new coop design help
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I'm new at this and just finished building a coop w/run and after many months of planning, probably too many. I'd say it depends on your location. I'm in the low desert in a semi-rural area so I'm more concerned about predators and less about drafts. Actually drafts are good on my end when it gets hot. Without knowing your details I'd just say as a general rule it shouldn't be "sealed" but rather well ventilated to allow moisture from the birds to escape and carry any ammonia from chicken poop out with it. Also you'll definitely want to keep rain out - nothing worse than a wet chicken on wet bedding - not good for the birds or you. Other than those two generalities the rest depends on your location needs and personal preferences.
As ejcrist said, you want the coop dry. Wet bedding is not something you want.
As for the run, you don't have to give it a roof, but if you don't, the ground will be however the ground is when you get rain, stomped on and kicked up by little chicken feet, otherwise known as mud. LOL Also, it depends on how big the coop is and how much other shelter you've got. You could have an open run, with some little "huts" in there for the chickens to shelter under when it rains. Also, if you get a lot of rain, consider the site where you are putting the run, you want drainage away from it, and you don't want it in the path of water draining from elsewhere (so, don't put the run downhill of the coop roof, for example).
You're coming into spring and summer aren't you? Is your rain in winter? You could defer adding a roof for six months or so, if you are on a budget. You could also have part of the run with a roof, and part open. If it's hot there, you should have some sort of shade/shelter/roof.
Height of the run is for us, rather than the chooks. It is a pain in the neck having to crouch (or crawl) into it and you'll get sick of it very quickly. Full height is MUCH better for people. The chooks are fine with chook height, you could make it chook height if you wanted.
Amen on the coop/run height issue! I kept my coop height at 7 1/2' at the peak (6' on the sides), and 8' on the attached run peak (6 1/2 at the ends) because the coop foundation is on blocks 1' high while the attached run is not - wanted them to be even and continuous. I do enough stooping in the vegetable gardens and picking wine grapes and didn't want to have to be crawling around in a confined space coop full of fertilizer dust, etc. That was one part of the project I was sure of. Don't get me wrong, I love my birds, the outdoors, etc., but I try to make the chores as easy as possible or I won't want to do them. It might cost you a few dollars more to make it walk-in height but just my opinion, it's very well worth every penny.
Depending on how large your run is, I would cover the entire thing. When I built my first coop last year, I did not cover my run, and ended up putting a tarp over the top after a week or two. This year I'm adding a roof to the rest of it. I try to let my birds free range as much as possible, but when the weather is bad, I prefer to keep them in the coop/run. Having a cover run really helps to give them extra space that they can use year round. The tarp worked well but is pretty tore up after this winter's winds. I could see it getting expensive to buy a tarp every year for it. For the winter, you also may want to consider covering the sides up to help protect them from the wind. I did the two sides that get the direct wind and my birds didn't have any problems.