MEEB FINAL CHPT 6

Sunpath projections (gnomnic, equidistant, rectilinear and stereographic)

The *gnomonic projection* (used with sundials and sunpeg charts) is derived from the sundial. The observer is at the center of the projection; therefore, low sun angles (sunrise, sunset) extend to infinity. For this reason, this method is rarely used for solar charts but is easily applied to building shadow studies. The *equidistant projection* (horizontal, polar) is used almost exclusively in the United States because of the ready availability and wide acceptance of the sunpath charts provided in the Pilkington (formerly Libbey Owens Ford) Sun Angle Calculator. The observer moves around the skydome, like the sun's view to the earth. Figure 6.11 shows a sample equidistant projection sunpath diagram. The *rectilinear projection* (vertical, cylindrical) is a two‐dimensional graph of the sun's position in Cartesian coordinates. Azimuth is plotted along the horizontal axis and altitude on the vertical axis. The development of this type of chart is shown in Fig. 6.12. These charts are actually graphs superimposed on the eye of an observer. At the vertical center of each chart, the observer is looking due south. The *stereographic projection* (circular, equal spacing) also represents the sun's changing position in the sky throughout the day and year. The format is like a fish‐eye photograph of the sky pointed to the zenith directly above. The various paths of the sun throughout the year can be projected onto the sky, then "flattened."

Declination

The Earth's axis of rotation is tilted at 23.5° (precisely, 23.47°), also known as its declination.

Altitude and azimuth

The position of the sun at any instant with respect to an observer on the ground is defined by its altitude angle and its azimuth angle. The altitude of the sun is the angle between the horizon and the sun's position above the horizon. The altitude varies during the day, beginning and ending at 0° at sunrise and sunset and reaching a daily maximum at solar noon. The azimuth (also called the solar bearing angle) is the angle along the horizon between the projected position of the sun and true (solar) south. (See Fig.6.3)

Equation of time and analemma

The speed of the Earth in its orbit around the sun is nonuniform; the planet moves less rapidly when farther from the sun. As a result, the actual length of the solar day varies as defined by the equation of time. (See Fig. 6.6a) The extent of this variation can be determined from a curve called the analemma (Fig. 6.6b) or from tabulations in various sources. The analemma is the shape that results if the sun's position in the sky is recorded at the same time of day throughout the year.

Solar time and clock time

*Location within a time zone.* The 360° circumference of the Earth is divided into 24 one‐hour time zones, each with a width of approximately 15° of longitude, which corresponds to approximately 1000 miles (1610 km). An observer located at any point other than directly on a standard time zone reference longitude (normally in the center of a time zone) must make a time correction for his/her distance from the reference longitude. *Equation of time.* The speed of the Earth in its orbit around the sun is nonuniform; the planet moves less rapidly when farther from the sun. As a result, the actual length of the solar day varies as defined by the equation of time. (See Fig. 6.6a) *Daylight saving time (DST).* During DST, clocks are moved forward one hour to effectively give (from the morning) one more hour of daylight in the evening during the summer months. (Note: The official term is daylight saving time, not daylight savings time.) The purpose of DST is to make better use of daylight.

Shading masks (context, use and reading of)

A shading mask is a sunpath chart (horizontal projection) that shows the shadow cast by a particular shading device, as shown in *Fig. 6.29.* For a horizontal shading device, the leading edge of the shadow cast by all horizontal elements with the same VSA (profile angle) projects as a segmental line, and when plotted on the sunpath chart, it is shown as a segmental mask. To draw this segment, a protractor is required.

Shading for orientation

Because of the high altitude of the sun, the most effective shading device for south‐facing windows during the summer is a horizontal overhang. On east‐ and west‐facing windows, a horizontal overhang is somewhat effective when the sun is at high positions in the sky, but is not effective at low‐altitude angles. A variety of shading devices are illustrated by the diagrams and examples in Figs. 6.14-6.18.

Designing finite horizontal shading

Deciding upon shading coverage is the first step in design. The second step is to establish the required depth of the shading device (the distance it projects from the wall). *Figure 6.32* shows how the required depth and the corresponding segmental mask are determined. At times, because of window areas left unshaded by the original overhang, it is necessary

Shadow angles (VSA and HSA) be able to draw these and describe them

Note that the shadow is defined by two angles: the vertical shadow angle (VSA), which indicates the position of the leading edge of the shadow as defined from the leading edge of the overhang, and the horizontal shadow angle (HSA), which defines the leading edge of a shadow cast by a vertical element (indicated by a dashed line) as defined with respect to that element's leading edge. (See Fig. 6.27)

Operable shading

Operable exterior shading devices are useful because they respond to daily and seasonal variations in solar and weather patterns in ways that fixed shading devices simply cannot do. The operation of a movable shading device can be as simple as twice‐a‐year adjustment—for example, manually extending roller shades, awnings, rotating fins, or louvers at the beginning of summer and retracting the shade after the hot season has ended (in fall). These devices are very effective at blocking low sun angles from the east or west. More complex movable devices are typically on automated daily and seasonal programs.