Oct 7
Map Projection Methods: Plaining the World
- Gökçe Bal
- Oct 7
- 6 min read
Updated: 5 days ago
Carl Gauss long ago demonstrated the impossibility of transferring the world onto flat paper . Just as it's impossible to peel an orange and make it perfectly flat, creating a map of the Earth's surface inevitably distorts some of it. Projections are mathematical methods that show us how to manage these distortions. When deciding which feature to preserve, we ask ourselves: shape, area, or distance. Ultimately, every projection perfectly preserves a limited feature, while other features are distorted.
In this article, we will discuss, in a technical but understandable language, why different projection types are preferred, which projections offer solutions to which geographical problems, and application examples in Türkiye.
Contents:
Projection Methods: Angles or Area?
Map projection methods fall into three main categories: azimuthal (plane), cylindrical, and conical. Each has its own distortion tolerances, and the preservation preferences are grouped into three main categories:
Conformal (angle-preserving) projections: Represent shapes and angles at a small scale without distortion. For example, the Mercator and Transversal Mercator (Gauss-Krüger/UTM) projections are conformal. They preserve the angles between parallel coordinate lines. Therefore, the Mercator is useful for charting routes in navigation; drawing a straight line between two points facilitates orientation with a compass.
Equal-area projections: Consistently preserve the surface area of each region on a map. The Albers or Gall–Peters projections accurately represent the relative size of regions. For example, the Albers equal-area conical projection is generally preferred for large east-west areas, especially for countries like the United States.
Planar (Azimuthal) Projections: Planar projections are created by projecting the Earth's surface onto a plane tangent to a specific point. In these projections, distances and directions measured from the center point are accurately preserved. The azimuthal equidistant projection is a typical example. These features make planar projections widely preferred in applications such as polar region mapping and flight path planning. However, distortions increase with distance from the center, making them unsuitable for mapping large areas.
There are also stereographic (polar) projections, called reverse projections , a special case of Mercator, and various hybrid projections (pseudoconical, pseudocylindrical) . For example, navigation also uses a spherical equidistant projection in this category. But the general rule is that every projection does one thing well and spoils the others .
Cylindrical Projections: Gauss-Krüger and UTM
When a cylinder is placed vertically (east-west) and rotated around the Earth, the resulting map is called a transverse cylindrical projection . Gauss-Krüger and UTM are the most well-known members of this category. Both are based on the Transverse Mercator (TM) projection. In the TM projection, the cylinder is tangent to a meridian, not the equator. This ensures that both shape and distance are not distorted at that central meridian, and the scale there is true; distortion increases as one moves toward the periphery.
Gauss-Krüger Projection: This type of projection projects the Earth onto a cylinder, preserving its angles. The Earth is divided into slices of 3° or 6° width, and a separate cylinder is tangent to each slice. In Gauss-Krüger, distortion increases with distance from the central meridian; maps are generally produced within 3° of each slice. In Turkey, topographic maps at a scale of 1:25,000 were produced using Gauss-Krüger (6° slices, with central meridians at 27°, 33°, 39°, and 45°).
Dilimlenmiş Harita Projeksiyonu: Coğrafi Bölgelere Özel Yaklaşım UTM (Universal Transverse Mercator): This system, developed based on Gauss-Krüger, is a globally standardized system. It is divided into 60 6° slices, starting from the 180° prime meridian. In each slice, the cylinder is tangent to the meridian at the center of that slice. UTM is also conformal: it preserves shapes and angles in small areas, but distortion increases, particularly toward the slice edges. Today, national maps are produced using this system in many countries (USA, Canada, Turkey, etc.). For example, a significant portion of US states are based on Transverse Mercator; large areas in Canada and Turkey are also mapped with UTM/GC. UTM's greatest advantage is its adaptability to any geographical area : 60 slices ensure a similar level of distortion across the globe.
National Mapping Infrastructure (UTM/Gauss-Krüger)
Consider the large-scale topographic maps of a country. If we are creating a scaled map based on geographical latitudes and longitudes (GPS coordinates), Gauss-Krüger/UTM is suitable. For example, in the Turkish National Map Application, maps at 1:25,000 and 1:50,000 scales are produced using UTM based on 6° gradients, with only approximately 0.1% distortion at each gradient. This allows coordinate values in meters and a consistent system to be used everywhere, in many applications, from urban planning and land engineering to infrastructure projects and agricultural land delimitation. With new technologies, these systems are automatically converted and harmonized by GIS software , making it possible to flexibly use different gradients in our projects.
Lambert Conformal Conic: Fine Scaling at Mid-Latitudes
A conical surface is more suitable than a cylinder for maps with wide east-west extensions. In this projection, the cone is tangent or cut to the Earth through the northern and southern hemispheres. The Lambert Conformal Conical is the most common and technically preferred conical projection. As its name suggests, it is a shape-preserving (conformal) projection. Two standard parallels are generally chosen, and distortion is minimal at these parallels. Distortion increases north and south. Parallels are concentric circles radiating from the center on the map, while meridians are lines drawn through the center.
Area of Use: The Lambert projection is ideal for mid-latitude countries, where latitude is small but longitude is large. For example, it is widely used in countries with large east-west areas, such as the US, Canada, India, and Egypt . US states with east-west orientations (such as Florida and California) often use the Lambert projection. Another advantage of this projection is that all parallels appear as balanced circles around a central center, minimizing distortion.
Regional Flood Maps (Lambert Conformal Conic)
Let's say we're creating flood maps for a region stretching from coast to coast (or a country with homogeneous latitudes, such as Turkey). Minimizing scale distortion (distortion of length) is crucial in these maps. In such a case, the Lambert Conical Conformal is chosen. For example, maps of the Mississippi River basin in the US, Italy, or intercity maps along the west-east route of Turkey can easily be created using the Lambert projection. This allows for realistic area and distance comparisons for engineering projects.
Projection Solutions for Different Map Needs
There are also various projections for different needs. For example, Mercator remains very popular in navigation maps because loxodromes (constant heading angles) appear straight, allowing aircraft and ship routes to be easily followed with a compass. Web Mercator, used in digital maps like Google Garitas, is essentially a cylindrical projection and is preferred because it accurately displays street directions. Equal-area projections are used in intercontinental maps: For example, projections like Gall-Peters or Mollweide can be used to keep continental sizes close to reality. Thus, an atlas can depict Africa as larger than the Americas, as it actually is.
Which projection should you choose? The answer to this question depends on the purpose of the map. In summary:
Local/City Maps typically use Gauss-Krüger/UTM (for metric accuracy).
Transversal Mercator (UTM) is suitable for long-distance country maps .
For large continental or state maps, the Lambert Conic or Albers Equal-Area is preferred.
Loxodromic projections such as Mercator or Stereographic (polar) are used in Marine/Air Navigation .
Global View (Atlas) includes Gall-Peters or globe models for world perspective.
Solutions Offered by Technology and the Future
Today, we no longer need to worry so much about the complexities of map projections. Geographic Information Systems (GIS) software can quickly convert between different projections. For example, while we use UTM when collecting topographic data in Turkey, converting the project to Web Mercator for global presentation takes seconds.
For example, Google Earth or VR applications can virtually eliminate the distortion problem by presenting the map as an interactive 3D sphere rather than a flat one. GPS in most modern devices operates on an ellipsoid model of the Earth, making accurate coordinate calculations easier. Ultimately, technology offers ways to automatically correct and manage the "distortion" problem in map projections. Instead of being bogged down in the mathematics of projection, designers and engineers prioritize the scale, accuracy, and scope they need.
In summary, while map projections are still fundamentally a mathematical necessity, it is now much easier to achieve innovative and user-friendly mapping applications with modern solutions.
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