Hello Johnny,
I'm not a professional wood worker but have spent quite a few hours cutting compound angles for geodesic domes of various sizes, mostly on compound mitre saws, but also on a radial arm saw. Do you want to make triangular frames with butted joints (as opposed to mitred joints) for a panel dome? If so, you can cut all the pieces on most types of compound mitre saw since no angle, whether mitre or bevel, will exceed 45 degrees. For this type of work, a compound mitre saw is probably safer and faster than either a table saw or a radial arm saw.
-- If you're cutting struts for butted joints, play close attention to the consistency of your lumber dimensions. If one batch of wood is, say, 1/16th of an inch thinner than another batch, perhaps due to a longer drying period, some triangular frames may end up differing from their theoretically correct size and shape. This could result in an accumulation of errors and therefore gaps and stresses when you bolt your panels together.
-- Make sure you have an accurate calculation of strut length reduction to accommodate the thickness of the lumber. The calculation for corner braces (between two struts, parallel to the third strut) differs from that for struts because the plane of the narrow face of the corner brace lies in the same plane as the triangle.
-- If you are using 1.5" x 1.5" lumber, you have to be careful about the orientation of the lumber on the saw table. It's easier to keep track of things when the lumber stock has a narrow face and a wide face, as with 2 x 3, 2 x 4 or 2 x 6 lumber.
-- For each type of strut and corner brace, make a master piece (a template) that can be used to measure all other pieces of that type. Mark it clearly so you so it's easy to find when you need it.
-- Before starting the compound cuts, cross-cut your stock into lengths about an inch longer than their final lengths. This results in a bit more wasted lumber, but it ensures you are manipulating and cutting only short, light lengths of lumber on the saw. These are easier and safer to deal with than long, heavy pieces, especially when compound angles are involved.
-- If the dome model you're building is only 30" tall, then even 1.5" x 1.5" lumber is quite "hefty". The large ratio of lumber thickness to strut length will make it difficult to bolt the frames together if there are even tiny errors in the angles and lengths you cut. The lower the ratio of lumber thickness to length, the more forgiving the components will be during assembly. If you want to use 1.5 x 1.5" lumber, it might be a good idea to double the diameter of your model.
-- I once built a 3 ft diameter 2v icosa dome model -- 40 triangular frames bolted together, made from commercial spruce kindling, 1.5" by 1/4". I glued and stapled the strut ends together to secure the three corners of each triangle. This didn't work very well because the staples ran parallel to the wood grain and the whole thing came apart after I accidentally knocked it onto the floor. (There were no corner braces in the frames.)
Good luck & let us know how you do with your model construction.
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