Cartography is the art and science of portraying a three-dimensional planet on two-dimensional surfaces, maps. Many projections have been developed to solve the challenges of this transformation. Among them, the Winkel Tripel projection stands out as one of the most balanced. It is also widely accepted. The Winkel Tripel is not as familiar to the public as the Mercator or Robinson projections. Still, it has gained significant respect in academic and professional cartographic circles.
National Geographic notably adopted it as its standard world map projection in 1998. The Winkel Tripel is not as familiar to the public as the Mercator or Robinson projections. But, it has gained significant respect in academic and professional cartographic circles. National Geographic adopted it as its standard world map projection in 1998.
This article explores the history of the Winkel Tripel projection. It examines its advantages and disadvantages. The article also evaluates its comparative value. Additionally, it discusses the factors that led to its institutional acceptance. This occurred by one of the most influential geographic organizations in the world.
I. The Challenge of Map Projections
Before we examine the Winkel Tripel, it’s essential to understand the broader problem it attempts to solve. The Earth is a geoid, an oblate spheroid shaped by gravity and rotation—yet maps are flat. The transformation from globe to flat surface necessarily involves distortion of one or more geographic properties:
- Area
- Shape
- Distance
- Direction
Every map projection makes compromises. Some prioritize navigation (like the Mercator), while others focus on maintaining area (like the Gall-Peters) or shape (like conformal projections). The Winkel Tripel aims to reduce overall distortion, offering a visual balance that neither overemphasizes nor underrepresents any one property.
II. The History of the Winkel Tripel Projection
The Winkel Tripel projection was developed in 1921 by German cartographer Oswald Winkel (1873–1953), a professor of mathematics and geography. Winkel was concerned about the shortcomings of existing world map projections. He sought a compromise between the precision of mathematics and the needs of visualization.
The word “Tripel” is German for “triple,” and refers to Winkel’s goal of minimizing three types of distortion:
- Area
- Direction
- Distance
To achieve this, Winkel mathematically averaged two existing projections:
- The equidistant cylindrical projection (also known as Plate Carrée), which preserves distances along meridians but grossly distorts area and shape.
- The Aitoff projection, which emphasizes aesthetics and reduces shape distortion but doesn’t preserve scale.
The resulting hybrid was the Winkel Tripel. It is a pseudocylindrical projection with curved parallels and meridians. It features visually pleasing curves and moderate distortions across all key categories.
III. Characteristics of the Winkel Tripel Projection
1. Type of Projection
The Winkel Tripel is pseudocylindrical. It depicts the central meridian and equator as straight lines. Meanwhile, it curves other meridians and parallels. This produces a familiar “oval” or elliptical world map.
2. Distortion Profile
While no projection can eliminate distortion, the Winkel Tripel minimizes root mean square errors in area, distance, and angular distortion. None of these properties are perfectly preserved. Nonetheless, they are less severely distorted than in most other projections.
3. Visual Balance
The resulting map is aesthetically pleasing, with:
- Moderate area distortion near the poles
- Less stretching of high-latitude landmasses (e.g., Greenland and Antarctica)
- Natural curvature that avoids the abrupt corners seen in many cylindrical projections
This balance makes it ideal for general reference and educational purposes.
Winkel Tripel Projection China / Australia / Japan Centered
IV. Comparison with Other Map Projections
To appreciate the strengths of the Winkel Tripel, it helps to compare it with its major competitors.
1. Mercator Projection
- Purpose: Designed by Gerardus Mercator in 1569 for navigation.
- Strengths: Preserves direction and rhumb lines, essential for maritime navigation.
- Weaknesses: Grossly distorts area; Greenland appears as large as Africa (in reality, it’s about 1/14th the size).
- Winkel Tripel Advantage: Better for general-use maps where exact visual proportion is important.
2. Robinson Projection
- Developed: In 1963 by Arthur H. Robinson, aimed to create a more visually appealing world map.
- Strengths: Smooth, rounded shapes; reduced pole exaggeration compared to Mercator.
- Weaknesses: Still distorts area, direction, and shape, and is not mathematically derived but rather constructed empirically.
- Winkel Tripel Advantage: More mathematically rigorous, with smaller average distortions overall.
3. Gall-Peters Projection
- Purpose: Equal-area projection designed to emphasize the relative size of developing nations.
- Strengths: Preserves area.
- Weaknesses: Severely distorts shape, particularly near the equator and poles. Landmasses look stretched.
- Winkel Tripel Advantage: More natural-looking shapes, which are often more intuitive and informative for educational contexts.
4. Goode’s Homolosine Projection
- Strengths: Excellent area preservation with interruptions to reduce distortion.
- Weaknesses: Discontinuities in the ocean make it unsuitable for some thematic or navigational maps.
- Winkel Tripel Advantage: Continuity across oceans, better for depicting global connections.
V. National Geographic’s Adoption of the Winkel Tripel
The National Geographic Society (NGS) is one of the most influential map publishers globally. Its decision to adopt the Winkel Tripel in 1998 marked a turning point in the projection’s popularity and validation.
1. Why the Change?
From 1922 to 1988, National Geographic used the Van der Grinten projection. This projection showed the entire Earth in a circular format. But, it greatly distorted high-latitude areas. In 1988, the society switched to the Robinson projection, which reduced this distortion and improved aesthetics.
Yet, continued cartographic research into distortion led to the choice of the Winkel Tripel as a superior choice.
2. Evaluation Criteria
NGS evaluated projections based on:
- Visual accuracy
- Distortion minimization
- Aesthetic appearance
- Balance of land and ocean representation
The Winkel Tripel scored highest across all categories, particularly for its low average distortion and visually pleasing proportions.
3. Impact of the Switch
National Geographic’s endorsement played a pivotal role in popularizing the Winkel Tripel, especially in educational materials and atlases. Today, many schools, universities, and textbook publishers use it as a default world map projection.
VI. Advantages of the Winkel Tripel Projection
1. Balanced Distortion
By minimizing overall distortion, the Winkel Tripel serves as a compromise projection, making it ideal for general-purpose maps.
2. Realistic Visual Representation
Landmasses are more proportionally correct. For example:
- Africa retains a shape and size closer to reality.
- Greenland appears appropriately smaller.
3. Mathematically Grounded
Unlike the Robinson projection, which was hand-drawn for aesthetic purposes, the Winkel Tripel is based on a defined mathematical formula. This makes it reproducible and analyzable by cartographic software.
4. Well-Suited for Thematic Maps
Because it doesn’t drastically distort spatial relationships, it’s good for thematic maps showing climate, population, or migration.
5. Adoption by Educational and Scientific Communities
Its growing use in textbooks, encyclopedias, and academic atlases speaks to its credibility and functionality.
VII. Disadvantages and Limitations of Winkel Tripel
1. No Property Fully Preserved
Unlike conformal, equal-area, or equidistant projections, the Winkel Tripel does not perfectly preserve any single cartographic property. It’s a compromise.
2. Not Ideal for Navigation
Like most pseudocylindrical projections, it can’t be used for plotting precise directional routes.
3. Edge Distortion Remains
Though reduced compared to cylindrical projections, distortion near the edges, especially in polar regions, is still noticeable.
4. Computational Complexity
Its formula involves trigonometric averaging of coordinates, which is more complex than simpler projections like Mercator. This was a limitation in earlier mapmaking eras, though it’s negligible today with digital tools.
VIII. Mathematical Formulation
For those interested in the technical side, the Winkel Tripel projection uses a formula. This formula averages the coordinates of the equirectangular projection. It also averages the coordinates of the Aitoff projection.
Given a spherical latitude φ and longitude λ (in radians), the Winkel Tripel uses:
- An average of the equirectangular coordinates:
xe=λcos(ϕ1)x_e = \lambda \cos(\phi_1)xe=λcos(ϕ1), ye=ϕy_e = \phiye=ϕ - And the Aitoff coordinates, which involve a transformation of the spherical coordinates into an azimuthal-like format.
The final coordinates are:
- x=12(xe+xa)x = \frac{1}{2}(x_e + x_a)x=21(xe+xa)
- y=12(ye+ya)y = \frac{1}{2}(y_e + y_a)y=21(ye+ya)
Where xax_axa and yay_aya are the Aitoff projection coordinates, and φ₁ is a standard parallel (usually set at 50°28′).
While not trivial to calculate by hand, modern GIS software handles these equations effortlessly.
IX. Conclusion: Winkel Tripel Modern Standard for Global Mapping
The Winkel Tripel projection does not offer the precision of conformal or equal-area maps. Yet, its versatility, visual appeal, and moderate distortions make it an ideal choice for global overviews. We live in a world increasingly reliant on maps to understand global phenomena. These include climate change, migration, and geopolitical shifts. The need for a projection that shows the world fairly and accessibly has never been greater.
The adoption by National Geographic solidified its place as a default projection for general world maps. Our cartographic needs continue to evolve. The Winkel Tripel is a reminder. Sometimes, the best solution is not the most extreme. Instead, it is the most balanced.
Further Reading:
- Snyder, John P. Flattening the Earth: Two Thousand Years of Map Projections. University of Chicago Press, 1993.
- National Geographic’s Cartographic Policies and Map Projections Overview
- Bugayevskiy, Lev M., and Snyder, John P. Map Projections: A Reference Manual. Taylor & Francis, 1995.