosmographer and cartographer from the County of Flanders. Without a doubt, the most famous map projection is the Mercatorprojection. Gerardus Mercator. 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. Gerardus Mercator: 3 ways influential cartographer changed the way we look at the world. A method of making a flat map of the Earth's surface so that the meridians and parallels appear as straight lines that cross at right angles. 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. Gerardus Mercator was a geographer, cartographer and mathematician born in Flanders. In a Mercator projection, the areas farther from the equator appear larger, making the polar regions greatly distorted. Although Mercator borrowed the geographic framework from Fine, his map is more similar in content to Frisius’s terrestrial globe. For example, the basic transformation equations become. On the Mercator projection parallels of latitude and meridians of longitude are drawn as straight lines so that they are useful for navigation. The 16th-century cylindrical projection by Gerardus Mercator, a Flemish cartographer, makes life easier for navigators by keeping parallels and meridians as straight lines. 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. 16(3): 222–223. 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. Gerardus Mercator (March 5, 1512 – December 2, 1594) was a cartographer with interests in theology, philosophy, history, mathematics and magnetism as well as being an accomplished engraver, calligrapher and maker of globes and scientific instruments.He is best known for the 1569 world map based on a new projection which represented sailing courses of constant bearing as straight lines. Please refer to the appropriate style manual or other sources if you have any questions. An additional feature of this projection is that all local shapes are accurate and correctly defined at infinitesimal scale. Mercator projections are a common sight in classrooms across the planet, but who invented them? Ring in the new year with a Britannica Membership, This article was most recently revised and updated by, https://www.britannica.com/science/Mercator-projection. His most famous work, the Mercator projection, is a geographical chart where the spherical globe is flattened into a two-dimensional map, with latitude and longitude lines drawn in a straight grid. 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 is a cylindrical map projection first introduced by the Flemish geographer and cartographer Gerardus Mercator in 1569. Much Web-based mapping uses a zoomable version of the Mercator projection with an aspect ratio of one. 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. Mercator projection, type of map projection introduced in 1569 by Gerardus Mercator. Biography Gerard Mercator's parents were Hubert and Emerentia Kremer. Originally intended solely for ocean navigation, the map has found its way into the classrooms of many western schools including those in the United States. Select from premium Mercator Map of the highest quality. Title: Wv11700a.cdr Author: Paul B. Anderson Created Date: 8/20/2002 2:33:11 AM Corrections? The classic way of showing the distortion inherent in a projection is to use Tissot's indicatrix. Therefore, the Mercator projection is adequate for mapping countries close to the equator. At this time, many of Europe’s top cartographers and explorers used elliptical projections derived from Ptolemy’s latitude and longitude grid. This map's grid is rectangular and lines of latitude and longitude are parallel throughout. More general example of Tissot's indicatrix: the, Fisher, Irving (1943). 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).) Mercator’s view of the world is one that has endured through the … However, if the map is marked with an accurate and finely spaced latitude scale from which the latitude may be read directly—as is the case for the Mercator 1569 world map (sheets 3, 9, 15) and all subsequent nautical charts—the meridian distance between two latitudes φ1 and φ2 is simply. Find the perfect Mercator Map stock photos and editorial news pictures from Getty Images. For cylindrical projections, the axes of the ellipse are aligned to the meridians and parallels. 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. 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, https://en.wikipedia.org/w/index.php?title=Mercator_projection&oldid=1011981804, Creative Commons Attribution-ShareAlike License, Greenland's real area is comparable to the, Africa appears to be roughly the same size as. The Mercator projection is a transformation of a cylindrical projection used for navigation. For Greenland, taking 73° as a median latitude, hk = 11.7. 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. Longer distances require various approaches. 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. The word "atlas" to define a collection of maps was coined by Gerardus Mercator, who is best known for his 1569 invention of a new system of projection for marine charts, called the Mercator projection, which revolutionized cartography as well as nautical navigation.. [19] This section discusses only the last of these cases. The interpretation of such bar scales is non-trivial. This is much smaller than the scale inaccuracy, except very close to the equator. For Great Britain, taking 55° as a median latitude, hk = 3.04. Updates? The corresponding distances for latitudes 20°, 40°, 60° and 80° are 846 km, 689 km, 450 km and 156 km respectively. Gerhard Kremer - alias Gerardius Mercator The difference is 3,338 km so the ruler distance measured from the map is quite misleading even after correcting for the latitude variation of the scale factor. Even if you've never seen Gerardus Mercator, you've almost certainly seen his work. [19], The above formulae are written in terms of the globe radius R. It is often convenient to work directly with the map width W = 2πR. Omissions? 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. 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. American Cartographer. 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. Mercator projection definition is - a conformal map projection of which the meridians are usually drawn parallel to each other and the parallels of latitude are straight lines whose distance from each other increases with their distance from the equator. Gerardus Mercator was an engraver and globe-maker in 1500s Flanders. 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°. Though the bulk of his fame stems from his career in cartography, Gerardus Mercator was a Renaissance man metaphorically as well as literally, having studied theology, physics, mathematics and Latin. Using the latest reports of new discoveries, he created innovative maps which became known throughout Europe. The area scale factor is the product of the parallel and meridian scales hk = sec2φ. Gerardus Mercator (1512-1594) was a great Renaissance cartographer whose work shaped the identity of the modern world. The quality of his maps made them a copy source for generations of mapmakers. However, the projection devised by Gerardus Mercator in 1569 continues to be used since, in order to represent cities or regions, it is very adequate, the calculations necessary to manage it are relatively simple and it is proportional, that is, it distorts the space in both the north-south and east-west axes in order to maintain the forms. Such a line is called a rhumb line or loxodrome. 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 Mercator Projection has many flaws and it is a prime example of how map bias can shape one’s world view. 1512-1594. It is often described as a cylindrical projection, but it must be derived mathematically. 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