The Speed of Light for Building Pyramids

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

RM: Steve Burrows is a principal of an engineering consulting company called Arup.

Steve Burrows (SB): I’m Steve Burrows CBE and I’m a professional engineer.

RM: And when he saw the great pyramid in Egypt for the first time, he reacted the same wayI imagine most people react.

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

RM: But then that structural engineer brain kicks in.

SB: 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?

RM: 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.

SB: 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.

RM: 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 the most of the descisions as a present-day engineer would.

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

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

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

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

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

RM: You’ve got to make a decision.

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

RM: That was number one.

SB: Secondly, they had to build it in the Pharoh’s lifetime. And I’m pretty sure that somebody, you know a contractor, said ” you know, 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.”

RM: 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.

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

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

SB: And I would think, depending on where the quarry was relative to the actually 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.

RM: 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.

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

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

SB: 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 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.

RM: 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.

SB: 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.

RM: 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.

SB: 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.

RM: But the material throughout the pyramid is consistant.

SB: 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.

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

SB: 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, you know, the longer buildings last, the more sustainable they are. So the longer their life and the less materials we use in the long run.

RM: 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.”

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

SB: And I think they will have learnt that.

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

SB: If they had a bucket of sand and they poured it on the floor, then it actually natrually 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 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 this is sort of a maximum angle about which should never exceed.

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

SB: 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, you know, 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.

RM: 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.

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

RM: 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 theories to explain them. They are the product of smart architects and designers and engineers 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. And 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 enought durability and flexability to last for 4,000 years.

  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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