Solar Geometry Is Predictable - Which Means Shading Devices Can Be Designed With Mathematical Precision
The sun follows a predictable path across the sky every day of every year, varying in height (altitude) and compass direction (azimuth) in ways that are calculable from latitude alone. Because solar geometry is predictable, architects can design shading devices - overhangs, fins, louvers, brise-soleils - that block direct sun precisely during specific periods while admitting it during others. A south-facing window in a building at 40°N latitude (roughly New York, Denver, or Beijing) can be designed with a horizontal overhang that completely blocks the summer noon sun while admitting the winter noon sun - because the sun's altitude angle at noon is dramatically different in summer (70°+) than in winter (27°). This mathematical design approach is a core passive design skill tested on the ARE PPD exam.
Solar Altitude and Azimuth
Solar altitude is the angle of the sun above the horizon, measured in degrees from 0° (horizon) to 90° (zenith, directly overhead). At the summer solstice (around June 21 in the northern hemisphere), the sun reaches its highest altitude at solar noon. At the winter solstice (around December 21), the noon altitude is at its lowest. The difference between the summer and winter noon altitude angles equals twice the tilt of the Earth's axis - approximately 47°. At 40°N latitude: summer noon altitude ≈ 73°; winter noon altitude ≈ 27°. Solar azimuth is the compass direction of the sun measured in degrees from north (0°) clockwise. At solar noon, the sun is due south in the northern hemisphere (azimuth 180°).
Sun Path Diagrams
A sun path diagram (stereographic or orthographic projection) maps the sun's position throughout the year on a circular chart. The center of the chart is the sky directly overhead; the circumference is the horizon. The sun's path for each month of the year appears as a curved line across the chart; hour marks on each path show the sun's position at each hour. By overlaying a shading mask (the arc of sky blocked by a proposed shading device) on the sun path diagram, an architect can determine exactly which hours and months of the year the device will provide shade to the point of analysis. Sun path diagrams are available for every latitude; digital tools (Ladybug Tools, Climate Consultant, Sefaira) generate them automatically for any location.
Overhang Design
For a south-facing window, the key design calculation is the overhang depth needed to fully shade the window at the summer solstice while allowing full sun at the winter solstice. The shadow angle - the angle from the window sill to the tip of the overhang, measured in the vertical plane - determines the shading effectiveness. At 40°N latitude, a shadow angle of 55° above horizontal will block the summer noon sun (which is 73° above the horizon) while the winter noon sun (27° altitude) easily shines under the overhang. The overhang depth equals the window height divided by the tangent of the shadow angle. Software tools automate this calculation, but understanding the underlying geometry explains why the same overhang is effective at one latitude and ineffective at another.
Key Exam Points
- Solar altitude: angle above horizon; highest in summer at noon, lowest in winter - 47° difference at all latitudes.
- At 40°N: summer noon altitude ~73°; winter noon altitude ~27°.
- Solar azimuth: compass direction; sun is due south at noon (azimuth 180°) in northern hemisphere.
- Sun path diagram: maps sun position by hour and month; overlaid with shading mask to evaluate device effectiveness.
- Overhang geometry: shadow angle designed to block summer sun, admit winter sun - latitude-specific calculation.
AREprep's PPD solar design content covers sun path geometry, shading device design principles, solar analysis tools, and the integration of solar geometry with daylighting and passive heating strategies - giving ARE PPD candidates the solar design knowledge they need to answer sun path, shading, and passive solar questions that appear in the PPD exam's environmental systems content area.
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