There is no shortage of theories about how the Great Pyramid of Pharaoh Khufu was constructed, but so far they have all failed in various respects. From ramps that are as large and difficult to construct as the pyramid itself, to ramps that by their nature would make its construction even more difficult, we can’t even really explain how the blocks were moved into place.
But a French architect by the name of Jean-Pierre Houdin may be changing that. He has put forth the first comprehensive explanation of how the Great Pyramid was built that stands the tests of physics and common sense, and his work continues to gain support from prominent architects, engineers, and Egyptologists.
Jean-Pierre has kindly agreed to work with Em Hotep! to put his theory into terms that are accessible to those of us who may not be professional architects or engineers, but who may be amateur and professional Egyptologists of varying degrees. In Part One we take a close look at the evolution of ramp theories, how they work and fail to work, and what was involved with building the only remaining Wonder of the Ancient World.
In the Introduction to Hemienu to Houdin: Building a Great Pyramid we met the primary characters of our story. Hemienu, who was vizier and Master of Works for Pharaoh Khufu, and who designed, planned, and built the Great Pyramid. Henri Houdin, a French engineer who became enthralled with Khufu’s Pyramid and took up the task of reverse engineering its construction. And the protagonist of our tale, Jean-Pierre Houdin, Henri’s architect son and heir to the Great Work of figuring out how Hemienu accomplished one of the greatest architectural and engineering feats of human history.
We traced out a short biography of these three master builders and examined how the times they lived in, the circumstances of history, and even their family lives drove them toward their respective quests. We were also introduced to some of the shortcomings of the many theories that have been offered by others regarding how the Great Pyramid was constructed, and touched on insights that set this father and son team on the trail of Hemienu’s secrets.
I also proposed an outline and timetable for how I wanted to approach this project, namely, that this series of articles would be posted over the course of several weeks, and that Part One would get into the specifics of Jean-Pierre’s internal ramp, and Part Two would look at how he proposes the interior architecture of Khufu’s Pyramid was planned and carried out. Now, more than a month later, it is obvious that the timetable is out the window, and for that I apologize.
But after much correspondence with M. Houdin, I have decided that this subject deserves more than just a rush-through. There are numerous short introductions available online and in print that can give you the basics of Jean-Pierre’s work, and for the full treatment you really must read his and Bob Brier’s book, The Secret of the Great Pyramid, which has just become available in paperback. As for Em Hotep!, my goal is to provide news and reference articles about Egyptology for “the Curious Layperson and the Budding Scholar,” and that means being both comprehensive and comprehendible.
So Part One: How Do You Prefer Your Ramp? is going to be a detailed look at the primary theories that have preceded Jean-Pierre and exactly why they simply cannot work. This will lay a good foundation for Part Two, which will deal with Jean-Pierre’s innovations on the various ramp theories, and as you will soon see, foundations are very important with this topic!
The first section of this article will deal with the straight ramp theories, which really serve as a sort of negative benchmark against which all others are measured. This may sound a bit harsh, but an understanding of what these theories attempt to accomplish and why they fail is vital to following their evolution and how each theory moves us closer to the answer. In order to make 100% certain I got this rather important aspect of our discussion right, the first section takes the form of a dialogue with Jean-Pierre.
The next section will take a look at external spiraling ramp theories. These theories suggest that the Great Pyramid was constructed by use of a ramp that corkscrews up the outside surface. They resolve a number of the problems that make the straight ramp theories impossible, but leave several major issues unresolved, and come with their own set of issues.
The third section will take a closer look at Henri Houdin’s eureka moment—Hemienu constructed the Great Pyramid by building from the inside out, and he accomplished this by using internal ramps. Henri’s epiphany resolved nearly all of the remaining problems with the previous theories, but as his son realized, a couple of snags remained.
The External Straight Ramp: A Dialogue with Jean-Pierre Houdin
The straight ramp theory was first worked out by Ludwig Borchardt and completed by Jean-Philippe Lauer. The basic idea was that a straight ramp constructed of mudbrick and filler would be used to haul the blocks into place. As each level of the pyramid is completed, work on the pyramid stops so the ramp can be built up to the next level. The base had to be fairly wide, about 50 meters, so that its top surface would still be both wide enough and stable enough as it rises. Keep in mind that as the pyramid grows narrower, so must the ramp.
As the ramp reaches the 35 meter level, where construction on the King’s Chamber begins, Lauer believed his and Borchardt’s ramp would be short enough and shallow enough in terms of its slope to enable men to pull the large blocks, some of them weighing in excess of 60 tons, up to the construction site of the King’s Chamber where machines using sacks of sand for counterweights and smaller ramps cut into the core masonry to maneuver the huge blocks and stone beams into place.
For the top of the pyramid, Lauer’s ramp would increase in gradient as the width decreased. He believed that blocks weighing a ton could still be moved to a height of 112 meters on a 14 degree incline, and that the last stretch could be as steep as 18 degrees to reach the final 146 meters. Lauer postulates that to compensate for the very steep gradients smaller blocks would be used to complete the pyramid.
A couple of problems present themselves right away with the Borchardt-Lauer ramp. First, contrary to Lauer’s assumption, the blocks do not grow progressively smaller higher up the pyramid. The thickness of layers continues to alternate pretty much from the bottom to the top, and blocks weighing as much as 2.5 tons are used at least as high as 90 meters.
Then there is the pyramidion. The pyramidion was the capstone of the pyramid, a sort of small solid pyramid itself. Constructed of limestone and covered in electrum, the pyramidion would have weighed at the very least 5.5 tons, and possibly as much as fifteen tons! Plus, although the top layers of stone are now missing, as is the pyramidion itself, they would have been especially thick to support the pyramidion. Several layers of smaller blocks would have been crushed over time. It is simply implausible that a 5.5-15 ton pyramidion, plus its supporting masonry, could have been moved up an 18 percent incline.
Jean-Pierre: In fact human strength falls very quickly above 10% grade. You must keep an optimum ratio of force-to-grade: 7-8% grade is the highest figure to consider.
So forget the gradually increasing incline. To build the pyramid using a straight ramp you have to maintain a 7-8% grade from bottom to top. In The Secret of the Great Pyramid, Jean-Pierre Houdin and Bob Brier talk about the straight ramp being a mile long. But in order for the ramp to reach the top of the pyramid, about 146 meters, while maintaining a 7-8% grade, it seems the ramp would have to be even longer.
Jean-Pierre: Discussions of a straight external ramp always talk about reaching the summit. That is wrong. No ramp can go above the 130-135 meter level—the ramp would be wider than the pyramid. So to reach a level of 130-135 meters at a 7% grade, a frontal ramp has to be 1,860 meters long, about 1.15 miles. To build the same ramp with an 8% grade it would be 1,625 meters long, about one mile, which is why I always talk about a mile long ramp.
This means that, in order to maintain a manageable 8% slope, the straight external ramp has to be about a mile long, and comes about eleven meters (about 36 feet) short of the estimated apex of the pyramid. So, where could Hemienu have built such a ramp?
The terrain has a lot to say about that. The Great Pyramid was built on a bluff, and there is a steep drop to the north, so no ramp there. To the east and west there are cemeteries contemporary with the pyramid, so no ramps there either. That leaves the south, which is far from ideal for such a construction.
Jean Pierre: Absolutely. A single frontal ramp has to be perpendicular to the south face of the pyramid which puts it cutting through the quarry before filling the wadi on the other side! The topography speaks for itself.
So the ramp would not only overshoot the quarry, it would have to account for the rise and fall of the terrain, which would mean filling in the wadi, a sort of canyon made by a dry river bed, which would add even more material and labor to the ramp project. Keep in mind that the further you have to build the ramp downward to account for the dip created by the wadi the wider the base has to be in that section.
Everywhere you look in the Great Pyramid you see signs not only of Hemienu’s architectural genius, but of the economy of his methods. Nothing is wasted in terms of time or materials. A ramp that requires the workers to drag the blocks in the opposite direction of the pyramid before mounting the ramp just doesn’t seem to make sense.
The volume of material and man-hours required in making such a ramp raise their own set of questions. Building a mile-long ramp that reaches 135 meters on its high end would require a huge amount of material and labor even if it was built on a flat surface, which it wasn’t. And where did all the millions of tons of stone go?
When you account for the terrain you are talking about a project similar in scope to the pyramid itself, just to build the ramp. Even allowing for filler material, a significant portion of such a ramp would have to be solid masonry. Remember, some of the blocks it would have to support weighed more than sixty tons. Think about it. If the ramp was, say, two-thirds the mass of the pyramid, then where would you dispose of two-thirds of the Great Pyramid, without a trace?
Another nagging problem with all external ramp theories, from Lauer onward, is the notion of stopping work on the pyramid while constructing the next layer of the ramp. Hemienu built the Great Pyramid in about 21-23 years. This task simply could not be accomplished in the time frame if practically all work on the pyramid had to stop every time the ramp had to be raised another level.
Jean-Pierre: Nor was it. Up to now, “rampists” have always talked about a ramp being raised and lengthened as the pyramid rises, which means that you have to stop the construction to enlarge the ramp. My theory, which you will see does include an external ramp along with an internal ramp, is the first to describe an external ramp that is being built as the pyramid rises.
The ramp was built at its maximum length, about a quarter of a mile, but with two parts, or lanes, built horizontally, layer by layer, following a 7-8% slope. While one lane is used to pull the blocks, the other is raised by 2 layers to be ready for the next step. The ramp is always rising with the pyramid and so there is no need for work on the pyramid to stop.
Lastly, with regard to the “rampists” theories, there is the issue of logistics. The higher you go, the less workspace you have on both the ramp and the top surface of the pyramid. And the logistics involved with moving the 60 ton blocks to the top of the King’s Chamber and maneuvering them into place..
Jean Pierre: On a 7% grade ramp, 600 men are needed to pull a 60 ton block. Can you imagine 600 guys? With six hauling lines, that gives a 100 meter-long line for each.. It is impossible to coordinate such numbers. And at the 60+ meters level you have only 50 meters of work space left on the north side to work around the King’s Chamber.
A single straight mile-long ramp just seems to create more problems than it solves. Not only would it have required as much work and material as the pyramid itself, there is no evidence for such a huge ramp. Where did it go? And how was the pyramid completed in time if work had to stop in order to build up the ramp at each level. Jean-Pierre’s two-lane ramp works fine up to the level of the King’s Chamber, but what about twice that height, about 135 meters? The ramp would be far too narrow at that height.
Perhaps a straight ramp may have worked on other pyramids, but Hemienu wasn’t building just any pyramid. He knew he was facing multiple challenges that would require complex answers, all of which had to be worked out before hand.
The External Spiraling Ramp: The Corkscrew Solution
For several very good reasons the long, straight ramp theory doesn’t seem to work. One can imagine that Hemienu might have figured this out pretty quickly. A fast survey of the landscape, lining up the only feasible approach for the ramp to the pyramid’s south face, calculating the amount of material it would take to keep the grade constant even as the ramp spans the wadi, the ratio of the width of the base to the width of the top, the length of the ramp—It would have been obvious from the outset to Hemienu that the long single ramp wouldn’t work.
It was probably an early lunch for Hemienu and his crew after a morning walk around the building site, checking surveying points, taking mental notes. As the architect and his crew sat around the table sipping karkade and brainstorming while the servants cleared the tableware, someone might have proposed what seemed to be the perfect solution.
“Think about a length of papyrus,” he might have said. “Stretched out it would cover this entire table, and spill over each end. But if you roll it up, it can fit into your robe. What if we fold the ramp to fit into the usable terrain and onto the surface of the pyramid itself?”
Hemienu would have pondered this idea. With his chin resting in his palm, he probably considered the advantages. What problems would a spiraling ramp address?
Several advantages of a spiraling ramp are immediately apparent. Terrain is no longer an issue, as the terrain would be the pyramid itself. Using the surface of the pyramid to support the ramp would mean a constant 7-8% grade could be easily maintained and the supporting surface would be a constant—no wadi to span and no 50-meter wide base to support a ramp 135 meters high. As it winds up the pyramid, the ramp itself would maintain a fairly regular height, except at the top, where it would actually grow shorter. This would also reduce the amount of material and man-hours required to build the ramp.
Hemienu’s assistant would have been pleased with his epiphany. The problem of the ramp, which was turning into as large a project as the pyramid itself, had been solved. Perhaps Vizier Hemienu, Master of Works for Pharaoh Khufu, would honor him with a memorial stela praising his genius? But his exaltation would have been short lived.
“What about the blocks for the King’s Chamber?” the Master Architect would have asked. “How do we navigate those, or any of the other blocks, for that matter, around the corners of your folded papyrus?”
The Spiraling Collapse of the Corkscrew Theory
Hemienu would have seen right away that for all its advantages, and there were admittedly several, there were also some flaws with the spiraling ramp, and they were deal breakers. The most obvious, and perhaps most vexing, would be how to handle the corners. The most common blocks used in the building of the pyramid weighed 1.5 to 2.5 tons and were moved on a type of sled. Wheels would not work because they would have sunk in the sand, and besides, there is no evidence of the wheel in use in Egypt this early. So turning the sled 90 degrees to face the next course of the ramp at the corners was an issue—simply spinning it on its rails would have destroyed the sleds.
There is also the issue of time. Keep in mind that every time you stop the production line to reorient a sled at the corner, the entire chain below you has to stop as well. Hemienu is believed to have completed the pyramid in about 21-23 years, which means that a block was being put into place during every minute of construction. How were the workers moving the sleds around in less than one minute on the tight corners of the corkscrew ramp?
Even if the problem of orienting the standard blocks at the corners of an external winding ramp was solved, there was still the problem of the huge blocks used to construct the King’ Chamber. The largest of these slabs weighed in excess of 60 tons and were over eight meters (a little over 26 feet) in length.
If you can picture trying to maneuver such a block around a corner, even if there was someplace where the workmen could stand while pushing/pulling (which there would not be), at around 45 degrees into the turn the full weight of these blocks would be balanced entirely on the corner of the ramp. Given that the corner of the ramp, obviously, would be built on the corner of the pyramid, we are talking about a tiny segment of the ramp pressed between a wedge below (the edge of the pyramid) and 60 tons of weight from above! This isn’t a model for supporting a weight, it’s a model for splitting something in half!
Another issue Hemienu would have realized was that you just wouldn’t be able to build a winding ramp against the surface of the pyramid that would be stable enough. Again, ignoring the problem of the 60 ton blocks, if you were to build a ramp wide enough and sturdy enough to move the average block up the pyramid, then the external ramp would obscure the corners of the pyramid, and that is another big problem.
In order to ensure that the four corners of the pyramid were rising at the same constant angle, Hemienu would have needed to take regular measurements. If the slope of one side of the pyramid was off by as much as a fraction of a degree, then the shape of the entire pyramid would be off and the four edges would not meet at a single point at the top. In order to make these exact measurements the corners and edges of the pyramid had to be visible, and a sturdy ramp corkscrewing around the pyramid would make this impossible.
It seems that for every problem the external corkscrew ramp solves, another is uncovered. You can’t build a ramp that allows the corners to be surveyed that will also be stable enough to bear the load of the blocks. Such a ramp would entail trying to build a pyramid consisting of four perfectly equal triangles, with exactly the same slope on each side, without being able to survey the slopes and angles as construction proceeds. If you build a ramp narrow enough to allow the measurements to be made, then it will be too unstable for the 1.5 to 2.5 ton blocks. Keep in mind that at any given time there will be multiple blocks on each stretch of the ramp.
The external corkscrew ramp could not work, not for the standard blocks, and certainly not for the huge blocks required for building the King’s Chamber, or for that matter, the Queen’s Chamber. Of course, other models have been offered—multiple ramps, zigzagging ramps, and some ramps that seem to have leapt from an M. C. Escher drawing. But down through the ages the long single ramp and the external spiral ramp have stood the test of time.
And failed the tests of physics and engineering.
The Internal Spiraling Ramp: Now We’re Getting Somewhere!
As we learned in the Introduction, the question of how the Great Pyramid was built caught the attention of an engineer named Henri Houdin back in 1999 after he viewed a television program called The Mystery of the Pyramid. Henri was one of the many French youth who inherited a post-WWII France, with all of the reconstruction that went with it. Soon after receiving his Ph. D. from École des Arts et Metiers, 24-year-old Henri found himself in charge of rebuilding the Conflans Bridge outside of Paris (Brier and Houdin, pp. 2, 38). The year was 1947, and a long and impressive career lay before young Henri.
In 1999, Henri was retired, but far from tired. He needed something to occupy his mind, which was as sharp and hungry for activity as ever. He approached the problem of Khufu’s Pyramid the same way he approached any other engineering problem he had ever taken on—How do I build this?
The advantages of the spiraling ramp still held true. A workable ramp that would maintain a 7-8% grade would have to be around a mile long, and the only way to do that with the terrain where Hemienu built the Great Pyramid was by wrapping the ramp around the pyramid itself. Multiple straight ramps would not work because the only side where a straight ramp could be built was on the southern side, and the terrain there only allowed for one ramp to approach the pyramid.
Making use of the artificial terrain of the pyramid itself would have the benefit of a regular surface free of obstacles, if there was only some way to construct a sturdy enough ramp that would also leave the site lines visible for surveying. So how would the engineer Henri Houdin build this?
Henri’s epiphany came as he pondered how he would deliver the building materials to the worksites. In this sense, the worksites are different from the construction site. The construction site was the entire project, but the construction site was made up of many worksites that were all over the structure, and many of which were in constant movement as the pyramid rose. Henri’s epiphany was that if he were to build the pyramid using the tools available at the time he would build it from the inside out, and the ramp would likewise be located on the inside.
An internal ramp would retain all of the benefits of the corkscrew ramp while solving many of the problems. The pyramid would not only be the building surface, it would be the ramp itself. The sight lines would remain visible because the ramp would be concealed within the pyramid. This meant that there would be no need to trade off between visibility and stability, which became doubly moot because the ramp would be as sturdy as the pyramid itself.
This solution also was in keeping with the economy Hemienu expressed throughout the rest of the pyramid. There was no wasted material—the material would already be in place. No wasted man-hours because virtually every block put in place for the ramp would have been required in the construction of the pyramid anyway. And there would be no need to explain why there are no ruins of the ramp, or how its materials were disposed of. The ramp is still there, within the core of the pyramid.
Henri Houdin’s first drawing of this ramp looks even more like a corkscrew than the external corkscrew model did. The external spiral ramp models follow the contour of the pyramid and are square in shape, with right-angle turns at the corners. Henri’s first model was a curving spiral that started on the eastern corner of the southern face and curled its way up at an 8% grade.
Henri revised his model to include four separate ramps, one entering on each face of the pyramid. Each of these ramps would reach a different level of the pyramid, but also allowed for multiple ramps to be in use at different levels. For instance, at the lowest levels, where most of the work took place and most of the material had to be transported, there would be four ramps in use at the same time. As each ramp reached its maximum height, and thus usability, the pyramid also became smaller requiring less material and labor.
The idea of building the pyramid from the inside out by using four spiraling internal ramps answered more problems than any model proposed so far. Perhaps most importantly Henri had put the train on the right track by moving the works inside. Building the pyramid layer by layer by use of an external ramp alone might make good sense to a layperson, but an engineer knows that the inner structures within the core of the pyramid would not only have to come first, but would dictate how the rest of the pyramid would have to be constructed.
Henri had shared his ideas with his architect son, Jean-Pierre, who had taken up the task with a relish of his own. But Jean-Pierre Houdin brought the skills of a seasoned architect to the table, and he saw problems even the engineer had missed. Obviously the ramp would have to be inside the pyramid, that much had been settled. But the circular spiral simply couldn’t work.
The 1.5 to 2.5 ton blocks had to be pulled by teams of men, and this cannot be done from around a curve. The men would have to be standing in a straight line in order to effectively pull the lines connected to the sleds, and the constant curve would place uneven pressure on the sleds that would lead to a rapid breakdown.
Henri’s model also left the problem of the large 60+ ton blocks unresolved. Even ignoring the weight, the length of these blocks would preclude them from fitting into the circular internal ramps. Jean-Pierre knew that he was back to a square spiraling ramp, which brought him back to the question of how to navigate the right angles. There was really only one answer—the sleds would have to be lifted and turned 90 degrees at each corner. Easier said than done.
And what about the masonry of the King’s Chamber? No internal ramp could manage that. Henri had set the train on the right track, but now it was up to Jean-Pierre to move it forward. A straight ramp, perhaps one that was an internal/external combination, could reach the King’s Chamber worksite with a 7-8% grade, and would still be short enough to fit into the terrain. But would it be long enough to accommodate enough men to pull the 60+ ton blocks? Probably not. And even if the blocks could be hauled to the worksite, how would they be maneuvered into place?
Jean-Pierre knew that the solution had to involve both an internal and an external ramp, and both straight and spiraling ramps, but how? How were the blocks turned at the corners? How were the giant slabs of the King’s Chamber pulled up the straight ramp and fitted into place with such precision?
In Hemienu to Houdin: Part Two we will get into the details of Jean-Pierre Houdin’s theory starting with his own ramp theory, and how it answers all of the above questions, and more.
Photograph ”Statue-of-Hemiun.jpg” by Einsamer Schütze is provided courtesy of Wikimedia Commons and are licensed under the Creative Commons Attribution ShareAlike 3.0 License. In short: you are free to share and make derivative works of those files under the conditions that you appropriately attribute them, and that you distribute them only under a license identical to this one. Official license.
Copyright by Keith Payne, 2009. All rights reserved.
Tags: Bob Brier, Dassault Systemes, External Ramp, Hemienu, Henri Houdin, Internal Ramp, Jean-Philippe Lauer, Jean-Pierre Houdin, Khufu's Pyramid, Ludwig Borchardt, The Great Pyramid, The Secret of the Great Pyramid