The map conic projection It is characterized by projecting the points of a spherical surface onto 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.

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

Figure 1 shows that the conical projection does not allow both hemispheres to be represented. In addition, it is clearly observed that the distances are distorted away from the parallels that intersect the cone.

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

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## Advantages

The Earth can be approximated to a sphere of 6378 km of radius, considering that all the terrestrial and aquatic masses are on that great sphere. It is about converting this surface, which covers a three-dimensional object, such as a sphere, into another two-dimensional object: a flat map. This brings the inconvenience that the curved surface is distorted, when trying 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 features are distances, surface area, angles, and more. The best way to preserve them all is by representing the Earth in 3D to scale. But this is not always practical.

Transporting a globe everywhere is not easy, since it takes up volume. You also can’t see the entire surface of the Earth at once, and it’s impossible to reproduce every detail 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 orange’s surface. It is clear that a lot of information will be lost in the process.

The projection options are as follows:

– Project on 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 on the parallels chosen to intercept the projection cone.

In addition, it keeps the orientation along the meridians largely intact, although it may distort the scale along the meridians a bit for latitudes far from the standard or reference parallels. That is why it is appropriate to represent 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 and 170. c. Later in 1745 it was improved.

It is frequently used in atlases of regions with intermediate latitudes. It is adequate to show 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 intersect 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 its center of projection.

**Disadvantages**

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

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

## The Albert conic projection

It uses two standard parallels and preserves area, but not scale and shape. This type of conical projection was introduced by HC Albers in the year 1805.

All areas on the map are proportional to the corresponding areas on Earth. In limited regions, addresses 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 that show 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 tangent or secant cone 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, distances are true along standard parallels.

On the Lambert conic projection the directions remain reasonably precise. The areas and shapes are slightly distorted at positions close to the standard parallels, but the disturbance of shape and area increases with distance from them.

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

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. In contrast, the national atlas of Canada uses 49ºN and 77ºN.

## References

Geohunter. The Lambert Conformal Conic projection. Retrieved from: geo.hunter.cuny.edu

Gisgeography. Conic Projection: Lambert, Albers and Polyconic. Retrieved from: gisgeography.com

Gisgeography. What are Map Projections? Retrieved from: gisgeography.com

USGS. Map projections. Retrieved from: icsm.gov.au

Weisstein, Eric W. «Albers Equal-Area Conic Projection.» Retrieved from: mathworld.wolfram.com

Weisstein, Eric W. “Conic Projection” Retrieved from: mathworld.wolfram.com

Weisstein, Eric W. “Lambert Conformal Conic Projection” Retrieved from: mathworld.wolfram.com

Wikipedia. List of map projections. Retrieved from: en.wikipedia.com