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Temporary solutions for the present dome would involve taping the seams. Finding a suitable tape becomes the main problem. 3M do aluminium tape but the complex bends at panel corners are likely to be very difficult to form neatly.
Or I could glass over the joints with polyester resin and cloth or tape. Both resulting in likely ugliness compared with the semi-crisp bends of the present, monocoque, plywood panels. I have no interest in glassing over the entire dome. Very poor working access and previous experience with GRP are enough to avoid such a major project. Externally laid up GRP is also extremely ugly IMO.
I have looked at using tarpaulin to clad the dome with some reservations regarding its life and gaining skill at welding the joints. I'd also need a decent heat gun.
Another option would be to drop full gores of aluminum sheet to cover the existing plywood dome. This should solve the rain leakage and improve both the lifetime and strength.
Internal, aluminium ribs could be fashioned from T-section profile and riveted and sealed to the new aluminium covering. No plywood, at all, greatly reduces the weight! The ribs sections would run from top to bottom of the dome. The web can be easily "nicked" to make the bends across the base of the profile. The partially cut bends then need reinforcing on the web. T-profile is more expensive than angle and much harder to find.
Two angles "back to back" make a T profile. Allowing bolting or riveting together means gores can be dismantled. Or lifted individually to observatory height. T's can't be separated. Downside is that the cost rises and proper sealing between the gore ribs becomes essential. Where the base of a T profile would be bridging each bend unless distorted to fit but would theoretically provide better protection against rain down its "back."
Crossbars at the bends between panels ought to be reinforced. Angle profile can manage this task. Provided they are placed above or below the bend. Angle profiles have the advantage of a suitable web to rivet or bolt panels together side by side. While the other leg provides stiffness at right angles to the base. Every panel has a dihedral angle where is meets the next panel along or above.
Now we are talking about a whole new dome! Trapezoidal works well. Without any ugly buckling of the aluminium sheet down near the bottom of a hemispherical dome. I could make the dome slightly larger too. To guarantee a decent overlap at the bottom edges where the base ring must overhang the walls. Without using the present strips of flashing.
Or, there is the barrel roofed observatory. Which would require I form quite gentle curves along angle profiles for the wall to roof joint. I have no doubt that this could be done with a suitably profiled former. Using a long lever and profiled roller to apply the rotation and curvature. The main problem is keep the profile flat in the other dimension. Where it wants to form a curve. A local engineering company failed on this score despite using a professional roller/bender.
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