Sun polar chart III

How to build your own Sun polar chart:

It has been some time since my last blog, but I did not want to leave in abeyance how to draw a Sun chart. Before the summer we could see what it was and how it is used a Sun polar chart:

Sun polar chart I

Where is exposed how a Sun chart allows us to determine when sunlight falls through a window or a skylight. However, we need a Sun chart for our latitude and is therefore important to know how to draw it. So I wrote the following post:

Sun polar chart II

Where was solved how to start drawing a stereographic Sun chart ... the problem is that the drawing is a bit tedious, so I decided to solve it step by step in two posts. This is the second and last post on sun charts.

After a fifth step, determined in the previous post, we draw the solar chart with the months of the year:

The sixth step corresponds to the drawing of the hours on the trajectories of the months of the year. Let's start with the six o'clock in the morning. As we have indicated the hours on the trajectories of the equinox, we just have to choose the point corresponding to the six, which indicates the change from night to day. From that point we draw a plane perpendicular to the ecliptic, which cuts at two points on the sphere. These two points are projected in stereographic form (to the lower vertex of the sphere) and are indicated on the axis noon. Then we draw a circle passing through the two points and the center is located on the axis:

Likewise, we draw the rest of paths hours. The drawing shows the trajectory of the seven o'clock:

With hourly and monthly paths we have our solar chart:

Although we need an important drawing: the parallels:

Once we have drawn parallels, are projected in stereographic form (to the lower vertex of the sphere) as shown in the picture:

That's it! We have our Sun polar chart and it may be used to calculate when light falls through a window, a courtyard or a skylight. Of course, for a given latitude:

And that's all for now. There is still much to discover (skylights, atriums, design methods, and a long etcetera) and I'll try to show it in the next few weeks.

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:

Sun polar chart II

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.

Sun Polar Charts I

How to use your own Sun polar chart:

The Sun polar charts allow us to determine when sunlight falls through a window or a skylight.

A Sun polar chart is a representation of the path of the sun throughout the year for a given latitude. The representation of a window or skylight on a solar chart allows us to see when the solar incidence occurs through the opening.

Sun polar chart at latitude 40º, drawing by author.

Is set out below how we use a solar chart:

1.- Define a window with an orientation and a point of study.

2.- Set the viewing angle from the point of study in plan view.

3.- Set the viewing angle from the point of study in section view.

4.- Transfer the plan angles to the Sun polar chart.

Set the section angles to the Sun polar chart.

Define the window in the solar chart.

As we can see, the window occupies an area of ​​the solar path. If we look closely, we can determine that this area corresponds to a number of hours, days and months of the year. This time interval shows us when solar incidence occurs through the window.

Coming soon we will explain how to build our own solar chart. See you soon.