Conic Projection

A conic projection is a fundamental map projection technique that mathematically transfers the Earth’s spherical or ellipsoidal surface onto a cone, which is then unrolled into a flat map. This approach generates map graticules where latitude lines appear as concentric arcs and longitude lines radiate from a central point, providing an elegant solution for representing mid-latitude regions that are wider east–west than north–south.

Historical Development

The geometric basis for conic projections dates to ancient Greek mathematicians, but practical and explicit forms emerged during the Renaissance and Enlightenment. By the 18th and 19th centuries, influential cartographers such as Johann Heinrich Lambert (Lambert Conformal Conic, 1772) and Heinrich Christian Albers (Albers Equal Area Conic, 1805) formalized the most widely adopted conic projections. Today, standards from the USGS, ICAO, and other organizations rely on these projections for national and regional mapping.

Geometric Construction

A conic projection is created by conceptually placing a cone over the globe so that it is:

• Tangent to the globe at a single latitude (one standard parallel), or
• Secant, intersecting the globe at two latitudes (two standard parallels).

After projecting the Earth’s features onto the cone, the cone is “cut” along the central meridian and flattened. This process produces:

• Parallels: arcs of concentric circles,
• Meridians: straight lines radiating from the apex (typically outside the mapped area).

The central meridian and latitude of origin further define the map’s center and coordinate system.

Mathematical transformation between geographic coordinates (latitude φ, longitude λ) and planar coordinates (x, y) varies by projection type and selected parameters (see Snyder, “Map Projections—A Working Manual”).

Distortion Patterns

All map projections introduce distortion. In conic projections:

• Scale is true and distortion is minimized along the standard parallels.
• Distortion increases northward and southward from these parallels.
• Secant conic projections (two standard parallels) distribute distortion more evenly than tangent projections (one standard parallel).

Tissot’s indicatrix visualizes these distortions: in Albers Equal Area, circles retain area but not shape; in Lambert Conformal, local shapes are preserved but not area.

Major Types of Conic Projections

Albers Equal Area Conic

Preserves area, making it ideal for thematic and statistical maps where accurate representation of spatial quantities is required.

• Distortion: Shapes and angles are distorted away from standard parallels.
• Use cases: USGS thematic maps, census, land use, environmental studies.

Lambert Conformal Conic

Preserves local shapes and angles, essential for navigation and meteorological applications.

• Distortion: Area and distances not preserved except along standard parallels.
• Use cases: State Plane Coordinate System (SPCS), aeronautical charts, topographic maps.

Polyconic Projection

Every parallel is projected as if it were a standard parallel, creating true-to-scale arcs for all parallels and a straight central meridian.

• Distortion: Neither conformal nor equal-area; distortion increases away from center.
• Use cases: Historical topographic mapping by USGS.

Comparison with Other Projection Classes

• Versus Cylindrical Projections: Conic projections minimize distortion at mid-latitudes. Cylindrical projections (like Mercator) are better for equatorial regions but distort high latitudes.
• Versus Azimuthal Projections: Azimuthal projections are best for polar or point-centered maps; conic projections excel for regions spanning wide longitudes at mid-latitudes.
• Tangent vs. Secant: Secant projections (two standard parallels) are superior for broader regions, as distortion is spread evenly.

Mathematical Formulation

The transformation equations depend on projection type and parameters:

• Lambert Conformal Conic: Preserves angles; uses trigonometric and logarithmic functions.
• Albers Equal Area Conic: Preserves area; modifies arc radii and spacing for area fidelity.
• Polyconic: Projects each parallel individually, resulting in complex but locally accurate shapes.

For detailed formulas, see Snyder’s “Map Projections—A Working Manual” (USGS Professional Paper 1395).

Applications

Government and National Mapping

• USGS: Uses Albers Equal Area for thematic maps and Lambert Conformal for topographic and base maps.
• State Plane Coordinate System: Many states use Lambert Conformal Conic for surveying and engineering accuracy.

Aeronautical and Meteorological Charts

• Lambert Conformal Conic is the standard for flight navigation and weather charting, due to its preservation of local angles and shapes.

Thematic & Statistical Mapping

• Albers Equal Area Conic is preferred for population, climate, and resource maps where accurate area measurement is crucial.

Selecting a Conic Projection

When choosing a conic projection, consider:

1. Geographic extent and orientation: Suited for regions wider east–west than north–south at mid-latitudes.
2. Purpose: Choose Albers for area accuracy, Lambert for shape and directional accuracy.
3. Parameter selection: Position standard parallels to bracket the area of interest for minimal distortion.

References

• Snyder, J.P. (1987). Map Projections—A Working Manual. USGS Professional Paper 1395.
• NGA (2020). Department of Defense World Geodetic System 1984—Its Definition and Relationships with Local Geodetic Systems.
• ICAO Doc 9674, Manual on Air Navigation Services.

Summary Table

Conic projections continue to serve as versatile tools in modern mapping, balancing the cartographer’s perennial challenge of representing a spherical world on a flat surface.

For additional guidance on selecting or implementing conic projections in your mapping projects, contact our experts or schedule a demo .o/).