So, the most fundamental question that needs to be asked and answered is simply, How many manors does it take to support an urban population of a certain size? My gut feeling is that the rural population must exceed the urban by about 3:1. That is, an urban population of 5000 would require a rural population of about 15,000 - or, assuming an average manor has a population of 150, 100 manors. Harn and Venarive in general has a rural:urban ratio of a little less than 10:1, which indicates that there is potential for urban growth, and is consistent with the oft observed underpopulation of the world.
Tough question. I'd guess more than say C 1100AD England, as Harn uses a less efficient 2 field rotation. On the other hand, I think the grain requirments would not be as high as 12th century England - because with the 2 field system, more land is theoretically used for pastorage, therefore more livestock, hence more meat/dairy in the diet.
To reflect this along with the rules for HarnManor - the 80% grain diet proposed should probably be more in the 70% grain, though if anything like terra ale would constitute a larger portion of the diet.
The other thing is that the percentage of land under plow can vary - but should it be a random variance, or would lands around cities have larger percentages of arable cropland?
My guess is it varies more by geography, or more specifically type and quality of land, which would also seem to mean that land closer to a city would be of batter quality to allow a city to be built there. Last but not least, I think (am not sure) that in general lands near rivers are more fertile than those not as close to rivers, which would mean more of the products of better quality land are easily transportable.
Just a quick off the cuff though, with some of the following assumptions:
1) Harnic Diets are 70% grain, 10% Ale for a total of 80% grain.
2) Urban Diets located near a large body of water are a bit different, the 20% fish Harnplayer mentions, which would then indicate 20% Fish, 64% grain and 14% "other".
3) Harnic production of grain is similar to 14th century England, other than less land being under plow due to the 2 field rotation
4) Manors around cities are of the Harnmanor averages for % of arable land and land quality.
5) "spent" Barley used for ale will also be used for human and livestock feed, so the total calories needed for ale will only require a 1 to 1 ratio of barley calories, as the spent grains will still be used, just will have less calories as grain (there are recipes for bread using spent barley).
6) For simplicity, grain will be a mixture of 1/3 oats, barley, and wheat, their net production per acre and calories per pound averaged equally. This results in 360 pounds per acre, and 1600 calories per pound (359 and 1599 actually)
A survey of English manors show these three grains being about equal in production, with rye being a very small portion.
So, what we need to figure is the average amount of grain produced by a manor, the amount needed for personal consumption, the amount fed to lifestock, and the excess grain per manor minus spoilage.
At 10,000 Calories per day, A harnic Household needs 3,600,000 per year. If urban populations bodies of water 64% grain, that is 2,304,000 calories from grain, which is 1,440 pounds of grain per husehold.
Rural populations would probably be closer to the 80%, or 1800 pounds of grain per household.
An "average" Harnic manor is 1800 acres, 20% of this being under plow on average, or 360 Acres. Harnmanor includes hay in cropland - this is not a seeded and harvested grain type product, but from pastorage lands that are not grazed upon. Taking this out of the equation, Harnic crop mix is about 60% grain, so 216 acres.
216 acres is 6 acres per household on the manor. That would be a net yield of 2160 poounds per household. They need 1800 pounds, so the net surplus is 360 pounds per household.
Pretty simple to factor here - 1440/360 = 4 huseholds rural surplus to feed one urban household. Of course, we are not factoring any grain for livestock in here, which would change this dramatically I would think.
I would think at least 1/3 of this surplus is going to livestock grain - or 4320 pounds of grain per manor. This actually IMO is a bit low. But this changes it to 6 rural housholds to support one urban household.
And we have not factored in spoilage, though the manor surveys these numbers are based upon may have already factored this in (it is thought that some of the production numbers were after some "theft" by the serfs doing the threshing, harvesting, etc.).
So with these numbers, a city of 5000 needs 30,000 serfs to support it, or 6000 serf households. That's about 166 manors and 300,000 acres.
This to me seems rather excessive, but the modifications I have made to stats from Harnmanor have actually increased agricultural production for the most part, such as the crop mix.