This question arose while looking at pictures of early keeps (such as Chateau de Loches and Chateau de la Madeleine) and the wondering curiosity of whether they had a latrine built into them, as other keeps do.
The second half of the question comes from the thought that keeps such as Rochestor, the White Tower, and Norwich castles don’t seem to have a visible place where waste would be deposited (and if they do, please forgive me as I haven’t had the chance to visit :D), so I’ve curious to know about how waste would be removed from the latrines.
The earliest latrines found in a medieval building can be dated from the 11th century: they were identified by archeological excavations under the main keep of the Castle of the Counts (Gravensteen) in Ghent (Mesqui, 1993, Ubregts, 2006). The current castle was built in 1180 over a previous (and lower) building that included a large hall with latrines (a latrine is visible in the current building, much to the joy of tourists). For castle specialist Jean Mesqui, who dedicated a chapter of his book about French medieval castles to latrines and hygiene issues (Mesqui, 1993, from whom I borrow most of the text below unless mentioned otherwise), identifying the presence of latrines in castles from the 11th century and earlier is difficult because 1) few of these buildings have survived and 2) those who have survived have been so thoroughly reshaped and remodelled over the centuries that minor structural elements like latrines are no longer visible. Much of what we know about castle latrines is from the 12th century onward.
Latrines were a important part of castle design: medieval castles were not just defensive facilities but also large residential buildings, the permanent or temporary home of many inhabitants, lords, domestics, and soldiers, could not be expected to go outside the castle grounds every time they needed to relieve themselves. Nobles, at least, could use close stools (chaise percée), a form of portable toilet that appears in the record in the late 1300s: Louis, Duke of Touraine, ordered one in 1390 to be used when he was with his wife. But even if close stools (and portable urinals, which also existed) allowed their aristocratic users to do their business wherever they were in the castle - people of lower status would have to walk to the nearest latrine -, the portable toilet had to be emptied by the domestics, and the latrines were used for that.
Latrines were usually built within the castle wall, which was usually thick enough to include a narrow closet or room made for that purpose. In some cases, the latrine was found at the end of a short corridor and/or closed by a door. The latrine could be for private use (for the most important residents) or it could be collective (for domestics, soldiers, prisoners etc.). Privacy was relative: noble users would be accompanied by a servant who held a candle or provided hygienic tissues. Smell was an issue: architects built vents to evacuate the foul air, and there is at least a bill dated from 1396 for 12 bottles for "water of Damas", an hygenic preparation containing several perfumed ingredients meant to deodorize (or purify?) the Queen's privy.
Latrines were built next to bedrooms (in residential towers), or they were adjacent to halls, or to defensive structures (walkways...). There are also numerous examples of towers (turrets) built specifically as latrines and that provided some privacy (there's one in the Palace of the Popes in Avignon). The set up of latrines could be rather sophisticated in large households, and medieval architects devised ingenious ways to allow several people to do their business at the same time: in the Château de Pierrefonds, for instance (Baillie-Hislop, 2016):
the ground-storey latrines were directly over the pit, while those on the upper storeys were over stone-enclosed shafts that also dropped to the pit.
Architect Viollet-le-Duc (who creatively restored Pierrefonds and the Notre-Dame cathedral in the 19th century) mentioned the existence of staggered latrines at the Château de Montagu, where each level had its own vertical shaft leading to the pit.
There were three basic latrine designs in medieval castles.
In the first design, called "cesspit latrine" by Mesqui, the latrine was above a vertical shaft that went down to a (usually) closed cesspit at the bottom of the castle. This arrangement contained the diffusion of smells within or outside the castle, thought the shafts themselves may have been smelly. How were the pits emptied? It is possible that the bottom of many pits was made of soil and sand, and that the liquid part of the excrements was filtered out naturally. Still, the pits had to be emptied at some point. In some cases, documents show that the drainage had to be carried out once a year, a difficult and dangerous operation (emptying cesspits was still a problem in 19th century Paris!). In the case of the Castle of Blandy-les-Tours, archeologists speculate that the pits almost impossible to drain, and that they were used only for one century (Coste et al., 2006). In other cases, cesspits had an opening at the bottom of the wall that allowed excrements to flow outside the castle. This solved the problem of manually cleaning the pits, but it introduced a security issue: in 1204, when Philippe Auguste lay siege to Château Gaillard, some of his soldiers entered the castle through the cesspit opening... Let's note here that in castles, often built on high ground, flowing water was usually not readily available, unlike in monasteries built next to rivers, where latrines were often more sophisticated and easier to clean. However, there are castles where existing watercourses were put to use to evacuate foul water from the latrines and the kitchens, and there is at least one example of a castle (Warkworth, in Northumberland), where rainwater collected in a cistern was used to flush the contents of the main drainage shaft (cited by Baillie-Hislop, 2016).
In the second design, called "angled shaft latrine" by Mesqui, the shaft opened on the outside face of the wall, sometimes right below the latrine (the materials then flowed directly down the wall), sometimes after running vertically through the wall (the materials then flowed only at the bottom). In some cases, such openings were first understood to be murder holes used by defenders to drop heavy objects or liquids on attackers, but they were actually the end of latrine shafts. The angled shaft design was simple (though it still required the building of internal shafts) but not much used in practice, possibly because it left ugly streaks of excrements on the walls that could be only washed away by rain (so much for prestige). Mesqui claims that such streaks can actually be seen on the painting of the Château de Saumur in the illuminated manuscript Les Très Riches Heures du Duc de Berry but I cannot find them.
The third design, that became popular from the 13th century onward, was the "corbel latrine", where the latrine was built on the external wall face like a machicolation: users did their business over empty space. This type was easier to build (it did not require putting internal shafts in the wall), and it did not leave streaks of urine and fecal matter on the walls, and it could double as an arrowslit if necessary. However, it was also dangerous to use during a siege, and architects added some protection so one could not be shot by an arrow while sitting on it! Waste disposal was facilitated when the corbel was put over a watercourse, a moat, a cliff, or the sea, like in St Andrew Castle in Scotland.
Finally, it should be said that castle latrines were not only used for excrements: they were general waste disposal facilities where people threw out various types of organic refuse, as shown by numerous excavations that have provided archeologists with extraordinary insights on the daily lives of castle inhabitants.
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