Galileo's Thirst for Knowledge: Priceless. Quenched: $470 Billion.

Over the past three entries I wrote about Galileo’s mistaken approach toward analyzing masonry domes and arches, where he invoked his Square Cube Law to wrongfully criticize the work of ancient master masons. One of the insights gained from a proper and correct stress analysis, which involves thrust force lines describing a catenary curve within the thickness of an arch wall, is that extra weight, or loading, applied to the outside of an arch actually makes the arch stronger by keeping the thrust force lines closer to the center of the arch wall.

The implications of this correct structural analysis are far-reaching and insightful, for numerous applications of masonry structures: some of which I have already been discussing in this blog.

If a complete sphere is assembled, and this complete sphere is submerged below water, the water applies a load to the outside of the sphere. Water pushes in on the round sphere fairly equally, all the way around the sphere from all directions. This external loading keeps the thrust line forces equally distributed around the entire sphere, and it keeps these thrust line forces located in the center of the wall thickness, resulting in an optimal loading of compressive forces. Any other shape, whether it is a cube, rectangular, elliptical, etc., will not distribute this external loading in an equal, symmetrical manner as a sphere does.

This attribute of a masonry sphere subject to external compressive forces bearing such loading equally and symmetrically about its surface means that a below ground storage tank, built as a sphere, is an ideal configuration for any below ground tank. If a below ground tank is used to store water, then the weight of the water will apply an interior force, or head pressure, against the inside of the sphere, so that this force weakens the sphere and must be countered by an external force. Given that the density of water is 1.0 grams/cubic cm, and that average soils have a density of around between 2 and 3 g/cc, it is obvious that the external forces of the surrounding soil are 2 or 3 times the internal pressure of the water held in the tank. In other words, there is substantially greater compressive force acting on the outside of the sphere from the surrounding soil than there is acting on the inside of the tank by the water stored there.

These examples further illustrate that a masonry sphere used as either a below-ground water storage tank or as a means of desalination, as discussed here and there in this blog, are ideal solutions to the growing global problem of potable water use, storage and procurement. This water problem can be addressed by the existing manufacturing capability of the concrete block industry, using its existing methods, materials, and infrastructure. This can be done in an economical, sustainable and easily implemented manner.

This represents a huge market, and the proposed technology could be a big part of the answer to a pressing problem which is expected to worsen with climate change and the growing needs of humanity. Currently, the size of the market for potable water is estimated at $470 billion. One in eight people around the globe lack access to fresh water; that’s almost one billion people. The solution described here could help address this problem.

To see a completed prototype for water storage, please look here.

The Wonder of Stupas

The stupa is a mound or domed structure which serves as a Buddhist reliquary, or container for relics. Stupas are a form of Mandala, or sacred form of circle in Buddhist religious traditions. The Mandala is comprised of a square within the circle. This geometric pattern is thought to symbolically or metaphysically represent the Cosmos in microcosm.

Stupas were originally simple crude piles or heaps of mud which contained artifacts of Buddha. Several thousand stupas were built after the third century, with the advent and spread of Buddhism. They eventually evolved into engineered domed structures. This evolution of structure reflected the change in the stupa from an object of memorial to one of veneration.

Most of the stupas were built as corbelled arch domes, not as true arch domes (as I discussed in an earlier blog). These corbelled arch structures require a very large amount of masonry material, resulting in very strong structures which are robust, long lived and somewhat reminiscent of the Romanesque in their extensive use of material.

Some of the great stupas famous to us today are the Great Stupa at Sanchi, India; the Dhamek Stupa in northeastern India; the Ruwanwelisaya Chedi in Sri Lanka; and the Borobudur in Indonesia: the largest Buddhist structure in the world.

The existence of such a large number of ancient stupas today is testament to the fundamental strength and stability of this domed structure. Many of these stupas have survived a long history of seismic activity and major earthquakes. This domed structure also points to the cultural acceptance and reverence for the dome in Buddhist cultures, as seen in Muslim culture relative to the mosques.
The square within the stupa (as described by four sacred gates) is an interesting manifestation of “squaring the circle” as discussed earlier on this blog. This superposition of circle and square seems a fundamental archetype of human nature, and is found across many cultures and societies. As described in An Introduction to Stupas, “"The shape of the stupa represents the Buddha, crowned and sitting in meditation posture on a lion throne. His crown is the top of the spire; his head is the square at the spire's base; his body is the vase shape; his legs are the four steps of the lower terrace; and the base is his throne." This strong cultural acceptance and reverence indicates that a domed masonry structure is readily accepted and embraced by Buddhist societies.