Mercator's projection

Also called: Mercator projection · Topic: Map Projections · NCERT: Class 11, Ch 4 "Map Projections"

Meaning

Mercator's projection is a mathematical, cylindrical and orthomorphic (conformal) map projection made by Gerardus Mercator in 1569. On it, parallels and meridians are straight lines that cross at right angles. Parallels are spaced farther apart towards the poles, so the shapes of small areas stay true but areas grow larger and larger towards the poles [3].

• It matters because it is the standard chart for navigation: any straight line on it is a line of constant compass bearing.
• A simple spherical form of it, Web Mercator, is the projection behind most online maps today [2]. That is why most people picture country sizes wrongly.

Explanation

What kind of projection it is

• Map projection means a way of moving the network of latitudes and longitudes from the round globe onto a flat sheet. Every projection distorts something: area, shape, distance or direction.
• Maker: Gerardus Mercator (birth name Gerard de Kremer). He was Flemish, from Flanders in today's Belgium. NCERT calls him "Dutch", which is wrong.
• Year: 1569. The projection was first designed and used by him in that year [3].
• Mercator fits three classes at once:

Basis of grouping	Mercator's class	What it means
Method of making	Mathematical (conventional)	It is drawn from a formula or table. It is not a real shadow cast on a cylinder.
Developable surface (a surface that can be laid flat)	Cylindrical	Picture the globe inside a cylinder that touches it at the equator. The cylinder is then unrolled.
Property kept	Orthomorphic (conformal)	It keeps angles, scale and shape correct for small areas [3].

• NCERT error: NCERT calls it "azimuthal". It is not azimuthal. An azimuthal (zenithal) projection is drawn on a flat plane that touches the globe at one point.

How it keeps shape: the secant rule

• Step 1: parallels are stretched.
• On a globe, a parallel gets shorter as you go towards the poles.
• On Mercator, every parallel is drawn as long as the equator.

• So a parallel at latitude φ is stretched by sec φ (secant of the latitude, which is 1 ÷ cos φ).

• Step 2: the gap between parallels is widened by the same amount.

• Mercator also spaces the parallels farther apart towards the poles, by the same factor, sec φ.

• Result: local shapes stay true.

• At every point, the scale along the meridian equals the scale along the parallel.

• So a small shape is not squashed or pulled in just one direction.

• Cost: area grows by sec² φ.

• A small area is enlarged in both directions at once.
• At 30°: length × 1.154, area about × 1.33.
• At 60°: length × 2, area about × 4.
• Near the poles sec φ grows without limit, so the poles can never be drawn.

Construction (NCERT example)

• Problem: draw Mercator's projection at a scale of 1:250,000,000 with a 15° interval.
• Radius of the reduced globe: R = 250,000,000 ÷ 250,000,000 = 1 inch.
• Length of the equator: 2πR = 2 × 22/7 × 1 = 6.28 inches.
• Meridian spacing: 6.28 ÷ 24 (because 360° ÷ 15° = 24) ≈ 0.26 inch. Meridians are equally spaced vertical lines.
• Parallel spacing: not equal. It is read from a table:

Latitude	Distance from the equator (inches)
15°	0.265
30°	0.549
45°	0.881
60°	1.317
75°	2.027

• The gaps keep growing: 0.265 → 0.284 → 0.332 → 0.436 → 0.710 inch. The 90° parallel would be infinitely far away, so the drawing stops at about 75°–80°.
• Steps:
• Draw the equator 6.28 inches long.
• Divide it into 24 parts and draw the meridians at right angles to it.
• Mark the parallels on both sides of the equator using the table.
• Draw each parallel as a straight line as long as the equator.

Properties, limitations and the rhumb line

• Properties:
• Parallels and meridians are straight lines that cross at right angles. The graticule (the grid of latitudes and longitudes) is rectangular.
• Every parallel is as long as the equator. So the 30° parallel is 1.154 times its true length. On the globe it is only cos 30° = 0.866 of the equator.
• Parallels get farther apart towards the poles, while meridians stay evenly spaced [3].

• Shapes of small areas are correct, but areas get more and more enlarged towards the poles.

• Limitations:

• High latitudes are hugely enlarged. Area grows about 4 times at 60°. Features near the poles, such as Greenland, look much bigger than they are [3].
• Greenland looks as big as Africa or the USA. Its true area is only about 2.2 million sq km. The USA is about 9.8 million sq km and Africa about 30 million sq km. In reality Africa is about 14 times as large as Greenland [3].
• The poles cannot be shown.

• Great circles look curved. So the shortest route does not look like the shortest route.

• Rhumb line (loxodrome): a line that crosses every meridian at the same angle. A ship following it keeps one constant compass bearing (for example, always N 60° E).

• Why it is straight on Mercator:

  • Meridians are drawn as parallel vertical lines.
  • The projection keeps angles true.
  • So a line that meets every meridian at the same angle has to be straight.

• Great circle: a circle on the globe whose plane passes through the Earth's centre, such as the equator or any pair of opposite meridians. An arc of a great circle is the shortest route between two points.

• On long voyages (NCERT Fig. 4.6), navigators combine the two:
• Plot the great circle, which is the shortest path.
• Break it into short stretches.
• Sail each stretch as a rhumb line with a fixed bearing.

Where it occurs

• Navigation charts, worldwide: used for sea and air routes, because a straight line on the chart gives a fixed compass bearing.
• Atlas world maps: used for distribution maps where direction and shape matter more than area:
• drainage patterns
• ocean currents
• winds
• temperature

• rainfall.

• Best near the equator: it works best for areas close to the equator, where distortion is small. Examples are India, the East Indies and equatorial Africa.

• Worst at high latitudes: Greenland, Canada, Russia and Antarctica look far bigger than they are. Tropical lands such as India, Africa and Brazil look smaller by comparison.
• Web Mercator (online maps):
• Web Mercator (code EPSG:3857, earlier EPSG:900913, popularly called the "Google Maps" projection) is a simplified, spherical form of Mercator [2].
  • An EPSG code is an ID number from a public list of map projections. Software uses it to recognise a projection.
  • Spherical means the formulas treat the Earth as a perfect sphere, not a slightly flattened one. This makes the maths simpler.
• Google Maps took it up around 2005. Today most online maps use it, including Google Maps, Bing Maps and OpenStreetMap [2].
• A variation of Mercator is used by popular services like Google Maps and ArcGIS Online [3].

• Why web maps use it: it keeps north up and the grid square. So the world can be cut into square tiles at each zoom level and joined without seams [2]. Streets and buildings keep their shape at any zoom.

• NASA GIBS (Global Imagery Browse Services):

• In April 2014, GIBS began offering satellite imagery in Web Mercator. This lets the imagery sit directly on top of Google Maps, Bing Maps and OpenStreetMap.
• GIBS also offers Geographic (EPSG:4326), Arctic Polar Stereographic (EPSG:3413) and Antarctic Polar Stereographic (EPSG:3031) projections [2].
• The polar stereographic projections are used for the Arctic and Antarctic, because Mercator cannot show the poles [2].

Don't confuse with

• Azimuthal (zenithal) projection: drawn on a flat plane that touches the globe at one point. Mercator is drawn on a cylinder. NCERT wrongly calls Mercator "azimuthal".
• Great circle route: the shortest path between two points, but its bearing keeps changing and it looks curved on Mercator. A rhumb line is the straight line on Mercator. It keeps one bearing but is longer, except along the equator or a meridian.
• Equal-area and compromise projections (Robinson, Winkel Tripel): these show area more fairly and are often chosen for general world maps [3]. Mercator keeps shape, not area.
• Web Mercator vs classic Mercator: Web Mercator (EPSG:3857) is a simplified spherical form made for online map tiles [2]. Classic Mercator is the 1569 projection used for navigation charts. Both enlarge high latitudes.

Prelims Hooks

• Mercator's projection (1569, Gerardus Mercator, a Flemish cartographer, not Dutch) is cylindrical, mathematical and orthomorphic (conformal). It is not azimuthal.
• Both the length of each parallel and the spacing between parallels grow by sec φ, so area grows by sec² φ: about × 4 at 60°. The 30° parallel is 1.154 times its globe length.
• A straight line on Mercator is a rhumb line (loxodrome): a constant compass bearing that cuts all meridians at the same angle. It is not the shortest route. The shortest route, the great circle, looks curved and bends towards the pole.
• The poles cannot be shown on Mercator, because the scale becomes infinite at 90°.
• True areas: Greenland (about 2.2 million sq km) < USA (about 9.8 million) < Africa (about 30 million). Africa is about 14 times Greenland [3]. Trap: "Greenland is 1/10th of the USA" is wrong. It is about 2/9.
• Web Mercator = EPSG:3857 (also EPSG:900913), used by Google Maps, Bing Maps and OpenStreetMap [2]. It keeps local shape but not area.

Mains Points

• Why the most-used world map shows sizes wrongly (GS-I):
• The secant stretch makes high-latitude lands (Greenland, Canada, Russia) look bigger than tropical ones (India, Africa, Brazil).
• This shapes how students and the public judge the size and importance of regions, a common example of "map bias".

• For general world maps of population, resources or development, equal-area or compromise projections (Robinson, Winkel Tripel) are better [3].

• Choose the projection by purpose:

• Use Mercator for navigation and for flow maps (winds, ocean currents), where direction matters.
• Use equal-area maps to compare distributions such as forest cover, crop area or population density.

• On long sea and air routes, plan along the great circle and steer by rhumb lines, stretch by stretch.

• Geospatial relevance:

• Web Mercator underpins online maps and satellite-imagery services, and its tile system makes zooming smooth [2].
• But area and distance measured on it at high latitudes must be corrected, or worked out again on an equal-area system. Examples are Arctic shipping routes and the extent of Himalayan glaciers.
• A map is a model, not a mirror. Knowing each projection's trade-off (shape vs area vs distance) is basic to reading atlas plates, thematic maps and GIS (Geographic Information System) outputs correctly.

Related concepts

• Rhumb line
• Web Mercator

Read more

• Mercator's projection, rhumb lines and Web Mercator