As discussed in a previous blog post the other day (see link below), dome roofs protect domes from moisture damage, shade the structure, reduce plaster work and capture rainwater. If you’re building in a rainy or snowy climate, your dome will likely have a longer lifespan and require less maintenance if you have a durable roof.
The drawings above show my recommended techniques using either wood poles or milled lumber. Wood poles are less expensive (or free), although they’re more tedious to work with. The basic ideas shown above can be altered to meet your needs. For instance, you could use purlins instead of roof sheathing. You could leave a gap between the roof and the dome for ventilation, add a skylight, gutters, etc.
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