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# Sun-Path Diagrams

Sun path diagrams are a convenient way of representing annual changes in the path of the Sun through the sky within a single 2D diagram. Their most immediate use is that the solar azimuth and altitude can be read off directly for any time of the day and day of the year. They also provide a unique summary of solar position that the designer can refer to when considering shading requirements and design options.

Figure 1 - An example sun-path diagram.

### What a Sun-Path Diagram Shows

The best way to conceptualise a sun-path diagram such as the one shown above is to liken it to a photograph of the sky, taken whilst lying on your back looking straight up towards the zenith with a 180Ã‚Â° fish eye lens. The paths of the sun at different times of the year can then be projected onto this flattened hemisphere, as shown in Figure 2.

Figure 2 - Conceptualising how the sun-path diagram actually represents the entire sky dome.

The generation of each sun-path line is done by determining the exact position of the Sun as it passes through the sky in sub-hourly increments for each date - in most cases on the 1st or 21st of each month. This is then projected from the sky dome onto the flat image, as shown below.

Figure 3 - Projecting the annual path of the Sun on a hemispheric view of the sky dome to create a sun-path diagram.

### Types of Projection

Mapping sun-path lines directly onto a fish-eye camera view such as that shown in Figure 2 requires a simple spherical projection. In this projection type, lines of equal solar altitude are spaced widely apart near the zenith of the sky but are concentrated quite closely together near the horizon. This makes distinguishing detail just above the horizon quite difficult, which may not be appropriate if you are looking at low level overshadowing by surrounding buildings, for example.

To overcome this, a range of different types of projection have been developed - all based on the same overall ideas but differing in two important ways:

1. Whether they use Polar or Cartesian co-ordinate mapping, and
2. How azimuth and altitude are distributed along each axis.

The following images show examples of the most commonly used projection methods. All the circular projections use some form of polar co-ordinate system to map solar altitude and azimuth whilst the rectangular projections use cartesian co-ordinates, usually with altitude in the Y (vertical) axis and azimuth in the X (horizontal).

Spherical Projection

Equidistant Projection

Stereographic Projection

BRE Sun-Path Indicator

Orthographic Projection

Waldram Diagram

The major types of projections using to create sun-path diagrams.

See the pages below for more detailed information on each of these projection types.

Solar Position: Variation
Sun-Path: Components