Sun-Path Diagrams

Article 013

Jul. '98

Sun path diagrams are a convenient way of representing the annual changes in the path of the Sun through the sky on 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. There are quite a few different types of sun-path diagram, however we look here only at the two main forms.
 
   
 
 

The Stereographic Diagram
 

Stereographic diagrams are used to represent the sun's changing position in the sky throughout the day and year. In form, they can be likened to a photograph of the sky, taken looking straight up towards the zenith, with a 180° fish eye lens. The paths of the sun at different times of the year can then be projected onto this flattened hemisphere for any location on Earth.

 
 
 
 

Figure 1 - Click on the image above to view a short animation describing the stereographic diagram (307k).

Images taken from ECOTECT v4.
 
 

The actual process of generating altitude lines on the stereographic diagram is not as simple a translation as appears in the animation above. A simply linear projection of altitude lines around the sky dome straight down onto a flat surface makes angles near the horizon very close together and those near the zenith very far apart. In most architectural situations, most of the overshadowing from surrounding buildings and vegetation occurs near the horizon. Thus, to give more detail at the horizon and less at the zenith, a stereographic projection is used. The differences between the two projection methods are explained in the following animation.
 
 
 
 

Figure 2 – Click on the words Stereographic or Orthographic above to display the different methods of projection.

Shows the derivation of altitude lines on the stereographic
diagram compared to simple orthographic projection, to give
greater emphasis to angles nearer the horizon.

 
 

Once the altitude lines have been established, the path of the sun can be drawn by simply plotting its altitude and azimuth for each hour of the day at different times of the year. It is unlikely that you will have to construct your own stereographic diagram from scratch, however it is worth knowing the basics. The following diagram shows an example full stereographic diagram, with all its components.
 
 

Diagram Components:
 
 

Figure 3 – Components of the stereographic diagram,
in this case drawn for latitude -32°. Use the selector box to
highlight individual components.

Images taken from THE SOLAR TOOL.
 
 

Azimuth Lines

Azimuth angles run around the edge of the diagram in 15° increments. A point's azimuth from the reference position is measured in a clockwise direction from True North on the horizontal plane. True North on the stereographic diagram is the positive Y axis (straight up) and is marked with an N.

 
 

Altitude Lines

Altitude angles are represented as concentric circular dotted lines that run from the centre of the diagram out, in 10° increments from 90 to 0. A point's altitude from the reference position is measured from the horizontal plane up.
 
 

Date Lines

Date lines represent the path of the sun through the sky on one particular day of the year. They start on the eastern side of the graph and run to the western side. There are twelve of these lines shown, for the 1st day of each month. The first six months are shown as solid lines (Jan-Jun) whilst the last six months are shown as dotted (Jul-Dec), to allow a clear distinction even though the path of the Sun is cyclical.
 
 

Hour Lines

Hour lines represent the position of the sun at a specific hour of the day, throughout the year. They are shown as figure-8 type lines (Analemma) that intersect the date lines. The intersection points between date and hour lines gives the position of the sun. Half of each hour line is shown as dotted, to indicate that this is during the latter six months of the year.
 
 

Reading the Sun Position
 

The position of the Sun in the sky at any time of the day on any day of the year can be read directly from this diagram. The animation below details the process required to find the position of the Sun at 9:00am on the 1st of April. If the animation stops, simply hit the Refresh or Reload button at the top of your browser.
 
 

9:00am on the 1st of April
 
 

Figure 4 – Animation detailing the process required to read
azimuth and altitude values from a stereographic diagram.
To restart this animation click the Reload or Refresh button
in the toolbar of your browser.

Images taken from THE SOLAR TOOL.
 
 

Follow the steps below to read the Sun position from a stereographic sun-path diagram:

  • Step 1 - Locate the required hour line on the diagram.
  • Step 2 - Locate the required date line, remembering that solid are used for Jan-Jun and dotted lines for Jul-Dec.
  • Step 3 - Find the intersection point of the hour and date lines. Remember to intersect solid with solid and dotted with dotted lines.
  • Step 4 - Draw a line from the very centre of the diagram, through the intersection point, out to the perimeter of the diagram.
  • Step 5 - Read the azimuth as an angle taken clockwise from North. In this case, the value is about 62°.
  • Step 6 - Trace a concentric circle around from the intersection point to the vertical North axis, on which is displayed the altitude angles.
  • Step 7 - Interpolate between the concentric circle lines to find the altitude. In this case the intersection point sits exactly on the 30° line.

This gives the position of the sun, fully defined as an azimuth and altitude.
 
   
 
 

Cylindrical Diagrams
 

A cylindrical projection is simply a 2D graph of the Sun position in Cartesian co-ordinates. The azimuth is plotted along the horizontal axis whilst the altitude is plotted vertically. Reading off positions is simply a matter of reading off the two axis, as shown in the animation below.
 
 

9:00am on the 1st of April
 
 

Figure 5 – Animation detailing the process required to read
azimuth and altitude values from a cylindrical projection.
To restart this animation click the Reload or Refresh
button in the toolbar of your browser.

Image created using THE SOLAR TOOL.
 
 

Follow the steps below to read the Sun position from a cylindrical sun-path diagram:

  • Step 1 - Locate the required hour line on the diagram.
  • Step 2 - Locate the required date line, remembering that solid are used for Jan-Jun and dotted lines for Jul-Dec. In these diagrams, the highest altitude line at noon is always in midsummer (either 1st July or 1st Jan, depending on hemisphere). Each other line represents the 1st of each month, solid Jan-Jun, dotted Jul-Dec.
  • Step 3 - Find the intersection point of the hour and date lines. Remember to intersect solid with solid and dotted with dotted lines.
  • Step 4 - The azimuth is given by reading off the horizontal axis. In this case, the value is about 62°.
  • Step 5 - The altitude is given by reading off the vertical axis. In this case the intersection point sits almost exactly on the 30° line.
 
 

 

 

 

This information is brought to you by  SQUARE ONE research PTY LTD.
 

Internet Site: www.squ1.com               Electronic Mail: sales@squ1.com