Dome Build: Compound miter angles.


My continuing thanks to Paul Robinson of Geo-Dome.Co.Uk:   

Trapezium Dome calculation tools

I was able to find a drawing on his website of a trapezium dome 'gore' with the internal angles shown. I then subtracted these angles from 90 degrees and printed these in red.

These are the vertical angles I need to set on my compound miter saw for cutting the horizontal struts.

These numbers certainly explain the difficulties I had in getting the correct compound miter angles for each horizontal strut. I had falsely assumed that the angles would all be the same. Then found each rib was pulled in or out as I tightened the screws. I noticed that the lower struts needed hardly any vertical miter at all. While the upper struts obviously needed more. Though my choice of 5-6° was still more than required.

Tomorrow is wet again but I can still use the miter saw in the shed. This time I shall set the horizontal miter angles to 11.5°. Then cut new struts to the correct lengths and vertical miter angles.

I am most grateful for the continuing advice given on Cloudy Nights DIY Observatory  discussion forum. Without which I would not have made so much progress. Nor made anything to a reasonable accuracy. Those who make sawdust for a living develop experience and tricks of the trade to succeed.

It is not simply a matter of saving time and materials but of simplifying seemingly difficult tasks and procedures. There are checks and working methods which ensure accuracy which are very unlikely to occur to the average hobbyist.

If carpenters had to reinvent their work practices every single morning then mankind would still be living in caves! Their willingness to offer free advice based on their long experience is an invaluable gift to a bumbling amateur like myself.

In that light I have been advised to mark the base ring to avoid nasty surprises from cumulative errors. Multiples of 16 soon add up. Using simple measuring jigs and sticks is another vital piece of advice. This will depend on my having dry weather so I can set out the complete ring, of course but that day must come eventually. Then I can use their practical advice to help ensure success.

And then there were 11 [ribs.]

Sooner said than done. I pinned the half lap joints of the base ring with screws and proceeded to scribe 16 segments using a batten and two nails as a divider. A couple of hours later I managed to find the exact division after repeatedly under and overshooting my start point. 60.5cm was the final measurement obtained by gently bending the nails in and out to change the divider's radius. It is easy to imagine one is marking off the circumference of a circle when in fact these are flat sided segments of the circle. A straight line [a chord] is shorter than the arc it subtends.

A forum member suggested using a long tape measure and I realised that it could be held in place by clothes pegs without needing to pin through it. 

Friday is a still, sunny day with 60F, so I am cutting out more ribs. I job I can't do in the shed for lack of room to handle full sheets of plywood. Reached 11 ribs in total. Both sides of the rib have to be cut twice because of the difference in radius. Leaving a long thin ans curved, tapered piece of waste.

Saturday is another fine, still day and I just finished the last 5 of the 16 ribs required before morning coffee. Which makes me realise that I had better start building something soon before it starts snowing!

Click on any image for an enlargement.

Click on any