Constructing the Cheops Pyramid Through Multispiral Ramps

The Cheops Pyramid is the largest Egyptian pyramid and is therefore also known as the Great Pyramid. It was built around 2600 BC and is considered the tomb of the Pharaoh Cheops with the Egyptian name Khufu. The pyramid is the oldest of the Seven Wonders of the Ancient World and the only one to remain largely intact.

The image from Mozaik Education shows the Pyramids of Giza from 4500 years ago. There is also a 3D representation of this.

The casing out of white limestone made the pyramids appear like diamonds in the sunlight.

Contents

Overview
External Ramp
Seven Misfortunes
Uniform Pyramid
Ramp Construction
Multispiral Model
Tow Team
Construction Time
Workforce
Turning At Corners
Huge Blocks
Pyramidion
Outer Casing
Magnitude
Real Pyramid
Stability
Measurements And Precision
North-South Direction
Strategy
Numerology
Seven Historical Evidences
Summary
Archaeological Finds
Publications

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Although the Great Pyramid is one of the most impressive structures of mankind, there are almost no documents or archaeological finds that indicate its construction technique.
The pyramid builders belonged to a high guild, which probably kept their knowledge extremely to themselves. They made sure that all notes were destroyed.
According to the two historians Herodotus and Diodorus, the construction time was only 20 years.
How could the Egyptians in the Old Kingdom build this pyramid?
There are many theories about this. However, most of which are completely absurd and none of them can explain the construction completely and satisfactorily.
Therefore, this problem is considered as a mystery of mankind.

Overview

This section contains the essential informations on the theory of Multispiral Ramps. Detailed information, including calculation tables, is provided below.

The construction of the pyramid was the largest and most important project in the state.
This required a clear and controllable technology, otherwise the project would never have been started.
The pharaoh had to be alive when the pyramid was completed.
Therefore, the construction period was set at 20 years.
The slope of the pyramid was determined for religious reasons:
Slope = 4/π
Then the task was to build the largest possible pyramid in this format.
There were two limitations:
– Construction time of 20 years,
– Average number of workers of 12,400 under normal working conditions.
This determined the height of the pyramid to be 146.59 m.
Overall, this is an early optimization problem:
To create the largest possible pyramid under certain constraints.
This task could only be solved by the earliest mathematicians.
A precise construction plan and schedule had to be submitted, specifying which height would be reached at what time.
For example, „After one-third of the time, 50 % of the material has been used, but only 20 % of the height has been reached.“
See the Overview Image.
Therefore, the most efficient method had to be applied at every stage of the construction process.
Deciphering the construction process is therefore quite analogous to convergent evolution in biology.
Using several spiral ramps is the most efficient construction method:
– The system has sufficient delivery lanes,
– There is a separate return path to avoid collisions,
– The delivery of stone blocks and the construction of the ramps can be carried out independently of each other,
– The ramp material accounts for only 6 % in comparision to the pyramid’s volume.
See the Multispiral Model section.
The transport method using wooden rollers is the most efficient.
The method using sliding sleds on wooden beams also requires numerous water carriers and wider ramps.
See the Tow Team section.
The bottleneck of the system is not the number of delivery lanes, but the number of workers.
See the Construction Time section.
The multispiral ramp theory is the first coherent and complete proposal for the construction of the Great Pyramid.
This was published in 2024.
The construction method is consistent with the few archaeological finds and historical evidences.
The task of future archaeologists will be to examine the outermost layer of the pyramid for ramp traces.

External Ramp

Using an external ramp seems to be the most immediate method. This ramp model was proposed by Ludwig Borchardt in 1928.

With an inclination angle of 6.6 degrees or 11.6 %, the ramp would have a length of 1.2 km and a volume of 135 % relative to the pyramid.

Since the two neighboring pyramids did not exist at that time, the ramp could have looked like demonstarted in the image. This is probably the only way to place an external ramp in this landscape.

It would take more than 10 years to remove this ramp. Therefore, it is impossible to complete this monument within 20 years
If this critical time limit would not exist, then the external ramp would have been considered as a possible solution to the problem for long. Therefore, other possibilities must be considered.
The Sphinx probably already existed at this time and had an animal head that was larger than today’s. Sculptures as hybrid creatures only existed from around 1500 BC.

Seven Misfortunes

In 1799, the Rosetta Stone was found containing Egyptian hieroglyphs and ancient Greek texts. Within just three years, the physicist Thomas Young partially succeeded in deciphering the hieroglyphs, what was completed by Jean-François Champollion.

On the other hand, the mystery surrounding the construction of the Egyptian pyramids has not been solved in the last 200 years. What are the causes for this?

1) The ancient Egyptians left no written documents regarding the construction of the pyramids. This meant that historians had no way of solving the mystery.

2) After the pyramids were completed, the Giza Plateau was considered a representative location. Therefore, it is understandable that all building rubble was cleared away, depriving the archaeologists of their work base. In addition, plenty of mastabas for higher officials were placed next to the pyramids later on, so possible archaeological traces may have been removed.

3) There are some archaeological finds at earlier pyramids. However, these were smaller and different in structure. The construction method did always change. Only the previous construction, the Red Pyramid, was the first real pyramid.

4) The historian Herodotus reported in 450 BC that the pyramids were built by slaves. But he had his information from dubious sources.

Accordingly, his description of the stepped stairs was misinterpreted. This was supplemented by a description of lifting devices.

The picture by Antoine-Yves Goguet from 1758, which was probably recolored, represents the distorted view of history.

Such a block of stone weighs more than 15 tons and cannot possibly be transported in this way by 12 workers. In addition, the wooden beams of the lifting devices would not be able to withstand this load.

5) The Museum of Science in Boston developed a model for building the Pyramid of Menkaure in 1950.

The archaeologist Dows Dunham from Harvard University played a key role in this project. He received the gold medal from the Archaeological Institute of America in 1979.

Walter Vose from the Massachusetts Institute of Technology provided practical engineering advice on the project.

The artist Peter Jackson made this lithograph probably based on this project.

In 1956, Dows Dunham made a corresponding publication in the journal Archaeology.

This includes the recolored graphic, which shows how a spiral path starts on each of the 4 sides. That was a tremendous innovation at the time.

This ramp model is briefly mentioned in the books by Georges Goyon and Mark Lehner, it is stated to be interesting but unsuitable.

Ultimately, it is completely inexplicable why this pioneering work has received little attention from experts for 70 years and no one has tried to develop it further.

6) A possible explanation is that spiral ramps were discredited for three reasons and therefore, not considered a serious solution. Firstly, it was impossible to explain how the huge blocks were turned 90 degrees at the corners. Secondly, the spiral ramps were criticized for not having enough transport capacity in the lower and middle areas of the pyramid.

All other models were widely discussed. In particular, the models by Georges Goyon, Mark Lehner and Jean-Pierre Houdin received a lot of attention, although for each model there are several reasons why it is not a solution. One reason they have in common is that in the upper half of the pyramid they use one spiral path with only one transport lane without a separate way back. Thus, the construction time would be more than 30 years.

In the first two models, the outer casing is completely covered by the ramps. Therefore, measurements are hardly possible, which led to a third discredit.

7) Overall, the opinion among archaeologists has emerged that ramps are the most tenable method of lifting the blocks. However, this is an incomplete method that must be supplemented by another device. That’s why so-called combination models have been favored since 1980.

These are suggestions for completing the Four Spiral Model by Dows Dunham:

The huge blocks don’t need to be turned at all, since they only take up a maximum of 2 % of the pyramid’s volume. See the Huge Blocks section. This eliminates the first discredit of the spiral ramps.
In the lower half of the pyramid, some ramps must have a lager width so that there is enough transport capacity. See Multispiral Model section. This eliminates the second discredit.
When building on levels, measurements can be done at any time. The precise measurement is carried out in a top-down process when attaching the outer casing. This eliminates the third discredit.
Some ramps end at different heights since space becomes narrower at the top.
Only one ramp with a width of at least 6 m leads to the top of the pyramid. This allows the pyramidion to be placed on top.
This system of ramps has enough transport capacity in the middle and upper areas of the pyramid. See Construction Time section.
The ramp material is made of dried mud-bricks. These are transported using the chain principle.
Last but not least, the system needs a reasonable transport method. There may well be historical evidence for the method of sliding sledges on wooden beams, but this is completely unsuitable for the construction of the pyramid. A comparable method using sledges on rollers requires only half the towing team. See Tow Team section. In addition, the sliding sledge method requires an enormous number of water carriers and the barefoot workers would constantly slip on the wet Nile mud.

Conclusion:
The adapted model is not a combination model. None of the sublimentary devices are required, which are generally not suitable for mass transport. It is the optimization of a dynamic ramp system.
The construction of the Great Pyramid was the most important project in the state. This was always linked to the fight against time. If there had not been a clear and manageable technology, the project would never have been started.

The following image shows the evolutionary lines of the ramp models. The dashed lines indicate that the corresponding models were created independently and without knowledge of the previous model by Dows Dunham, since it was almost not mentioned in the literature.

Uniform Pyramid

To better understand the construction of a pyramid, let’s consider a uniform step pyramid with 5 levels. All stones or blocks have the same shape.

The number of blocks is calculated from top to bottom as follows:
B = 1 + 2⋅2 + 3⋅3 + 4⋅4 + 5⋅5
= 1 + 4 + 9 + 16 + 25
= 55

Then the inner step pyramid is decorated with an outer casing. The corner and deco stones of the casing are placed on the steps of the inner pyramid.

There is an additional level with a gold-plated keystone at the very top. This stone is a mini pyramid and is called pyramidion.

The Great Pyramid consists of 210 levels including the Pyramidion. As a uniform pyramid, the Great Pyramid would have 3 million blocks.

The lowest red line indicates the height at which half or 50 % of the material was installed. This process took 7 years and only a height of 20.5 % was reached at that point.

The blue line shows the height after half of the construction period or after 10 years. Two thirds of the material was installed at that point.

The green line stands for half of the height or the median. This construction phase was reached after three quarters of the construction time or 15 years.

Thus, for many years the Pharaoh saw only a truncated pyramid which did slowly grow.

Multispiral Model

The main green path begins on the south side, about 400 m from the quarries, from where 99 % of the material is delivered. See the image of the Giza Plateau.

The main ramp leads to the top of the pyramid. In the upper third of the pyramid, the ramp paths partially rest on the path below. This creates a working platform at the top of the pyramid, allowing the pyramidion to be placed on top.

When transporting a block from the bottom to the top, a distance of 1.8 km is covered and 7.5 circuits are made. The transport takes 9.8 hours. The values are given in detail per level in Table 3.

On the other 3 sides there start 2 ramps with only one transport lane.

These 6 single paths end at different heights. The ends are marked in red.

The entire model consists of 7 spiral paths.

The dark blue ramp ends at the north entrance which is marked in black. This was a restricted access area.

The green main ramp has 6 lanes in the initial phase. The outer 3 lanes are marked by orange lines. After the first turn of the ramp after 5 years, the outer 3 lanes can be dismantled and the ramp material can be reused further up. Compare the images Construction Time and Huge Blocks.
This is dynamic ramp construction which saves 25 % of the ramp material.
The total ramp material has a volume of only 6 % of the volume of the pyramid. This is a huge advantage over the external ramp, which has a volume of 170 %. The values are given in detail per level in Table 3.
The many ramp paths make it possible to create a working platform at any location for the later application of the outer casing.

Tow Team

A tow team of 20 workers is required to transport a 2.3 ton block.

At the command of the commander (4), 12 workers (5) pull simultaneously for 1.5 seconds with a force of 23 kp. This moves the sledge with the block by 25 cm. During the pulling movement, the workers make the same sound.

The two workers (6) on the right are enjoying the break.

The two workers (3) with the wooden bares ensure that the rollers remain parallel and do not jam.

After the pulling movement, the sledge stands for 2.5 seconds while the tow workers (5) reposition themselves.

The two workers (3) clamp the wooden bars between the rollers, what prevents the sledge from rolling back.

The worker (1) on the far left must always stand behind the sledge and catch the rollers. This prevents the rolls from falling off the pyramid, which is a massive risk of accidents.

The two workers (2) transport the rollers from back to front and reposition them.

Within 4 seconds the team moves 25 cm, which corresponds to a speed of 3.75 m/min.
The teams have a freedom of movement of 15 m. This is marked with the blue lines.
One block can be delivered per lane every 4 minutes.
Thus, 0.25 blocks are delivered per minute.
This corresponds to 15 blocks per hour.
For a working day of 12 hours per day in two shifts, this corresponds to 180 blocks per day and per lane.
All teams must move at the same speed to avoid jams.
The workload of the workers over 6 hours with rotating breaks and relaxation on the way back can be compared to today’s working conditions and in no way corresponds to slave conditions.
To ensure smooth transport with rollers, the surface of the ramps should be kept flat and stable.

In the literature, there are almost exclusively presented a transport method in which sledges were pulled over wooden beams. The beams were constantly lubricated with Nile mud to reduce friction. See the picture by Peter Jackson.

A towing team would consist of 18 workers and would be the same size as for transport with wooden rollers.

However, water carriers were required in addition when using Nile mud.

The water carriers would have to deliver the Nile mud not only at the end of the delivery lane, but for all tow teams along the entire transport lane.
When building the upper half of the pyramid, the routes are longer than 1 km and more than 50 teams would be on one transport lane. Therefore, the number of water carriers would increase considerably.
The water carriers would require a separate walkway as they are large in number and would move at 8 times the speed of the towing teams. This way is marked by the two blue lines. Therefore, the ramps would need to be 20 % wider. This would increase the ramp volume by 44 %. The same applies to the number of workers for ramp construction.
For example, let’s look at level 112, where 90 % of the volume was built up. At this point, 2,442 water carriers would be needed and only 6,586 workers would be available for towing, which is presented in Table 4. In comparison, if wooden rollers were used, 8,405 workers would be available for towing, which is shown in Table 1.
In addition, the workers would have difficulty moving on the slippery transport paths.
Under the same working conditions, it can be said that with this transport technique, the construction time would increase by 4.3 years and the total work by 24 %. The detailed values and comparison are shown in the appendix of Table 4.
The greatest possible efficiency was required because the project was a fight against time.

Construction Time

The image shows level 112, where 90 % of the material has been installed.

The pyramidion was transported up to there from level to level by zigzag-lifting. All the huge blocks had been installed by then. Compare the image Huge Blocks.

The main green path leads to this level with 3 lanes. In the lower area, the ramp material of the 3 outer lanes was transported upwards (dynamic reuse).

There are also the light blue and dark purple paths, each with one lane. So a total of 5 lanes lead to this level. When subtracting one lane for the way back, there are still 4 lanes left for delivering the blocks.

This level has a width of 210 – 112 = 98 block widths.
Therefore it consists of 98 ⋅ 98 = 9,604 blocks.
There can be 180 blocks delivered per day and per transport lane.
With 4 transport lanes, a total of 4 ⋅ 192 = 720 blocks could be delivered per day.
Due to the length of the paths, this would require more than 20,000 workers. Therefore, a maximum of 630 blocks can be produced and delivered per day. This only applied during the 3 months of the Nile flood.
Of the 4 available transport lanes, only 630 / 180 = 3,5 lanes can be used to their maximum. The bottleneck of the system is therefore not the number of transport lanes, but the number of workers. Detailed information is presented in Table 1.
In the remaining 9 months outside of the Nile flood, there were only 10,000 workers. Therefore, only 315 blocks can be delivered per day, using 1.6 transport lanes.
This results in an annual average of 394 blocks per working day, using 2.1 transport lanes.
Therefore, this level has a construction time of 9,604 / 394 = 24.4 working days.
Since there were 300 working days per year, this corresponds to 0.081 years or about one month.
In this way, the values for all 210 levels can be determined. Adding the values up to level 112 results in a construction time of exactly 15 years at this point. See the Overview Image.
By adding the values for all 210 levels results in the construction time of 18.4 years for the inner step pyramid. Detailed values are shown in Table 2.
This leaves 1.6 years of the total construction time of 20 years. This is enough time to install the outer casing, remove the ramps, and construct the perimeter wall.
The outer casing requires only 0.7 % of the material, but must be polished smooth.
Table 1 gives a condensed overview of how the number of transport lanes decreases with increasing height of the pyramid, but the number of workers for towing increases.
Table 2 shows how, with increasing height, the individual levels have fewer blocks. Overall, the construction times for the different levels decrease slightly with increasing height.
Table 3 contains some key figures, e.g. the „number of blocks per minute“ which has a value of 1.29 at the lowest level and 0.01 at the highest level.
This model proves that the system of spiral ramps has sufficient transport capacity in the upper range of the pyramid. This is in contradiction to the literature. There are only models used that have only one transport lane in the upper two thirds of the pyramid without a separate way back. In this case the construction period would be at least 30 years.
The transport problem can be completely solved with the described system of ramps. No further technology is necessary. This is contrary to the literature where it is mentioned that ramps require supplementary devices.

The diagram shows how the volume and height of the pyramid developed within the construction period of 20 years.

The blue dashed line indicates that after 10 years a height of 30 % was reached and the volume of 67 % was built. See the corresponding image in the Uniform Pyramid section.

The black dashed line indicates that the height of 100 % was reached after 19.1 years when the pyramidion was placed.

Then the outer casing was installed from top to bottom in 0.7 years, so that the construction was completed after 19.8 years.

Huge Blocks

In the first 5 years, the huge blocks were brought onto the pyramid using the green ramp. That’s why they didn’t have to be transported on ramps around the corner. This saved the difficult turning at the corners.

The huge blocks were transported upwards from level to level. The temporary brown ramps with a slight slope of 2 degrees were used for this purpose. This method is called zigzag-lifting.

The area on the pyramid was always so large that the huge blocks never required more than 15 % of the area.

Outer Casing

When the pyramidion was placed, the bottom-up process is completed.

Then the outer casing was installed in a top-down process. At the same time the ramps were removed.

The white limestone was delivered from Tura, 30 km away.

In January 2024, the Mitteldeutsche Zeitung published a newspaper article entitled Mystery of History Solved on this theory.

There will be an additional scientific paper that will cover this website in detail and include the mathematical proofs. It will give an insight into the mathematical thinking at the time 5000 years ago, explaining exactly how they were able to use these methods to create this monument with such precision. The work includes positioning the roof over the north entrance with blocks of 100 tons and erecting obelisks of 400 tons.
The work is titled Scientific Methods In Ancient Egypt and will be published in the Journal of Humanistic Mathematics of the Claremont Colleges in California at the end of 2025. It comprises 200 pages, including 50 pages of calculation tables.

The idea, proof finding and implementation were developed by Dr. Rudolf Volz. He is a qualified mathematician, has developed software for many years and is interested in the central problems of humanity.

Sources: Image 1 and the background of Image 3 are courtesy of Mosaik Education.
Image 2 uses elements from 123rf.com.
Image 4 is by Gouchet and image 6 is by Dows Dunham.
Image 5 is by Peter Jackson, Bridgeman Images.
All other images are copyright of Dr. Rudolf Volz.

Imprint (2023 – 2024) – Deutsche Mediengesellschaft mbH – Auf den Steinen 2 – D-06485 Quedlinburg, Germany – info@cheops-pyramid.net