MAP CONIC PROJECTION: CHARACTERISTICS, ADVANTAGES, DISADVANTAGES - GEOGRAPHY - 2024

The cartographic conic projection is characterized by projecting the points of a spherical surface on the surface of a cone, whose vertex is located on the axis that passes through the poles and is tangent or secant to the sphere. The cone is a surface that can be opened in a plane, forming an angular sector and without deforming the lines projected on it.

The mathematician Johann Heinrich Lambert (1728 - 1777) was the one who devised this projection, appearing for the first time in his book Freye Perspective (1759), where he compiled various theories and reflections on projections.

Figure 1. Conical projection. Source: Weisstein, Eric W. "Conic Projection." From MathWorld – A Wolfram Web Resource.

In conical projections of the earth's surface, the meridians become vertex-centered radial lines with equal angular spacing, and the earth's parallels become circular arcs concentric to the vertex.

Figure 1 shows that the conical projection does not allow to represent both hemispheres. Furthermore, it is clearly observed that the distances are distorted away from the parallels that intercept the cone.

For these reasons, this type of projection is used to represent regions of mid-latitude, extensive from east to west and of lesser north-south extent. Such is the case in the continental United States.

Advantage

The Earth can be approximated to a sphere with a radius of 6378 km, considering that all land and water masses are on that great sphere. It is about converting this surface, which covers an object in three dimensions, such as a sphere, into another object in two dimensions: a flat map. This brings the disadvantage that the curved surface is distorted, when wanting to project it onto the plane.

Map projections, such as the conic projection, try to solve this problem with as little loss of accuracy as possible. Hence, there are several options to make a projection, depending on the characteristics that you want to highlight.

Among these important characteristics are distances, surface area, angles, and more. The best way to preserve them all is to represent the Earth in 3D to scale. But this is not always practical.

Transporting a globe around is not easy, as it takes up volume. Nor can you see the entire surface of the Earth at once, and it is impossible to reproduce all the details on a scale model.

We can imagine that the planet is an orange, we peel the orange and spread the peel on the table, trying to reconstruct the image of the surface of the orange. It is clear that much information will be lost in the process.

The projection options are as follows:

- Project onto a plane or

- On a cylinder, which can be developed as a rectangular plane.

- Finally on a cone.

The conical projection system has the advantage that it is exact over the parallels chosen to intercept the projection cone.

In addition, it keeps the orientation along the meridians practically intact, although it may distort the scale along the meridians somewhat for latitudes far from the standard or reference parallels. That is why it is suitable for representing very large countries or continents.

The equidistant conic projection

It is the conical projection system originally used by Ptolemy, a Greek geographer who lived between AD 100-170. Later in 1745 it was improved.

It is used frequently in the atlases of regions with intermediate latitudes. It is suitable for showing areas with a few degrees of latitude, and that belong to one of the equatorial hemispheres.

In this projection, the distances are true along the meridians and in the two standard parallels, that is, the parallels chosen to intercept with the projection cone.

In the equidistant conic projection, a point on the sphere extends radially to its intersection with the tangent or secant cone, taking the center of the sphere as the center of projection.

Figure 2. North America with equidistant conical projection. Source: Radical cartography.

Disadvantages

The main disadvantage of the conic projection is that it is not applicable to equatorial regions.

Furthermore, the conic projection is not appropriate for mapping large regions, but rather particular areas, such as North America.

Albert's conic projection

Use two standard parallels and preserve area, but not scale and shape. This type of conical projection was introduced by HC Albers in 1805.

All areas on the map are proportional to those on Earth. In limited regions, the directions are relatively accurate. The distances correspond to those of the spherical surface on the standard parallels.

In the United States this projection system is used for maps showing the limits of the states of the Union, for which 29.5º N and 45.5º N are chosen as standard parallels, resulting in a maximum scale error of 1, 25%.

Maps made with this projection do not preserve the angles corresponding to those of the sphere, nor do they preserve perspective or equidistance.

Lambert Conformal Conic Projection

It was proposed in 1772 by the Swiss mathematician and geographer of the same name. Its main characteristic is that it uses a cone tangent or secant to the sphere and the projection keeps the angles invariant. These qualities make it very useful in aeronautical navigation charts.

The United States Geological Survey (USGS) uses the Lambert Conic projection. In this projection, the distances are true along the standard parallels.

Figure 3. Different conic projections of the northern hemisphere, on the right, the date of creation. Source: Wikimedia Commons.

In the Lambert conic projection the directions remain reasonably precise. Areas and shapes are slightly distorted at positions close to standard parallels, but the alteration of shape and area increases with spacing to them.

Because the objective of this projection is to maintain directions and angles equal to the original ones on the sphere or ellipsoid, there is no geometric method of obtaining it, unlike the equidistant projection of Ptolemy.

Rather, it is an analytical projection method, based on mathematical formulas.

The USGS base maps for the 48 continental states use 33ºN and 45ºN as standard parallels, yielding a maximum map error of 2.5%.

For navigational charts in Alaska, the base parallels used are 55ºN and 65ºN. Instead, the national atlas of Canada uses 49ºN and 77ºN.

References

1. Geohunter. The Lambert Conformal Conic projection. Recovered from: geo.hunter.cuny.edu
2. Gisgeography. Conic Projection: Lambert, Albers and Polyconic. Recovered from: gisgeography.com
3. Gisgeography. What are Map Projections? Recovered from: gisgeography.com
4. USGS. Map projections. Recovered from: icsm.gov.au
5. Weisstein, Eric W. "Albers Equal-Area Conic Projection." Recovered from: mathworld.wolfram.com
6. Weisstein, Eric W. "Conic Projection" Recovered from: mathworld.wolfram.com
7. Weisstein, Eric W. "Lambert Conformal Conic Projection" Recovered from: mathworld.wolfram.com
8. Wikipedia. List of map projections. Recovered from: en.wikipedia.com