I'm in NH, USA; about 40" of rain yearly, much in the form of snow which is on the ground November - April. Fall and spring tend to be wet periods -- we'll get a week or two of rain/dampness at a time with no real chance for anything to dry.
I'm planning on building a small family-size cob oven. I have no experience with cob. Should I plan on building a roof over it or otherwise protecting it from moisture?
I'd suppose that using it regularly will bake away dampness...
You can get away with a tarp when not in use, but it is a pain. A roof would be much more convenient.
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Do you want to be able to use the oven during bad weather? If not, you can use a simple solution like a piece of corrugated metal lashed down on top of the oven. Otherwise, you need something more elaborate.
In my oven construction, the roof ended up being the most complicated part of the project.