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A member of the Cloudy Nights Observatory discussion forum has kindly
provided guidance to calculating horizontal strut lengths using simple
trigonometry.
My own memory of trigonometry was so old and rusty I had
no idea where to start. Once provided with the simple formulae and helpful drawings it was a matter of entering a few figures in my dusty, scientific calculator and pressing a few buttons. If only I could be excused typos! I made a mess of calculating R3 and C3 which threw everything off.I have underlined the corrected figures and they make a dramatic difference!
Original "made to measure" strut lengths are on the left under Orig. Calculated lengths on the right after subtracting the 1.8cm thickness of the ribs. The differences are not exactly trivial! I shall now cut a couple of new struts for the complete, full height gore to see how it compares.
Having cut new struts to the calculated lengths they made no sense. The ribs were curved sideways and the spacing at the tops of the ribs was about a foot!
I have now returned to my more generous "made to measure" strut lengths. The glue on the plywood patches for a second, full length, gore/segment is drying over lunch. A third gore will be made this afternoon to the same generous strut lengths and the rib extensions glued.
In the image above the base ring has been placed underneath to ensure the gores were following the correct radius. A plank on the wall fixed the center height of the ribs at 1.5m. [5'] The ribs lie nicely flat together without gaps between them. The base has been carefully checked for level.
At this point I have run out of clamps. The timber yard had not restocked with the Rawlink clamps as promised. Despite their numerous drawbacks the Rawlink clamps offer plenty of clamping pressure for the modest investment.
A couple of contacts have kindly suggested alternative means of building my dome accurately. For which information I am very grateful. I think I have been too afraid to continue after a couple of minor failures. Though I have certainly not lost the will to succeed. I had rather lost my nerve without any real insight as to how to improve the strut dimensions. I seemed to be shooting in the dark. My trepidation was largely due to a fear that I'd have to cut each covering panels individually to match each facet on the trapezium dome's skeleton.
I have now realised that with a complete gore completed I can check the radius directly at each strut out from the shed wall. This will be a good check for the calculated radii and perhaps explain where I went wrong with the calculated upper strut lengths. The bottom and second struts match both the physical and the calculated lengths. Things go awry on the third and fourth strut level.
I can also set up the three gores at 120° to each other to see how that looks. Once I have confirmed I am on the right track I shall mass produce more struts to the new lengths. It is now certain that I shall need to buy more 9mm [3/8"] birch plywood to complete the upper ribs. Which is a bit of a shame because most of them will be lopped off halfway once the observation slit demands it. I shall just have to use the "waste" as local reinforcing material.
Having cut new struts to the calculated lengths they made no sense. The ribs were curved sideways and the spacing at the tops of the ribs was about a foot!
I have now returned to my more generous "made to measure" strut lengths. The glue on the plywood patches for a second, full length, gore/segment is drying over lunch. A third gore will be made this afternoon to the same generous strut lengths and the rib extensions glued.In the image above the base ring has been placed underneath to ensure the gores were following the correct radius. A plank on the wall fixed the center height of the ribs at 1.5m. [5'] The ribs lie nicely flat together without gaps between them. The base has been carefully checked for level.
At this point I have run out of clamps. The timber yard had not restocked with the Rawlink clamps as promised. Despite their numerous drawbacks the Rawlink clamps offer plenty of clamping pressure for the modest investment.
A couple of contacts have kindly suggested alternative means of building my dome accurately. For which information I am very grateful. I think I have been too afraid to continue after a couple of minor failures. Though I have certainly not lost the will to succeed. I had rather lost my nerve without any real insight as to how to improve the strut dimensions. I seemed to be shooting in the dark. My trepidation was largely due to a fear that I'd have to cut each covering panels individually to match each facet on the trapezium dome's skeleton.
I have now realised that with a complete gore completed I can check the radius directly at each strut out from the shed wall. This will be a good check for the calculated radii and perhaps explain where I went wrong with the calculated upper strut lengths. The bottom and second struts match both the physical and the calculated lengths. Things go awry on the third and fourth strut level.
The triangle represents the latest gore dimensions and angles. In reality the gore is curved away from the viewer. Later, panels will be laid over the gores to achieve an angular profile. Note: I have underlined changed dimensions and angles compared with earlier versions. R is the Radius, measured from the shed wall to the outside of that particular strut. I also lifted the base to achieve a true 160cm radius at the center of the strut and show the difference with hyphens. The larger angles on the left are direct altitudes measured from the wall base.
I can also set up the three gores at 120° to each other to see how that looks. Once I have confirmed I am on the right track I shall mass produce more struts to the new lengths. It is now certain that I shall need to buy more 9mm [3/8"] birch plywood to complete the upper ribs. Which is a bit of a shame because most of them will be lopped off halfway once the observation slit demands it. I shall just have to use the "waste" as local reinforcing material.
Click on any image for an enlargement.
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