Geo-Dome.Co.UK's Trapezium Dome Calculator Pt.2.


I have been binging [binge-ing] on Paul Robinson's videos on geodesic dome construction and already have a better idea on constructing a trapezium dome.The latter provides a much more friendly geometry for cutting observation slits and doors.

The image [left] shows my attempt to draw the dome ribs and cross section full size on the rather worn lawn. The grass hasn't completely forgiven us for wheel-barrowing 20 tons of self compacting gravel across it. The light blue ring is drawn on with software. While the red string shows the rib form. Not how the flats, where the panels would fit, come very close at the panel centers to the arc drawn just inside. Either the rib depth must be considerably increased or matching flats made on the inside to ensure full rib depth is maintained throughout. Maximum internal radius [inside the dome] must be matched by minimum external dimensions. 

Several options exist for the assembly of such a dome. Panels can be joined at the corners. A jointed 'stick' construction is possible. Or even a hub and stick, hub and panel, or stick and panel arrangement. The slight dihedral angle between adjacent components and panels must be taken into account. A solid metal or plywood hub might not suit the dihedral angle between vertical and horizontal segments. Flats would have to be bent or cut on the hubs to allow everything to rest snugly and strongly in place.

Paul Robinson of Geo-Dome.co.UK shows his build method for his geodesic domes which deliberately avoids both glue and hubs. The angles cut on the mitered struts brings the joints together and provides the curve of the dome automatically. He shows how he builds a simple, but accurate , triangular, plywood jig. Which ensures all the angles and lengths of the struts are achieved repeatedly from triangle to triangle. All without having to measure and cut the very odd angles involved. As each triangle finds its place in the geodesic structure the struts are doubled. Providing a very firm structure of amazing strength. Even his idea of making one cut from larger material on the table saw, to make two struts with the correct angles is a very valuable lesson. 

The trapezium dome does not enjoy all the self-reinforcing features of a Paul's geodesic domes but has certain other advantages. Most of which apply to domed observatories. I am now thinking furiously how I can build a trapezium dome which is both strong and self-supporting during the actual build. I can't have flimsy panels waving about in the wind! Even the plastic conduit rocks like mad in the slightest breeze up there on the bare platform.

Making complete vertical segments which can be slotted into place side by side seems most logical. It reduces construction time and exposure while working up high. Using half thickness pre-cut ribs provides guaranteed angles between panels and automatically doubles the rib thickness when brought together as a dome. Gluing and laying slotted batten 'covers' over pairs of ribs as they are brought together offers a simple clamping mechanism during segment erection.

The vertical ribs provide self-support even before the panels are added. I keep wondering how the ribs could be considerably increased in stiffness and strength without adding considerable weight. A full box section of four thin sides could be foam filled. The thickness of these box ribs adds complication to the geometry. Constructing the box sections out of 4mm ply would not be very easy. The joining angles are complicated and the material too thin to be pinned or screwed. Though a jig is a possible way of holding everything together.

Variations on blocks between spaced ply strips offer increased stiffness. As do I-beams and T-beams made up from ply strips. With four changes in direction for each facet the joints would have to carry the increased strength through the bends. It would be tempting to introduce extra complication, much like a model aeroplane wing. The weight is kept down by using small sections but distributing loads in all directions with diagonal reinforcement in all planes. Each panel has a "Union Jack" of bracing applied. Usually between covering both inside and out or top and bottom.

The problem is that the plain plywood rib segments are not likely to be very self supporting as individuals. Starting at opposite sides of the dome with opposing segments might make good sense. They can support each other. So I can work around the ring adding more segments in opposition. Clockwise on one side of the dome and anti-clockwise on the other. Though I'd need a base plate on each segment to screw to the dome's main base ring to make it stand up.

Providing a central support pole is possible. Except that I would have to remove the heavy mounting and telescope from the pier. I could erect the builder's stepladders in opposition. Just as I did to lift the mounting onto the pier. This would give me access to the top of the dome and provide support at the center while I erect the segments. Side by side pairs of segments might still be manageable in both weight and size to provide more self support. Or I could erect a simple, triangulated timber support structure from the octagon posts to bypass the pier. This is not rocket science!

Perhaps I should build a complete segment and decide how to proceed from there depending on its stiffness and weight? I may be exaggerating the weight in my mind. Two 9mm[?] ribs + 9mm base plate, plus four cross batten braces? Or four ribs and eight braces and base plates. How thick and deep to make the ribs? Is 18mm total thickness enough?

I do have a chain hoist and a boat winch. Though I'd need a jib to be able to lift any structure from the ground and then bring the structure inboard and place it on top of the neck-high walls and rotating base ring. I really ought to get some more clamps. Some oversized "clothes pegs" too.

Note: I'd much rather "waste" time thinking [and writing] about construction now. Rather than have a floppy mess teetering or even a collapsing dome high above the ground. Where I obviously can't be in several places all at the same time. Not while the glue is going off and it starts to rain cat's and dogs and blow a squally gale!

Click on any image for an enlargement. 

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