How to read a sun path diagram

Altitude and azimuth: the two coordinates

Altitude, also called elevation angle, is the sun's angle above the horizon: 0° at sunrise and sunset, 90° when the sun is directly overhead. Azimuth is the compass direction the sunlight comes from, commonly measured clockwise from north (north 0°, east 90°, south 180°, west 270°). Some tools measure azimuth from south instead, so check the chart's convention before reading angles from it.

Because the Earth's axis is tilted by about 23.45°, the sun's declination swings between +23.45° and −23.45° over the year and is 0° at the equinoxes. On the equinoxes the sun rises due east and sets due west at every latitude. At solar noon the sun is due south in the northern hemisphere and due north in the southern hemisphere, except between the tropics, where it passes on the other side for part of the year.

How to read the chart, step by step

• Check the latitude: a sun path diagram is drawn for one latitude, and its shape changes as you move north or south.
• Find the date line: the arcs are the sun's path on particular days, often the 21st of each month. The highest arc is the summer solstice, the lowest the winter solstice, with the equinoxes in between. Months that mirror each other around a solstice, such as May and July, follow almost the same arc.
• Find the hour line: the lines crossing the arcs mark the hours. Where your hour meets your date is the sun's position at that moment.
• Read the angles: altitude from the concentric rings of a polar chart or the vertical axis of a cylindrical one; azimuth from the outer ring or the horizontal axis.
• Check the time basis: hour lines may be in solar time, where 12:00 is when the sun is highest, or in local clock time, which differs because of time zones, daylight saving and the shape of the Earth's orbit.

A worked example: the noon sun through the year

In the northern hemisphere, the sun's altitude at solar noon is 90° minus the latitude plus the declination. At 40°N that gives about 73.5° at the June solstice, 50° at the equinoxes and 26.5° at the December solstice. That 47° difference between the summer and winter noon sun is what allows a horizontal overhang over an equator-facing window to block much of the high summer sun while letting more of the low winter sun in.

Polar, stereographic, equidistant and cylindrical charts

Polar sun path diagrams flatten the hemisphere of the sky into a circle: the horizon is the outer edge, the zenith is the centre, azimuth runs around the rim and altitude is read from concentric rings. The spacing of the rings depends on the projection. An equidistant projection spaces the altitude rings evenly. A stereographic projection expands the area near the horizon and compresses the zenith, giving more room to low morning, evening and winter sun. Orthographic projections are also used.

Cylindrical, or Cartesian, charts unroll the sky onto a rectangle, with azimuth on the horizontal axis and altitude on the vertical axis. The information is the same; only the drawing changes. Because the axes are simply azimuth and altitude, the outline of surrounding buildings, trees or hills, measured as an altitude angle for each bearing, can be drawn straight onto the chart.

Shading masks: testing overhangs, fins and neighbours

A shading mask protractor, developed by Olgyay and Olgyay at Princeton University in the 1950s, describes the part of the sky that a shading device hides from a point at the base of a window. Rotate it to the façade's orientation, lay it over the sun path diagram, and every sun position inside the masked area is a month and hour when that point is in shade.

Horizontal overhangs mask the upper part of the sky and vertical fins mask the sides. Their angles follow from simple trigonometry: the overhang's cut-off (vertical shadow) angle, measured up from the horizontal at the window sill, is the angle whose tangent is the window height divided by the overhang's projection. Neighbouring buildings, trees and hills can be drawn on the same chart as a skyline, which shows when the site itself is overshadowed.

How C4B shows the sun path

C4B draws the sun path for the exact location as a polar diagram (its 'globe view'), a section and a 3D sky dome for the solstices and the equinox, and pairs it with monthly daytime cloud cover, because geometry alone overstates the sun in cloudy climates. Its solar radiation analysis adds direct, diffuse and global radiation and the radiation reaching vertical surfaces facing any direction. Both are available on the Free plan.