About a year ago, I made several additional preliminary housing block designs, but was dissatisfied with them all. The southwest spacious manor block design was complicated by not knowing how many cattle ranches would be built and whether lettuce would be stored nearby. The city center design had similar complications. Those designs, while not final, are close enough to be used for estimates such as the distances from weavers to mortuaries.
Soon after restarting work on Itjtawy, I realized that I had miscounted the number of houses back in reply #11. I decided to redo the housing and consumption calculations. Then, instead of resuming housing block design, I tackled most of the remaining industries.
Housing AgainMy estimate for the number of workers has gradually increased, so I decided to reduce the fraction of scribes to just over one-third. Assuming that there are 5 common manors in the small block and 1 in the block near the west bank ferry terminal, the new expected housing mix is:
10 stately manors,
10 elegant manors,
42 spacious manors,
6 common manors, and
163 fancy residences,
for a total of 231 houses (including 68 manors) with 22532 people.
Pottery consumption is 5544/year. The 11 planned potters will be sufficient, with 668/year overproduction for requests.
Beer consumption (with 1 senet house) is around 6264/year. The 13 planned breweries will be sufficient, assuming that the senet house isn't too far away. Barley imports of 6264/year should be possible, but are very close to the maximum of 6500/year.
Linen consumption (with 4 mortuaries) is around 8616/year.
Luxury goods consumption is reduced to 1632/year.
Papyrus consumption (9 schools plus 1 library) is unchanged, around 4746/year.
Grain consumption is 26124/year.
Meat consumption (5 common manors plus 14 fancy residences) is 2112/year.
Combined lettuce and pomegranate consumption (houses not getting meat) is 24012/year. The amount of each depends on how many fancy residences are on each bank.
Straw consumption (cattle ranches producing the meat plus 8 brickworks) is 3242/year.
Changing a few planned spacious manors into fancy residences will make designing some of the remaining housing blocks easier, since those houses will need less space and desirability.
Farm TypesI tentatively chose the type of each farm. A few farms may change types later, when I finish designing the housing blocks (and determine the exact consumption of each food), make careful estimates of floodplain farm productivity, and decide the storage space for each food.
Grain farms will be a majority on the west bank, those that are closest (by road) to the southwest, to minimize the distance to cattle ranches (which won't be very far from the brickworks). Grain farms will include 16 meadow farms of 44%-48% fertility, and assuming that they are harvested twice/year, each of them will produce 8/year less than it would if harvested once/year. Therefore, total meadow farm production will be only 39656/year.
Flax farms will be on the northwest meadow, just north of grain farms, to minimize the distance to weavers. There will be 14 of 42%-43% fertility and 5 of 44%-47% fertility. Total flax production will be 9064/year, 448/year overproduction for flax or linen requests.
Lettuce farms will be scattered--a few on northwest meadow, more on northwest floodplain, all of the farms on northeast floodplain and meadow, and some on southeast floodplain. (There will be no southeast meadow lettuce farms, since they would be a long distance (by road) from the lettuce storage on the west bank, and their cart pushers (unlike floodplain farm cart pushers) must return to their farms before the next harvest.) Since most lettuce farms will be on the floodplain, considerable lettuce storage will be required (in case there is a series of terrible floods), making the west bank even more crowded. Pomegranate farms will be all of the southeast meadow farms and some of the southeast floodplain farms.
WeaversAt full efficiency, a weaver produces 100 linen every 34 production increments. A production increment is 2 days (1/192 year), so the linen production of a weaver at full efficiency is 100*192/34 = 564.7/year, and the production of 16 weavers would exceed the required 8616/year by about 419/year. But weavers will not be running at full efficiency, for several reasons, so more weavers will be needed.
Some weavers may receive an odd lot (not a multiple of 100) of flax. When a weaver contains over 100 flax, more flax is not delivered to it. When a weaver with less than 200 linen finishes producing a batch of 100 linen, it will not start producing again until more flax is delivered to it. I haven't seen more than about 1/4 of a large group of breweries or weavers with an odd lot, but the conditions in Itjtawy might be different enough to change that behavior, so I'll assume the worst case: every weaver will have an odd lot of flax.
The production with an odd lot depends on the time spent to resupply the weaver with flax. There will be 4 flax storage yards, with a maximum delivery distance of 18 tiles and an average of around 9 tiles. If a cart pusher always started delivering flax (going 1.7 road tiles/day) as soon as a weaver needed it, this would mean a maximum delivery time of around 11 days and an average of around 5 days. However, sometimes a cart pusher will not be immediately available. This shouldn't happen too often, but I'll assume that it will, with a typical time from when linen is produced to when flax is delivered to be 11 days. Therefore, because of odd lots, weavers will typically stand idle for 5 production increments each cycle, and the linen production of a weaver should average 100*192/(34+5) = 492.3/year.
Some weavers may be supplied flax directly from farms instead of from storage yards, which could delay starting the next batch of linen. The only significant effect will be at the harvest, since at other times cart pushers with flax will already be near weavers. The average distance from a flax farm to a weaver is about 36 road tiles. Therefore, a weaver supplied by a just-harvested flax farm would typically stand idle for about 10 production increments instead of 5. However, such a weaver would not have an "odd lot" for at least the following production cycle (and probably for several more). Therefore, under these assumptions, delivery of flax directly from farms will not reduce average production.
A weaver may deliver linen directly to a mortuary. Assuming the worst case, weavers will try to deliver all of the linen that mortuaries need, an average of 7.68 deliveries/year to each mortuary. Let's first consider the effect on linen production if only weavers deliver to mortuaries, and then consider the complications of storage yard deliveries.
Linen production will not be affected by deliveries to the 2 closest mortuaries (in the northwest block and the best block). For deliveries to the other 2 mortuaries, I'll assume the worst case of delivery from the most distant weavers. The average road distance from the 4 most distant weavers to a mortuary in the southwest spacious manor block is about 101 tiles (requiring about 119 days for a round trip) and to a mortuary in the other spacious manor block (next to the best block) is about 76 tiles (requiring about 89 days for a round trip). A weaver that delivers to the most distant mortuary will not be able to deliver again for 60 production increments, standing idle for 21 production increments in addition to the usual 5. A weaver that delivers to the second most distant mortuary will not be able to deliver again for 45 production increments, standing idle for 6 production increments in addition to the usual 5. If only weavers deliver to mortuaries, the lost linen production is 7.68*(21+6)*100/34 = 609.9/year.
Now let's consider the negative effects of storage yard deliveries to mortuaries. This occurs when the storage yard cart pusher delivers his linen to a mortuary first, so the weaver cart pusher cannot deliver all 100 linen, requiring the weaver cart pusher to deliver the remainder somewhere else. As usual, I'll assume the worst case: weaver cart pushers will never be able to deliver 100 linen to a mortuary. Storage yards that accept linen will be placed so that a weaver cart pusher can deliver his remaining linen on the way back to his weaver without going any extra distance. However, sometimes a weaver will try to deliver his remaining linen to another mortuary. I think that the probability of a weaver cart pusher at a given mortuary delivering to another mortuary would be the fraction of linen consumed by mortuaries excluding the given mortuary, or (4-1)*768/(8616-768) = 29.36%.
Weaver delivery to a second mortuary affects all 4 mortuaries. We'll assume that all extra travel by weaver cart pushers going to another mortuary causes lost production. For each mortuary, I estimated the extra distance required to return to the weaving area caused by detouring to each other mortuary. Over the 12 cases, an average of 24.25 production increments are lost, for a total lost linen production due to weaver deliveries to a second mortuary of .2936*4*7.68*24.25*100/34 = 643.3/year.
In addition, a weaver cart pusher might deliver to a third mortuary, with additional lost production of .2936*643.3/year. And he might deliver to a fourth mortuary, with additional lost production of .2936*.2936*643.3/year. He will (of course) run out of linen at some point, but (for simplicity) we'll assume that this can go on indefinitely. Summing the infinite series, the total lost production caused by weaver deliveries to multiple mortuaries is 643.3/(1-.2936) = 910.7/year.
But there is also a positive effect of storage yard deliveries to mortuaries, since the total amount of linen delivered to a mortuary will, on average, be greater than the 100 linen that the mortuary cart pusher would deliver by himself. I expect that the 2 cart pushers will deliver an average of a least 120 linen. This means that mortuaries will need to be supplied no more than 5/6 as often, and the lost linen production from deliveries to mortuaries can be reduced by 1/6. The total lost linen production due to weaver deliveries to mortuaries is (609.9+910.7)*5/6 = 1267.2/year.
Stop for a reality check. Is the positive effect of storage yard deliveries to mortuaries greater than the negative effect, which would invalidate at least one of my assumptions? No, not even close, so the assumptions are still valid.
Considering everything (that I can think of), the number of weavers required to produce 8616 linen/year is (8616+1267.2)/492.3 = 20.08. 21 weavers will be built, with overproduction of 455/year for requests. (Just in case I missed something, I'll leave space for 1 more weaver.)
Papyrus Delivery Storage YardsImported papyrus will be purchased from caravans at 2 storage yards (set to "Accept all" papyrus) in the southwest. Papyrus makers may deliver to those storage yards, but will deliver directly to a school or library that is running low. Cart pushers from those storage yards and from other storage yards (set to "Get 1/4" papyrus, perhaps also filled with an unused good) will deliver to the schools and library. Should the papyrus storage yards have enough capacity to deliver all of the papyrus that the schools and library use? If we ignore requests then the answer is no--being able to deliver the maximum imported papyrus (2500/year) would be sufficient. But I want Itjtawy to be able to satisfy requests that aren't too large.
Excess papyrus will accumulate, so papyrus requests will simply be dispatched. I'll also try to accumulate excess reeds, but that may not happen--there may be enough papyrus makers to use all gathered reeds, and filling the papyrus storage yards may reduce papyrus imports instead of reducing papyrus production. Therefore, a reeds request may require stockpiling reeds (which will shut down papyrus production) temporarily. When reeds are stockpiled, storage yard cart pushers should keep the schools and library supplied (at least enough to prevent housing devolution), as long as papyrus supplies last. (Since reeds will rarely if ever be stockpiled, I won't be as careful with papyrus delivery calculations as I tried to be with linen delivery calculations.)
For these calculations, I chose tentative locations for the schools in the northeast and east housing blocks (which I haven't started designing). Fortunately, each of those blocks has to give labor access to quite a few buildings, so their locations can't vary very much.
I'll assume that the average delay at a ferry crossing is equal to the crossing time, which is reasonable if the ferry traffic isn't too heavy. (If there is too much cross-river traffic for the ferry to handle then the city will fall apart, so I won't worry about that now.) Ferries and cart pushers appear to travel at the same speed. Since a ferry crosses the river in 17 tiles, a cart pusher river crossing will be considered to be equivalent to 34 road tiles.
I'll assume that the papyrus storage yards will be among the 9 planned storage yards on a narrow loop road (along with 5 brickworks) getting labor access from the small block. (Anywhere else that the papyrus storage yards may be located should be closer, on average, to the schools and library.) Of those storage yards, the 2 that are farthest north will "Accept all" papyrus. Weighting the library by 1.5 (since it consumes 1.5 times as much papyrus as a school), the average papyrus delivery distance from those 2 storage yards is 96 tiles, for a average round-trip delivery time of 113 days. A cart pusher may wait up to 2 days before starting delivery, so we'll assume that 100 papyrus is delivered every 115 days, for an average papyrus delivery rate (by an "Accept all" storage yard) of 100*384/115 = 334/year.
If a papyrus distribution storage yard is filled with an unused good (such as plain stone), then both cart pushers will be active. Each cart pusher will usually go to an "Accept all" storage yard and pick up 400 papyrus, return to his storage yard, deliver to a school or library, deliver to another school or library, perhaps deliver one or more additional times, and (when empty) return to his storage yard. If total papyrus deliveries are barely enough, then schools are likely to have no more than 100 papyrus when it is delivered, and the cart pusher will usually deliver papyrus to only 2 buildings. The average distance from one school or library to another is considerably less than the average round-trip distance from the storage yard to a school or library, so the cart pusher will usually take less than twice as long to deliver 400 papyrus as an "accepting" storage yard cart pusher takes to deliver 100 papyrus. The cart pusher will sometimes deliver to 3 buildings, and will sometimes pick up less than 400 papyrus, but those shouldn't happen too often, so I'll assume that their effects can be compensated by increasing the average delivery time to twice that of an "Accept all" storage yard. Each of the 2 cart pushers delivers 4 times as much papyrus in twice as much time as an "Accept all" cart pusher, for an avererge papyrus delivery rate (by a "Get 1/4" storage yard filled with an unused good) of 2*4*334/2 = 1336/year.
Not filling a papyrus distribution storage yard with an unused good has the advantage that 3/4 of the storage yard can store useful non-deliverable goods (such as pottery, bricks, or meat). But only 1 cart pusher will be active, who will usually deliver 100 papyrus to a school or library, return (empty) to his storage yard, go to an "accepting" storage yard and pick up 400 papyrus, return to his storage yard and drop off 100 papyrus, deliver to a school or library, deliver to another school or library, perhaps deliver one or more additional times, and (when empty) return to his storage yard. Using the same reasoning as in the previous paragraph, the cart pusher delivers 4 times as much papyrus in 3 times as much time as an "Accept all" cart pusher, for an average papyrus delivery rate (by a "Get 1/4" storage yard not filled with an unused good) of 4*334/3 = 445/year.
As the stored papyrus runs low, only 1 "Accept all" storage yard may hold papyrus. Therefore, the "Get 1/4" storage yards should deliver 4746-334 = 4412/year. As a minimum, I'll probably have either 4 "Get 1/4" storage yards including 3 filled with an inert good, or 6 "Get 1/4" storage yards including 2 filled with an inert good. I may decide to have a bit more than the minimum papyrus delivery capacity.
Papyrus MakersRoughly half of the papyrus used (at least 2246/year, preferably around 2466/year) will be locally produced. Some or all of that will be delivered directly to the schools and library by papyrus maker cart pushers. To minimize the distance to most of the schools and the library, the papyrus makers will be near the east bank ferry terminal. Using assumptions similar to those in the previous section, the average delivery distance from a papyrus maker to the schools and library is 88 tiles.
A papyrus maker cart pusher may not be able to deliver all of its papyrus to the school or library, if a storage yard cart pusher delivers papyrus there first. I don't want to make "worst case" assumptions similar to those made for weavers, since that will result in far too many papyrus makers. I think it highly likely, and will assume, that an average papyrus maker cart pusher will deliver its 100 papyrus by going to 3 buildings (schools, library, or "Accept all" papyrus storage yards). Since the average distance between those buildings (whether or not the storage yards are included) is less than the average round-trip distance from the papyrus makers to the schools and library, an average papyrus maker cart pusher will deliver its papyrus and return in less than 3*2*88/1.7 = 311 days. Therefore, an average production cycle will be less than 156 production increments, for an average papyrus maker production of more than 10*192/156 = 123/year.
20 papyrus makers should be plenty, and will be planned. However, I won't build that many unless I determine that they are really needed, which probably won't be decided until after the library is built (when the city is nearing completion).
Reed GatherersThe reed gatherers will be built near the center of the marsh, to maximize reed production. The average distance from the reed gatherers to the 8 most distant papyrus makers is 55 tiles, so an average reed gatherer cart pusher will deliver 100 reeds and return in 65 days. Therefore, when sufficient reeds are available, 100 reeds will be delivered every 33 production increments, for an average reed gatherer (building) production of 100*192/33 = 582/year.
5 reed gatherers will be built. Assuming that the marsh regenerates as fast as expected, the reed gatherers will produce the desired 2466/year, plus around 444/year extra until the marsh is fully harvested.
[This message has been edited by Brugle (edited 06-03-2004 @ 07:26 PM).]