INTRODUCTION

Great-Pyramid-of Khufu

Five years ago I visited Egypt on an excursion and was intrigued by the craftsmanship of the builders of the old monuments. After a lifelong in building, both as an architect and a contractor, I realized that the traditional construction theories could not be correct for the simple reason that they were practically inadequate. And as I don’t believe in giants or ET’s there must be a logical explanation on how humans with relatively simple means could have built the great pyramid in about twenty years.

And if they could then, we should be able now, as will be proven in this paper.

A pragmatic approach is indispensable to finish with good results a building task like the Great Pyramid of Cheops, more than 4400 years the largest man-made construction. Like any modern contractor uses all available technical means to build as effective as is possible, so must have done the builders in ancient times. It implicates that not just one specific technical solution or theory was used, but a number of complementary ones to tackle the different tasks at hand. Hence the solution of this old riddle is a description of a combination of technical solutions, of course based on the possibilities of 2550 years BC.

There are scores of theories in the Internet on how the pyramids were built, some more fantastic than others, but with two exceptions they all have one feature in common: they just describe only one part of a building process, mostly theories on transportation of the heavy blocks, never a complete and practical working method. Nevertheless, among the majority of inadequate and sometimes ridiculous ideas there are some very useful. I gratefully based this construction hypothesis on those, sometimes unchanged and sometimes improved. Because this paper has no scientific pretensions, it is just a description of a working method, no sources are systematically mentioned with the same exceptions, Franz Löhner and Henk J. Koens, who published wide and thorough studies in the Internet with an admirable informative value.

This paper is exclusively focused on the technical execution of building the great pyramid, so it is only the “how” and not the “why” or the “wherefore”. And interesting as such a study would be, it is neither about the bearing on the North or West or on the constellation of Orion or Sirius and neither about the relationship of its measurements with Pi or the Golden Mean.

I am sorry that this paper is more than twenty pages long, but trying to give a complete description of the building process made that unavoidable. Especially the seemingly unimportant details are decisive for the successful result of the proposed building method.

Ir. Ben J. Hendriks

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2.   SUMMARY,  WHAT  IS  NEW ?

This working method is based on 6 OLD and as far as I know 12 NEW ideas:

  • NEW is the proportion between height and base of very probably 500 feet or 145m and 800 feet or 232m which gives an easily to produce measuring and controlling tool for the gradient and thus for the facing stones.
  • OLD is egalizing only 5m peripheral area,  4700m2, in stead of the total base area of   ± 54000m2.
  • OLD is the construction in layers.
  • OLD and inevitable is the necessity to place the facing stones first on horizontal planes in every layer. There is no other simple way to converge the four sides in one point straight above the center of the base.
  • OLD is the placing of the peripheral stones from the inside out against well aligned casing stones. Their height must have been adapted to the casing stones forming a horizontal surface  for the casing stone of the next layer.
  • NEW/OLD is the idea to fill the core partly with sand, smaller stones and clay-lime concrete, necessary to level the surface for the transport of the stones of the next layer. Great benefit of this is the shift from skilled to unskilled labor of which there is plenty available.
  • OLD is the transformation of a rectangle in a cylinder because the friction of rolling is 5x to 10x smaller and the surface of the route is much less demanding.

  • NEW is the simple way this is done without nails or screws.
  • OLD is making the ramps in the flank of the pyramid with the proportion         Height/Width  = 5/4, so the ramps are parallel to the face at any level.
  • NEW is the rather short horizontal end of the ramps, because less transport workers are required.
  • NEW is the simple and easy way the cylinders are turned 2x 90º on turning plates at the top and bottom of a ramp and the freedom of direction on the leveled layers of the pyramid.
  • NEW is the way the counterweight of the small hoist is placed on a sled on rollers so the bin does not have to be emptied after the placing of each stone.
  • NEW is the zigzag lift that can be used from level 131m up to 143m to place the capstone and maybe later to assist in filling in the ramp area from the top-down.
  • NEW is the way the capstone is encased to form a dismountable cylinder.
  • NEW is the idea to tilt the capstone using half of its own mass as counter weight.
  • NEW is the crane with the adjustable floors every 40cm to build the top and to fill in the ramp area top-down.
  • NEW is the hoisting rope in the crane with nooses every 40cm.
  • NEW is the use of tables in combination with a hoist.

 3.   DECIMAL  MEASURING  UNITS  

Interesting is that if the height is 145m and the base is 232m this gives a very easily to reproduce tangent of 5/4 for the angle between the horizontal plane and the face of the pyramid, which is very practical for producing the hundreds of “un-square” try tools for the stonemasons and foremen. Both measures differ only slightly from the traditional assumptions of 146m and 233m. And when their unit (probably a foot) was 29cm than the pyramid was in their system 500units high on a base of 800units square. This coincidence can not be accidental. You could even conclude that they used a decimal counting system.

Of course, the pyramid could have been 146m high, but if it was, than their foot was very probable 292mm and the base 233.6m and the tangent of the angle would be again 5/4. The slight difference with the mean angle is probably due to the fact that the stones in the lower levels are bigger than average and so were the casing stones probably deeper with as result that the sides are a little less steep, 51º34’02” in stead of 51º41’21” or 0,24%.

4.   DIMENSIONS  AND  QUANTITIES 

Height 500 ancient feet                               210 layers?                   145  m

Base 800×800 ancient feet of 29cm =        232x232m             53 824  m2

Gradient faces / horizon                       H / 0.5B = 5 / 4        51º 34’ 02”

Volume                                                     1/3 x H x B x B         2 601 000  m3

Weight                                                           2500kg/m3         6 502 500  Ton

Top above 131m 0.09%            1/3 x 14 x 22.4 x 22.4                2 342  m3

Weight of capstone                       160 x 160 x 100 cm                2 048  Kg

Casing surface                              4 x 232 x 185.7 x 0.5              86 165  m2

Total length slopes 10%                 ± 10 x 131 + 50 x 6             ± 1 600  m

5.    STARTING  POINTS

This hypotheses of how it could be done (= how I would have done it) is based on the following assumptions to make it comparable with the possibilities of 4500 years ago.

  • The building of the pyramid must have been excellently organized and so the managers must have been very intelligent and effective with relative great mathematical insights and well understood communication. The still very impressive monuments in Egypt illustrate their ability to make round and square stones with very exact measurements. So this craftsmanship was also available for the building of the chambers and galleries in the pyramid.
  • They disposed of simple but effective levels, plummets, long straight rulers and square angles probably based on the proportions 3/4/5 and 5/4.
  • They used cranes and hoists sparingly as well as scaffolding and only around the top and during the filling up of the ramps.
  • They must have had harder chisels than copper ones for the cutting of granite and so those were probably available for the quarrying and finishing of the limestone blocks too. That none are found is due to the scarcity and hence the high cost of iron then. There are no copper chisels found either.
  • They disposed of sufficient construction timber and were good carpenters as is proven by the found boat.
  • They were masters with ropes and there was plenty of material to make strong cables.
  • The stones were mostly rolled in stead of dragged on sleds.
  • They used a kind of concrete mortar based on dehydrated clay and powdered limestone.
  • Next to specialized craftsmen an almost limitless number of unskilled workers were available during the flooding periods of the Nile.

·6.   PROJECT PREPARATIONS

Everybody will no doubt agree on one thing – especially the technicians – that to realize those gigantic buildings there must have been an enormous organization with very complex working schemes and high quality building drawings, supported by an efficient administration and catering. How all this was done is not known. There are no rests found of this administration or of their mathematical knowledge, but there are many rests found of a laborer’s village.

Because construction wood had to be imported from Lebanon or more southern Africa and because granite was chosen for the construction of the chambers and gallery and because the very heavy stones that cover these rooms had to be present at the start of the works  one can safely state that project preparation must have been at least 1 to 2 years. Furthermore special boats must have been built to transport the very heavy stones from Aswan and roads from the quarries to the harbors and the pyramid had to be constructed and/or leveled. All in all it is an enormous achievement to realize this in this short period.

That the archaeological accepted construction theories can not be correct is evident. It simply is impossible to achieve a good result that way in time. A logical consequence is that they must have preferred labor-saving methods. Given the result they obviously succeeded.

Carpenters with drill and saw

7.   MEASURING AND SITE PREPARATION

To make sure that the four sides of the pyramid meet in one point exactly 145m above the midpoint of the base square it is necessary that all four sides rise with the same constant gradient.

The first step was to mark the four corners. This could be done with measuring cords, pickets and 3 / 4 / 5 proportional cords. It is of course very important that the four sides are of exactly the same length and form a perfect square.

The second step was to level the base of the pyramid. Probably not the whole building site was leveled according to Mark Lehner, but only the peripheral strip, 4 to 5m wide, so 4x5x235m = 4.700m2 in stead of 235x235m = 55.225m2. But this whole area had to be very exactly horizontal. The surrounding grounds could also have been leveled, but were probably later and did not have to be as accurate horizontal. For leveling they must have used sighting lines along levels with plummets and pickets, about the same way surveyors work today. Using water  is practically not feasible over more than 200m on sand and or sandstone in that climate.

It is quite possible that the pyramid is built over a small hill and maybe therefore the Queens Chamber is situated at ± 30m above base level. Lehner was probably the first to mention this possibility. Sand and loose small stones were taken from the core area and later on together with mortar used to fill in the gaps between the bigger stones in the core area to make each layer flat enough for the transportation of the bigger stones of the next layer. This could also explain why the stones at the lower levels are bigger. Most of these bigger stones could have been moved down on the building site and not up from a distant quarry.

It is indeed not very logical to take away a large amount of material to replace it with stones that have to be quarried and transported with considerable efforts. Yet almost all papers on the internet stipulate that the total base surface was leveled and the whole pyramid was filled with 2.5 million stone blocks as are now visible. I suppose that the builders then had more common sense. For example, when the core area has a mean height of only 5m above the base level, it would result in a saving of ca. 260 000m3 or ± 10% of the total volume.

Great Pyramid of Cheops  Source: Franz Löhner

1. Entrance   2. Entrance cut by grave robbers    3. Subterranean chamber   
4. Grand Gallery  5. King’s chamber + relieving chambers + granite portcullis slabs    6. Queen’s chamber  7. Slabs 8. Limestone plugging the air shaft   
A = Air shafts     

 

8.      QUARRYING AND SHIPPING

There were three quarries:
1.   Granite for the chambers and gallery in Aswan at 700km.
2.   White limestone for the faces at 50km on the east side of the Nile.
3.   Sand-limestone for the core at about 700m.

Both the white limestone and the granite had to be shipped. Franz Löhner has published in his internet site an excellent description on how this shipping was organized and how much manpower was required. The loading of the stones on sledges or rollers on the ships is not identical, but on principle not very different. So my advice is to visit his site for more detailed information.

As iron was available, although scarce and expensive, it was probably used in the quarry for the casing stones, simply because it would be cost-effective. The number of rejects would be amply diminished and the production of casing stones would no longer be the bottle-neck. For this building method this is not essential.

As this limestone is a sedimentary stone, it is structured in layers. By forcing a horizontal row of wedges between these layers it is possible to split it free with a rather flat base. Vertically a second row of wedges is placed. Source: Franz Löhner.  The result is a rectangular stone, to split  or saw  in two along the oblique line of 5/4. Then they let the stone fall on a heap of sand at the bottom of which the first part of the roller is buried. When the two stones are corrected and the base is well flattened the faces and the top will be finished and controlled. Empty rollerWith levers and rams or a small crane it will be well placed on the buried part of the roller. Then the second casing stone is placed on top of it and the two stones are fixed to one another with ropes. See chapter 12. Then the other three parts of the roller are installed and the whole is bound together with two strong ropes around it. Then the stones are secured with wedges. After removing the rest of the sand the stones are ready to roll to the harbor and from there to their final destination.

9.   SETTING  OF  THE  CASING  STONES      

From the point of view of implementation it is by far most simple to start each layer with the casing stones, because placing them later against less exact placed stones is practically impossible to combine with a good fitting in the faces of the pyramid. To make this fit would require a multiplication of the finishing time and it would complicate the logistics enormously; above all, transportation would be near impossible along the steep sides.

The casing stones are formed as a trapezium with six faces. Of these faces only three are very important. The base must be very flat, the outer face must make exactly the same tangent of 5/4 with the base for all stones and the small upper face must be precisely parallel with the base. On top of that the height of the casing stones should be as regular per layer or per part of a layer as is feasible to make a brick pattern of vertical joints easily possible and thus the surface more stable. Checking if the casing stones meet the right level of exactness could be done by each mason with his own wooden standard models based on sides of 5 and 4 units. Placing and joining the stones is much easier if the side and back faces are square on the base, but this is not essential.  After the base area is well prepared and exactly horizontal, the casing stones of the first layer could be adjusted with rams along sighting lines and with long straight rulers. For easier adjusting the base could be
lubricated with clay-lime cement. After finishing the almost 1km long range of casing stones (4x232m) the second row could be set rather easily from the inside out against these casing stones. How this is done will be explained later. It is of the utmost importance that this second row of stones is exactly as high as the casing stones thus forming a smooth and horizontal surface for the second layer of casing stones. There is plenty of time to make the necessary adjustments during the filling up of the first layer.

Behind this second row of on the upper site equalized stones a third row of bigger stones is placed and behind those probably the rejected casing stones and rubble from the quarries. The smaller stones could be carried in baskets by donkeys or oxen. The spaces between these core stones could have been filled with sand and lime, also to be transported in caskets or barrels. A provisional external ramp for the lower levels can be made for carriers, so the rollers could have the exclusive use of the smoother ramps along the side of the pyramid.

5. First row of on the upper side horizontal stones. Horizontal joints filled and equalized with mortar.

10.   CORE AREA

After the filling out the core of the first layer and equalizing and stabilizing it with tampers it is rather easy to place the second layer of casing stones, just like the first layer. Then the second row of stones can be placed and finished, than the third row and the filling out and stabilizing of the core of that second layer. The same sequence is used in the third layer, and so on up until 2/3 of the layer at 131m.

It is quite probable that the core area was partly filled with smaller stones and sand because it would be very difficult to make a flat surface per layer with only bigger stones and a flat surface of the core is indispensable for the transportation of the rather heavy stones of the next layer. At least 30% seems a fair estimate.

The horizontal pressure on the peripheral stones and the casing stones is negligible because the natural slope of a heap of sand and stones is ± 50º. An extra benefit of this solution is the extensive use of unskilled labor for up to 80% of the mass of 2,600,000m3.

It is noteworthy that the pyramid is built with an astounding exactness. The four sides of the pyramid will automatically converge in one point above the center of the base if the deviations of the faces are kept within an acceptable limit. But even if the casing stones are less precisely made, it is possible to correct them when the next row of stones of a layer is placed and the upper faces are made horizontal again for the next layer of casing stones.

The logical conclusion of this is that all theories based on the presumption of placing the casing stones last can’t be very probable for three reasons:

1.   Much more preparation work because every casing stone has to be made fitting to the first row of core stone(s) behind it as well.

2.  More than ten times more work in the transportation and the placing of the casing stones since the stones have to be lifted tier by tier in stead of continuously rolled over ramps and over the flattened core of the previous layer.

3. It is very difficult if not impossible to make an exact symmetrical pyramid based on less exact  stones. Correcting the surface later is very difficult on the steep slope, but it is possible without damaging the surface with hanging scaffolding if it is done immediately after the  placing of the casing stones.

11.   ROLLING THE STONES

The found cradle

A double circle segment of wood like a cradle was found with the appropriate size to envelop a stone of about one cubic meter with three similar segments and thus to form a cylinder, that could rather easily have been rolled with levers and/or ropes. (Unfortunately this found cradle seems not strong enough to transport a 1m3 or 2½Ton stone and it lacks the necessary holes to combine it with three others with ropes.)

Different persons are mentioned for the idea to transform a rectangle stone into a cylinder to make it possible to roll it. Engineer John D. Bush was probably the first in 1978. Henk J. Koens has published some very convincing calculations about friction and the number of required transport workers. He also gives a practical method on how to put a stone between roller disks. Although our proposal is different almost the same method could be used.

Rolling the stones has three great advantages:

  • The friction of moving the stone in a roller is at least 10 times less than sliding on a sled on a well lubricated sand road, so less transport workers are needed.
  • The preparation of the road, leveling, is less demanding and small changes of the slope of the road are no problem.
  • The changing of direction is very easy, see chapter  Turning Points.

USE OF MANPOWER FOR TRANSPORTATION PER  AVERAGE CASING  STONE

Men     Hours     Sliding     Rolling
Road to harbor 36 15 540
Ditto rolling 12 3.3 40
Loading and unloading 36 5 180
Ditto rolling 12 2.5 30
Return to quarry*) 36 2.5 90
Ditto rolling 12 2.5 30
Road from harbor to pyramid 36 2 72
Ditto rolling 12 1 12
Ramps on pyramid*) 36 18 648
Ditto rolling 12 0.5 6
Movements on pyramid 36 1 36
Ditto rolling 12 0.5 6
TOTAL 1566 124

*) Assumed is that the transport crews don’t embark and that sliding along the zigzag ramps is possible by using hoists for turning.

12.   NO  NAILS  NOR  SCREWS

Empty roller

 Based on this rolling principle there is a simpler method to transform a square stone in a cylindrical form without complicated carpentry work. All you need is two square frames adapted to the size of the stone, surrounded on each side by five or six small bars of different height, four of which are a little longer for a pulling device. The whole contraption is pressed together by two strong ropes around. The stone is placed on one part with a tripod crane and then the three other sides are installed. The rather elastic rope is put on pressure with a turning stick and at last the stone is secured in the frames by wedges adapted to the size and the form of the stone to place the center point of the stone in the ax of the roller. The enveloping rope is fitted in a small slot to avoid wear by touching the ground. Probably about 500 rollers of different sizes would be enough due to the capacity of the transportation road and ramps and the quarry crews. For the transport of an average stone of 1.5T or 0.6m3 is a crew of ten men sufficient who can do four trips a day at 2 to 3km/h. Loading and placing the stones is done by teams of specialists so the transport teams can rest.

An advantage is that the roller always touches the ground with at least 800cm2, so the pressure is seldom more than 2.5kgf/cm2 and the roller will not sink into the ground once it is on the leveled core. Tracks could be made on the ramps of beams of 100x100mm to reduce the friction to 2.5%. Total force will be then 12 .5%, comparable with the friction on the horizontal leveled layer of the core.

The Greek historian Herodotus was told by Egyptian priests that the stones were lifted “with machines formed of short wooden planks”. This roller fulfills this description, as does the zigzag lift. Source: Jason Baldridge and Henk J. Koens.

 13. VERTICAL TRANSPORT

There are two possibilities with both advantages and disadvantages:

1.   Zigzag ramps along one side of the pyramide, ± 3.2m wide and 4m rising (proportion 4/5).

2.   A stairway of elevators of each ± 3.2m deep and also 4m rising.

Both systems have stops per layer and are adapted to the rolling of the stones. And both systems require maintenance for efficiency and safety.

The greatest advantage of ramps is that one does not have to wait till the preceding stone has passed. The ramp is large enough for most teams to pass another one if need be. A second advantage is that the material for the ramps, smaller stones, sand and lime concrete (±2000m3) can later on be used in the core, so it does not have to be transported twice. A third and perhaps very important advantage is that no more than 52m3 wood  was required for these ramps and no extra manpower. Since the ramps are at every level parallel to the face no traces can be seen once they are removed.

No small disadvantage of ramps is that it can’t go farther up than ± 131m, so for the last and small part of the pyramid (2340m3 or 0.09%) an elevator system must be made. See chapter 14.

Zigzag ramps parallel to face at any level  

The advantage of this method is that up to a height of about 131m  vertical transport of the stones is relatively easy for more than 98 % of the building mass. In this way 89 % of the casing stones can also be placed easily.

A minor disadvantage is that the small area of the ramps  must be filled in top down, which requires the use of cranes and is at least five times more work than the filling in of the casing stones directly from the ramps. Although it is a very small volume,  compared to the volume of the pyramid, of which still 1/3 can be set directly from the ramp. See also the paper by Henk J. Koens. Above 131m for ca. 2400m3 the transport method described below could be used.

14.   TOP  14m

Building the top is no problem with the use of a lift or crane that can put the stone, still in the roller, on the right level. Once there it is exactly the same as on the lower levels starting with the casing stones and so on. Of course the spaces for the lifts and/or cranes must be left open.

        Top 14m with zigzag lift on highest level            Top 14m with open spaces                                                                                                                              for lifts or cranes.

 Because level 131m can be attained by ramps then almost 80% of level 132m can be filled up without the use of cranes. Perhaps with extra manpower and a steeper slope level 133m could also be done this way. This would reduce the filling up of the top with cranes from 2342m3 to 1474m3 or 0.056%.

15. TURNING POINTS

Turning at the horizontal end of a ramp can be done with a flat turning plate or block. The encased stone is rolled on the turning block lifting the sides A and B of the wooden bars 2cm off the ground. Then the stone can be rotated 90o with levers and a small slope inward eases the rolling of the stone to the next turning plate at the base of the next ramp to be turned again 90o. Off course, some guard rail or threshold is placed to prevent that the stone would fall down. All in all this is a work of just a few minutes and much space or manpower is not needed; probably 4 men would be enough for stones up to 2Ton.

16.   HOISTS  FOR  SETTING  THE  STONES

As stated, the pyramid is built up in layers and the stones are rolled from the quarry to their final location. This implies that each layer must be fairly flat and therefore it is unlikely that only big stones were used in the core area. When the stone is almost in place the bars and frame of the roller are disassembled and the stone glides of the last section with the help of levers. The stone can not be placed directly against its predecessor because it slides of the roller with a small angle, so the stone will have to be moved or lifted. Because sliding without moving the underlying layer is only possible with very smooth surfaces it is probably less work to lift the stone with a simple crane a few centimeters and then set it in place by turning the jib. For stability the base joint is filled with lime concrete.

11. Principle of hoist

If the counter weight, ca. 20% of the weight of the stone, is put in a box or basket on a small sled on rolls then it is not necessary to empty the basket almost completely each time the crane is replaced. By loosening some wedges the counter weight can be hanged free just enough so the sled could be moved out of the way and the counter weight can be loaded or pulled down by men to descent about 50cm lifting the stone 10cm. After the placing of the stone, the tripod with the jib could easily be moved with a few men and seldom more than a meter. The sled with the base counter weight could be moved with levers over beams. To free the rope under the stone small wedges are used.

17.   MOVING VERY HEAVY STONES

The traditional view on the transport of heavy stones (more than 5m3) is the use of sleds on leveled lubricated roads pulled and pushed by large groups of men, assisted by pack animals. This is very ineffective for great masses of stones and above all because changes in the slope of the road make gliding impossible.  There is a mural depicting rollers under a sled so probably this method was also used, because the friction of rollers is perhaps up to 8 times smaller than sliding, so for horizontal transport 8 times less men are needed.

The very heavy slabs, up to 60Ton, covering the Kings Chamber could not have been moved on sleds with hardwood rollers. The pressure on the rollers would be too strong and they would deform too much. The rollers must have been used directly under the flattened slabs over broad hardwood beams as rails or tracks. The slabs must have been put in the core area right from the beginning of the works and must have gone up with the rising of the pyramid on beams that would go along too and with special teams of movers assisted by oxen or perhaps elephants.

The stones did zigzag slowly up. To mitigate the forces the slope was probably not more than 2%, but that would still result in a too sharp angle at the change of slope. A possible solution would be to tilt the track beams under the slab by removing some sand or pebbles, so going down a few inches after going up. As it is also problematic to make bends it is essential that the tracks were in alignment with the future place of the slabs. This implicates that probably 9 or 10 parallel tracks were used.

                            Big roller made of short beams of 200x200x1000mm.

A probably still better alternative would be the method of Koens, making 2 very broad hoops around the slab and raising the slabs by zigzagging up the core tier by tier. The hoops are made of two disks hold together by ropes. For extremely heavy slabs a combination of 2 times 3 hoops could be made. Tracks made of large beams will be unavoidable to avoid sinking in the sand or crushing of the hoops on protruding stones.The hoops will be removed when the slab is resting in the sand above its final destination.

Two advantages next to less manpower would be:

  1. Freedom of direction.
  2. Less space for storage in the core area.

18.   BUILDING  THE  CHAMBERS  AND  CORRIDORS 

Building these interior spaces seems not much different from any other big palace or temple. This work could be done in the open air with the advantage that as the pyramid goes up the surrounding “ground” level rises too, so all work could  be done on a rising ground level and no stones have to be hoisted to a higher level.   Walls of quarried stones are erected around these chambers to avoid or diminish horizontal pressure on the vertical walls.

Fig. 13 King’s Chamber. Source: Franz Löhner

Obviously the builders knew beforehand exactly what they were going to build, for it is unlikely that they would bring up haphazardly a lot of very heavy stones to decide later what could be done with it. To get the heavy decking stones of the rooms and corridors in place the underlying space was filled with sand and emptied again later. The out coming sand could be used as a filling material for the core around it.

19.    STAIRS AND SCAFFOLDINGS

Because material and hence people went up, so people had to go down again. There were two possibilities. By way of stairs along the ramp ends of 6.4x6m or simply down the ramps. Being 3.2m is wide enough to pass most of the up-going traffic. Stairs would be used mainly at the top of the pyramid, because the ramps there could only be 2.4m wide. Passing stayed possible on the flat end of the ramps. The rollers were rolled back for reuse by the same team that had them raised.

                            Scaffolding  at level 139m next to zigzag lift

As stated before it is essential that the width and the height of the ramps have the same proportion as the angle of the faces of the pyramid, so if the ramp is going up 4m then the width must be 3.2m, if it is 3m rising then 2,4m. In this way the base of the ramps is parallel to the face of the pyramid at any level. This will simplify the filling up of the ramps when they are no longer needed after the capstone is set and the higher ramps are filled up.

                      Exemplary of highest part of still to fill up ramp area 

That the yellow area can be filled up with a reasonable effort will be proven hereafter. As this is feasible, so the total area of the ramps can be filled up top-down. See chapter 26.

20.  THE ZIGZAG STONE LIFT

Above 131m the pyramid is too small for a ramp. Up from this level the stones – still enclosed in the cylinders – must be brought up with a stone lift or a crane. There are two possibilities to finish the top 14m and to fill the area of the ramps top-down: A crane for stones not heavier than 1500kg or the Zigzag stone lift, necessary for the capstone because it is too heavy and too large for the cranes.

Zigzag stone lift

The zigzag stone lift is made of two small towers of approximately 2.2×2.4m2 with a varying height of up to 4m. These towers could be made of timbers like a log-cabin. In each tower a floor can be placed every 20cm. These floors are connected by 2m long beams with a slope of 5% to 10% from one tower to the other alternately. 

How the zigzag lift could be made.   Diagonal stabilizing ropes are not drawn

With a gradient of 5% the horizontal force to roll capstone of 2.8T up to the other tower is ca. 100Kgf. With 4 men on each side the stone can be moved and secured easily. For going up only one lift is required, first for layers 132m to 135, then the stone is parked on level 135 and the building up of the same zigzag lift can be done for the layers between 135 and 139m and ditto for the layers 139m to 143m. With a well rehearsed crew the capstone could be lifted 1m in 30 minutes by 8 men to move and secure the capstone and 12 more men to adjust the lift towers. Total time to lift the capstone is 12x30min, so it is just a day’s work (plus preparation, transportation, setting and finishing less than one week).

The zigzag lift is much too inefficient for the transportation of the stones, because it has to be built entirely up for every new stone and taken apart after each one. The crane is much more efficient.

21.   CRANES

The crane is built with 6 vertical beams forming two connected towers, Tower A for hoisting the stone and Tower B mostly for stability. The horizontal beams of tower A and the diagonals can be dismounted so the stone in its cylinder can leave the crane at any level. Turning the stone in the right direction is of course no problem once it hangs free. The hoisting rope has nooses every 40cm so attaching the stone can be done in a few seconds. As soon as the stone is hauled up the floor is set one level of 40cm higher by pulling it up. The workers stand on a small adjustable platform next to tower A.

The hoisting beam has a total length of 7m and weights ± 175kg when the section on the turning point is 10x40cm. At least 8 men (40kg/man) are required to pull up the stone in its cylinder and 5 to 6 men to push up the hoisting beam after a haul of 40cm.

Because level 131m is attainable by ramps there is no need for a crane for level 131.8m. So to raise 1 level of 80cm only 2 hauls are for level 132.6m, 4 for 133.4m, 6 for 134.2m and 8 for 135m and 10 for level 135.m. Then the stones have to be moved by the second crane and again after a raise of 4m with the second crane the third crane will be needed. For the last layer at 143.2m the stone is 20 times 5 minutes in vertical transportation and luckily it concerns but 16 stones.  At 142.4m it is 15 times 5 minutes for 36 stones. A great advantage is that the three cranes can work at the same time.

22.    CAPSTONE  OR  PYRAMIDION

Although it is difficult to fix the Pyramidion or capstone, ca. 2000kg (160x160x100cm), between the circles, it is quite possible and without nails or screws. The circles are fixed with wooden pegs, ropes and a kind of glue based on resin. The center of gravity is approximately 25cm above the base. Thus there will be 3x more weight on one circle of about 2.5m diameter than on the other.

Capstone in roller, 8 diagonal stabilizing ropes are not drawn

When the stone is rolled and lifted up to level 143m there still remains a difficult operation. The stone must be tilted from a vertical position between the disks to a horizontal position on rollers. The safest way is by making use of its own weight as a counter-weight. Special notches or a bar could be attached to the base circle just under the center and after the removal of the upper part of this circle the stone can be tilted and laid on a kind of bridge between the pyramid and the lift. With a 4m long lever on the outer circle the forces seem manageable with 6 to 10 men. After the stone has come to rest on the rollers the remaining parts of the circles and the turn-over bar must be removed and the stone can be pushed till halfway up the pyramid. The last 80cm can be overcome with rams. Of course the pyramid and the surrounding scaffolding must be well secured with ropes. In the layer below the capstone one casing stone must be set later to make a safe support for the bridge.

23.    TILTING AND SETTING OF THE CAPSTONE 

The work sequence for tilting and setting of the capstone:

  1. The capstone is 160x160x100cm, including the roller ± 2500Kg
  2. The stone is rolled up to level 131m
  3. Then lifted to level 143m with 3x the zigzag lift with stops in between at 135m and 139m
  4. Part of roller is removed and tilting beam is fixed
  5. Capstone is tilted over on wooden rolls
  6. Rest of roller is removed
  7. Capstone is rolled to final place and adjusted with tampers
  8. Joints and faces are corrected if necessary.

24.    FILLING OUT THE RAMPS TOP-DOWN

The relatively small volume of the ramps must be filled out from the top down starting from the capstone, because it is virtually impossible to get the stones to the upper levels when the ramps beneath are filled out. The direct consequence of this is that still approximately 2.5% of the 80,000 to 100,000 casing stones will have to be adapted to the behind lying core stones. It could be considered therefore to start at a lower level with shorter ramps of more than 10% so there is less ramp volume to be filled. Thus the transport distance will also be greatly reduced, but of course more men will be necessary for pulling the stones. The number of turning points will not change (= ± 2x the number of layers).

Of course there has been more than sufficient time to rehearse the whole process on  ground level several times and for making and trying out the necessary fittings and scaffolding, so there would not be any surprises on a height of 143m. With the use of the zigzag lift this job is feasible;  even though a lot of extra attention will have to be paid to the first row of core stones to make the later insertion of the casing stones less difficult. If the casing stone is well measured and smoothed with fat lime-mortar on the upper and under site, then it can slide in by means of a ram. Vertical joints can also be closed by means of the ram. Of course the last stone of a layer must be very well prepared, because it has to fit on all sides. An advantage is that adjustments can be made easily because the stone is good attainable when the stones under it are not yet set in place.

Hoist and tables to set every 4th layer of the left open space for ramps

See for sample sequence the filling up of the open space of the top of the levels 139-142m. The other open spaces 135-138m and 131-134 can be done in the same way. The stone is rolled from the crane over a small bridge on the levels 139-141m to its final place and positioned with a hoist and/or rams. The facing stones of level 142 are also rolled on level 140m and than lifted up to level 141m with the hoist, tables and is pushed in place with some small rollers and rams.

25.    SCHEME  OF  FILLING  UP 143m – 139m TOP-DOWN 

This sketch is based on stones of 80x80x100cm to simplify the sketch. In reality the height of a layer in the top was probably around 65cm. This does not have an impact on the principle of filling up the ramps top-down.

Although the use of cranes is less efficient than rolling from ramp to final place the average time loss per stone is 7 x 3 minutes x 10 men is approx. 5 man-hour. As there are three lifts needed at the top three lifts can be used simultaneity on the lower levels.

26.    FILLING  UP  RAMPS  AT  LEVELS  32m  AND  33m

The casing stones are set first on every level except on the highest. The filling in sequence is:

  1. Remove ramp on level C33 and fill in C33 without a crane
  2. Removeove ramp B32 and fill in AB32 without crane.
  3. Fill in ABC33-34-35-36-37 with crane.
  4. Fill in 38-39 combined with the use of hoists and tables.

27.  SOME  ARGUMENTS  PRO

This building and transporting method I would have used for the following reasons:

  • First and foremost, because this solution is simple and would require much less (skilled) manpower and could probably have been done within a period of about twenty years.
  • By rolling the stones not only much manpower is saved in the transportation from the quarry to the right level of the pyramid, but it is also much faster.
  • Furthermore the work on the smoothness of the roads could be less demanding.
  • Making the circle segments does add some carpentry, but sleds have to be made also, and of course the rollers could be reused many times. As the friction is much less, the wear down is much less compared to sleds.
  • By setting the casing stones first in each layer they can work very accurate without too much effort. Small angular deviations per layer are corrected automatically when the top of the casing stones and the first row of core stones are adjusted horizontally.
  • With sight lines and long rulers it can simply be tested whether the casing stones are within the allowable ranges. If not, then it is relatively easy to correct this before the next layer of casing stones is placed.
  • Since the casing stones are completely finished, it is not necessary to make improvements after placement. Working against a surface of 51° is rather troublesome. Arms are too short to work standing, so a worker can only do something when squatting or kneeling.
  • Because the casing stones are finished and inspected in the quarry, no unnecessary and/or incorrect casing stones are transported.
  • There is always a risk of serious damage when the finishing has to be done after the placement in the pyramid. To replace a damaged stone is a major problem because it is not easily attainable later on.
  • Filling out the core with smaller rocks is much easier from the point of view of transportation. However, it must be ensured that the core is filled adequately so no settling could occur later. Smaller stones could have been stabilized with sand and a kind of lime concrete. Horizontal pressure on the peripheral stones will be zero.
  • There will be less rejected casing stones because depth of the back site of the stone is not important and so the front site can simply be corrected. It is however very important that the height of the stone is correct and that the upper site is smooth and perfectly parallel to the base. Each mason can simply check his own work with his own 5/4 try square.
  • By using the flank of the pyramid as a stable base for the ramps no extra material has to be replaced. All material used for the ramps could be placed in the core behind the 3rd row of each layer.

28.   TENTATIVE CONCLUSION

This theory answers to at least four of the five requirements formulated by Franz Löhner that every pyramid construction theory should fullfil:

+    A solution using a technology that is as simple as possible.

+   Continuity in technical matters and craftsmanship.

─   Verification through pictures and/or text (neither are the other theories)

+   Technology in keeping with time and culture.

+   The supposed technique and/or method must really be a practical solution.

If you see what is necessary for the vertical transportation of just 0.09% of the mass of the pyramid you will realize that it is absolutely impossible to finish the construction in time if you have to do it following the traditional views and by placing the facing stones last. Cranes are nothing more than a  necessity that uses up at least 10 times more manpower than rolling the stones directly from the ramps to their final destination.

Although there are still some minor details to refine, it certainly seems possible with these techniques to build the great pyramid of Gheops in about 20 years and probably with less manpower then in the traditional views.

But one question still remains: Was it really done this way?

De Lier, November 2014,

Ir. Ben J. Hendriks  b.i.

 

CONTENTS

1.    INTRODUCTION

2.    SUMMARY WHAT IS NEW ?

3.    DECIMAL  MEASURING  UNITS

4.    DIMENSIONS  AND  QUANTITIES

5.    STARTING POINTS

6.    PROJECT PREPARATIONS

7.    MEASURING AND PREPARATION OF BUILDING SITE

8.    QUARRYING AND SHIPPING

9.    SETTING OF THE CASING STONES

10.  CORE AREA

11.  ROLLING THE STONES

12.  NO NAILS NO SCREWS

13.  VERTICAL TRANSPORT

14.  TOP  14m

15.  TURNING POINTS

16.  HOISTS FOR  SETTNG  THE  STONES

17.  MOVING VERY HEAVY STONES

18.  BUILDING THE CHAMBERS AND GALLERY

19.  STAIRS AND SCAFFOLDING

20.  ZIGZAG STONE LIFT

21.  CRANES

22.  CAPSTONE OR PYRAMIDION

23.  TILTING AND SETTING THE CAPSTONE

24.  FILLING UP THE RAMPS TOP-DOWN

25.  SCHEME OF FILLING UP 143-138m TOP-DOWN

26.  FILLING UP RAMPS AT LEVELS 32m AND 33m

27.  SOME ARGUMENTS PRO

28.  TENTATIVE CONCLUSION

 

 

.

 

4 thoughts on “PAPER

  1. Loed de Bever

    Ben,
    Een bijzonder indrukwekkende studie, die ik nog eens in detail
    moet gaan bestuderen. Houd jij hierover wel eens lezingen, b.v.
    bij Probus ? In dat geval zou ik je graag eens in onze club in
    Eindhoven ontmoeten. Voorlopig heb ik leesvoer genoeg !
    Hartelijke groeten, Loed

    Reply
  2. Eise

    Ben,
    Goed stuk, vind het veel duidelijker dan de papieren versie, kan me voorstellen dat er inderdaad op een dergelijke manier gebouwd is indertijd.
    Groet,
    Eise

    Reply
  3. magueys

    Greetings! This is my first visit to your blog!
    We are a group of volunteers and starting a new project in a community in the same niche.
    Your blog provided us useful information to work on. You
    have done a extraordinary job!

    Reply

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