Planking the roof of the cone poses interesting problems. You can plank a cone radially, and every plank is straight. My rafters run radially, but that doesn't have to be a problem; I could put short purlins between the rafters to fasten radial planks to. I can even envisage some rather pretty joinery for those purlins. It isn't impossible.
But every plank would have to be cut longitudinally - identically, so I could make a jig and it wouldn't be a big deal, but it's a significant job. More significantly, radial planking also would not strengthen and stiffen the roof, and I'm still concerned by my friend Pete's comment that the roof could be floppy in strong winds. The tensile bracing which Pete suggested and which I've shown in the last drawings will help, but...
When I originally envisaged planking the dome I thought of short sections of plank between two rafters only. This has multiple problems. There's a lot of work in doing that cutting, and getting it right. In practice, every one would have to be fit and then cut individually, and there would be almost two thousand of them. There's two lots of nails at every crossing between plank and rafter, doubling the opportunity to miss the rafter and end up with ugly exposed nails. Actually more than doubling, because given that every nail is through a plank end it cannot go into the middle of the rafter, and must be on a diagonal. Finally, all those cut ends create areas of roughness which could potentially damage the waterproof membrane which will be laid over them. So it's entirely possible that the roof would have to be sanded before the membrane could be laid, which would be a huge job. The more I think of it the more I see the short-plank roof as a bad idea.
But, a cone is a developed plane surface; there are no complex curves. So, you could lay your planks perpendicular to one key rafter, and just keep planking like a floor. The problem with this is that the cone has a curvature, and the planks will only bend so much. As you get closer to the peak, the curvature tightens. However, it's a very shallow cone - for most of its area it does not curve much. This means, of course, that the planks will partially wrap around the cone, forming graceful curves themselves which will be visible from the interior (particularly if one in every five or so is stained a contrast colour - see later in this essay).
It also means that if you started perpendicular to one particular rafter, then the natural wrap of the cone would mean that on the opposite side of the dome where the wrap met, you would have planks which were crossing the rafters at a steep angle, and you would need to provide a 'king plank' where the wrap joined. This might look good, but I'm not confident.
The solution I'm presently inclined to try is to start planking perpendicular to the most east-westerly outer rafters, and have a king plank running north-south across the roof. This makes the eastern and western halves of the cone essentially separate structures, but it solves some of the problems of wrapping and I'm confident it would look well. There's a minor problem in that the inner rafters are offset from the outer rafters by 3.75 degrees, so a king plank which is perpendicular to an outer rafter cannot be perpendicular to an inner rafter and vice versa. It will probably look best if it is not perpendicular to either.
In the upper part of the cone, the curvature will get tighter, and the planks won't curve that much naturally. There are a number of possible solutions.
First, I could saw a series of transverse cuts across the plank, halfway through the thickness. It's an old joiner's trick to ease a piece of wood through a curve that's too tight for it. The problems are that the cuts are best done on the inside of the curve, where they would be visible from the interior. The technique weakens the plank anyway, but if done on the outside weakens it more. And the risk is that it snaps, which wouldn't be good.
Second is, I could build a steam box on site and steam the sections of the planks which need to curve most tightly. This would probably work. When steamed, wood goes (relatively) floppy. It also swells, and assembling toungue-and-groove joints when the wood is swollen might be tricky, but this idea has definite merit.
Third, when the curve gets tight I could switch to a different material which can take the curvature more easily. Specifically, for the uppermost 1200mm (or even 1800mm) of the cone I could switch from 22mm tongue and groove planking to three thicknesses of 6mm plywood or one layer of 6mm plywood and two of 9mm OSB (oriented strand board - although I'm not convinced that 9mm OSB will cope with the curvature required, and 6mm isn't readily available).
In some of my working drawings I've coloured different pieces of timber in bright contrasting primary colours, to make it clearer how joints are intended to work. I never intended that the timber in the structure should be coloured in this way. But I've come back to colour from a different angle.
What I'm building is a frame to support a roof, in Galloway, where it rains. A lot. It can, of course, be covered in polythene when not being worked on; but it's also an exceptionally windy site, so polythene is likely either to get blown away, or, worse, to act as a sail and damage parts of the uncompleted structure. So it would be a good thing if the structure were resistant to wet before it's assembled. Also, the timber needs some degree of protection from xylophilic invertibrates.
I don't like paint, and, in any case, on this scale, paint is simply far too much work - I don't have either the money or the time. But the sort of stains sold for outdoor timber would be quick and not outragreously expensive to apply. They're readily available in a range of browns and greens, from pale to dark, and less readily, in a range of more saturated colours.
So, I'm thinking about staining the main structural frame; and if I'm going to stain it I'm thinking of colour. A forest green frame would definitely be nice. A variety of toning colours, in browns, greens and greys, would also be nice, and could be done either to colour-code the structural function of the element or simply, as in my drawings, to draw attention to and explain joints.
The possibility of colour staining the roof planking, either in a regular pattern or, within the toning range, randomly, also appeals, especially if the 'long tangential' planking technique is used. It would show up the boatlike form of the roof.
All this is slightly complicated by the fact that an exposed timber roof in a kitchen is required to be finished in a fire-retardent varnish, and I assume my singlespace will be considered to be all kitchen from this point of view. But there is no problem with applying fire retardent varnish over a stain, so the solution of staining before erection and then applying varnish to the interior once completed is entirely possible.
I haven't decided on colour. For that matter, I haven't decided on long-tangential planking. But that's the way my thinking is running just now.