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A current trend in architecture has been green building design commissioning. Not surprising when one considers the rise in energy costs. More building owners are now taking green design seriously. This is best illustrated in the introduction of the Leed rating system for construction projects. This rating method assigns point values to various design strategies to minimize negative environmental impact of construction while maximizing performance in energy efficiency. It is design that goes beyond mere aesthetic intent. One might wonder if mathematical topologies could influence design in relation to the goal of energy efficiency. Simply put, building volume shapes and distribution of spaces determine certain characteristics that influence directly a building's energy use.

For example if we examine closely the relation of exposed exterior envelope in cold climates, and heat loss, it becomes clear that reducing a building's surface will improve its efficiency. In plain terms, ideally we should want to use the least envelope surface to enclose a given volume of space. The optimum shape for that purpose is the sphere. The sphere can be seen as a three dimensional expression of the a circle. Throughout history, the circle from its aboriginal roots has been a shape well appreciated for its properties. Circles and related ovals and parabolic shapes explored and exhausted long ago by African sculptors, so fascinating mathematically to Pythagoras and Archimedes, are brilliant in the compactness of their volumes. A perfect sphere has a volume to surface area ratio of 2.2. That is to say that a 1000cubic meters can be enclosed in a sphere with only 483square meters of exposed exterior surface (for simplicity's sake we will assume a wall thickness of zero). Ancient Inuit igloo architecture is a good example of hemispherical volume enclosing the most usable floor area with the least amount of wall and roof area.

But, if we consider other shapes there are some interesting permutations. Consider a building 50 meters long and 5meters high with a depth of only 4 meters. Such a proposal would also enclose 1000cubic meters but would have an exposed surface area of 940 square meters. Almost twice the surface area of the sphere. Ideally, a building built for hot climates would expose the maximum amount of surface to cooling winds while exposing the least amount of surface to direct sunlight. Traditionally, in Mediterranean countries, the courtyard is an often used design feature. A shaded interior courtyard exposes the interior building volume to outside cooling air and minimizes exposure to direct sunlight. In Polynesian and Filipino coastal architecture, houses raised on stilts with porous straw or bamboo envelopes maximize air flow on all surfaces.

But in countries where space heating and air conditioning are used all year round, the heat loss or gain through exterior wall systems would again favour the sphere. If we compared any given shaped building to a hypothetical sphere shaped one in winter and summer; and both had identical volumes, footprint and fenestration areas, opacities and orientations to wind and solar exposures; then the sphere building by virtue of least surface area would be less prone to leaking temperature differences of inside and outside air.

Now, with cost of construction up the roof, one can hope there are other volumes that will save in heating/cooling energy. In practical terms a spherical building enclosing a huge volume equivalent for example to a 40 story skyscraper, usable floor areas would be compromised by complex structural requirements. Fortunately, there are other volume shapes that have high volume to surface ratios. The cube and cylinder have similar ratios and have the added benefit of more reasonable structural options and usable floor areas. The cylinder has a better vol./surf ratio of 1.88 in comparison to the cube (1.66). Cylinders like spheres are based on the circle whose circumference encloses the most area with the smallest perimeter length. The cylinder, the simplest of these circular topologies, makes a compelling case being easy to implement with minimal structural gymnastics. Its efficacy in enclosed a maximum amount of volume is But in pragmatic terms, architecturally, it lacks the even simpler structural grid of a cube. It hasn't stopped Frank Lloyd Wright and Douglas Cardinal from elaborating cylinder geometries into museums. But arguably, the cube and cylinder stands to reason as optimum shapes strictly in terms of energy footprint and structural simplicity.

Can we foresee a future skyline of stacked cubes in modern cities? Or perhaps concatenations of spheres and squat cylinders? Probably not. Instead, we might envision, through environmental considerations, the re-thinking of envelope shapes and compositions to improve building energy signature. SM.05/06

About the Author

Steve Michel is a designer, free lance writer, and editor of Dalani News. www.dalani.com