The Millers' Guild needs all aspiring Mathemagicians!

Medieval Damascus has been expanding its crop-growing land because all these European Crusaders are eating too much bread. Unfortunately the millers' guild does not have enough operating capacity to mill it all.

The Shah of Damascus has been convinced of the necessity for a new Super Windmill! The Millers' Guild will need to repay the cost like a normal loan, but the detailed monetary amounts are not important.

The windmill itself has most of the obvious decisions already made, now we must estimate the operating cost to properly estimate our loan details

The windmill itself is:

  • Tower Style Windmill
  • 125 ft tall
  • 6 Sails of cotton cloth measuring 3 ft wide and 35 ft tall
  • avg 35 mph rotating speeds, a persistent wind blowing 24/7

What we need to know to complete the deal

  1. The Millers' guild needs to know what the most cost effective milling stone is for this operation
  2. how often the milling stone and sails will need to be replaced if operation is expected 24/7 with the wind.

We can figure out the approximate cost for the materials.

This is the 11th century. It is notable that you have access to Damascus Steel if it is desirable, but we would not like to use it.

  • 1
    $\begingroup$ The real answer is a plague. Don't have to feed the dead. $\endgroup$ – cde Jan 21 '19 at 22:06
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    $\begingroup$ Damascus steel was an excellent alloy for weapons as the technique in making it made the blade allowed it to hold up in combat, but for other applications, it was not the best metal for many jobs. $\endgroup$ – sonvar Jan 21 '19 at 22:16
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    $\begingroup$ What do you mean by "most effective millstone"? What's wrong with sandstone, which has been used for this purpose since forever? And millstones typically last for quite a long time, they just need to be dressed (resurfaced) from time to time. Have two of them, one in operation, and one ready to replace it. $\endgroup$ – AlexP Jan 21 '19 at 22:54
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    $\begingroup$ Centralized milling means longer (more expensive) transport for bulky unmilled grains from distant fields, and longer transport of milled flour to distant bakeries. In exchange, you get a single point of failure that those pesky crusaders will quickly identify and target...or that a usurper can use to their advantage by discrediting the Shah. $\endgroup$ – user535733 Jan 22 '19 at 2:42
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    $\begingroup$ What do you expect to gain from building one oversized windmill? There's a general theme to the size of mills which suggests that scale does not increase efficiency past a certain point. (Tallest towermill in the UK (Moulton Mill), is 100ft tall) $\endgroup$ – Separatrix Jan 22 '19 at 11:33

For the best millstone option seems to be actually a composite stone, built up from pieces of emery.

While not being the most cost effective exactly these stones are more durable and thus they could be considered more effective because of reduced downtime in operations. Also, given that presumably the stone is large (matching the large construction elsewhere in the tower) the outer velocity of the stone would move at higher rates than a smaller stone might, which matches the real-world development of this type of milstone.

Unfortunately this millstone was developed In the 1800s. However this development seems to be because of the necessity of tougher stones and not because of the craft of making the actual stone being restricted by the period.

Actually estimating the cost of such a stone would be wildly dependent on the local (or relatively local) supply, industry of harvesting the stone, transportation logistics, and other matters that you can easily adjust to your needs. The stone itself, generally speaking, historically was not particularly rare or expensive.

As to how long the supplies will last, I can't find any good data for that. Since modern flour milling following historic practices is almost exclusively for novelty or artisan sake, it could be that this information is largely lost to time. In Kodak, Tennessee, for example, there is a still functioning water mill where you can buy (somewhat crudely) ground flour. Even then, watching the flour mill work through the old, decrepit, wooden-framed windows, you can see a number of components have been modernized (ranging in apparent age from the 40s to the 80s). To this end there simply might not be information out there about this to extrapolate upon for your question, nor historic record that people bothered to keep.

I would imagine, however, that the sails would last in the measure of years, and the stone would measure in the measure of either months or years, even with 24/7 operation, with the caveat that fierce storms may reduce the sails' lives.

  • $\begingroup$ Could you please add a picture or reference to such a composite stone? How does it differ from a traditional milling stone? $\endgroup$ – Elmy Jan 22 '19 at 7:16

As to the sails I wouldn't expect them to last much more than a single season, as both cotton and linen degenerate rather quickly when exposed to the elements.

Also the expectation to run the mill 24/7 is... Unrealistic. There is a very important reason that no miller would even consider working past evening. And those who did would quickly learn how powerful dust explosions could be.

Also sails would require frequent maintenance or their condition would deteriorate rapidly, and so would wooden elements of the drive.

As to the millstones, there wouldn't be many options out there and you probably would have to use multiple smaller units running in parallel.

  • $\begingroup$ A windmill relies upon the wind. They don't work 24/7 only because the wind isn't always blowing. If the wind picked up in the middle of the night, millers got up and started work because that is when they had wind and could do their job (get paid) despite the risks (which can be mitigated with a little care - they weren't stupid). $\endgroup$ – pluckedkiwi Jan 22 '19 at 20:36

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