In this blog post, we will take a closer look at various map projection methods for transferring the curved surface of the Earth onto a flat map, as well as their mathematical principles and characteristics.
The location of a specific shape on the Earth’s surface is expressed by longitude and latitude, which form a geographic coordinate system. Since a geographic coordinate system is a system for indicating locations on the surface of a spherical Earth, a map projection is necessary to accurately represent it on a flat map. A map projection is a method of creating a map based on the shadows formed when a light source is placed inside a transparent globe and the light is projected onto a projection surface. The projection surface can be a simple plane or a shape that surrounds the Earth, such as a cone or a cylinder. Accordingly, map projections are divided into plane projections, conic projections, and cylindrical projections.
A plane projection is a method of projecting the Earth onto a plane based on a specific center point, and since all great circles passing through the center point appear as radial straight lines on the map, it has the advantage of matching the actual directions on the surface of the Earth. In particular, when projecting around the poles, the parallels are represented as concentric circles, and the meridians are represented as straight lines extending radially from the poles. The conical projection method involves wrapping a globe in a cone shape and projecting it so that it touches the parallels, then unfolding the cone. In this case, the parallels appear as concentric arcs, and the meridians appear as straight lines extending radially from the poles. The cylindrical projection method involves wrapping the globe in a cylinder along the equator and then unfolding it, so that the parallels are represented as horizontal lines and the meridians as vertical lines.
However, in the actual map-making process, it is essential to make mathematical corrections to minimize the distortion that occurs during the projection process, rather than simply transferring the shadows cast on the projection surface as they are. There are four main geographical characteristics that are taken into consideration at this stage. First, the shapes on the surface of the earth and on the map must be similar (conformity). Second, the proportions of areas must be maintained (static). Third, the proportions of distances must be maintained (conversion). Fourth, the directions on the map must correspond to the actual directions (true direction). However, no map can satisfy all four conditions at the same time, and only a globe can do so. Therefore, in flat maps, certain characteristics must be maintained for specific purposes, while others must inevitably be sacrificed, and an appropriate projection method must be selected accordingly.
A stereographic projection is a projection method that maintains stereographic properties. This method is characterized by maintaining the same angle between the meridians and parallels as on the actual Earth and having the same scale in all directions from a single point. For example, shapes that are elongated in the east-west direction must be adjusted in the same proportion in the north-south direction. The Mercator projection is a typical orthographic projection method, which is suitable for navigation but has the disadvantage of exaggerating areas at high latitudes.
On the other hand, the equidistant projection is a projection method that keeps the area constant. In this method, even if the shape is slightly distorted, the actual area of the surface is adjusted to be proportional to the area on the map. If a specific part of the map is extended in the east-west direction, the north-south direction is reduced by the same amount to maintain the proportional area. Lambert’s equidistant cylindrical projection is a typical example of this, maintaining equidistance by offsetting the increase in the east-west scale with a decrease in the north-south scale.
The equidistant projection focuses on maintaining the proportional relationship between distances. In this projection, the straight-line distance between two points on the map is designed to reflect the arc on the great circle, which is the shortest distance on the actual surface. For this purpose, a flat projection is often used, and when constructed around a pole, the parallels are represented as concentric circles of equal spacing, and the meridians are represented as radial straight lines.
Azimuthal projection is a method of projection in which the direction from a central point to all other points is made to correspond to the actual direction on the Earth’s surface. This projection is characterized by its flexibility in that it can be implemented in conjunction with one of the three properties of maintaining azimuth, regularity, and constancy. Due to these characteristics, it is particularly important for nautical and aeronautical maps.
In conclusion, map projection is a scientific solution to the problem of how to deal with the inevitable distortions that occur when transferring positions on a sphere to a flat surface. Each projection method is the result of mathematical adjustments to accurately represent specific geographic information such as shape, area, distance, and orientation. Mapmakers must decide which characteristics to prioritize based on the purpose and context of the map, and then select the appropriate projection method. Ultimately, a map is not simply a picture of reality, but an intentional representation that combines science and purpose.
