01 The Pyramids

What can we learn from the design and build project

preeminent from 2500 BC until the modern age?

The Giza pyramids must have made an incredible visual impact – at the edge of the desert three abstract geometrical symbols were rising, huge luminous white triangles reflecting the blinding light of the sun! (1)

The pyramids on the Giza plateau are the largest of the 107 (30 major) pyramids built in Egypt.  Khufu was originally 480.9 feet tall with Khafre  just a few feet shorter. Built with about 2,300,000 to 2,500,000 blocks of average size 4ft x 4ft x 2.5 ft (5000 lbs each) in 210 (maybe 218) courses or layers.  Mostly limestone, a soft sedimentary rock, but with granite (very hard igneous rock)  in interior work and facing the entire outer surface..  From its construction around 2560 BC (radiocarbon dating +/- 400 years) (2) Khufu was the tallest man-made structure for 3800 years, until the spire of the Lincoln cathedral rose in AD 1300.

 

Introduction

First, a story illustrative of  four points.  I introduce these as a guide as we consider project fundamentals which worked for the Egyptians building the pyramids

Canadian Natural Resources (CNRL) was a small company getting really big with the construction of a large ($8 billion) oil sands plant with upgrading capability.  My bud Chris had been actively consulting with them since inception, I had dabbled during early design, but the call now was to get field construction back on track.  We would be working for L, project executive in charge of the upgrading units, and soon to be executive in charge of all units.  We like L a lot.  He had been a top executive at Petrovesa until a new Venezuelan president, Chavez, replaced him and his staff with more politically aligned cronies.

Here is a really interesting aspect of working for L: he was given stock options as part of his package for signing up; these were not insignificant, the project started up well, generating the kind of cash flows anticipated, and L would pocket something rumored to be $12 million dollars to his own personal account.  Nice.  So, we are working for a very bright, experienced man, who was focused on real results.  Ideal.

A couple of details.  Work at the Hydrotreater units was falling way behind because they didn’t have, or couldn’t find the piping materials for work scheduled to be done.  The Construction Manager made a standard observation: I can get anything built if I have the materials at site. But without them, I can do nothing.

Another unit was having problems because much of what they had installed had to be changed: the “Approved for Construction” drawings were being wildly revised.

Elsewhere there was the trouble with welding productivity – new welders were coming onsite and doing test welds on final field installations, and there were logistical, training and supervisory problems as well.  Instead of the 15-20 diameter inches of weld we expected for a crew, we were getting 2-4.  Argh.   (Footnote: less can be more – once low performers were removed from the unit, not only did rates get better, so did total work: with fewer people there were more welds per day.  Go figure.)

And the sequencing in another area was jumbled, because they were blowing and going on whatever materials and drawings they had available, but this availability did not follow the sequencing required for efficient constructability. Scaffolding was dismantled, later needing to be rebuilt in the same spot.  There was worker congestion causing low productivity in some spots, no work being done in others.  And cranes were seldom where they needed to be.

One unit, the Coker, was in really good shape.  I wasn’t called to help out on that one, they didn’t appear to need it, but I did have a really good conversation with their construction manager ,Steve Seguin, because I wanted to leverage on what was working for him, there, at my other units.  All of the above mentioned problems came together in what he called the four key points, from his Bechtel days. These are the four things that need to come together at the work package level to get the work done productively, safely and right. I share this because it is something I use every day in my consulting practice, it makes sense in so many ways:

 

I propose now to view the pyramids through this 4-point lens.

 

Khufu’s Great Pyramid of Giza – Lessons Learned

 

The Issue: How did they do it?  What can we learn?

 

Bold decisions:

  1. Design: Iterative Design and Build; Khufu’s father Sneferu improved the Step, then built the Meidum, Bent and Red pyramids in Saqqara.  His son Hemiunu built his son Khufu’s Great Pyramid, incorporating lessons learned from his father, Sneferu.
  2. Materials: built on the site of the quarry for  limestone blocks (97% of all blocks); built canal to the Nile for the imported Granite (large structural blocks and facing)
  3. Work sequencing: clever design to move blocks over “rolling fulcrums” (catenary quarter circles); possible internal ramp to the top. Lever lifts.  Low tech but really good tech.
  4. People: Probably 4,000 to 5,000 workers (some say 10,000) over 5-10 years (some say 20).  Archeologists have uncovered a nice city built for the workers, possibly all voluntary for the opportunity to learn and work on a great and enduring endeavor.

Resolution: the basic reasoning behind each of these bold decision, and especially all of them together, will make most modern projects better.  Read on.

1. Iterative Design Build.

While the earliest pyramid type things were more like large stone slabs (mastabas, benches) we will not discuss those.  Our primary focus is on the largest of the pyramids, Khufu, but we need to start with three pyramids built by his father.

 

A mastaba (bench) and the Step Pyramid in Saqqa

A mastaba was a burial tomb of religious significance for royalty. It consisted of an underground burial chamber with a vertical shaft that opened into an above-ground structure. This solid structure was generally rectangular with inward sloping sides. Early mastabas were fairly modest with the above ground structure being about ten feet high and about 30 feet on a side. Later mastabas grew in size and complexity. Thethi Kheneri’s mastaba was about 208 feet long and about 30 feet high. It contained five shafts, seven rooms and a number of corridors(all underground).

Enter one of the worlds first geniuses to be recognized by the monuments he left behind – Imhotep. called by some the Leonardo D’Vinci of his age.  He designed and built the first large construction that is generally classified as a pyramid: the “step” pyramid of Zoser (Djoser), around 2850 BC – or only about 75 years before Khufu.  This first Egyptian pyramid consisted of six mastabas (of decreasing size) built atop one another in what were clearly revisions and developments of the original plan. Each layer was built up of many sub-layers of stone about a foot thick. The pyramid originally stood 203 ft tall, with a base of 358 × 410 ft and was clad in polished white limestone.  The volume was about 10 million cubic feet, or about 11% of the Great Pyramid. This is still a considerably large structure.

Looking forward: Sneferu reigned from 2813 to 2790 BC; his son Khufu reigned from 2789 to 2767 BC; Khafre, Sneferu’s grandson, ruled from 2758 to 2742 BC. During this period of only 71 years, the four largest Egyptian pyramids were built. These four pyramids alone comprise over 270 million cubic feet of limestone. For about 1,000 years after this period, nearly all of the pyramids that were built were much smaller than even Djoser’s pyramid.  Note that the massive pyramids would all be built within 70 years, or about one lifetime. All the later pyramids are smaller by at least an order of magnitude

 

The Meidum pyramid in photo and cross section; the core of this pyramid is all that remains standing.

The next pyramid we see is the Meidum with a couple of new twists. They use a corbelled ceiling for tunnels and rooms within the pyramid. And they also smoothed the steps for the first true pyramid. Unfortunately they built us a bit steep and it collapsed.  Eventually, we find evidence that the Meidum pyramid was built for the king Sneferu.  The Meidum pyramid was built in different stages, beginning as a seven-step pyramid to which an additional step was added at a later stage.

Known as “the collapsed pyramid”, the outer layers of the casing began to collapse, leaving the exposed core showing. Because of its appearance, it is called el-haram el-kaddab — (Fake Pyramid) in Egyptian Arabic.  Some believe it was the collapse of this pyramid during the reign of Sneferu that led him to change the angle on his second pyramid at Dahshur to 43 degrees.   Original height 302 ft; Base 472.5 ft; Slope 51° 50′ 35″.

Take Away: Lot’s of successful innovations, but something went wrong in stability.

 

 

The Bent Pyramid and the Red Pyramid, each is about half the volume of the Great Pyramid

Sneferu’s second pyramid would be at Dashur, about 30 miles north of Meidum.  The Egyptians were to learn by trial and error, loading stones upon a beam until a collapsed for example, and there is no greater example of this in the second pyramid at Dashur the Bent pyramid.  Pyramid’s are built on bedrock not sand but a portion only one corner of the bent pyramid  was built on gravel which subsided.  Sneferu  is now in a very difficult position, he’s built the two largest  buildings on earth but neither was suitable for his burial.

Enter now the Red pyramid.  Just a mile from the Bent pyramid.  Not taking any chances it has a gentle 42° slope rather than the 53° slope of the other two.

Sneferu’s three pyramids : Meidum , the Bent, and  the Red – constitute the most intense building spurt in history. Under one pharaoh, Egypt built the three largest buildings on earth, developed the first true pyramid, and invented the corbelled ceiling so burials could be above ground, high up in the pyramid. In television programs and popular books about pyramids the focus is always on King Khufu the builder of the great pyramid at Giza. However it is really Khufu’s father Sneferu who taught Egypt how to build pyramids. 1000 years after Sneferu’s death, when someone does something impressive, he would say “not since the time of Sneferu has its like been done”.

 

Take away: We now have design details from these lessons learned.  How to build internals with corbelled ceilings to support the weight of the pyramid above.  Proper site selection and site prep for stability.  Optimized slope of the pyramid walls.  Details like keeping base blocks strictly horizontal and not tilted slightly inward avoiding what we today would call shear stresses.  And likely ways of how to  quarry, shape, transport, lift and align blocks.

 

Turning our focus back to the great pyramid, itself

 

Khufu’s Great Pyramid of Giza: modern photo; the internal chambers; 52% of the stone at elevation 98ft – 82% at elevation 164ft

Height: 485 ft.  each of four base sides:  763 feet.  ratio of height to width: 1.571 (one half of pi)  slope: 51.85 degrees

 

2. Materials

 

Orange = Limestone quarries on the Giza plateau.  Dashed line = harbor facilities


First idea of genius: build the pyramids at the site of the quarry for the limestone blocks!  And build a canal from the Nile for the granite blocks.

Take away: This is similar to the next success story we are going to consider, the Empire State Building, in which all of the steel was provided by a foundry dedicated almost solely to this building.  And the Empire State project also developed a transit method to deliver steel components, each clearly marked as to where it was to be installed, next day directly to the site.

 

3. Work sequencing (Constructability)

 

Did I mention transit?  Without cranes and trucks, how did they move these blocks to where they needed to be placed?

To understate the issue, there are plenty of theories.  I like the ones with some archeological evidence.

Here’s one. Tracks made of catenary shaped quarter-rounds allows a single man to “roll” a 4200 pound limestone block along level ground at walking pace!

The heavy lifting, intellectually here, has been done by Gerard C. A. Fonte in his book “Building the pyramids in a year: an engineer’s report”.  Cedar rounds of this roughly catenary shape have been found at site.  And the author has demonstrated that it will work, as this 5’10′ 135 pound man built such a track of catenary shaped quarter-rounds, loaded a 4200 pound block of average pyramid block dimensions, and moved it himself at walking pace, with local news videotaping the whole thing.  I like it.  What a great way to move blocks from the quarry to the pyramid site!  Photos and video of this work have been published. (3)

 

Next issue:even  if the above works along flats or gentle slopes, how do we get blocks to the top?

Giant ramps have been speculated and dismissed; they would take more material than seems to be available, not to mention that building such ramps may have almost doubled the total effort.  More clever thinking seems to be based on this; use the pyramid as it is built itself as your ramp!

It makes sense, though, to build a ramp to get from the quarry at least to the lower heights.  30% of the blocks are at elevation 49ft, 52% of the blocks are at elevation 98ft and below.  The efficient way to do thisfor the lower courses may have been to use standard size blocks (to be installed into the pyramid after ramp use completes).

But the higher levels would require more ramp materials and a longer ramp length for slope than appears to be feasible.  One school of thought would be to use the 52 degree side slopes  of the finished pyramid levels as ramps.  Have 4200 pounds of men walking down pull up a 4200 pound block on ropes, using water and oil lubricated “sleds” to make it easier.  And maybe fewer than 4200 pounds of men, by making use of their muscle power.  Hypothesized; crews of 48 men per block.

More clever: a series if internal ramps within the pyramid.  This possibility has been carefully explored in 3-D computer modelling, projected onto IMAX film.  Would be very clever, and some early gravity measurement type instrumentation seemed to find such internal ramps existing within the pyramid.  Thermal instrumentation may definitively identify these (hollow tunnels will be cooler) but such testing has not yet been authorized, so we are still in conjecture mode.(4)

Along with these, levers can lift blocks.  Such levers (shadoufs) were common on a smaller scale, in hieroglyphics showing how water was raised by a series of levers from the Nile to the higher surrounding countryside.  And carefully constructed stone ends, such as would be useful where the ropes meet long lever ends, have been found on site. Additionally, Brier and Houdin suggest that the internal great chamber may have been designed for counterweights used in heavy lifts.

Take away: While a naive project manger or planner might think that the first step in solving this problem would be to develop a work breakdown structure ( in fact, such has been published!), my thoughts are that clever engineers, work supervisors and workers discovered methods to make the transport of blocks not only efficient and effective, but fun.  So clever was the constructability that it became inevitable to build something based on it. An easy sell to the project executive and project manager.  High PEVA.   Clever constructability modes survive to this day on the projects benchmarked to be in the top percentiles.

4. People

The exeutive in charge of Khufu’s pyramid was  named Hemiuni.  He was a step-brother of Khufu and  also a son of Sneferu ( of a different wife).  He had been around during Sneferu’s construction of the pyramids at Saqqara.

The workers were also well taken care of.  Recent excavations have uncovered a nicely designed city for the workers near the building site of the pyramids.  It is not unlikely that some of the key supervisors had experience on the Saqqara pyramids.  While slave labor  as described in the book of Exodus was employed building the store cites of Ramses and Pithom, it is widely speculated that the Khufu pyramid workforce was volunteer, looking to develop skills and share in the glory of a magnificent endeavor.

Concluding remarks

1.  Design.

Learn all that is available from previous, similar endeavors.  And then feel free to strike out on some innovative new ideas yourself where the project justifies them and you have a good chances of success.  I like UCLA basketball John Wooden’s quote: the team that makes the most mistakes wins.

2.  Materials

Make sure you are selecting the right materials, secure them early, and get them to site when needed and marked for their intended final use.  Creative solutions to the materials and delivery issue have been the hallmark of many great successes.

3.  Work sequencing (Constructability)

In a utopian world, it would be great if there was some context-insensitive algorithm such as a work breakdown structure that would ensure success regardless of project specifics.  Alas, I strongly believe that it is necessary to elicit and coordinate context sensitive ideas: clever thinking on the part of those closest to the work, especially the workers on the tools and their direct and indirect supervisors who must be coordinated with the big picture executive, project manager, engineers and planners to get this done right.

4. People

I  am a fan of the ‘great man”or “great woman” concept.  There is nothing better than, at the top, an executive, project manager and/or his/her staff, who completely envision the entire project as a whole, with all of its PEVA inputs, making timely decisions and providing overall guidance.  As Frederick Brooks says, “conceptual integrity is the most important consideration in system design… The solo designer or artist usually produces works with this integrity subconsciously” (5)    And this can apply to a single person plus his/her tested and trusted staff, not necessarily to a single person alone.

Once this vision is secure, then having people signed up, trained and effective to get the work done makes it all happen.

 

 

 

Notes:

(1) http://www.cheops-pyramide.ch/khufu-pyramid/khufu-numbers.html

(2) http://web.archive.org/web/20080305031531/http://www.aeraweb.org/how_old.asp

 

Reading List:

(3) Gerard C A Fonte  “Building the Pyramids in a Year: an Engineer’s Report”.  . http://www.algora.com/147/book/details.html

(4) Bob Brier and Jean-Pierre Houdin  “The Secret of the Great Pyramid: How one man’s obsession led to the solution to ancient Egypt;s greatest mystery”

(5) Brooks, Frederick P. (2010-03-22). The Design of Design: Essays from a Computer Scientist (Kindle Locations 1170-1180). Addison-Wesley Professional.”

 

 

 

 

Giza 160
Great Pyramid SWS
Pyramid n Lo 1
tetra 03
khufu-interior-view
pyramid 3 in the sun
Mastaba
step pyramid in memphis
bent 2
red-pyramid-dahshur 2
medium
meidum detail
Khufu 1
Khufu 2
Khufu 3
Quarries at Giza
Giza sideview
catenary roll
catenary detail
roll 4
roll 1
roll 2
roll 1
roll 2
roll 3
ramp

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