Introduction to Cartographic Projections

Fundamentals of Map Projections Introduction Imagine trying to wrap the curved surface of a basketball in a single sheet of paper without tearing or stretching it significantly. This is essentially the challenge that cartographers face every day. The Earth is roughly spherical, but we want to represent it on flat surfaces—paper maps, computer screens, and other media. This transformation from three dimensions to two requires making deliberate choices about which properties of the Earth to preserve and which to distort. A map projection is a systematic mathematical method for transforming the three-dimensional surface of the Earth onto a flat surface. The fundamental problem is this: it is geometrically impossible to flatten a sphere without distorting it in some way. Any flat map of the Earth must sacrifice at least one important property. The art and science of cartography lies in choosing which properties to preserve based on what the map will be used for. Understanding Distortion in Map Projections Since no projection can preserve all properties perfectly, cartographers must understand the different types of distortion that can occur. Distortion of shape is called angular distortion. This occurs when angles and local shapes are not preserved on the map—coastlines or country boundaries may appear stretched or compressed in certain directions. Distortion of area is called areal distortion. This happens when some regions appear larger or smaller than they actually are relative to other regions. This is particularly problematic if a map is being used to compare the relative sizes of countries or regions. Distortion of distance is called scale distortion. When scale distortion occurs, the distances between points on the map do not accurately represent the actual distances on Earth. A map might have one scale true along certain lines but different scales elsewhere. Distortion of direction is called azimuthal distortion. This happens when compass directions or bearings are not preserved—a straight line on the map might not represent a true compass direction on Earth. The key insight is this: you cannot have a projection that minimizes all four types of distortion simultaneously. If you preserve shape perfectly, you will distort area. If you preserve area, you will distort shape. The choice of projection is fundamentally about deciding which distortion is most acceptable for your specific purpose. The Three Major Families of Map Projections Cartographers organize projections into families based on the geometric shape used to transform the Earth's surface. Understanding these families helps explain why each projection has its characteristic strengths and weaknesses. Cylindrical Projections Imagine wrapping a cylinder around the Earth so that it touches along the equator. A cylindrical projection is created by projecting each point on the Earth's surface onto this cylinder, then "unrolling" the cylinder into a flat rectangle. Key properties of cylindrical projections: They are conformal, meaning they preserve local shapes and angles. If you look at a small region on a cylindrical projection map, it maintains the correct angles and proportions. They display latitude and longitude as straight, perpendicular lines, making them visually simple and easy to use. Compass bearings appear as straight lines, which is tremendously useful for navigation. The critical tradeoff: While cylindrical projections preserve shape beautifully, they severely distort area, especially near the poles. Greenland appears roughly the same size as Africa on a typical cylindrical map, when in reality Africa is about 14 times larger. This is the areal distortion problem with cylindrical projections. The Mercator projection is the most famous cylindrical projection. Created in 1569, it became the standard for navigation because of its property of showing compass bearings as straight lines. However, the extreme exaggeration of polar regions—Antarctica appears as a massive band along the bottom of the map—makes it problematic for showing true area relationships. If you use a Mercator map to compare the sizes of countries at different latitudes, you will get seriously misleading results. Conic Projections A conic projection is created by placing a cone so that it touches the Earth's surface along one or two lines of latitude called standard parallels. The Earth's surface is then projected onto this cone, which is then unrolled into a flat map. Key properties of conic projections: They provide reasonable preservation of both shape and area in the region between the standard parallels. They are particularly well-suited for mapping mid-latitude regions, such as the United States, Europe, or most of the continental areas that humans inhabit. Distortion is minimized along the standard parallels and increases gradually toward the poles and the equator as you move away from these chosen lines. Important distinction: There are different varieties of conic projections depending on what property you choose to preserve: Conformal conic projections (like the Lambert Conformal Conic) preserve local shapes. These are useful for navigation maps and aviation charts. Equal-area conic projections (like the Albers Equal-Area Conic) preserve area relationships. These are useful for thematic maps where you want to accurately compare the sizes of regions. The genius of conic projections is that you can choose where to place the standard parallels based on your area of interest. If you're mapping the northern United States, you'd place the standard parallels across that region, minimizing distortion there. The tradeoff is that areas far from the standard parallels will experience more distortion. Azimuthal (Planar) Projections An azimuthal projection (also called a planar projection) is created by projecting the Earth onto a flat plane that touches the globe at a single point. This point of contact is often a pole or a specific location of interest to the mapmaker. Key properties of azimuthal projections: They preserve direction from the center point of the projection, making them excellent for showing routes radiating from a central location. They can be designed to preserve distance from the center point (making them equidistant), which is useful for measuring distances from a key location. They can also be designed as equal-area projections, preserving the relative sizes of regions, such as the Lambert Azimuthal Equal-Area projection. Distortion increases with distance from the center point—the further you move from the center, the more distortion you encounter. Common uses: Polar maps: For mapping the Arctic or Antarctic regions, an azimuthal projection centered on the pole is ideal. The poles themselves, which are problematic points on many other projections, become simple points at the center. City-centered maps: A map centered on a specific city can show all directions and distances accurately from that city. Airline route maps: The property of preserving direction from a center makes azimuthal projections useful for visualizing flight routes radiating from a major hub. Other Notable Projections Two other projections are worth knowing about, though they represent different strategies than the three major families: The Robinson projection is a compromise projection. Rather than perfectly preserving any single property (shape, area, or distance), it balances multiple properties to reduce overall visual distortion. While it doesn't excel at any one thing, many cartographers and organizations (including National Geographic) have adopted it for world maps because it produces a visually pleasing result with acceptable distortion across all properties. The Mollweide projection is an equal-area pseudocylindrical projection commonly used for global thematic maps. It preserves area precisely while distorting shape (especially at the edges), making it ideal when showing global distributions of phenomena like population density or climate where area relationships matter. <extrainfo> </extrainfo> Selecting the Right Projection for Your Map Understanding projection families is only half the battle. The real skill lies in selecting the projection that best serves your map's specific purpose. This requires thinking critically about your audience, your geographic focus, and which distortions you can tolerate. Matching Projection to Purpose and Extent The intended geographic extent of your map—the area you're trying to show—should strongly influence your projection choice: For mid-latitude regions (roughly 20° to 60° from the equator): Use a conic projection. This includes most of North America, Europe, and Asia. Conic projections excel in these regions. For polar regions: Use an azimuthal projection centered on the pole. The poles are special points in polar azimuthal projections; they appear as single points with no distortion, whereas they would appear as lines or highly distorted regions on other projections. For entire world maps: Consider a compromise projection like Robinson, or choose based on what matters more—preserving area (Mollweide or equal-area conic) or minimizing visual distortion (Robinson). Making Tradeoff Decisions Every projection involves choosing what to sacrifice. Here are the key tradeoffs you'll encounter: Shape vs. Area: When you use a conformal projection (which preserves shapes), areas will be distorted, especially at high latitudes. Greenland will look too large. When you use an equal-area projection (which preserves area), shapes will be distorted away from the standard parallels, making coastlines and country boundaries look stretched or compressed. Distance from Center: Azimuthal equidistant projections preserve distance from one central point, but distances everywhere else will be distorted. Directions away from the center may also be inaccurate. The key question to ask when selecting a projection: What would be most misleading or problematic if distorted for my specific map's purpose? If you're making a map for navigation, preserving directions (compass bearings) is critical—use a cylindrical conformal projection like Mercator. If you're making a thematic map comparing the sizes of continents or countries, preserving area is critical—use an equal-area projection. If you're showing global patterns where visual balance matters more than perfect accuracy, use a compromise projection like Robinson. Practical Adjustments An important detail: the parameters of a projection can be adjusted to minimize distortion in your specific area of interest. For conic projections, you can choose where to place the standard parallels. For cylindrical projections, you can choose which latitude the cylinder touches. For azimuthal projections, you can choose the center point. Smart cartographers use these adjustments to concentrate accuracy where it matters most for their map. Additionally, the scale of your map matters. A very large-scale map (showing a small area in great detail) will show very little distortion regardless of projection, because the distortion becomes obvious mainly when mapping large regions. A small-scale map (showing a large area) will show more obvious distortion, making the projection choice more critical.