Somewhere in the text I mention I need a better clock than the calendar. In the meantime I have designed the copper clock to do this, a full staffed copper mine delivering to a nearby warehouse at a steady rate, but I have been too lazy to redo my tests of the small pyramids, or test out the bigger ones. Again, any input is welcome.

Pyramid Construction

1. Introduction.

Building pyramids in Pharaoh usually is a lengthy procedure. Boring maybe, even with the pyramid speed-up on, considered a legal way of cheating by many experienced players. Actually with proper planning even the larger pyramids can be built quicker by manpower than by the gods themselves. So the pyramid speed-up is actually a misnomer, and should be called a pyramid discount offer instead.

Building the real pyramids in Egypt was a lengthy procedure too, so if it takes a long time in the game, due to limitations put in by the designer of the mission, it gives a fair picture of reality. I have done some testing about what you need to do to have a pyramid built rapidly at no high cost. I restricted myself to the stepped pyramids of sizes small, medium and large. The stepped pyramid complex and the grand stepped complex would take much testing time. I will try to extrapolate my findings from the smaller to the larger sizes.

To build a stepped pyramid you need a lot of plane stone and a bit of wood. In the test mission I designed, these both were available in abundance. If the goods need to be imported, that could be a limiting factor. Still the other parameters should be roughly similar. Most of the factors determining building speed can be influenced by the player. One can't, and that is the rate at which the sled pullers collect their stones at the storage yard. Only one sled at a time can leave the yard. Walkers from the work camps will all go to the same yard to collect their stones, and will only be convinced to turn to another yard once that one is empty. I couldn't fully figure out what yard that was, but it seems to be the last one built, then the one before that etcetera.

Knowing this, the goal of our design should be to have sleds leave the storage yards at a steady rate, without any delays. As we have no way to exceed that maximum rate, we must focus on optimizing the rest.

2. Foundations.

The first thing that must be done is the ground work. For that you need the workers from the work camp. Each camp will spawn a maximum of four workers consecutively. Each worker walks to the building site, enters it through the platform, walks across the site to the tile that needs work. He then works four tiles and disappears. The second walker will be sent out shortle after the first, the delay appears to be rather fixed, and doesn't depend on the whereabouts of the previously dispatched walker. To optimize the speed at which the workers reach the site there should be no road connection to the platform. That way the workers will walk diagonally cross the map, which is faster than along the gridlines the road must follow. You cannot control the movements of the worker on the building site, that is the limiting factor for this part of the construction.

As stated, a single work camp will dispatch a maximum of four workers. For the larger sites you never have four workers working at the same time, as the first has already done his four tiles before the third or fourth reaches his first tile. Below is a table on the preparation time in months for the different pyramids as a function of the number of work camps. It appears the unit of month is rather rough, introducing some rounding error. All camps are close to the platform and fully staffed. To ensure the last you may set food production to priority one, as the work camps fall under that department. There were no other camps that could spoil the issue, only meadow farming.

With two camps a small construction site is prepared twice as fast as with one, with three it's about three times as fast, but the forth one doesn't contribute as much. Workers travel larger distances on the construction site to find their four tiles, which causes delays. Also the average distance to the platform increases with the number of camps. Finally there is some delay in between different stages of the groundwork, during which time there are less or no workers at the site. That delay is independent of the number of camps.

The conclusion is that it doesn't pay to have more than 3 or 4 camps for a small pyramid, unless speed is of the essence. Even then 5 camps could suffice. If we compare eight and four camps we see that we need 80 employees extra to gain just three months. Those employees would probably have produced much more had they been employed in other industries. If we multiply the number of camps with the number of months we get an impression of the efficiency, as that is a direct measure of the wages involved. According to that criterium 3 camps is the best compromise between speed and economy. As the building costs of a work camp don't generally pose a problem, I have left that factor out.

For a medium size pyramid 5 camps is the best compromise, but if you can afford the 6 months, 3 camps is more efficient. If speed is important you need 8 camps. The ground work for the large pyramid is done most efficiently with 5 camps, if you want more speed 9 is a good compromise and for even more speed use 11 camps. The efficiency criterium is fairly constant here.

Extrapolation to the two larger sizes the following table applies. Given are the number of camps needed for the most efficient strategy. The size is the dimension of the square footprint on the map in tiles. The number of tiles increases quadratically with pyramid size, the walking distance on the size linearly. A simply used linear extrapolation. Probably second order polynomial gives a better result, provided we have more precise measurements. The rounding off error in the month unit is too large for more sophisticated tools.

3. Small stepped pyramid

Now we come to the building of the pyramid itself. Quarries will produce stones at a rate of about one per 1.06 months. You can increase production rate by having an altar of Amon in your temple complex for Ptah. Exact numbers can be found in the Nerdicus post on Pharaoh Heaven. Carpenters take about three months to prepare the wood for making an addition to the ramp. Stone masons each deploy four workers and work camps each deploy two sleds. This all is assuming there is no shortage of employees. To assure this, both set the food and the industry department to high priority, as carpenters, stone masons and quarries all fall under the latter. In practice it's best to have a small level of unemployment during the building stage.

Pyramids are built in layers. Every six consecutive layers contain the same amount of blocks. The small pyramid consists of 6 layers of 24 blocks (8 loads) and a further 6 six layers of 8 blocks (2 loads). As the pullers deliver their blocks in loads of four that is the better unit. The total size of the small pyramid is 60 loads (240 blocks). The medium pyramid has 6 layers of 18 loads and a full small pyramid on top of that. The sizes in loads and the total size in loads and blocks of the five different pyramids are in the table below.

The lower layers from the second layer up all need a section of the wooden ramp to be added by the carpenter for the sled pullers to have access. The six top layers don't need the ramp. The four workers from the stone mason work in pairs. Each pair will handle a single load at a time. Once they have finished that load they walk across the site and call for a new load. The maximum number of stone mason workers per layer hence is just twice the total number of loads. The conclusion is that the maximum number of stone masons (buildings) needed per monument is half the number of loads in the lowest layer. In practice you can do with less.

Each work camp will send out two sleds. That would imply there is no gain in having more work camps than there are stone masons. It seems, however, that the second sled will not leave the SY before the first one has arrived at the platform. Hence it can be quicker to have a few camps more.

As stated before, the limiting factor is the rate at which sleds leave the SY where the blocks are collected. You can optimize the building rate by having a lay-out with this SY next to the platform (see the Meidum-150 scenario by Cartouche Bee on Pharaoh Heaven). If my observation of the order in which the SY's are visited by the sled pullers is correct, this should also be the first SY for plain stone that is built. Below is a detailed table on the construction rate of a small work camp, layer by layer, for different setups. Indicated are the number of camps (C), masons (M), quarries (Q) and carpenters (J). The reported time is in months, after the finishing of the foundation (see above for times needed for laying the foundation). At the start there was a single SY full of blocks (32).

Having the extra camp in B speeds up the construction rate of the first 6 layers, for the last 6 layers it doesn't make any difference. The limiting rate for the last six layers is the time it takes to walk up the ramp to the building level of the construction site. This cannot be influenced by the player. The extra mason in C does give extra speed, the problem is a delay at the second level because the carpenter isn't ready. With the extra carpenter in D that problem is fixed. The two extra quarries are not enough to keep up with the building rate, so another two quarries are added in E. The top six layers still take 9-10 months, independent of the configuration, so they are not reported. Increasing the number of masons and camps to 3 in F reduces building time. Using the efficiency criterium (months) x (masons), we conclude F is less efficient than E, and E is as efficient as A. Actually E is a bit more efficient than A because we need relatively fewer quarries. With 4 masons (G) efficiency goes down further because logistics is bad.

Storing 128 blocks in 4 SY's and optimizing lay out (H) it is possible to decrease building time to 10 months, with even fewer quarries. Still efficiency is less than in (E). Using the same optimized lay-out we can bring down the time of the first six layers in (E) to 13, making it by far the most efficient one. If speed is of the essence it is possible to gain just one extra month with 4 masons, 6 camps, 3 carpenters and 4 complete full yards, setting the yard next to the platform, where the sleds leave, to getting and the other 3 to empty. This was the only example in all my tests where 3 carpenters were needed. Apparantly the presence of four masons to fully cover the lower layers is not needed. In the time it takes the later sleds to move up the ramp the stone masons that receive the first load can deposit the blocks and move across the building site to call for another load.

4. Optimal construction

Two carpenters are sufficient to have the construction rate of the ramp meet that of the layers. If both are ready to put in the piece, only one will go, and the other will do the next piece for the next layer. No micromanagement is necessary. This is different from the construction of the scaffolding, where all carpenters that are ready to build come to the construction site, but only one gets to build the piece. Nonetheless all start from zero again with preparations.

The six ground layers are optimally placed in 12 months. That means you need 192 blocks in 12 months, or 16 blocks per month. To produce these by quarries you would need 17, or 12 if you have the altar. You can do with less by having some in storage. If you store say 96 blocks, you only need to produce another 96 blocks in 12 months, and 10 quarries suffice. That is 5 quarries per camp for the optimal strategy (E). For the upper layers the construction rate slows down, and less quarries are needed. It will be difficult though to have a lay-out where all the quarry delivery men bring the block to the SY within the production time, which calls for more quarries.

Together with 9 months for the top layers and the time needed to lay the foundation, with 8 and 3 camps respectively, that brings the fastest construction time down to 23 months for a small stepped pyramid, as compared to 30 for the most efficient strategy.

It seems a bit odd to put so much effort in a detailed analysis of the optimal construction strategy of a small stepped pyramid. The construction of a small pyramid will hardly ever be the main bottleneck in completing a mission, but the larger pyramids frequently are the focal point of the strategy of citybuilding. From this study of the small pyramid we can derive the proper strategy for building the larger pyramids. The general conclusions are:

1. The limiting factor in the groundwork is the movement of the work camp workers over the building site.
2. The limiting factor in the construction of the pyramid itself is the rate at which sleds depart from the SY.
3. At a later stage the time to move up the ramp becomes a more important limiting factor.

This leads to the following rules of thumb:

4. Two carpenters suffice to have the construction rate of the ramp match that of the layers.
5. Use equal numbers of stone masons and work camps.
6. The number of quarries for the production rate to match the construction rate is
( 6 x 4 x [#loads/layer] - [#blocks stored] ) x 1.06 / ( 6 x [#months/layer] )
Another important point is that the upper 12 layers of a medium size pyramid just make up a small pyramid. That implies all of the conclusions above apply equally well to the larger pyramids. For the lower layers conclusion #2 is of relevance, and #3 for the upper layers.

5. Medium and Large stepped pyramid

The study for the medium size pyramid begins with construction of the first layer only. Above we have show that for the ground work 6 camps is a good compromise. During the construction of levels 7-12 we will need four camps and masons (conclusion #3). Two carpenters will suffice. The construction of layers 1-6 takes 18 loads per layer. These were stored before construction. The construction time in months of just the first layer as a function of the number work camps and masons is given by the following table

Five camps and masons is the best you can get, a bit further testing shows 5 camps and four masons is equally fast. For layers 7-12, each requiring 8 loads, four masons appears to be the optimum too, considering the ramp to be the limiting factor. The layers are produced in two months, so 2 carpenters are needed.

The problem is at the supply side. Suppose we have 128 blocks stored. The number of loads per layer is 18 and the number of months per layer is 2. According to the equation (6) we need ( 6 x 4 x 18 - 128 ) x 1.06 / ( 6 x 2 ) = 27 quarries. I tried with 16 quarries and didn't make it. Construction rate dropped to 4-5 months/layer for layers 3-6 because the storage was exhausted and the supply lacking. All in all the delay is 10 months, the next six layers are done in two months each, equally fast as for a stand alone small pyramid. With a storage of 192 blocks (6SY's) the equation gives 21 quarries. Again I tried with only 16. Now construction for layers 3-6 slowed down to 3 months, not because supply was lacking, but because sleds would collect blocks from SY further from the construction site. After layer 7 the rate went up to 2 months per layer, indicating a loss of only 5 months. Only the top layer took 3 months again, because of the long ramp. Construction of the full pyramid took 43 months. That may be reduced to 38 by putting in extra quarries that deliver to the SY next to the platform.

The construction time for the first layer of the large stepped pyramid (32 loads = 128 blocks) as a function of the number of work camps is given below. The number of stone masons is equal to the number of work camps.

Some further testing showed that 5 masons and 7 camps (B) would also do the work in three months, and 8 masons with 10 camps (C) finish in two months. On average 4 of each (A) is still the most efficient strategy, and it would allow for having just one carpenter. Also the number of quarries does not get too high. If we follow strategy (A) the number of quarries with 128 blocks stored according to eqn. (6) is 28, with strategy (B) we need 42 and with (C) we need 55. In practice the number will probably be a little less, as building speed will drop because of other factors.

I tried strategy (B), with 5 mason, 7 camps, 2 carpenters, 20 quarries and 192 blocks stored. The first three layers were constructed in 10 months, just a little below estimate, without supplies lacking, but at layer 4-6 the rate dropped to 7 months per layer. With 20 quarries the maximal production rate is 19 blocks per month, which indeed gives 7 months per layer. The following layers of 18 loads were done in four months each. Obviously the problem is on the supply side here, we really need say the 40 odd quarries to keep up, or store a whole lot more before starting. My design map didn't allow for more than the 20 quarries to be constructed near the building site, so I couldn't do that test. If we do have the possibility to have those quarries nearby, we can expect the pyramid to be constructed in about 60 months.

Results and discussion.

Small: Start with 3 work camps, store 128 blocks from 12 quarries, delete one camp after the ground work. Build 2 carpenters and 2 stone masons. Total building time 30 months.

Medium: Build 5 work camps, store 192 blocks from 16 quarries. Build 2 carpenters and 4 stone masons. Total building time 55 months.

Large: Start with 9 camps, store 256 blocks from 30 quarries. Build 5 masons and 2 carpenters and delete 2 camps. Total building time 75 months estimated.

The following two are just estimates based upon extrapolation of the previous results.

Complex: Start with 12 camps, store 300 blocks from 40 quarries. Build 7 masons and 2 carpenters and delete 3 camps. Total building time 95 months estimated.

Grand: Start with 15 camps, store 400 blocks from 50 quarries. Build 8 masons and 2 carpenters and delete 3 camps. Total building time 120 months estimated.

The Strategy used by Cartouche Bee in her Meidum scenario with a stepped pyramid complex and a small stepped pyramid is 72 quarries, 2 carpenters, 9 masons and 18 work camps. That at least is what is present in the save file after 94 months. I do not know whether she used different numbers at earlier stages and how many blocks she had stored before starting construction. The full scenario is finished in 150 months. Given the above measurements and estimates that's cutting it pretty sharp, mildly stated, considering the time needed to build up the potential work force. The monuments would need 125 months to build, leaving just 25 months before construction can start. This typically looks like a strategy with the emphasis on speed, but the other parameters for the map are equally well optimized. The Meidum mission, with its large space and many resources, allows for such an approach. Based upon my own estimates I would guess the mission can be finished almost equally fast with substantially less work camps, 9 to 12 should be sufficient.

Building the real pyramids in Egypt was a lengthy procedure, so if it takes a long time in the game, due to limitations put in by the designer of the mission, it gives a fair picture of reality.

(Included corrected tables and adjusted quarry production rate)

[This message has been edited by joshofet (edited 04-05-2002 @ 10:23 AM).]