2600 B.C. Lean Manufacturing (Tech Trends Feature)30 Jun, 2007 By: Kenneth Wong
French architect Houdin turns the pyramid theory inside out.
On January 2, 1999, a retired French engineer in Paris was watching a television program about the construction of the Great Pyramids. He wasn't satisfied with the hypotheses presented by the show. They just didn't pass muster, he thought.
Suddenly he felt he'd stumbled on the answer to one of the greatest archeological riddles. In a burst of excitement, he made a transatlantic phone call to his son, an architect living in New York.
"If I were to build a pyramid, I'd build it from the inside," he told his son. He asked his son if this theory could be examined, tested and, perhaps, proved with 3D computer models.
"I couldn't say no," said Jean-Pierre Houdin, the son, reflecting on the phone call eight years later, "because he's my dad."
But the more he explored the inside-out theory, the more seductive it became. The project eventually attracted the attention of Dassault Systemes, a French PLM (product lifecycle management) company. Under the Passion for Innovation sponsorship program, Dassault gave Houdin access to all of its digital tools. During the past two years, Houdin (figure 1) and a multidisciplinary team of 15 engineers, designers and developers painstakingly recreated the Great Pyramid of Giza in a digital environment. They rebuilt not just its stony façade but also its narrow corridors, ramps, passageways and inner chambers. Along the way, they learned just how efficient the ancient builders from the Nile were.
Figure 1. Jean-Pierre Houdin, a French architect, turns the pyramid theory inside out with the help of 3D products from Dassault Systemes.
One of the prevalent hypotheses is that the Egyptians used an external ramp to transport the bulk of the 5.5 million tons of stone that the project required. As the structure got higher, so did the ramp. In Houdin's view, this plan is implausible because "If it were to reach the top of the pyramid, such a ramp would be twice the volume of the pyramid itself. Or it would have an incline that's too steep." So he proposed instead that the external ramp was used for only part of the construction.
"As I understand, the Egyptians were very smart about volume," he reasoned. "In the beginning, they used an external ramp to build up to 43 meters' height [approximately two-thirds of the entire pyramid's mass], which is the base of the King's Chamber. At that stage, the ramp would have been one-third of the pyramid's total volume. So, after the King's Chamber was completed, they dismantled the external ramp, and brought these blocks inside to build the rest of the pyramid using an internal ramp [figure 2]. So they wasted nothing."
Figure 2. Houdin's theory is based on an internal ramp spiraling to the top of the pyramid.
Reverse-Engineering a Great Wonder
The first task was to build a 3D geometric model of the Great Pyramid, Pharaoh Khufu's ambitious tomb that measures approximately 53,000 square meters at its base, 146 meters to its summit. Houdin and his team used CATIA, the industrial design software used by Boeing and Lockheed Martin, to replicate the pyramid's massive structure on a 1:1 scale.
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Rotating and inspecting the model from different angles, Houdin and his collaborators obtained a better understanding of its cross-sections, internal corridors and inner chambers. Houdin was now able to visualize in 3D what he'd imagined all along—a spiraling internal ramp climbing to the top of the pyramid. With the ability to easily measure the distance between any given points, he was able to check clearances and verify the soundness of his theory.
Houdin had obtained the dimensions of the pyramid and the 2D plans from the measurements that were made by another French architect, Gilles Dormion. But Houdin had an advantage over his predecessor. "Jean-Pierre was thinking in 3D, so he was able to visualize the pyramid differently, understand the relationships between its elements and ask new questions," remarked Mehdi Tayoubi, Dassault's online marketing and communication director.
In addition to the geometric model, the team also produced a physical model reflecting the granite block's elasticity and density, among other variables. This was done by embedding the materials' characteristics as defined by François Schlosser, a geology specialist, in the geometric model. In the digital experiments to reproduce the lever actions and counterweight systems that the Egyptians might have used, the physical model would serve as a stunt double, if you will, behaving identically to the real pyramid in how it reacts to the laws of motion.
A Crack in Time
Stacked on top of one another, five stout granite beams sit above the King's Chamber, at the heart of the pyramid. Some weigh as much as 60 tons, so they represent yet another archeological conundrum. How did the Egyptians place them there? (It's not as if they had mechanical cranes to hoist them.)
The visible fractures on some of the beams also have generated many speculations, with some scholars "going so far as to suggest that the builders abandoned the King's Chamber after the crack, in favor of another yet-unknown design," noted Houdin. That, of course, assumed the accident occurred mid-construction. Using SIMULIA, Dassault's stress test and structural analysis software, Houdin and his colleagues were able to prove the crack occurred long after the chamber was completed (figure 3).
Figure 3. Using SIMULIA, Houdin and his team were able to under-stand how the cracks in the King's Chamber occurred.
"So we built the first [level of] the ceiling [in the software]—nothing happened," recalled Houdin. "We put the second ceiling up—nothing happened. Then the third, the fourth, the fifth and the rafters—nothing happened. We put the whole load of the pyramid [on top of the chamber]—still nothing happened. We were confused."
Houdin admitted, for a brief moment, that he doubted the software's fidelity to real-world physical conditions. But eventually his faith was restored; the cracks corresponding to the ones in the pyramid appeared once they introduced the collapse of the south wall. Armed with this evidence, he proposed that the King's Chamber's ceiling cracked "under the combined effect of the substance of the south wall and the separation of the rafters."
With a combination of geometric and physical modeling, Houdin and his colleagues tested the counterweight system the ancient builders might have used to transport the granite beams to the site of the King's Chamber (figure 4). In their simulations, the Grand Gallery, a narrow passageway devoid of liturgical embellishments, revealed itself to be an efficient mechanism for pulling the blocks. Relying on gravity and friction, the system would have employed trolleys, sledges and counterweights built with ropes and wood.
Figure 4. Physical modeling (left) allows the researchers to recreate the mechanisms the Egyptians might have used to pull the granite beams (right) to the King's Chamber.
Using DELMIA, Dassault's software for organizing factory-floor operations, the team was able to assess the amount of human labor and the length of time the whole project would have required. The digital simulation indicated it would take 20 years, which accurately corresponds to the span of Khufu's reign as well as the testimony from the Greek historian Herodotus.
"Due to the Dassault Systemes V5 architecture, no data conversion was needed to go from the initial CATIA model to DELMIA or SIMULIA," said Houdin.
A Classical Platform
Writing nearly 2,000 years after Khufu's time, Herodotus recorded the supposed construction methods of the Egyptians. "The method employed was to build it in steps, or, as some call them, krossai or platforms. When the base was completed, the blocks for the first tier above it were lifted from the ground level by contrivances made of short timbers; on the first tier, there was another, which raised the blocks a stage higher, then yet another, which raised them higher still . . ." (Herodotus, Histories, Book Two).
Houdin didn't set out to prove Herodotus's account in particular. In fact, he'd prefer to rely on architectural instinct than on the Greek historian's secondhand narrative, set down long after the event. But as it turned out, his theory produced a workflow not so different from what Herodotus wrote. For instance, he postulates the blocks were lifted from one flight to the next using wood-and-rope contraptions, operated on notched landings or corner platforms (figure 5).
Figure 5. The platform that the laborers might have used to raise the blocks from one level to another.
Skip the Camel Ride
On March 30, Houdin publicly unveiled his theory at the Paris Geode Cinema, a dome-shape auditorium with a 1,000–square-meter seating area. His findings, captured in an immersive 3D environment, now reside permanently on the Internet. At www.3ds.com/khufu, you can let Houdin's digital avatar guide you through the episodic reenactment, or you can circumnavigate the Great Pyramid and its environs on your own. The public site is powered by Virtools, Dassault's 3D content-creation software for the Internet and game consoles. Houdin's book, Khufu: The Secrets Behind the Building of the Great Pyramid (Farid Atiya Press, 2006), is now available at Amazon.com as well as other booksellers.
Kenneth Wong is a former editor of Cadence magazine. As a freelance writer, he explores innovative usage of technology and its implications. E-mail him at Kenneth.Wong at cadalyst.com.