Projections and navigation [School]

The specialty of Air Navigation, denominada “Aeronavigation”, the teachings of a specialized aeronautical engineering make use of geometry for making charts.

Students who have made this work are sensitive to it and therefore highlight one of the applications of the teachings they have received.

The group “HAFF” gives us another interesting example of cross-learning in the field of projective geometry.

The aeronautical chart is defined as representing a portion of the earth, its landscape and buildings, specially designed to meet the requirements of the Air Navigation. Is a map which reflects the routes to be followed by aircraft, and aids are provided, procedures and other critical data to the pilot.(W)

por HAFF

In this post I will address the main types of projections made in cartography to produce charts. In the field of aeronautics, This has some importance to air navigation, today as pilots use navigational charts despite the existence of radio, radar and GPS.

The main problem that arises is that the Earth's surface is not developable and therefore it is not possible to project with total fidelity on a plane. So, each type will have its limitations projection, in which a crew to select a map based, depending on the type of route.

In aeronautics, las projection surfaces used are the plane, the cylinder and cone, projections resulting flat, cylindrical and conical.

PLANE PROJECTIONS

Depending on the point from which all points of the planet projected on the plane, We can divide them into:

• Spell: Is projected from a point improper (infinite) so as to project the sphere perpendicular to the plane of projection.
• Scenographic: The origin of the projection corresponds to a point outside the Earth's surface and a finite distance.
• Stereographic: The origin of the projection is located on the surface of the Earth, at a point diametrically opposed to the plane.
• Gnomonic the centrográfica: The center of the earth is the origin of the projection.

CONFORMITY, METHOD AND CIRCLES MAXIMUM

To make a chart, is important to note certain items described below.

• CONFORMITY: We say that a projection is as if the angles are preserved. Namely, if we measure the angles of a triangle formed by three towns, in the letter must match these three values.
• METHOD: A projection is equivalent if you keep the areas.
• Equidistance: if it preserves the actual distances between various points on the map.

A good projection should be as and equivalent. But it is impossible to have a projection that satisfies these features completely. Thus, intermediate solutions are sought. Conformity and equivalence are not easy to be at once as a projection of a figure that preserves angles not retain your area.

Other items to consider, fine to navigation, are how transform a line loxodrómica and orthodromic on projection. Consider these two concepts:

• An flat the shortest distance between two points is given by straight line
• On a spherical surface, Earth is approximately as, to get from one point to another by the shortest path, you should go for a circle arc.

It is called circle to the intersection of a sphere with a plane passing through its center. Namely, a circle of maximum radius in the area. For example, all meridians are great circles. But not all parallels, since they are reduced as we increase the radius of latitude or down from Ecuador (which is a circle).

Well, a line (o ruta) orthodromic is one that is a circle arc and, thus, the fastest path between two points. Sin embargo, when moving with a steady course with our aircraft, We are not doing this kind of experience, but we are flying on a loxodrómica, that is the one route that intersects the meridian at the same angle (what happens to maintain a constant geographic direction). Would describe a path like the image. Namely, to fly a great circle would have to be constantly changing course. Although we must keep in mind that this happens on a large scale and for short-range travel this much less influence.

loxodromica

Said, for the pilot of the ship, is important to know how to render a rhumb line and great circle. One way to look quickly is to look at the way they meridians (great circles) in our letter. If we see that are as straight possible, We will be more useful. See below for various types of projection and how these qualities are present in them.

PROJECTIONS

Polar gnomonic: Not satisfied and, As in the previous, as we move away from the pole shapes are distorted to a greater degree. The parallels and meridians are orthogonal. Orthodromic lines are rhumb lines are straight and curved lines.

Cilíndrica Mercator: It conforms and distortion of areas and shapes increases with distance from Ecuador (not suitable to represent the entire globe). The parallels and meridians are orthogonal. The parallels are presented as unequally spaced parallel straight lines. The meridians appear as equally spaced parallel lines. The lines are curved orthodromic, except meridians and Ecuador. The rhumb line is a line. The origin of the projection is the center of the sphere and the projection plane is tangent to it in Ecuador. It is widely used in navigation for ease of draw rhumb. A mathematical description of the projection can be found in: Mercator Projection

Lambert Conformal Conic: This is the projection used in General Aviation (letter including ICAO 1: 500.000). It conforms and distortion of areas and shapes is very light. The parallels and meridians are orthogonal and the distance scale is practically constant. The parallels are arcs of concentric circles as almost equally spaced. Meridians appear as straight lines which converge on the pole. The great circle are approximately straight and are curved rhumb. Projecting from the center of the sphere towards a conical surface, intersecting the projection plane (letter) in the parallel llamados the standard automecoicos. Is used for virtually all types of navigation.