The Speed of Light for Building Pyramids

Roman Mars:
This is 99% Invisible. I’m Roman Mars.

Roman Mars:
Steve Burrows is a principal of an engineering consulting company called ARUP.
Steve Burrows: I’m Steve Burrows, CBE, and I’m a professional engineer.

Roman Mars:
And when he saw the great pyramid in Egypt for the first time, he reacted pretty much the way I imagine most people react.

Steve Burrows:
When you actually go and see something that’s somewhere in the region of 40 stories high that was built 4,000 years ago, you just have this incredible “wow” moment.

Roman Mars:
But then that structural engineer brain kicks in.

Steve Burrows:
Every time you look at something, you think, first of all, “how did they do that?” Then I start thinking, “how would I do that?”

Roman Mars:
And in a recent article in “DesignIntelligence,” he took those questions head-on. As if a client gave him a brief to build something like the Great Pyramid today.

Steve Burrows:
We get these incredible challenges, where you’re doing something that’s never been done before. So one of the incredible facts, for me, was that the Great Pyramid stood as the tallest building in the world for centuries.

Roman Mars:
And as someone who, in the present day, is hired to engineer seemingly impossible structures, Steve Burrows thinks that the engineers of 600 BC really knew what was possible and made most of the decisions as a present-day engineer would.

Steve Burrows:
So some of the things they knew were that if they built on the Giza Plateau, they could put stones to a certain pressure and the ground didn’t collapse beneath it.

Roman Mars:
You can look at other pyramids and see the previous mistakes that were made.

Steve Burrows:
And they got to know what the ground capacity was. And I think that determined the size of the Great Pyramid.

Roman Mars:
Because if you’re going to build the tallest building in the world, how tall do you want it to be?

Steve Burrows:
Do you want it to be a mile? Or just a bit taller than the last tallest building?

Roman Mars:
You’ve got to make a decision.

Steve Burrows:
And I think the decision was made for them, by the quality of the ground that they were building on.

Roman Mars:
So, that was number one.

Steve Burrows:
Secondly, they had to build it in the Pharoh’s lifetime. And I’m pretty sure that somebody, you know, a contractor said, ”With the best will in the world, we can only lay this number of stones a day and I can only assemble this many men.”

Roman Mars:
And assembling men seems to be the right word in here, because, and I totally missed this historical revision, but the consensus now is that it was a rather privileged, well-treated class of Egyptians that built the pyramids. Not slaves. That blew my mind. Cecil B. DeMille is going to be pissed.

Steve Burrows:
20,000 men can only lay this many stones a day and the pharaoh typically lives 35 years, so that many men times that many stones times 35 years means it’s going to be this high.

Roman Mars:
So the ground can only hold so much mass without buckling, the workers can only build so much in a pharaoh’s lifetime, and finally, the material had to be delivered to the site in time to build the thing.

Steve Burrows:
And I would think, depending on where the quarry was relative to the actual site, which was chosen for its known ground-bearing capacity, and also height and visibility of Cairo, they also figured out that they could only get so many stones there. They only had so much material of the quality at the quarry.

Roman Mars:
So Steve Burrows thinks that these practical engineering considerations determine the size of the pyramid – its height, the number of stones – and ultimately, what we all marvel at, thousands of years later.

Steve Burrows:
It wasn’t so much mystique as just practical necessity.

Roman Mars:
Another practical consideration that led to the pyramid’s longevity is material chemistry. There are other ancient buildings that have not held up as well as the pyramids.

Steve Burrows:
The buildings I saw had lasted thousands of years. And they hadn’t all performed perfectly well. So it was pretty clear to me that the Egyptians had a pretty good understanding of the material that they were working with. But it wasn’t 100% perfect. For example, the first large mud-brick structures that I looked at had massive vertical cracks in them. And it was very clear to me that they were thermal cracks. What had happened is that they were used to building walls, but when a wall turns a corner, that point becomes very stiff. And because the temperatures vary hugely between day and night, these materials, these walls, expand and contract, and when it contracts, masonry will always break next to the stiff point. So every time there was a corner, I found a huge vertical crack. So they clearly didn’t understand the thermal performance of mud bricks.

Roman Mars:
And that problem is exacerbated by the fact that they lay these mud bricks on a mortar bed. So they effectively have two materials for building.

Steve Burrows:
So they’d use mud brick and mortar. And by putting these different materials together, they thermally move at different amounts. And they had cracked.

Roman Mars:
So somebody must have said, “If we’d only use one material, lay the bricks dry, would they have performed better?” And the answer is yes.

Steve Burrows:
And the pyramids are exactly that. So there is only one material that’s used. That means that the pyramids, you know, they get very hot in the day and very cold at night.

Roman Mars:
But the material throughout the pyramid is consistent.

Steve Burrows:
So it didn’t crack. Because they move together, they effectively breathe. And because they breathe to account for the changes in temperature, they’re able to last a long time without cracking or breaking up.

Roman Mars:
So this prompted Burrows to think of modern buildings, where we put so many materials together all the time.

Steve Burrows:
Steel and glass, and aluminum and concrete, and cementitious materials and plasterboard. And I started walking around modern buildings and looking at where all the cracks were. And every crack is at the joint between different materials. And I started to think, maybe we could think about this a little bit more and if we did, we could actually make buildings last longer just by thinking harder about those joints, which presently we solve by putting, you know, gooey material in the joint to try and take up that thermal movement. But if we just detail them better in the first place, they would last longer. And I think, the longer buildings last, the more sustainable they are. So the longer their life, the less materials we use in the long run.

Roman Mars:
Longevity is probably the most basic route to sustainability, and the pyramids are the poster children for longevity.

[You know there’s an old Arab saying, “Man fears time. Time fears the pyramids.”]

Roman Mars:
In addition to chemistry, adhering to basic principles of physics keeps your building around for millennia with little or no maintenance. A pyramid is a nice, stable shape.

Steve Burrows:
And I think they will have learned that.

Roman Mars:
But it isn’t as simple as the way I was thinking about it.

Steve Burrows:
If they had a bucket of sand and they poured it on the floor, then it actually naturally makes a pyramid shape. So, intuitively, they know that that is a stable thing to do. But actually, one of the interesting things is that the gradient of the sides of the pyramid is not determined, like sand, by its natural angle of repose. You can actually make it whatever you want to make it. But you can see from the prior pyramids – from the step pyramid and the bent pyramid, the pyramids that preceded the Great Pyramid – that they were sort of going a little bit steeper but they never really got above 50 degrees. Because I think that somebody felt that there’s sort of a maximum angle about which should never exceed.

Roman Mars:
So, again, in empirically-derived knowledge sets the agenda.

Steve Burrows:
If you put these things together, how much stone you can get, the bearing pressure that you can put on the ground, and the angle, it determines the height of the building. And I’m pretty sure the simple mathematics and the work between the architect, engineer, and contractor, gave a practical limit to what could be built.

Roman Mars:
This exercise in using engineering principles to augment the archeological data might give us some insight into why the great pyramid is both the oldest and the largest pyramid of Giza. Because people probably thought it was the limit of everything. It’s the biggest bearing capacity, it’s as steep as they go, and it’s as many stones as can be laid in a lifetime. You can’t do any bigger than that.

Steve Burrows:
It was the speed of light, if you like, for building pyramids.

Roman Mars:
I know it’s no revelation that the pyramids are well-designed. I’m not an idiot. But learning about these practical considerations from Steve Burrows just made me appreciate their majesty in a new way. These structures are not other-worldly. You don’t need to come up with crazy theories to explain them. They are the product of smart architects and designers and engineers and skilled workers who applied knowledge that was gained over time and passed down over generations. And through that perfectly understandable and repeatable process, they discovered their limit. But don’t get me wrong. I don’t ever want to see the tallest building we could possibly build. But I might like to see the one designed with enough durability and flexibility to last for 4,000 years.

Roman Mars:
99% Invisible was produced by me, Roman Mars, with support from LUNAR, making a difference with creativity. It’s a project of KALW 91.7, local public radio in San Francisco, the American Institute of Architects in San Francisco, and the Center for Architecture and Design. To find out more, go to the website. It’s 99percentinvisible.org.

  1. Tina

    I am Egyptian and I loved what you did in this episode and how you discussed the great pyramid in a new and different perspective. Love the arabic song in the end, Chapeau =)

  2. tim

    The latitude of the pyramid in decimal degrees can match a sequence of numbers expressing the speed of light if you look hard enough for it, but that phenomenon is nothing more than coincidence.

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