Thursday, September 11, 2008

Pyramids: Engineering by Trial and Error?

The Bent pyramid. The lower portion of this pyramid rises at the same angle as the pyramid at Meidum, but ancient Egyptian engineers reduced the slope for the upper portion to ensure its stability. The Bent and Meidum pyramids were apparently constructed concurrently with engineers decreasing the angle of the Bent pyramid once they learned of the failure at Meidum.

The pyramid at Meidum. Built at a steep angle, the outer casing of the pyramid at Meidum collapsed around its central core during construction.

Monumental architecture in the form of pyramids, temples, and palaces is diagnostic of high civilization and is remarkable in the history of technology, not only as a set of extraordinary technical accomplishments, but also as indicative of the institution and practice of architecture and the developed crafts and trades associated with engineering. The Egyptian pyramids provide the classic example of monumental building by an early civilization. The case is well documented, and it encapsulates the themes raised thus far regarding agriculture, civilization, and the Urban Revolution.

Consider first the sheer immensity of the Great Pyramid at Giza. Built on the west bank of the Nile during the zenith of the pyramid-building era between 2789 and 2767 bce (or possibly 2589–2566 bce) by Khufu (Cheops), the first pharaoh of the Fourth Dynasty, the Great Pyramid is the largest solid-stone structure ever built: it consists of an unbelievable 94 million cubic feet of masonry, made up of 2.3 million blocks averaging 2.5 tons apiece, with a total weight of 6 million tons; it covers 13.5 acres, in 210 courses of stone, and stands 485 feet high and 763 feet on a side; chambers, buttresses, and passageways lie within. Sheathed with polished stone, the scale of the construction—not to mention the beauty of the finished structure—has not been surpassed in the nearly five millennia of human history since the Great Pyramid was built.

The architects and engineers who built the Great Pyramid and the others like it commanded some elementary and some not-so-elementary practical mathematics. Design and material requirements demanded such expertise, as did the very exact north-south and east-west alignment. Ancient Egyptian engineers and architects understood the mathematics and appreciated the elegance of perfect pyramids, but the Egyptian pyramids (and monumental building generally) need to be seen primarily as stupendous engineering achievements.

According to a report by the fifth-century bce Greek historian Herodotus, 100,000 people toiled for twenty years to build the Great Pyramid; perhaps 4,000–5,000 craftsmen worked at the site year round. The techniques of pyramid construction are now well understood, and excepting the possible use of a cantilevered machine to lift stones, no categorically new building methods developed compared to what one finds in Neolithic building techniques. Simple tools and practical procedures carried the day but, characteristic of the new powers of civilization, more people, by orders of magnitude, were deployed and construction completed that much faster than at Neolithic sites.

Such an extraordinary monument did not suddenly appear in the Egyptian desert. Rather, the Great Pyramid culminates a clear progression of pyramid building coincident with the growth and expansion of the Egyptian agrarian state.

Several fanciful theories have been put forward to explain why the Great Pyramid and preceding and succeeding pyramids were built, but the function of these structures as tombs for pharaohs seems irrefutable, even if it may not have been their only purpose. A problem exists, however: at some periods at least, the number of new pyramids exceeded the number of pharaohs; and several pyramids were built simultaneously by a single pharaoh. Moreover, most of the truly monumental pyramids came into being in just over a century in the late Third and early Fourth Dynasties. According to one account, in four generations over 112 years between 2834 and 2722 bce, six pharaohs built thirteen pyramids. Clearly, something more than burying the dead is needed to explain the extraordinary socio-cultural phenomenon of the Egyptian pyramids.

One explanation of pyramid building from an engineering point of view attempts to explain the more or less continuous construction that took place on the west bank of the Nile during the heyday of pyramid building. In this interpretation, pyramid building was an activity pursued in its own right as an exercise in statecraft. The sequence of the early pyramids comprised giant public-works projects designed to mobilize the population during the agricultural off-season and to reinforce the idea and reality of the state in ancient Egypt. More than one pyramid arose simultaneously because a labor pool—and surely an increasingly large labor pool—was available and because the geometry of pyramids dictates that fewer laborers are required near the top of a pyramid than at the bottom, thus permitting the transfer of labor to newly started projects. Monumental building was therefore a kind of institutional muscle-flexing by the early Egyptian state, somewhat akin to the arms industry today.

The engineering key to this argument comes from two particular pyramids. The first, the pyramid at Meidum, begun by the pharaoh Huni (Uni), who reigned for 24 years between 2837 and 2814 bce, and continued by his son Sneferu, stood 80 feet high and ran 130 feet on its side. It was to have been the first true pyramid with sheer, sloping sides and no visible steps. However, the pyramid at Meidum turned out to be an engineering disaster and a monumental structural failure, as the outer stone casing collapsed in rubble around the inner core of the pyramid. Designed with the evidently excessive slope of 54 degrees, the collapsed ruin may still be seen by the traveler.

The second pyramid at issue is the succeeding “Bent” pyramid at Dashur, also built by King Sneferu. It is a huge pyramid 335 feet high, 620 feet on a side, with a volume of 50 million cubic feet. Extraordinarily, the Bent pyramid is truly bent, angled, like Meidum, at 54 degrees on the lower half and 43 degrees on the top. One supposes that when the pyramid at Meidum failed, engineers reduced the slope of the Bent pyramid, still under construction, as a precaution. The next pyramid built by Sneferu, the Red pyramid, retained the safer slope of 43 degrees. (The Great Pyramid and later pyramids returned to increased elevations over 50 degrees, but used improved internal buttressing techniques.)

One does not have to follow every detail in order to accept the general point. The Egyptian pyramids were large state-run construction projects. A surplus of idle agricultural workers available seasonally for three months a year during the Nile floods provided the labor pool. (Agricultural productivity was thus not affected by the demand for labor for pyramid building.) Contrary to a once-common belief, forced slave labor did not build the pyramids, but labor was conscripted (like military conscription today) and organized in work gangs. Workers received food supplied by state granaries, and the completed pyramids served as tombs for departed pharaohs. Inevitably, elaborate theologies, priestly ceremonies, and ancillary technologies (such as mummifying) grew up around burying pharaohs. But in their construction the pyramids functioned primarily as gigantic public-works projects, the effect of which helped maintain the economy of irrigation agriculture in the Nile River Valley and bolstered centralizing political and social forces, notably the state. Indeed, the heyday of pyramid building was the heyday of political centralization in Old Kingdom Egypt. The pyramids were symbolic as well as literal exercises in state building.

Pyramids without Wheels

A new Pyramid building method by Franz Löhner

Architect Jean-Pierre Houdin theory at Dassault

Mysteries of the Past

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