Spherical structures enclose the greatest volume with the least surface. Every time the diameter of a spherical structure is doubled volume increases 8 fold & surface area increases 4 fold. Dome volume increases @ a 3rd power rate while the structural component lengths increase @ only a fraction more than an arithmetical rate. The gain of weight in structures as ratioed to basic linear dimensions, is as 1 is to 1-(1/x) weight ratio, as the same structure is multiplied in relative size. Every time the linear dimension of a symmetrical structure is doubled (ie. 1 to 2), the surface area of the enclosure increases @ a 2 to the 2nd power rate and its volume increases @ a 2 to the 3rd power rate. Wind drag on a dome, as quantified in the Net Pressure Coefficient, is less than for most other shapes. See chart at the end of this chapter.
THERMODYNAMIC
Bernoulli Chilling Effect As the suns radiation is outwardly and diffusingly reflected by the domes convex outer surface, vertical thermal-column movements of the sun heated outside atmosphere develop. The spirally rising volumes of heated atmosphere will draw air out from under the domes large lower edge summertime openings. This voluminous outward drafting in turn pulls air into the dome through the small cross sectioned ventilators at the domes apex. The pressure differential between the small air entry and the large exhaust openings produces the BERNOULLI CHILLING EFFECT, which in hot weather will swiftly cool the domes interior atmosphere.
Upward draft is caused
by polar heating of the outside surface
which then heats the surrounding air.
The warm air rises creating a thermal column.
Air is sucked out
of the large openings @ ground level
causing reduced pressure inside the dome.
Reduced pressure causes air near the top vent
to rush in through the small openings.
Increased air flow through these small openings
cools incoming air.
This aspect of dome behavior maybe one of the hardest to replicate.
Perhaps it is a matter of adequate insulation and reflectivity in dome
construction. As of 5-31-94, I (the author) have not been able to achieve
Bernoilli cooling.
HEAT SINKING
When the spherical structures diameter doubles, the amount of enclosing surface through which an interior molecule of atmosphere can gain or lose energy as heat or cool is halved. So heat energy is more efficiently retained in large spherical structures than by smaller domes. Every time a geodesic domes diameter is doubled, it has 8 times as many molecules of atmosphere but only 4 times as much shell; therefore each progressive doubling of dome diameters halves the amount of enclosing surface ( relative to the enclosed volume ) through which a molecule may lose or gain heat energy Every time we enclose a geodesic dome within a greater diametered geodesic dome, whose radial concentric inter-spacing is greater than the depth of the frost penetration of that area while at the same time avoiding use of any metal connections between the inner and outer domes structures, the heat losses and gains of the innermost dome is halved with respect to those of non-domed-over-domes of the same dimensions. Next Table of Contents