jueves, 4 de julio de 2013

Sun polar chart II

How to build your own Sun polar chart:
The stereographic solar charts allow us to determine when sunlight falls through a window or a skylight. Previously, I made a brief entry which set out how they should be used:

As can be seen, its handling is easy. However, each solar chart serves only to a given latitude, so we must learn to build our own solar chart. As it is a laborious process, I will discuss it in two different entries.

The first thing to know is that the stereographic solar chart is a representation of the ecliptic, or sun path on a horizontal plane. However, the paths are directed to a central point, instead of using an orthogonal projection. This singular projection allows us to discern the sun path in the lower latitudes.

The first step is to draw the Sun's path on a sphere in the days of the equinox. This path corresponds to an arc, which is projected as a line on the sphere representing the sky. Then we draw the solstice paths, which are also circumference arcs, which are separated from the equinox by the tilt angle of the axis of the Earth; 23.44º.

When drawing circumference arcs equidistant from both solstices, we obtain the trajectories of the Sun in each month.

The second step is to project the position of the hours on the ecliptic equinox, knowing that every hour is separated from the previous 15 degrees.

The third step is to tilt the solar paths, according to the latitude where we are. Following the example we consider latitude 40º. Accordingly, the ecliptic will be tilt 40º.

In this same step we will project the ecliptic on the horizontal plane of the sphere. To do this, the points that are on the plane are projected directly onto the ground, while the points on the sphere will be directed to lower vertex. Thus, we draw the sun path on the day of the equinox.

In the fourth step, we operate in the same way with the trajectories of the solstices: the points on the horizon are projected directly onto the ground, while the points on the sphere are directed towards the lower vertex.
In the fifth step, we operate in the same way with the rest of the year. Thus, we have sun paths drawn every month for a latitude of 40 °.

In the next post I will explain how to find the hours in solar paths. Soon.

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