Geometry of Seasonal Shading

Architects and homeowners who pursue passive solar design aim to maximize solar gains during winter while minimizing overheating in summer. A fixed horizontal overhang is a simple yet effective tool for controlling sun penetration. The basic geometry involves the apparent height of the sun in the sky at solar noon on key design days. When the sun is high in the summer, the overhang should cast a shadow that fully covers the window, whereas during winter the lower sun angle allows light to reach deep into the space. Determining the correct overhang length requires a bit of trigonometry.

The solar altitude angle, $\alpha$, at solar noon for a given day is given by $\alpha =90°-\phi +\delta$, where $\phi$ is latitude and $\delta$ is the solar declination for the chosen date. Declination varies between ±23.45° over the year and can be approximated for specific days using astronomical formulas or tabulated values. For the summer solstice, $\delta$ is roughly +23.45°, while for the winter solstice it is −23.45°. By selecting a design day—often the summer solstice—we ensure that the overhang blocks the highest sun of the year.

Once the solar altitude is known, the required overhang projection, $L$, is calculated using the tangent relationship $L=\frac{H}{+}/\tan \left(\alpha \right)$, where $H$ is the window height to be shaded and $O$ is the vertical offset between the top of the window and the underside of the overhang. If the overhang is flush with the window top, $O$ equals zero. The calculator implements this relation to output the projection that will just shade the bottom of the window at the selected solar altitude. Designers may choose a slightly longer or shorter length depending on whether partial shading is acceptable.

To appreciate how sensitive shading is to the input parameters, consider the comparative table below. It lists overhang lengths for different latitudes assuming a 1.5-meter-tall window with an offset of 0.3 meters and a design declination of 23.45° (summer solstice). Notice how higher latitudes with lower summer sun angles require longer projections to achieve full coverage.

The difference is substantial: a home at 50° latitude may need an overhang nearly three times longer than one at 30° to provide the same shading. Failure to account for this can result in discomfort and higher cooling loads. Conversely, an overly deep overhang might block too much winter sun, reducing passive heating. This is why some designers model sun paths for multiple dates to fine-tune the dimensions.

Beyond sizing, the material and color of the overhang influence thermal performance. Light-colored surfaces reflect more sunlight, reducing heat conducted into the building, while dark surfaces may absorb heat and radiate it downward. Vegetated overhangs or pergolas with deciduous vines provide dynamic shading: leaves block summer sun but fall away in winter. Nevertheless, the underlying geometric calculation remains unchanged.

When planning retrofits, practical constraints such as property lines, aesthetics, and structural limitations must be considered. Cantilevered projections require adequate support, and wind uplift can be significant in hurricane-prone regions. The calculator provides the necessary starting point for structural engineers to evaluate loads based on the proposed length. By combining solar geometry with engineering judgment, one can create overhangs that are both functional and durable.

Software tools like SketchUp or specialized sun-path applications can visualize shadow patterns throughout the year. However, the fundamental math implemented here offers quick insight without complex simulations. Understanding the role of latitude and declination empowers homeowners to adapt designs for different climates or to compare the effectiveness of horizontal versus vertical shading devices such as fins or louvers.

For those interested in more advanced calculations, incorporating the equation of time and hour angle allows analysis of sun position throughout the day, not just at solar noon. This is valuable for east- or west-facing windows where morning or afternoon sun can be problematic. The methodology extends naturally: compute the sun altitude at the relevant hour and apply the same tangent relationship to size side fins or angled overhangs.

Ultimately, a properly sized overhang enhances comfort, reduces energy consumption, and prolongs the life of interior furnishings by preventing UV damage. Whether you are a do-it-yourself builder or a professional architect, this calculator and explanation aim to demystify the process so that passive solar principles can be integrated into any project.

Further Considerations for Overhang Design

Because the sun's path changes gradually around the solstices, some designers select a date a few weeks before or after the extreme to ensure comfortable margins. For instance, choosing a declination of 20° rather than 23.45° yields an overhang that shades earlier in the season, which can be beneficial for south-facing rooms that tend to overheat in late spring. Conversely, a smaller declination may be appropriate for colder climates that value winter gains. The calculator allows any declination value so that users can experiment with these nuances.

Another layer of complexity comes from window orientation. The equations above assume a true south-facing window in the northern hemisphere (or true north in the southern hemisphere). If a window is rotated away from cardinal directions, the solar altitude at solar noon changes less dramatically, but the azimuth—the compass direction of the sun—causes the timing of shading to shift. In such cases, designers might combine horizontal overhangs with vertical fins to handle low-angle morning or afternoon sun. Although the calculator does not model azimuthal effects directly, understanding the limitations encourages deeper exploration.

Historic buildings often present unique challenges. Preservation guidelines may restrict visible alterations, requiring creative solutions such as interior blinds or removable awnings. Temporary shading devices can be modeled with the same trigonometric relationships to ensure effectiveness. Additionally, when multiple stories are involved, designers must consider shadow interactions between overhangs and balconies. A second-story deck can act as an overhang for lower windows, but the geometry changes if railings or balusters block light. The principles outlined here remain applicable, yet on-site measurements and seasonal observations provide essential validation.