Monday, September 16, 2019

Castle Construction Times

Chateau Gaillard
Previously I looked at some real-world data for medieval castle construction costs and found, somewhat surprisingly, that if we read the costs from OD&D in silver pieces (groats; 1/3 shilling) that they're quite close to the actual prices involved. I'm still jazzed at how sweet that was!

But one thing I couldn't figure out at the time was a way to estimate castle construction times. The real-world data was all over the map and not consistent; a small single keep at Peveril could take 2 years; medium to large castles like Orford or Dover took 8 or 10 years; and then on the upper end the "vast" castle of Gaillard which cost twice as much as Dover (and on a difficult-to-reach precipice) itself took only a lightning-fast 2 years. So I left that puzzle for a later day.

Well, that day is today. The players in my ongoing campaign are advancing in experience and treasure enough that they're starting to ask about options for castle-construction. The night of this writing I sat down and played with some numbers and discovered a remarkably simple rule that gives fairly realistic results. Here it is:

The base time for construction is the square root of the OD&D total cost, read in weeks. If speedier construction is desired: Each multiplied cost factor divides time by a like amount, up to quadruple cost/speed.

Let's compare that to the real-world data; it's a small sample size, but for game-design purposes I'm comfortable making a decision on this basis. Gray and yellow highlights are things added to the spreadsheet since last time. The bottom row for Gaillard is special, because it's the only one where we're applying our quadruple speed-up rule.

Castle Construction Time Estimates

In the 8th column, we have our squart-root estimate for time in weeks. For example, with the top row of Peveril, we take the square root of the D&D cost (identical to real cost in this case): sqrt(12,000) = 110, rounded to nearest whole number. Dividing that by 52 weeks in the year comes out almost exactly to 2 years, exactly the real-world time it took to build it (in the 4th column). Doing that for Orford and Dover likewise comes out within 1 or 2 years of the actual figures.

Now let's look at the last case of Chateau Gaillard. Just looking at a map of the place, it looks smaller than Dover Castle (compare "Details" in the 5th column). My estimate using the OD&D tables it that it should cost about 208,000 sp or so; and construction time ought to be sqrt(208,000)/52 = 456/52 = 8.8 years or so. But to this we will apply a speed-up factor of 4, quadrupling both price and speed of construction; then the price jumps to 832,000 sp and the time drops to 2.2 years. Note that these figures now align with the real-world prices: Gaillard cost some 720,000 groats (i.e., 12,000 pounds) and did indeed get built in just 2 years time.

Consider: Gaillard was the major work of Richard the Lionheart, who worked feverishly to stake the world's finest castle directly in the heart of his French enemies. He personally supervised the work and drove laborers unrelentingly, even through reported rains of blood. Said one observer: 

... the king was not moved by this to slacken one whit the pace of work, in which he took such keen pleasure that, unless I am mistaken, even if an angel had descended from heaven to urge its abandonment he would have been roundly cursed.

Note also at least one nifty side-effect of our square root rule: Designing a large castle up front will take overall less time than if you build a small construction and add to it over time. Say, two separate rounds of 10K construction would take sqrt(10K) * 2 = 100 * 2 = 200 weeks. But one round of 20K value construction would be just sqrt(20K) = 141 weeks. This sort of jives with the classic engineering experience that it's more efficient to get a design right early rather than late; and provides a neat in-game dilemma on whether a PC should get started with something small with available resources, or wait to gain more treasure so as to start on a larger (and ultimately faster) construction.

(N.B.: There's a bolt from the blue waiting for the first person who suggests Agile castle construction methodology.)


35 comments:

  1. Split your stories. What is the smallest piece of a castle that has value to the user?

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  2. The gamist in me says, “let the castle be finished in one calendar year.” This is what I will do when my first player builds a castle.

    But as usual your application of real world data and smart maths makes so much sense from a simulationist standpoint.

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    1. I think sometimes in these case (particularly big-ticket campaign items) letting the facts of reality lead me in a place I wouldn't have made up on my own provides freshness and productive struggle.

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  3. "If speedier construction is desired: Each multiplied cost factor divides time by a like amount, up to quadruple cost/speed."

    Well, Dwarves, Profit Minded Stone Giants, and binding earth elementals ain't gonna come cheap.

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    1. Oh wow, nice. Now I'm fantasizing about different pros/cons to pursue for each of those. :-)

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  4. The things to keep in mind that castles were fantastically expensive especially considering they were not productive in of themselves.

    So it likely the widely variable construction times doesn't represent the true time but rather that the builder spaced out their outlays over a period of time to match what they had in revenue.

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  5. What Robert says. Also, my understanding is that (at least in northern Europe) construction pretty much stopped during winter (because e.g. mortar wouldn't set, ground too hard, etc). So probably productivity is higher in summer, standard in spring/fall (maybe lower than expected because of planting & harvest requirements), and very low in winter.

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    1. I'd like to see a citation for that. Related: I'd gotten the impression that in that same area, travel basically stopped in the winter. But when I pursued the academic literature on that, the data shows pretty strongly it was a myth.

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  6. I can't recall where I read this, but my understanding has been that medieval peasants owed a certain numbers of days of free labor to their lords - in pre-Black Plague Europe, anyway, peasants in general had greater bargaining power due to the labor shortage and began to wrest better terms from their landlords starting in the 14th century. But I digress. Point being, to the best of my knowledge most castles would be built using this free labor, keeping costs down but limiting its speed based on the number of days' labor that a lord's peasants collectively owed. Whereas for Chateau Gaillard, King Richard was presumably using hired laborers since it wasn't in England, so the cost skyrocketed, but it also meant that he could have construction progressing continuously for 6 to 8 months out of the year instead of only 1 or 2.

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    1. I'll wager that some/many of those peasants also saw the castle's construction as benefiting them with protection down the road. But most peasants probably weren't highly trained craftsmen. So, lots of 'dumb' labor for clearing land, digging moats and foundations, and filling walls with rubble. But the finished stonework and carpentry are going to be expensive and time consuming.

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    2. The word you're looking for is corveƩ. Peasants would be required to work approximately one day out of every 12 on public works, or about 30 days a year.

      It sounds like a lot but peasants actually didn't work a lot of days in the fields - something like seven months.

      It was the exception rather than the rue for a peasant to labor on the lord's private property but undoubtedly it happened. More frequently it was to maintain public works such as roads and ditches.

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    3. Sure, I never said that it was excessive or coerced, just that it was owed. The most detailed estimates I've read are that medieval commoners worked between 240 and 250 days out of the year, which is actually pretty close to what you work at a modern Monday-Friday job, just the work days are distributed differently across the calendar. And for sure some experts were needed in addition to peasant labor, which is why even the (relatively) cheaper castles were still expensive. But actually, the daily rates for carpenters and masons weren't that much higher than for unskilled laborers. When labor was plentiful and cheap, a carpenter might make double what a laborer did, and a mason 2.5 to 3 times as much. However, at times when the labor supply was lower, such as post-plague, the rates might be something along the lines of 4 pence per day for a laborer, 5 pence per day for a carpenter, and 6 pence per day for a mason.

      Point being, just needing to hire any kind of worker using actual money, instead of receiving labor as a type of rent payment, was expensive no matter what - and it sounds to me like King Richard was probably relying exclusively upon hired hands for Gaillard.

      Also agreed that a peasant's labor was usually allocated to more mundane works like roads; castles lasted centuries. As a ballpark figure just from ones that I've anecdotally looked into, a smaller 12th-century castle might be expanded/improved somewhere around the 15th century, and by that time the peasants were almost certainly paying their rents in coin rather than in goods and services. Between 2 and 10 years spent castle-building out of 300 or more is quite a small percentage.

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    4. It's something that I definitely wrestle with from time to time in regards to issues like this, early knights-service versus later scutage, levies vs. standing army, etc. There are times that I want to model all of those systems that feed into support of medieval armies.

      But the truth of it for our D&D games that practically all of us play PCs as showing up with no land or fiefs and big sacks of coins instead. So it makes for a pretty crisp simplification to assume some kind of late-era economy with everything based on cash payments. Gives us a thinner system and interfaces with our PCs better in that regard.

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    5. That's fair to just assume all labor will be hired; my real point was conjecturing that much of the true cost of those first three castles was obfuscated by non-hired labor. And that Castle Gaillard might have cost nearly the same amount of money to build whether it was built in 2 years or 10 years.

      My hypothesis is that for "cheap" castles that leaned heavily on peasants' manorial labor obligations, construction time was largely a factor of that labor supply. Meanwhile, for castles relying on hired laborers it would be a matter of financial throughput rather than absolute cost - if you could only afford to devote £2000 per year to building, then a castle equivalent to Gaillard would take 6 years to complete.

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  7. Slower or no construction cold climes during winter, but also slower or no construction in warm climes during summer.

    I know many departments of transportation reschedule roadwork during the summer for overnights (probably not an option for castles) or pass altogether. There are other summer weather factors too - hurricanes and just summer thunderstorms. So at the extreme northern/southern limits I'd bet that there's an equal amount of time lost to weather/climate.

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    1. I don't think that summer slowdown would hold in Europe. Hurricanes are few and far between there, and when they do get something one it's nowhere near as bad as what hits the US South. As for thunderstorms, the warmer parts of Europe are along the Mediterranean, and have a reputation for very dry summers. As for the DOT scheduling construction at night, that's primarily due to the fact that there's less traffic as night, so they can work on three lanes out of a four-lane highway without causing a 20-mile traffic jam. They're out during the day if it's only a one-lane job.

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    2. Admittedly for me I might say that those two characteristics mostly cancel each other out. Maybe. :-)

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  8. I prefer the waterfall method of castle construction, where a castle is built on a suitably scenic waterfall.

    (Your math more-or-less lines up with my math: https://coinsandscrolls.blogspot.com/2017/09/osr-building-castles.html)

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    1. Why, I oughta... oh, actually that's an extremely pleasant idea.

      And a very nice system on your blog, thanks for sharing that!

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  9. I'm assuming you take the square root of the cost because you're dealing with square footage... so if you were building a wall instead of a castle, you'd be dividing the cost instead. Although I'm thinking you could work out a standard unit of square footage that would make sense in the game and just multiply the number of areas you are building in by the base time.

    I would probably have to go that route, since I came up with an idea of estimating costs by using the cost of a ship as the base cost and asking "how many people are going to be housed in the structure?" and adjusting the cost accordingly... then doubling or tripling the cost because it's stone rather than wood. But I never got to the point where any players actually needed to build anything, so I never worked out building times, anyways.

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    1. Actually, no, it's just a simple mathematical model that seems to match the real-world time data pretty well.

      Or in other words: Perhaps more research needed for why that's the case.

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  10. To add to my previous conjectures that, if the PCs are paying entirely in coin and don't have any feudal peasants contributing labor, that something on the order of 3 to 4 times the OD&D price might me needed:

    From the UC Davis Medieval Price List web archive (http://medieval.ucdavis.edu/120D/Money.html) there is a section about Langeais, a rectangular, tapering stone tower built in 992-
    994. The dimensions at the base were 17.5
    meters by 10 meters; the height was 16m - so about equivalent to the Peveril Castle tower.

    Labor Costs, in Average Working Days (AWD):
    procurement: 14 250
    transport: 2 880
    labor:
    unskilled: 63 500
    mason: 12 700
    smith: 1 600

    Later in the list, they give pay for a laborer circa 1300 as "£2/year max," which would translate to 2d/day. Rolling the year back to 992, let's assume half the pay, or 1d/day for simplicity. The mason and smith might earn 2d/day, and I'm unsure on the procurement and transportation costs, but I've read accounts qualitatively claiming that it was costly to transport goods in the medieval period, so let's say those are at least twice as expensive as unskilled labor as well.

    We end up with labor costs in the ballpark of 120,000d = 10,000s = £500. That doesn't even count the cost of any materials that the lord was unable to extract from his own lands and had to pay for. So adding in an unknown amount extra for material costs, it's looking like at least triple the £200 for Peveril, and over 100 years earlier as well so possibly some inflation occurred during that time, perhaps making the inflation-adjusted cost of Langeais in 12th-century pounds closer to £800 - or 48,000 coins in your 1 groat = 1 silver piece system.

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    1. That's great data, I'll have to think about that. Thanks so much for pointing that out!

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  11. Here's some more data points:
    https://erenow.net/common/castle-a-history-of-the-buildings-that-shaped-medieval-britain/3.php

    Rochester Keep.
    Cost ~£3,000
    Time (actual) 8-10 years
    Time (predicted) 8.15 yrs

    Dover Keep
    Cost £4,000
    Time (actual) 10 years
    Time (predicted) 9.4 years

    Orford
    Cost £1,500
    Time (Actual) 6 years
    Time (Predicted) 5.7 yrs

    That's from that article. All of those times match the formula about perfectly.


    Flint Castle (https://en.wikipedia.org/wiki/Flint_Castle)
    Cost 6068L
    Time (actual) 9 years
    Time (predicted) 11.6 years
    - Pretty close!


    Two More: http://www.castlesandmanorhouses.com/architecture_08_building.htm

    Rhuddlan Castle
    Cost £9,000
    Time (Actual) 5 years
    Time (Predicted) 14 yrs
    - Possibly a rush job? Probably a hired workforce.


    Beaumaris Castle (part 1)
    Cost £11,000
    Time (Actual) 5 years
    Time (Predicted) 15 yrs
    - Hired workforce of ~2500 personnel, wages of 270L/week (for first summer; work slowed second summer, then came to a trickle years 3-5). The wages thus account for somewhere between 3.5K pounds for the first summer alone.

    This is an interesting case. A quick look at the plan of the castle indicates six large towers (10K SP each in OD&D), two gatehouses (3K SP each in OD&D), 12 small towers (4.5K SP ea) and about 2000 feet of wall (75K SP)... As a WAG, about 2350L in construction costs. That sort of castle should take 7 years to complete. That's pretty close to 5 years. Also bear in mind that the "phase 1" of construction was only the "80% solution;" constructed dragged on for another 30 years at a slow rate to get to the finished version I priced out in OD&D costs.

    WHAT ABOUT CHEAP CASTLES?
    Another common reference point is the Norman Tower House, probably costing about 10 pounds and taking a year to throw up. Our formula indicates 24 months.

    Also on the cheap end is a motte and bailey. Paying cash wages for all labor, one example costs 20 pounds and took about 4 weeks for a crew of 50 laborers.
    http://www.castlesandmanorhouses.com/architecture_08_building.htm

    Our formula suggests a time of 34 weeks, which is way longer than the actual Motte and Bailey. Tentatively, this could suggest that the formula works for stone castles, but perhaps wood & earth construction is way faster (10x faster?). Alternatively, if we assume that like Beaumaris, the actual castle cost is 1/4 of the price (with 3/4 being hired labor) then we get a construction time of 17 weeks... perhaps a smaller crew of about 15 laborers?

    WHAT ABOUT GRAND PROJECTS?
    At the other end of the spectrum, Wiki says:
    "Edward I's campaign of castle-building in Wales cost £80,000 between 1277 and 1304, and £95,000 between 1277 and 1329;"
    (also here http://www.castlesandmanorhouses.com/architecture_08_building.htm)

    80K over 27 years (actual) vs. 42 years (predicted)
    95K over 52 years (actual) vs. 45 years (predicted)

    Those values are at the outer end of our formula but even so they're not completely out of there.

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    1. CONCLUSIONS
      - The formula given seems to work for "typical" construction, or at least be in the ballpark.
      - The formula probably works when corvee labor is available for the job with minimal hired workers.
      - Use of a hired (vs. local) labor force seems to be a major cost driver. Edward's Welsh castles were "rush jobs" and had to use imported labor. You can see the impact that causes on the cost directly with Beaumaris. We showed there that at least 2/3 of the cost (3500L the first summer, 3500L more spread over the next four summers) were due to labor. We also showed that our formula accurately predicts the construction time when you look at the finished works and price them out in OD&D values. This is a solid data point backing up a previous poster's suggestion that if sufficient free-of-charge labor isn't available, costs will double or treble.
      - The nature of the formula suggests that as projects become larger, efficiency grows higher. On one hand, this makes sense -- larger projects probably justify investmentment in specialized tools, expert craftsmen, etc. On the other hand, there are probably some C2/management bottlenecks that cause efficiency to come down. Anyone who has worked on a large enough project knows that even with modern management and workflow efficiencies there are some productivity losses with larger teams.

      NEXT QUESTIONS -- WHAT IS "SUFFICIENT" LABOR?
      Its hard to define what "sufficient" labor is to qualify for the "BTB" prices for castles. As an order of magnitude estimate we know that Beaumaris needed 2500 laborers the first summer (32K man-weeks). On the other end of a spectrum, I find it hard to believe that a Norman Tower House had a population much larger than a few villages supporting it (maybe 10% of 1K villagers over 5 weeks, for about 500 man-weeks). This is definitely an area for further research.

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    2. Holy cow, that's flat-out amazing! Thank you so much for that added data & analysis! Completely invaluable.

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  12. Here's a rough stab at the manpower requirements to build for the BTB (aka cheap) price. Data is from https://opendomesday.org.

    Peveril Castle, in Hundred of Blackwell (224 households). 3 households local. 200L.
    Orford Castle, in Hundred of Walshcroft (999 households). 0 households local. 1400L.
    Rochester Castle, in Hundred of Rochester (39 households, plus 493 in the next hundred inland and upriver of Larkfield). 16 households local. 3000L.
    Dover Castle, in Hundred of Bewsbery (791 households). 420 households local. 7000L.

    I've included all the households in the Hundred, which is an administrative subdivision called a "barony" in Ireland.

    When I graph it, Orford is a clear outlier. That said, there is a loose relationship between having more peasants and finding more expensive castles:
    Castle Cost = 3.2 x Peasant Households + 922, R2 is .1452

    Without Orford, there is a near perfect linear relationship between the cost of the castle and the number of households in the hundred:
    Castle Cost = 12 x Peasant Households - 2326, R2 is 0.997.

    Finally, our D&D villages are not in households -- they're in people. I assume 5 people per medieval household.

    That gives us a workable rule of thumb for the local workforce needed (with some rounding) to qualify for cheap construction:
    Castle Cost in L = 2.4 x Peasants - 2300

    Or put another way, to figure out how many peasants you need to build a castle on the Delta Timeline and OD&D price point:
    Peasants Available = (Castle Cost in L + 2300) / 2.4

    For example, if you have, say 5 villages of 250 villagers (OD&D standard population), that's 1250 villagers. That means you can build a castle up to 700L (42,000 SP) without needing to bring in a hired workforce.

    42K SP will get you a small to mid-size castle. Anything bigger will require hired labor (which double or trebles the price), or will take longer (I'd imagine a doubling of construction time if the workforce is half the required size). As a concrete example, with 42K you can design:
    4 x 90 foot castle wall segments (14K)
    4 x small towers for the corners (18K)
    1 x Gatehouse with Gate (3K)
    3 x Buildings (7.5K) -- great hall, barracks and a temple, for example

    An alternate design could shorten the walls by half, cut the buildings, and put a keep in the middle or on a corner.

    Clearly OD&D envisions larger castles than this: A "modest" paladin's castle is described as having a cap of 200K in cost. But this is in line with real world data.

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    1. That's spectacular! There should probably be a supplement or something making use of this analysis.

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    2. Thanks!

      I think I finally cracked the relationship here between the variables. I actually did a deep study of Guedelon (prob should make a post on my own blog about that) then applied the rule of thumb to our historical cases. Voila! It works.

      Here's my general rule of thumb: One man-week of labor is needed for every shilling of castle cost.

      Construction is actually a little slower than that (about 25% slower) but its close, and suitable for small-scale projects. The proofs below will use a more precise calculation using the more precise but less eloquent rule of thumb: "30 man-weeks of labor are needed for every L of castle cost."

      Finally, for my examples I am assuming that each household in Domesday contributes two corvee laborers for 40 days each year, or 16 man-weeks (5 days a week -- no work on sundays or feast days, plus some sick days...).

      I think that Delta's square root formula reflects the fact that wise rulers designed castles that could be built by the available labor force in a reasonable period of time. Castles were built for specific problems: to guard conquered areas, keep unruly nobles in line, etc. You wanted it built in a few years, not for your grandkids. So the designs were probably drawn up with the local manpower and resources in mind. The largest castles are thus found in areas where the population density is highest.

      Here's some examples:
      A) Peveril (200L/2 yrs/224 households):
      Man Weeks Required: 200L * 30 = 6000
      Man Weeks Available: 224 * 16 = 3584
      Est Construction Time: 1.7 years

      B) Dover Keep (4000L/10 yrs/791 households);
      Man Weeks Required: 4000L * 30 = 120K
      Man Weeks Available: 791 * 16 = 12.6K
      Est Construction Time: 9.5 years

      C) Rochester (3000L/8-10 yrs/532 households):
      Man Weeks Required: 3000L * 30 = 90K
      Man Weeks Available: 532 * 16 = 8.5K
      Est Construction Time: 10.5 years

      D) Orford (1400L/8 yrs/999 households):
      Man Weeks Required: 1400L * 30 = 42K
      Man Weeks Available: 999 * 16 = 16K
      Est Construction Time: 2.6 years

      Again, we ask -- Why does Orford take so long?

      I finally figured this one out!
      http://www.castlesfortsbattles.co.uk/east/orford_castle.html
      "...work on Orford Castle commenced in 1165 and the Keep was complete no later than 1167 although work would continue for another 6 years finishing the outer walls and out buildings."

      If we assume that most of the construction was done at Orford in 2 years (i.e. building the keep proper) then the work in the previous posts and this one comes out just right.

      E) RUSH JOB: Gaillard (3400L OD&D cost + 8600L surcharge/2 yrs/0 households):
      To see how robust our model is, we'll see if it can explain the 8600L surcharge to build Gaillard. To complete this castle with no corvee labor, we need 102K man-weeks of labor (3400L * 30).

      Unskilled labor around this time was making 2 pennies a day (http://medieval.ucdavis.edu/120D/Money.html -- thatchers), or about 1.16 shillings a week. At that rate, the 102K man-weeks costs 5916L (a good chunk of our 8600L surcharges) -- and that's just for the unskilled labor, not accounting for room & board, skilled laborers, etc. The model works fine here too.

      \\\\

      On a related note, I feel fairly comfortable generalizing that the cubic yards of material required to build fortified structures equal the cost in L divided by 5. Round towers are more like divide by 8; houses closer to divide by 3. This is useful for estimating the number of tons of stone (one ton or wagonload per cu yd).

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    3. Totally spectacular work. Incredibly impressive, I'm convinced!

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    4. That total of 5916 pounds for Gaillard is also extremely close to being exactly half of the total actual cost. It would be interesting to see if that relationship holds for other castles built under similar circumstances.

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  13. rock to mud cement. Just sayin'... Castles tend to start looking more like bunkers circa 20th century.

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    1. This one I fall in the other direction on. I want my world to have medieval-style castles, therefore rock to mud must be interpreted a bit differently. See here (esp. the last section) for more.

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