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of the Great Pyramid:
Study by Peter Prevos

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Pyramid Construction: Desk Study by Peter Prevos

Maastricht, January 1997
Copyright Peter Prevos

1. Introduction

During 1995 I was working at the Jamuna Multipurpose Bridge Project in Bangladesh where we were doing so called river training works. The goal of the project was to fix the river between two guidance dikes. These are needed to protect the foundations of the newly built bridge from eroding. One part of the project was to build a dike in a bend of river, this to prevent the river from eroding too far inland and flow in front of the bridge instead of under it.

Because of unavailability of suitable equipment we employed approximately 5,000 local people to do part of the excavation works manually. All work, except the compacting, was done manually using so called 'headpans'. These are small baskets that are filled with soil and then carried on the heads of the workers to remove the material. Seeing these people move all that soil with, from our point of view, primitive tools made me think about how the pyramids Would have been built.

My goal was to analyse how a pyramid of similar size as the Great Pyramid at Giza can be constructed, with resources similar to those of the ancient Egyptians. Many books have been written about this subject, but none of these books have looked at this from a civil engineers point of view. It is not possible to give an detailed account on how the great pyramid has been built since there are no records on pyramid construction written by the Egyptians. The earliest account is written by the Greek historian Herodotus, more than 2,000 years after the actual construction. This study is therefore not about how the pyramid was built, but how it could be built. The goal of this study is to analyse the logistical aspects of pyramid construction.

For this preliminary desk study a simplified model is used. The pyramid shall be approximately of the same dimensions as the Great Pyramid of Khufu on the Giza plateau in Egypt, but shall have a massive core, without any passages or chambers. The building method to be used is described by Peter Hodges, in his excellent book How the Pyramids were built. In his view the problem of the vertical transport of the individual elements that make up the core of the pyramid was solved by using levers.

The basic outline of this report is as follows: First a general description of the object is given, stating the dimensions, materials used, equipment and manpower. Then the building method will be described in some detail, including estimates concerning lifting and transportation speed of the elements. With this data a plan is made, estimating the total construction time and the total use of labour resources. Finally a cost price is estimated, assuming that a pyramid would be built in Bangladesh.

The report is written as a 'project preparation report' as if a new pyramid would be actually built, using only the technology known to the Egyptians of the fourth dynasty.

Therefore, past as well as future tense is used in the text, this to distinguish between facts concerning the original pyramid in Khufu and the new idea's put forward in this study.

I hope this study is a valuable addition to all the previous work that has been done on this subject.


2. General description of the works

2.1 Geometry

The great pyramid was built during the reign of Khufu (Cheops in Greek), second king of the fourth dynasty 2,720-2,560 BC. It stands on the Giza plateau nearby Cairo and is the biggest pyramid in Egypt.

The pyramid itself now stands 137 meters high, its original height of 146.16 meters is indicated by an iron post erected on the apex. Each side originally measured 230.362 meters or 440 royal cubits (1 cubit=0.524 metres). At present the side measures 227 meters, due to the loss of the casing stones. The core masonry consists of large blocks of local limestone taken from the nearby quarries and built around and over a rocky knoll. The size of the knoll cannot be determined, since it is completely covered by the pyramid.

The entrance to the pyramid is in the centre of the northern face. It is located in the thirteenth course of masonry from the base. This entrance has a pointed roof formed of massive slabs of local limestone and opens into a long steeply descending passage. From there a 36 meters long ascending passage leads to a 35 meters long horizontal passage that leads to the so called 'Queen's chamber'. This chamber measures 5.2 by 5.7 meters and the maximum height of its pointed roof is about 15 meters. The north and south walls each have a small hole a few centimetres square about 1 meter from the floor. These lead into narrow channels that originally opened on the exterior of the pyramid. At the juncture of the ascending and horizontal passage is an opening of a shaft which descends to a depth of 60 meters. It opens into the lower part of the descending passage, close to the unfinished, underground chamber, and is believed to have been an escape shaft for the workmen who filed the ascending passage with huge stones after the king's funeral. From the horizontal passage the Grand Gallery, which leads to the king's chamber, starts. It is 47 meters long and 8.5 meters high, and has a corbelled roof. In the centre of the floor is a sunken ramp about 60 centimetres deep. The Grand Gallery ends in a horizontal granite passage which serves as an antechamber. It measures 8.4 meters long and 3.1 meters high, and has slots for three portcullises. Beyond the antechamber is the so-called 'King's Chamber' which is lined, roofed and paved with red granite. It measures 5.2 by 10.8 meters and is 5.8 meters high. Its flat roof is formed of nine monolithic slabs of granite The northern and southern walls each have an 'air channel', one of which is open to the outside. The Pyramid can be seen to have about two hundred level courses of squared stones. The layers all have a different thickness ranging between approximately 50 and 145 centimetres. The average block size is about 1 cubic meter.

On the Khufu pyramid all the casing elements were removed in the 14th century. The few casing stones which do remain in the Great Pyramid all lie in the 1.5 meter thick bottom course and cannot be representative of the stones which would have been used in the higher parts of the construction. The only examples of face work which remains are those on the pyramids at Meidum, Dashur and Giza (Khafre's).

Figure 1 shows a wire-frame model of the Pyramid. The wall around the pyramid and the temple are not included in this report.

Figure 1, Wire-frame model of the Great Pyramid

A simplified model of the great pyramid will be used for this study. The pyramid has a square base measuring 230 meters in length and the height of the apex will by 146 meters. The foundation is a level surface on which the first layer can be placed. Any settlement due to the pressures during or after construction will be disregarded. The pyramid is solid, without any passages or chambers. Because the volume of the passages and chambers is only 0.07 % of the total volume the passages and chambers can be omitted. The construction will be done in 200 subsequent layers of equal thickness being 0.73 meter. The standard element will be cubical with sides of 1.17 meters. This is a theoretical assumption since blocks of this size will not be able to balance on the already placed steps. To be able to estimate to construction time for the core, the used parameters, such as the number of layers and the element size, have to be as close as possible to those of the actual pyramid. During the actual construction the layer thickness has to be adapted according to the thickness of the strata at the quarry. The block size will have to be adapted to be able to balance on the steps. Each layer will have fitting elements that are slightly smaller or larger than the standard element size. The core elements will thus form a step pyramid. The size of the steps is 0.575 meters. The outer layer will consist of wedge shaped casing elements so the pyramid will have a smooth surface when completed.

2.2 Materials

The core of the great pyramid consists of solid limestone blocks. Limestone is a sedimentary rock with a density between 2.5 and 2.7 tonnes per cubic meter. It is quite sensitive to weathering, therefore the top layer was constructed of a more durable limestone. The Kings Chamber and the Grand Gallery are constructed of red granite. Granite, an igneous rock is more dense than limestone and has better general physical properties and is therefore used in the upper chambers. The bulk of the limestone was quarried on the plateau itself. The red granite had to come from near Aswan about 700 km upstream from Cairo.

The problem of opening and exploiting the quarries needed for the construction is a very interesting and complex problem but is not a part of this study. The pyramid for this study is completely made of limestone, assuming a density of 2,600 kg/m3. The weight of one element is: 1.17 * 1.17 * 0.73 * 2,600 = 2,598 kg.

2.3 Labour and equipment

The ancient Egyptians built the pyramids with the simplest methods. Both in quarrying and building workmen used copper chisels, as well as flint, quartz and diorite pounders. Further they used wooden crowbars, sledges and rollers to transport the elements. Figure 2 is a scene showing the transport of blocks of stone from the quarries in Tura, in which we see oxen dragging the sledges.

Figure 2, Transportation of stone blocks in a quarry at Tura

This method works very well for transporting over long distances, but usually manpower was used to move building elements. Figure 3 shows how 172 men work to drag an alabaster colossus of the twelfth dynasty monarch, Dhutihotep, from the quarries of Hatnub in Middle Egypt. This statue measured over 6.5 meters high and weighed about 60 tonnes.

The scene also shows men carrying levers and others pouring liquid, presumably water, from pots in order to reduce the friction between the statue and the surface. To transport a 2.6 tonnes element in a similar way, 172 / 60 * 2.6 = 7 to 8 people are needed. To transport the elements on the sledges special roads were constructed. They consisted of a base of rock rubble on which wooden planks where embedded at regular intervals in a layer of clay. The friction was reduced by wetting the clay, as can be seen in figure 3.

Figure 3, Transporting a statue from the tomb of Dhutihotep, El Bersheh

All lifting work will be done by means of levers. With these levers all elements can be jacked up along the sides of the already constructed part and put into position. The lifting method will be described in more detail in the method statement. Levers can also be used for horizontal transport, but only for short distances or to put an element at its correct place.

The levers are made of wood and have a length of 2 meters. At the fulcrum the lever measures 100*100 mm and is tapered to both ends for easy handling. The maximum lifting force for one lever is determined by the length of the lever, the place of the fulcrum, the section of the lever and the type of wood used for the lever. The section has to be able to resist the bending stresses induced by the levering action. When assuming that the leverage point is at 0.1 meters from the end, and the maximum downward force to be applied by one person is 600 N the upward force on the other end is 1.9 * 600 / 0.1 = 11,400 N. The actual bending stress in the lever will be 6.84 N/mm2 which is allowable for most timber. Three levers would be sufficient to lift a 2.6 tonnes element, but for reasons of stability four levers have to be used.

Work will be done on 350 days per year, taking into account any religious or other holiday that may occur. A working day is from dusk to dawn, since working with artificial light is not possible. Average daylight per day, measured over a year, is 12 hours. Any lunch breaks or otherwise will also be accounted for by means of an efficiency factor of 70%.


3. Method statement

The construction of the pyramid can be divided into four different activities:

  • Preparation of the work area;
  • Construction of the core;
  • Casing and trimming;
  • Production of the elements;

3.1 Preparation of the work area

The work area has to be cleared from sand and weathered rock and the surface has to be smooth to enable the horizontal transport of the elements.

Assuming that it takes 1 man about 2 hours to clear one square meter and that two teams of 115 men will work towards each other it will take 460 hours, or 5.5/0.7=9 weeks to clear the complete area. For each man doing the clearing and cutting a team of four more men have to remove the debris behind them and dispose it outside the work area. The total workforce needed for this activity is 2 * 115 * 5 = 1,150 men for a period of 9 weeks. This activity has to be completed before the construction of the core can commence.

3.2 Construction of the core

Many theories have been put forward concerning core construction. Most of these include the use of ramps to transport the elements to the work platform. There are three possible versions of a ramp. A long ramp or a short steep ramp with horizontal plateau and the spiral ramp. There are several problems with these theories. First the volume of the ramp to be built. In the long or short ramp scenario the volume of these structures would be more than the volume of the pyramid itself. In case of the spiral ramp stability will be a major problem. The slope of the pyramid itself is more than 50° and so the wall of the ramp has to be even steeper. Al this is very well analysed in Hodges.

Core construction is done in two actions. First the element has to be jacked up to the layer under construction after which it can be placed in its final position.
On the sides and the top of the pyramid teams can work in jack-up lines as shown in figure 4.

Figure 4, Distribution of work teams on the pyramid

Lifting teams can work from only two sides of the pyramid simultaneously. When working from more than two sides the work platform can not be divided into equal square area's which is needed to ensure a smooth flow of elements. Working from one side would not be a very efficient option. When working from three or four sides the placing teams will be in each others way. The remaining two slopes can be used to lift the big slabs needed for the construction of the chamber. For this the geometry can be changed by leaving bigger steps on which the big size elements can be jacked up the sides and placed on the platform. When no more odd size elements are needed, the steps will be filled with standard size elements. Between two 'jack up lines' there must be some space for supervisors etc. There must be working space between the teams in vertical direction also. Figure 5 shows the distribution of the jack up teams along the pyramid side.

Figure 5, Spacing between jack-up teams

Because there are blocks being jacked up every four meters there is an almost constant flow of material to the work surface. The horizontal transport on the work platform actually determines the construction time for that particular layer and not the time needed to lift the elements. When an element has reached the level under construction it will be moved to its final place in the pyramid by the same team that has brought it to the top. This will create a continuous flow of elements on the work platform. After a row is placed the teams go down the unused sides of the pyramid and start a new cycle down at the base where they receive a new element to bring to the work platform. At the moment the first two rows of a layer are placed, halfway along the work platform, the maximum number of workers are being employed. This gradually reduces until the last rows are placed. When placing the next layer the number of work teams increases again. This is a complex flow of people and material which needs very good management to make sure there is minimum time loss.

The big problem with this method is the safety while jacking up the elements. Is it quite likely that an element can lose its balance and tumble down the pyramid creating a very dangerous situation. Because of this danger the vertical transport has to be done very carefully. Except for the great time loss in such a situation, many human lives can be lost when workers are hit by a limestone block avalanche.

In the next paragraphs this method is being quantified and the total construction time for the core is estimated.

Vertical transport

The elements will be lifted to the required level by teams of 7 men using 4 levers. Four men operate the levers, two to insert the timber packing and one man to co-ordinate the actions. The jack up procedure is as follows:

  1. The levers are put in position for the first 'jack'. Two on each side, four in all. The element has been delivered on timber packing;
  2. After the first jack is complete extra packing has to be inserted below the stone at each end;
  3. An extra packing has to be inserted below the levers;
  4. Start the next jack;

This sequence is repeated until the element reaches the next level.

Figure 6, Jack-up procedure

According to Hodges, who has conducted full size tests of the above described procedure, it takes 25 seconds to complete one cycle. With every jack the element is lifted 100 mm, taking 8 complete cycles to lift the element to the next level. To move the element onto the next step it has to be moved horizontally. This horizontal transport can be done by using the levers in a paddling movement. Hodges mentions a horizontal travelling speed of 13 meters per hour for this method. A complete cycle of moving a block to the next step (0.73 meter vertical and 0.575 meter horizontal travel) takes 359 seconds. In the calculations 513 seconds (5.12 meter per hour) will be used, taking into account any loss due to resting, human error or otherwise (efficiency 70%).

Placing the elements

This is also done by using the paddling movement used in the lifting procedure. In the calculations a speed of 9.10 meter per hour will be used (70% of 13 meters per hour). The distance between two teams on the platform is the time that one team travels horizontally before the next team reaches the top. In our case this distance is: 9.10 * 4/5.12 = 7.11 meters. This is slightly more than the distance in horizontal direction and should be sufficient.

Calculation of construction time

In Appendix 1 the construction time for each layer is calculated using parameters listed below.

    W - Width of the pyramid [230 m]

    H - Height of the pyramid [146 m]

    z - Element height [0.73 m]

    l, b - Element size [1.17 m * 1.17 m]

    Vv - Vertical speed [5.12 m/h]

    Vh - Horizontal speed [9.10 m/h]

    Sv - Vertical spacing [4 m]

    Sh - Horizontal spacing [7 m]

    Sp - Spacing on the platform [7.11 m]

    n - Layer number [1 to 200 ]

For each layer n the height h(n), width w(n) and the number of elements to be placed e(n) are calculated.

The time needed to place all the elements is the time between the moment that the first row of elements arrives on the work platform and the moment that the last row has been placed. After every Sv / Vv = 0.78 hours a new batch arrives. This is repeated until the last row, ½ w(n) / b in number, is placed.

The elements also have to be moved sideways to fill up the rows. All elements have to be moved sideways over an average distance of ½.Sh meter. The above sequence has to be repeated Sh/l times to fill the platform.

In figure 7 the sequence of placing one row of elements on the platform is illustrated.

Figure 7, Placing sequence

Now the construction time per layer can be calculated by:

The total construction time for the core of the pyramid, 2,556,988 blocks, as calculated in Appendix 1 is 45,684 hours, or 10.88 years. In Hodges the construction time or the core is estimated at 17 years, but with completely different assumptions and method. The vertical speed in his calculations is 9.125 m/h which is to my point of view not possible. Also the efficiently is taken as 100%, which would mean 17 years of work without any mistakes and problems! The horizontal transport on the platform is not taken into account. Also the number of teams to be employed at any time is equal for every layer.

When placing at maximum capacity 56 blocks per hour can be placed on average throughout the almost 11 years the core is under construction. The in the above described way calculated capacity is the maximum capacity. In case the quarry can not supply sufficient elements the placing capacity will be equal to the quarry capacity, leaving no stock. In paragraph 3.4 the quarry production will be looked at in more detail and the placing capacity will be levelled.


At any stage there are teams working on two sides and on the top of the pyramid. By calculating the number of teams that can be employed at one time in horizontal direction Th(n), in vertical direction Tv(n) and on the work platform Tp(n) the total number of teams can be determined.

When a new layer is started only the two sides are occupied, the number of teams being:

2 * ( Th(n) * Tv(n) ). When the first row of elements reaches the middle of the work platform the platform is also occupied.

The maximum number of teams to be employed at one time for the construction of the layer is calculated with:

The actual number of elements being moved on the pyramid at one time lies between 2 * Tv(n) * Th(n) and T(n).

For each layer the maximum number of teams is calculated by using above mentioned formulas. In figure 8 the number of work teams is set out against the layer number. From this it can be seen that the total workforce will be smaller as the pyramid grows. This is because the surface to work on is getting smaller, although the pyramid is getting higher, less teams can be placed on it.

To estimate the total use of labour resources the workforce is multiplied by the construction time per layer and the number of men per jack-up team. This way the total use of labour resources is estimated to be 3,579,745 man weeks, or 71,595 man years. The maximum number of workers is at layer number 11, being 1,135 * 7 = 7,

In figure 8 the number of workers during the construction period are shown.

Figure 8, Number of labourers used for core construction

3.3 Casing and trimming

After the highest point is reached the final action, smoothing of the surface, can start. There are two distinctively different methods of shaping the surface of the pyramid, both of which will be analysed. The illustration below shows the principle of the two different methods of pyramid shaping.

Figure 9, Final shaping of the pyramid

Placing casing elements

The first method described is the placing of ready made casing elements. The wedge shaped elements measure 2 * 0.575 meters at the base and are 0.73 meters high.

To cover the core 45,970 elements have to be placed which is calculated with:

The elements have to be elevated to the required level and subsequently placed accurately on the face of the pyramid. Jack up teams can work on all four sides of the pyramid simultaneously using the same method as for the construction of the core. The first elements take 146 / Vv = 29 hours to reach the top. When working 100% efficient this action will already start right after the last core element starts its way up to the top. But when the highest point of the pyramid is reached a two week holiday will be very appropriate so the jack-up lines have to be established again. Every jack-up line has to move Sh / 2 = 3.5 elements to the work area. After every Sv / Vv = 0.78 hours a new element arrives. It takes 3.5 * 0.78 = 2.73 hours to fill one layer. Thus the total jack up time for all the casing elements is 200 * 3.5 * 0.78 = 546 hours, or 6.5 weeks. Placing the elements in the face will also consume a lot of time. It is assumed that it takes twenty minutes to position a casing element into the final position. This is a very crude assumption but no reliable data is available to me at present. The total placing time for all elements is 45,970 * 20/60 = 15,323 hours (3.65 year). Thus the total construction time for the casing action is 29 + 546 + 15,323 = 15,898 hours (3.79 year). The use of labour is calculated in Appendix 2. The layer numbers are in reversed order since the casing has to start at the top. For each layer the number of lifting teams is calculated in the same way as with the core construction, but working from four faces instead of two. Then the total construction time for the layer is calculated using 20 minutes placing time per block, adding the 2.73 hours per layer and for the top layer the 29 hours to position the first element. To get the total man weeks the construction time is multiplied by the number of teams working on that layer and the number of workers per team. From Appendix 2 it can be seen that the total use of labour to place the casing elements of the face of the pyramid is 1,088,028 man weeks, or 21,761 man year.

Trimming the pyramid

In this method the outer layer of the core is constructed of the casing material which is a more durable limestone than the core material. After the last core element has been placed the stone masons start to chip away material so that the final shape can be made.

This method implies that more core material has to be placed. Effectively this means that every layer will be 1.15 meters wider. One extra layer of 230 * 230 meters, consisting of 38,644 elements, has to be constructed. Using the formulas from paragraph 3.2 gives a construction time of 460 hours, using at maximum 1,126 teams (43,198 man weeks). This has to be added to the core construction.

The actual trimming is done at one layer at the time because all the debris has to be removed continuously. The volume of material to be removed can be calculated by:

    [ (2,556,988 + 38,644) * (1.17 * 1.17 * 0.73) ] - (2302 * 146 * 1/3) = 19,341 m3

Assuming that one stone mason can chip away 0.5 m3 per day and that they are positioned every two meters it takes one full day to complete one layer and 200 days to trim the complete pyramid. To remove the material two chains of workers are placed on the side of the pyramid. This method is often used in Bangladesh and is called the 'headpan' method. A basket, containing approximately 20 kg of material is passed on, over the heads of the workers, down the slope of the pyramid, hence the name headpan. The second row is used to bring the empty headpans back to the stone masons. This way a production of 4 m3/hour, or 48 m3/day, can be achieved. One 'chain' can remove the material produced by 96 stone masons.

At the bottom of the pyramid the chain has to continue to be able to deposit the material at its final destination. Behind every mason two labourers work to remove the debris from under his feet and bring it to the removal teams. This way the produced debris can be removed from the face of the pyramid very easily.

The total amount of workers needed per layer is calculated in Appendix 3. For every layer the width is calculated and the number of teams, using above mentioned parameters. The total number of labourers depends on the distance the material has to be transported from the base of the pyramid. In the calculations 100 meters are assumed. The figures from Appendix 3 have to be corrected for a efficiency factor of 70%. In total 348,052 / 0.70 = 497,217 man days or 1,421 man years are used to trim the pyramid. The total time needed to trim the pyramid face is 200/0.70=286 days or 40.8 weeks.


The trimming method is the fastest and most efficient way of giving the pyramid its final shape. The extra material that has to be placed in the core will be added to that activity bringing the total number of core elements to 2,556,988 + 38,644 = 2,595,632 elements. The construction time will increase by 460 hours. The total use of labour will increase by 40,710 man weeks.

3.4 Production of the elements

The production and transportation capacity of core elements has to be high enough to make sure that there is always sufficient stock.

In Appendix 1 the average placing capacity is calculated per layer. This ranges between 0.4 and 84 elements per hour. The average placing capacity is 56 elements per hour. The quarry capacity is mainly determined by the geometry of the quarries. The thickness and size of the strata to be used determines the number of elements that can be yielded at one time. The distance of the quarries and the number of quarries are also an important factor which is not known to met at this time.

When there is always sufficient stock, the construction time for the core will be as calculated in paragraph 3.2. When there are no more elements to be placed the core construction will be delayed. In this situation the placing capacity will be equal to the quarry capacity. In Appendix 1 the construction time as well as the stock are levelled for this situation.

An important parameter is the number of elements in stock before starting the actual construction of the core. Producing this stock will take extra time, but the construction time for the core will be reduced. The following table shows the relation between material in stock and the total construction time for the core, assuming a production capacity of 56 elements per hour.

In stock Preparation time Construction time TOTAL
0 0 52,429 52,429
100,000 1,786 50,742 52,510
200,000 3,571 48,864 52,435
300,000 5,357 47,079 52,436
378,000 6,750 45,684 52,434
2,556,988 45,684 45,684 91,368

Table 1, Construction time for different stock levels

The figures do not include the extra time needed to place the elements for core trimming as put forward in paragraph 3.3. From this data it can be concluded that no stock is really needed since the longer construction time is compensated by a shorter preparation time. The overall construction time stays more or less the same. Producing more then the 378,000 elements is not effective, because the core construction is on maximum capacity and the total construction time is at its minimum.

In case the quarry capacity is less than the placing capacity the construction time will be negatively effected. When the quarry capacity is equal to the maximum placing capacity (84 pcs/hour) the construction time will be lowest. Table 2 shows the total construction time for different quarry productions. No stock is produced beforehand.

Quarry capacity Construction time [hr] Construction time [yr]
84 45,684 10.88
70 47,116 11.22
60 50,384 12.00
56 52,429 12.49
50 56,444 13.44
40 67,369 16.04
30 87,168 20.75
20 128,707 30.64

Table 2, Construction time for different quarry production levels

To make a good estimate of the total construction time the quarry capacity has to be known as exact as possible. Since it is not feasible to give a reliable estimate of the quarry capacity at this time an arbitrary figure is used. For further calculations a capacity of 30 elements per hour is used. A higher quarry capacity is not very likely and a even lower capacity will increase the construction time considerable as can be seen in table 2. Assuming that it takes about 1 day to cut one element from the quarry face, 360 elements have to be in production at one time at the different quarries. There has to be enough space in the quarries to produce all these elements and enough transportation capacity to bring the elements to the construction site. Detailed study of the quarries sites is required to determine the quarry capacity more accurately.

Because of the extended construction time the use of labour will also be different to the situation in which there is always sufficient stock. To make sure there are not too many teams waiting for supply the placing capacity will be reduced. This is done by increasing the vertical spacing of the jack-up teams.

Figure 10, Optimizing the placing capacity

The vertical spacing can be changed in the spreadsheet so that the new maximum capacity can be calculated. In figure 10 the results of the calculations for the core construction time are given for different values of the vertical spacing, using a quarry capacity of 30 elements per hour and no stock produced before construction. The top line shows the use of labour in man-years. At a vertical spacing of 7.5 meters the use of labour is minimal. The other two lines are the construction time in hours, using the maximum placing capacity and the levelled capacity. The waiting time for the jack-up teams is proportional to the difference between the maximum capacity and the levelled capacity. The difference between these two is minimal at a vertical distance of more than 10 meters.


The quarry or production capacity can not be estimated properly since no data about the geometry of the quarries is available to me at this time.

From table 1 can be seen that production of stock before starting the construction of the core will not have a substantial beneficial effect on the total construction time for the core.

Because the placing capacity is different for every layer, but the quarry capacity is taken as a constant, the placing capacity has to levelled for that. Table 2 shows the construction times for the core for different quarry productions. A quarry production of 30 elements per hour is used for further calculations. The validity of this figure can not be properly established at this time.

The quarry capacity is most of the time lower then the placing capacity so there will be a lot of waiting time for the jack-up teams. To reduce this waiting the placing capacity is reduced by increasing the vertical spacing. Figure 10 shows that at a vertical spacing of 7.5 meters the use of labour is minimal.

Using this model the total time needed to produce the 2,595,632 elements is 1,030 weeks. The minimum construction time for the core is 85,233 hours, the levelled construction time is 97,758 hours (1164 weeks), using 128,641 man years to complete. The average placing capacity is equal to the quarry production capacity of 30 elements per hour.


4. Planning

To determine the total construction time for the pyramid all four activities will be summarised. The use of labour will not be levelled, assuming that an unlimited supply of workers is available at any time.

4.1 Preparation of the work area

This is the first activity to start and lasts for 5.5 weeks, using 1,150 workers, 6,325 man weeks.

4.2 Construction of the core

Starts directly after the preparation of the work area is completed. The total time needed to position all the core elements is 97,758 + 460 = 98,218 hour or 1,169 weeks. The total use of labour for this activity, as calculated in paragraph 3.4 is 6,432,039 man weeks. On average 5,500 people will be at work on the pyramid at any time.

4.3 Trimming the pyramid

The trimming method takes 286 days to complete (41 weeks) and will start right after the core construction is completed. 497,217 man days will be used for the trimming.

4.4 Production of the elements

The production of the elements will start the same time as the preparation of the work area. A small stock, of six weeks production, will be created. This will not have a great influence on the core construction. The time needed to produce all the elements has to be less than the core construction time. The total time to produce all the 2,595,632 elements is 86,521 hour or 1,030 weeks.

4.5 Total construction time

The total construction time is determined by adding up all activities as listed above including a two week holiday between the completion of the core and the start of the trimming activities.

9 + 1,169 + 2 + 41 = 1,221 weeks, or 24.4 years are needed to construct the pyramid. Figure 11 shows that the critical path in bold. The only activity with some float is the element production.

Figure 11, Planning chart

Although the core construction is in the critical path it has to be noted that the placing capacity has been reduced to minimise waiting time. When using the maximum placing capacity the element production will be critical.


5. Cost estimate

To give an impression of the actual volume of the work the costs of the total project are estimated. For this it is assumed that someone would want to built a pyramid, of similar size as the Khufu complex. The construction site will be situated in Bangladesh because of the abundance of cheap labour and the fact that the local people have a lot of experience with moving great volumes of material by hand. The local currency in Bangladesh is the Taka (BTK), all costs will be estimated in the European Currency, the Euro. The following exchange rates will be used:

1 Euro = 51 Taka

1 US Dollar = 40 Taka

At the 1995 price level the average salary for a unskilled labourer in Bangladesh is about 65 Taka for a 8 hour day. Overtime is paid 50% extra per hour. The working days at the pyramid are 12 hours, making the daily rate 114 Taka per day, or 2.23 Euro per day.

5.1 Element production

Because rock of any bigger size is not available in Bangladesh concrete will be used to produce the core and casing elements. Only boulders are found in Bangladesh, they are normally crushed and used as aggregate for concrete. The density of light aggregate concrete is about 2,00 kg/m3, the pressure in the bottom layer becomes 3.4 MPa. This gives an indication of the required compression strength of the core elements. Low grade concrete will be sufficient.

The mineral aggregate can be replaced by brick chips, which is a very common and much cheaper option. The price for concrete with brick chip aggregate, without reinforcement would be approximately 3,000 BTK/m3, including all costs for labour and transport. One core element would cost 2,998 BTK or 58.78 Euro per element.

5.2 Preparation of the work area

In paragraph 3.1 it was estimated that one team of five men will clear 6 m2 per day. The unit rate for the site clearing will be ( 5 * 2.23 ) /6 = 1.87 XUE/m2.

5.3 Core construction

In the used scenario, with a quarry production of 30 pcs/hr the total use of labour resources is 6,432,039 man weeks. The costs for core construction per element are: (6,432,039 * 7 * 2.23) / 2,595,632 = 36.68 XUE per element.

5.4 Trimming the pyramid

The trimming of the pyramid takes 286 days and a total of 497,217 man days. Total costs of this activity is 497,217 * 2.23 = 1,108,794 Euro lump sum.

5.5 Housing and accommodation

Housing and accommodation for all the labourers will cost approximately 350 Taka per man per week. The total number of man weeks over the complete project is:

Activity Man Weeks Duration Labour
Preparation 10,350 9 1,150
Core construction 6,432,039 1,169 5,502
Trimming 429,217 41 10,468
TOTAL 6,871,606 1,219 5,637

Table 3, Total number of man weeks

The occupation of the workers camp will change according to the need of labour. The average number of people to be taken care of at one time is 5,637. The element production is sub contracted, the costs of housing etc. are all included in the unit rate of the subcontractor. One week accommodation for one man will cost 6.86 Euro. The total costs for food and accommodation will be 47,139,217 Euro.

5.6 Total construction costs

In table 3 the costs for each activity are summarised and totalled. All the prices are exclusive of overheads, profit & risk.

Activity Quantity Unit Unit rate Amount
Element production 2,595,632 pcs 58.78 152,576,898
Preparation work area 52,900 m 1.87 98,923
Core construction 2,595,632 pcs 36.68 95,207,782
Trimming   LS   1,108,794
Housing 6,871,606 weeks 6.86 47,139,217
TOTAL 296,131,614

Table 4, Total construction costs


6. Conslusions

From all the calculations made in the previous chapters can be seen that it is very well possible to construct a pyramid of the gigantic size as the one at Giza by merely using the technology and resources from the ancient Egyptians.

The construction requires very good planning and management. The work has to be done very carefully to prevent a block avalanche which will set back the construction for weeks. It is very conceivable that such a disaster will actually happen but no risk analysis are made on that point.

The most important conclusion that can be made from this report is that when trying to analyse this problem the quarry production needs the most attention. All previous reports have focused solely on the problem of vertical transport. I have tried to show that this is not the real problem if all work is organised well. The maximum placing capacity is sufficient to ensure continuous flow of elements to the work platform. The production of the more than 2.5 million elements is the real achievement of the pyramid builders That build the great pyramid. Accommodation and feeding of the labourers is the second major task. Not to mention the great number of supervisors and other staff members to control the construction process.

6.1 Reliability of the assumptions

The reliability of the assumptions made to reach to the conclusions differs per activity. Preparation of the work are is only a very small part of the whole process. Core construction can be estimated quite well since the used data comes from actual experiments as described in Hodges. All figures include an efficiency factor of 70%. There is no actual data available to estimate the element production so an arbitrary figure is used. The total construction time highly depends on this activity so a good estimate would be essential. The figure of 30 element per hour is quite high, the reason I used it is because it leads to a total construction time of about 20 years which is what Herodotus mentions in his book the Histories as described in the next paragraph.

6.3 Herodotus comments

The oldest known document about the construction of the pyramid is written in Herodotus' book the Histories, part II. He visited visited Egypt in the fifth century BC. In Appendix 4 the relevant text about pyramid construction is given. Herodotus mentions several parameters that are also referred to in this document. One furlong, as mentioned in the text is 1/8 of a mile, 201.163 meters. A fathom measures 6 feet, 1.829 meter.

Line 11 states 'A hundred thousand men laboured constantly ...'

According to the calculations done in this report an average work force of about 5,500 men would be present at any time, excluding the labour needed to produce and transport the element to the quarry site. Assuming that it takes one whole day with two people to cut one element out of the quarry face and that 30 elements are produced per hour, 360 elements have to be in production and in transportation at the same time. Transportation from the quarries to the pyramid face is done by oxen sledges as shown in figure 2. To produce and transport 360 elements simultaneously not more then 3,600 men would be needed. The maximum number of workers employed at any time during the project, including staff, cooks etc. Would probably not be more then 10,000 at any time.

Line 20 states: 'The pyramid itself was twenty years in building.'

To construct the pyramid in this time frame a quarry production of 30 elements per hour would have to be maintained. It is still questionable if this is achievable.

Line 27 states ...machines formed of short wooden planks.

This passage could describe the levers that would have been used to transport the elements along the sides and on top of the pyramid. The lever method is the only way the vast volume of big size elements can be brought to the required levels.

Line 38 states ...1,600 talents of silver.

One talent of silver is equal to 26 kg. These were only the costs of food for the labourers who constructed the pyramid. These days 1,600 talents of silver would be equivalent to approximately 4,900,000 Euro (118 Euro/kg). Using the calculations from chapter 5 this would be 1.35 Euro per man per week to feed the workers.

6.3 Further study

There are several points not fully analysed in this study. First the quarry problem. I would need more data about the actual place of the quarries, the maximum yield per face and to get a better insight into the quarrying methods used by the Egyptians. I am planning a trip to Egypt, later this year, to study the possible quarry sites and try to analyse the quarry production process.Also the influence of the construction of the chambers on the construction process needs some further analyses. The lifting of the big size elements will need adaptations to the geometry of the core, which have to be filled up after the construction of the chambers is completed.

This report will be followed by a second one in which a more reliable estimate of the quarry production will be done and possible amendments to this report.

It was Archimedes who first described the mathematical aspects of using levers for moving heavy objects and I would like to end this report with a quote from him:

Give me a firm place to stand and I will lift the world.

Pyramidology | Pyramid Construction
Appendix 1 | Appendix 2 | Appendix 3 | Appendix 4

Peter Prevos
(January 1997)

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