31st August 2017 Mock-up of ribs and segment

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The rain never seemed to stop for two days so I wasn't able to get anything done. Having the base ring arcs handy I decided to mock up a segment. The weather actually cooperated with a brief burst of warm, 62F sunshine. 

The two ribs should actually meet at the top but I wasn't going to cut the arcs just for a mock-up. I leaned the structure up against the octagon and spread the base of the pretend "ribs" by 63cm as prescribed by Geo-Dome's trapezium dome calculator. The red lines on the inside of the distant rib are to simulate the flat panels. All of which, regardless of size and shape, will be 63cm tall. But only 63cm wide at the base ring.

When seen up close, like this, the dome shrinks into a manageable size. Up on the platform a single arc seems so unwieldy that I can hardly imagine erecting the complete dome up there. The old, aluminium satellite dish. leaning against the shed, is intended to reinforce the observation slit around the top of the dome. Probably protecting a laminated plywood collar for extra strength.

The next step is cut more arcs to make the ribs from 9mm birch plywood. Which is seen stored safely under wraps against the side of the shed. Each rib will consume one full, 1.5m arc with about another meter extending on top of that. With a halving joint between them just as I did with the base ring. The observing slit will save some length on the second, upper arc.  Though I may complete all the other ribs before constructing the observation slit.

With the ribs ready, I can start cutting the horizontal cross struts, for each level, from softwood. Probably using 2"x2" timber. The struts will need compound mitering to fit between the ribs. Not only do the ribs radiate from a central, vertical axis of the dome but the segments shrink constantly as they head upwards, towards the pole. Provided I can establish a pattern for each of the four cross struts I can cut more and know they will fit exactly into the next segment along. In theory the strut making should be a form of mass production. Not forgetting to saw two opposing bevels on the table saw of the outer surfaces for the panels to rest flat. 

A sixteen sided figure is a hexadecagon. The internal angles are 157.5°. So the miter angle to be cut on the ends of the horizontal struts is 180 - 157.5/2 = 11.25°. This is the same angle which must be double beveled on the faces of the vertical struts. Which will be laid on the 'flats' cut away from the ribs. Both to reinforce the ribs and provide a substantial bed for the flat, trapezoid, 4mm plywood sheathing panels.

I have bought some 43x43mm timber for some experimental struts to make up a single dome segment. However, the continuing bad weather has stopped most work on the build. I need to be outside to have enough room to cut the 9mm plywood arcs for the dome from 5' x 5' sheets. It is not the matter of a few moments to tidy everything up between sudden cloudbursts. September 2017 in Denmark is heading for an all time rainfall record. There was more rain on one particular day than the average for the whole of a normal September. The weather has constantly flip-flopped between sunny and cloudbursts. The regular gales don't help.

Thanks to Paul Robinson's Geo-Dome trapezium dome calculator
 http://www.geo-dome.co.uk/trap_tool.asp

 I can find the weight of the struts.
 More information here:
  http://www.geo-dome.co.uk/article.asp?uname=trap_dome

By a happy/unhappy coincidence 43x43mm softwood [pine] weighs close to 1kg per meter, or roughly 2.2 lbs/ per m or 39.4".

Vertical struts = 16 x 4 = 64 x 64cm  = 41m

Horizontal struts          = 16 x 64 cm  = 10.2 m
                                        16 x 59    "   =  9.5
                                        16 x 45    "    = 7.2 
                                        16 x 24    "    = 4
Total length of struts    = 71m
Weight                         = 71kg or about 156lbs. Eek?

To which must be added the weight of the 4mm plywood sheathing, of course.

Click on any image for an enlargement.

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Cutting the dome ring lap joints.

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I must say that I don't much like the Rawlink spring clamps. The jaws are as long as the slippery handles and this makes the required hand pressure uncomfortably high. The green, self-aligning jaws keep falling out to compound the irritating hand pressure to obtain a wide enough gape. That said they were cheaper than chips at 20 Kr. or about £2 each from memory. Luckily I only bought 6 small and two of the larger.

I shall definitely look elsewhere for another make since I could do with many more for the coming work. They do have a firm enough grip, at the jaws, to be useful and are far quicker and lighter to use than G-cramps. Particularly for thinner jobs like gluing or holding plywood.

But why bother to put green, entirely decorative panels on the handles if they aren't sticky enough to grip firmly with the major fingers and thumb? Even a drooling idiot can easily see that the shape of the handles makes the hand automatically slide down to the point of minimum leverage at the pivot/fulcrum! Leaving the reserve digits and pinky to apply any further leverage. Brain dead dullards could do better! Why can't the manufacturers?   

I went over and started marking out the half lap joints on the arcs. Then I realised that one can't just put a try square on a circle. Certainly not on the convex outside. So I used my newly acquired "speed square" and reversed it each time on the concave curve. Following on with a bisection line by eye. A quick check with a 6" protractor showed that I was spot on. So far so good. The odd thing is that my circle laid on the ground seemed to have far larger overlaps than these measly 3" joints. Perhaps I just didn't have them lined up well enough with each other? I'll have to lay them out to the new markings and see what happens.

My maths is worse than I thought! I carefully laid out the ring arcs on blocks to the pencil marks and clamped them together after close alignment. The overlaps at each end were 16cm or over 6". Exactly twice my calculated overlap. No problem though since it gives me more leeway.

The image above shows my measuring pole at half way and the 1/4 circle marked with another pole. I mark the poles with tape and this saves hours of fiddling with 10' of extended and floppy tape measure. I can quickly go around the circle checking the diameters are all equal without being in two places at the same time.

I brought out the table saw to do the half lap joints. Then couldn't summon the nerve to shove a 5' tall arc of wavy plywood through the blade set to full 3" cutting height! So I brought out the router instead and cut the material away with a 1/2" bit across all seven arcs laid out at the same time. A crude fence stopped it taking chunks out of the shoulders. I cleaned up with a block plane and checked the depth by reversing a pair of joints. I had already set the router's last cut with a vernier caliper on the plywood. Now I just have to do the reverse laps on the other ends. I just hope I remember to do them all the right way around!

The lap joints worked okay but the arcs were slightly too long. So I re-marked them all and used the miter saw to slot the joint surfaces prior to removing the waste material. The ring is now close to the correct size with the arcs well aligned.

After some reorganization of the parking area I was able to make room for the ring further away. This avoided problems with the car reversing into the previous outdoor work site. I shall have to build a work shelter as the weather becomes much more changeable. It would not be possible to "put away" a partially constructed dome every time there was a shower. Even throwing a tarpaulin over such a large object is not without difficulties. The cheap, lightweight tarpaulins really are absolute garbage and quickly become as waterproof as a fishing net. Even four layers of brand new, lightweight tarps has failed to keep my timber stock dry!

Talking of rubbish: I went in local search of better quality spring/glue clamps for the coming build. I found some small Bahco clamps at three times the price of the Rawlink but identical in shape. Unfortunately I did not have "Arnie" with me in full Terminator guise. So my feeble, human hand strength could not open the damned jaws without considerable strain and pain! Somebody actually designed and released these to an unprepared public? And they actually kept their job? Good grief!!

Lest thee think me a wimp: I regularly carry heavy, multi-stretch ladders and 18' lengths of 2x8s and 4x4s about, without effort, working alone. I moved over 20 tons of sand and gravel, 50 yards, by shovel and wheelbarrow alone, in only a couple of days. So get over yourselves!

I have now ordered a selection of Bessey Clippix XC spring clamps without having physically touched them. The handles just look as if they were designed for real human hands. Unlike the Rawlink and Bahco [half-baked?] spring clamps. Another pair of companies where such "alien technology" as basic human ergonomics has, quite obviously, completely escaped their attention.

Even the Ancient Egyptians knew about levers and moments. Why can't the Chinese plastic factories read the hieroglyphics? Has common sense completely evaded all of them before they stick 'Western" labels on their wares?  Has it got anything to do with being "cowboys?" [A derogatory British term for poor builders.]

Click on any image for an enlargement.

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Marking and cutting the dome base ring.

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I spent the morning marking and cutting out arcs in 15mm birch multiply form a 5'x5' sheet. These arcs will be joined to make the dome rotation/base ring. I decided to use a heavy brass plate to hold the pivot point board in place. Spring clamps just got in the way of the 5' long beam compass. Experts would probably have used double sided tape to hold the scrap of ply used for the pivot line.

 If you look at the image carefully you can just see the pencil lines I have drawn and the waste crescents between the arcs of different radii. 5'4' external and 5' internal radius. 3.1m and 3m.

I used a fine toothed blade in the electric  jigsaw to cut close to the lines. Then smoothed the curve with an angle grinder fitted with a coarse flap wheel. It was actually easier to remove an 1/8" with the sanding disk rather than cut too close to the line and then have no material to wear away into a nice, smooth curve. This also ensured there were no ragged edges left from the saw. Birch tends to fray upwards when sawn. Ear defenders and an industrial dust mask were worn for protection.

The second image shows the result of laying all seven arcs together. All the arcs are of the same, 5' linear length but naturally are slightly longer in circumference. D = 10'4" x Pi = 31.75ft.

It has reached a tropical 70F outside so I was glad when the lunch gong sounded. So I could go indoors and cool off.

With so many joints it will probably be a good idea to make a slot between the plies with the table saw. Then glue tongues of 4mm ply between skewed butt joints as reinforcement and to spread the loads more evenly. Or, I could make half lap joints. Moving the huge ring 'upstairs,' with just a butt joint between arcs, would have quickly found any weaknesses. I have no desire to cut two whole rings with overlaps between the joints just to make it safe. The weight of the seven, bare arcs is 26.2 lbs or just under 12kg.

My plan is to cut more arcs so that that shorter lengths can be fixed to the bottoms of the vertical dome segments. Hopefully no overlapping joints will occur between the base ring and the bases of the segments. There may be a rotation point [phase?] where this is possible. It is odd how large the complete ring seems down on the ground. I took an arc upstairs to check it against the octagon posts in case I had made a serious mistake in my radius measurements. It fitted nicely.

Joining the arcs into a full circle will require joints. I shall use half lap joints which will consume some of the length of each arc.
The diameter of the dome is 320cm  x Pi = 1005.4cm circumference.
My seven arcs are each 160cm long in outer circumference.
7 x 160 = 1120cm. 1120 - 1005.4 = 114.6 / 7 = 16.4 / 2 = 8.2 cm

Checking my sums: Required ring circumference = 1005.4cm.
Arc length = 160 - 16.4 [overlap] = 143.6 x 7 arcs = 1005.2. Near enough! 

16.4cm is the length of maximum circumferential overlap per arc.
So 8.2cm [3.2"] is the maximum length of joint overlap allowed at each end of the arcs to provide the full circle.

This assumes all arcs are intended to be equal in circumferential length. The seven arcs raises the question of whether I ought to use eight, shorter arcs? This would help to ensure all joints overlap when the 16 dome segment bases are added on top. Yet another thing to worry about?

Click on any image for an enlargement.

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Marking out dome rotation rings and ribs.

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The photo, of  a scale drawing, alongside shows how many arcs can be sawn out of a 5'x5' sheet with a 10'6" outer diameter. The arcs will be joined end to end and laminated to produce a complete ring to support the dome ribs.

My careful scale drawing suggests that I should reduce the width of the arcs by a small amount to allow more full widths and also for the saw cuts themselves. It should also be remembered that the inner arc should be of slightly shorter radius than the outer so that they are concentric with each other. My method of moving the pivot a fixed distance along a line produces identical curves. The two radii could be marked by adjusting the radius arm pivot each time. Or using two radius arms. [Oversized beam compasses] Or the sharper curve could be produced on the inside curve by the smoothing router which follows the jigsaw.  Jigsaws don't work well on radius arms in my own experience. It's hard enough to get them to follow a straight edge fence.

One saw kerf may not seem much but it soon adds up with multiple parallel cuts. For example: 9 x 1/16 = is over half an inch. Taking this into account saves wasted material when the absolute width of the ring is not [usually] critical. Some dome builders cut their arcs with a router. Obviously the width of the router bit takes its toll on the consumption of expensive materials. Some builders have set up two routers, side by side, to ensure perfect concentricity, the correct radius for both inner and outer arcs and a fine finish. Which probably doubles the kerf wastage and dramatically reduces the number of arcs per sheet.

I am thinking of saving money on birch ply by placing the rollers on top of the octagon posts. Timber plates between the posts can reinforce the arrangement and give a very good, bolt fixing. Simply wood screwing the roller support plates into end grain on the tops of the posts is not very clever.

Note that , line of pivot points, for the radius arm, must be perpendicular and well fixed to the sheet to be marked and cut. Any sloppiness or misalignment will badly throw off the arcs. With birch ply costing as much as it does in the thicker sizes it should not be wasted! The router arm pivot can be placed on each corner of the sheet to be marked and arcs struck off along the material providing the pivot line. Just as you learned to do in geometry class to draw a perpendicular to a line, now so many years ago. The router arm must be rigid. If it flexes or rocks it will not draw an accurate curve.

I took the trailer to the builder's merchants and bought 4 x 4mm, 2 x 9mm and 2 x 15mm birch multiply, all in 5'x5' sheets. Just to give myself some initial materials to experiment with. Plus half a dozen, plastic, 'clothes peg', spring clamps for when I am gluing plywood ribs together. Swift and firm clamping is essential when working high above the ground. There is usually no time to be messing about with heavy G-cramps, C or F clamps when working alone. I should really have bought more spring clamps as they are relatively inexpensive. I'll see how well the ones I bought perform before investing more funds. It's hard enough to find consistently good clothes pegs.

Click on any image for an enlargement. 

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

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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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Geo-Dome.Co.UK Trapezium Dome Calculator.

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Quite unexpectedly, while searching for an online dome gore calculator, I found this on the Geo-Dome.Co.UK website:

http://geo-dome.co.uk/default.asp

Trapezium dome design

Trapezium Dome calculation tools

By the most amazing coincidence the website offered an online trapezium dome calculator requiring only the radius of the dome as input. It doesn't care whether you choose meters or feet as long as the builder remembers which.

To add to the unbelievable level of usefulness the calculator had already chosen a dome with 16 gores by four segments high. Precisely the same specifications I had planned to use for my own dome! 👍

It then "printed out" the data for the struts to build a trapezium dome skeleton:

Geo-Domes UK's main area of interest seems to be geodesic dome and building construction. They offer plans, kits and the erection of greenhouse domes. The number of instructional YouTube videos is quite remarkable. The proprietor obviously wants to popularize geodesic construction.

https://www.youtube.com/user/pauly1060/videos

Some basic information:

'X' applies to the base ring strut lengths.
AND, all of the vertical strut lengths.

'A' is the next ring up,

'B & C' refer to the rings above A respectively.

A glance at the panel plans [below right] will clearly show what the terms X,A,B &C refer to.

The pole is the point where all the top triangles come together. All the other panels are trapeziums.

Important Note: The dimensions shown here are the output from the Geo-dome Trapezium Dome Calculator with an input of 160. This is the radius of my own 320cm [10'6"] diameter dome. This diameter should ensure rain is safely shed outside the octagon building which supports the dome.

I am most grateful to Geo-Dome.Co.UK for their helpful online calculators and wished I had learned of the website's existence earlier.  I searched for days just for an image of a trapezium dome but somehow missed this useful website until now. I must have been using the wrong search terms. "Trapezium dome" unlocks more avenues to explore.

Click on any image for an enlargement. 

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Building rhe Octagon Pt.73 The non-traditional approach.

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While the horizontal ring design had certain advantages I could see myself really struggling to build it well. With no self support, nor automatic concentricity, the horizontal rings would have to be arranged on a strong and accurate support structure during building.

A drawing showing vertical plywood ribs, with horizontal braces and flat panel segments. The plywood panels would have to be well sealed at all their edges.

Meanwhile, traditional vertical ribs, between gores, provide support and automatically provide the desired hemispherical shape. A ladder can be leaned up against the bare skeleton. With a simple timber crossbar applied to the top rung to ensure alignment and spacing are maintained while working up high. Since the dome must be erected in place, on top of 5' high walls, up on the raised platform, this is not [remotely] a trivial matter!

Though, heaven knows, I would much prefer to work on the ground and have a local farmer's [big bale] loader lift the finished dome into place. The question is whether the access is wide enough for a machine which can easily manage the big lift. Big bales can weigh between 600 and 2000 lbs so there is no doubt about these telescopic loaders lift capacity. The countryside is often littered with huge stacks of bales reaching to considerable heights. Well above my more modest altitude requirements.

The cross braces between the vertical ribs are wedged into place by the open angle during fitting and gluing. An F-clamp can easily be applied while the glue is drying. A slotted vertical brace can supplement the gluing and screw fixing area of the plywood rib.

In fact the crossbars could be assembled from a cross plywood rib with the slotted and mitered battens glued on top. That would give me a full plywood, grid skeleton but with a softwood batten [gluing and screwing] surface laid on top of the entire structure. This avoids having to fix the sides of the panels to the edge grain of the vertical plywood ribs.

The slot width will have to change to suit vertical or horizontal orientation. Unless I use the full rib width for the ply crossbars. I'm not sure it is worth the extra effort to make two different slot widths while mass producing the mitered battens. That said, ply crossbars will add some weight. 15 x 4  = 60 x 2' [average width] times rib depth [say] 4"? 120' x 4" = 40 square feet. Or one very large 8x5 sheet! I'd better make the horizontal ply cross ribs quite thin!

It has been suggested that I build the dome from sub-assembly segments like neatly cut orange peel. The sub-assembly ribs would employ half thickness vertical ribs until finally joined together to complete the dome. The crossbars would maintain the shape of the unit to allow easier handling than trying to assemble loose components almost twenty feet off the ground. Which suggests that the covering panels are not attached until the dome skeleton is assembled. Otherwise it will be impossible to work from relative safety inside the structure.

 

The ribs will provide support for a tarpaulin during final construction in what must inevitably become poorer weather as winter approaches. This insurance against having to work while fully exposed to the elements will hopefully increase speed, accuracy and comfort. I'm thinking of using net reinforced, clear plastic tarpaulin for its transparency, light transmission and whatever warmth the weak autumn/winter sunshine can offer.

Click on any image for an enlargement.

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Building the Octagon Pt.72 Boxing clever?

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It occurred to be that a dome could be built from shallow boxes, placed on edge, in rings. The four sides of the boxes would become vertical and horizontal ribs of twice the thickness where they joined. Somewhere in my mind I remembered seeing an inside view of a building or structure with a similar arrangement of ribs. The idea seemed so logical I thought I'd better see what could be accomplished. Thin [marine?] plywood is strong for its thickness. As a box it gains stiffness from the sides and base. Now stick lots of them together with glue and the strength is multiplied by the sheer number of self-reinforcing surfaces and huge number of stiffening ribs. 

Geodesic domes are sometimes built from folded cardboard. The joining edge flaps may be turned in or out to taste and can provide extra stiffness. It may be this which I am vaguely remembering from my earlier interest in geodesic domes and structures.

 IGLOO | MUT architecture | Archinect

Here is an image I found online of a spiral built, shelter igloo for hot and cool days on a Manhattan rooftop. These boxes have been deliberately spaced for air movement. Or simply to cater for the fixed geometry of the boxes.

Now imagine if they were all tightly snuggled up against each other. [Assuming that was possible] If the boxes were placed directly over each other they ought to get smaller as each ring of boxes rises up the dome. Now imagine each box was made to a precise size but kept shallow. Almost like a tray with raised edges. The sides will need a slight taper and be angled to bring the edges flat against each other. So that they are able to have a firm bond between adjacent boxes as they are stacked tightly together. To keep the weight down it is suggested that 3mm [1/8"] plywood would be a suitable building material. 

Such material needs rather unorthodox means of joining box edges to edges. Kayaks and boats are sometimes made of similarly thin, wood-based material and shaped panels are sewn together with copper wire. The joint is then filled with epoxy resin before the stitches are later removed after curing. The finished shape is then usually glassed over with glass mat or thin glass cloth and coated with resin. Requiring lots of patient sanding to obtain a high gloss finish.

Assuming a dome is to be constructed from similarly sized boxes stacked side by side and one above the other: The number of gores gives the inward angle required of the vertical surfaces. The number of vertical segments fixes the angle of the horizontal surfaces. The observation slit may "use up" two gores but this will not affect the inward angles of the box sides. The central rib of the slit area is simply removed.

A full circle has 360° so dividing by the number of gores [sectors] gives the angle of the ribs.

360/16 = 22.5° per sector in the horizontal plane.

Let's move onto the vertical plane which must be divided by the chosen number of vertical sectors. A quarter radius of a circle = 90 degrees.  Assuming four flat surfaces are desired then 90/4 = 22.5°. A happy coincidence where multiple components have to be cut.

These angles would only be correct if we were dealing with arcs but we are placing a straight line across each sector. The flat bottoms of the boxes will lie across the sectors and these become segments. Which means that the angle of the sector is shared between the two sides. 22.5/2 = 11.25°. This is the inward angle to be applied to all four sides of the box to make them fit snugly together. Though I doubt the 1/4 of a degree will matter much even if it could be measured, marked and then cut with a high degree of accuracy. Now I have to work out how to build a series of boxes with rather thin sides and bottoms. Preferably without adding reinforcement or using epoxy resin. 

But why build lots of boxes and then glue them together? The ribs are far more substantial once they are doubled in joining adjacent sides. Thick ribs provide thicker glue surfaces when the bottoms are added to form the outer skin of the dome. So why not cut the angles on the ribs out of double the thickness of the original assembled boxes? Why make lots of boxes when only the edges really matter for strength? Now join the vertical edges of all the uprights into strips. Or all the horizontal edges? Maintaining the strength of multiple ribs, in a grid pattern spread evenly over the dome, suggests the arcs are joined using halving joints. Basically you cut a deep slot to half the width of the rib in each piece at the joint and then glue them together. This joint is commonly used for making partitions in drawers. Accuracy of cutting the slots an their exact spacing is obviously desirable to avoid misaligned joints. Now I have a table saw I can cut such joints.   

The area of a hemisphere [dome] is 2 x Pi x r² 
1.5m x 1.5m = 2.25 x 6.284 = ~14.14m².
5'x5' = 25 = 6.284 x 25 = ~157' ²

Assuming a 3m or 10' diameter dome [hemisphere] has a surface area of 14m² or 157' ². 

4mm ply weighs ~15lbs per 5'x5' sheet. So ~160/25 = 6.4 x 15 = 100lbs for the covering alone without any skeleton.

Click on any image for an enlargement.    

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Building the Octagon Pt.71. Segmented domes.

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Searching for segmented domes threw up a small number of skylight manufacturer's wares and projects.
 

The first is an octagonal roof lantern with only four vertical facets. Still a most attractive structure with jewel-like qualities in special  glass. The crispness of the superbly narrow joints will have to be my target if I build anything similar.

 AutoSpec | Skybright Skylights glass domes and octagons | Browse

The next example is a much closer approximation to a perfect hemisphere thanks to multiple gores [24?] and five [or six] vertical segments. A most attractive form in blue glass. The original is 42' across and is visible in Street View if you find the client's address in the link below.

http://sky-techglazing.com/Half_Dome_Skylights.htm


The desired segmented observatory dome  now needs to be defined as to the number of gores and vertical segments. An octagonal dome is possible but would limit the free radius inside as the straight lines cut across the arc. Only increasing the radius will help here. Adding more gores produces a much more realistic [smoother] approximation to a hemisphere. Adding more segments also smooths the curve. Complexity rapidly increases as does the number of panels to be cut and fitted.

Here I have arranged a hoop of plastic conduit to ensure the telescope would swing freely within its limiting, minimum arc.  I then superimposed circles on the image to conform to the required height [equator] and diameter. Note that the white hoop is skewed relative to the camera so appears oval/elliptical.

By enlarging the dome to the red circle it projects safely out over the octagon below. A suitable dome skirt will ensure weatherproofing. The supporting base track can be reinforced with timber brackets attached outboard of the octagon's upright posts.

The hemisphere's equator needs to be raised to match the mounting's axis. Alternatively, the pier could be lowered but at the expense of a very low eyepiece height when observing overhead. The present height of 70cm, 27" is considered adequate with a star diagonal in place. A low seat helps increase comfort levels on those rare occasions when overhead observation appeals.

Modification of pier height would cause considerable extra work because the heavy mounting would have to be hoisted clear. Using larger [4"] industrial wheels, with their usual, heavyweight, steel frames, will automatically raise the dome. As will using two plywood rings with blocks in between. It is arguably the easier option to physically lowering the pier. Albeit at the cost of a larger object.

I marked each quarter arc of the conduit with four and five pieces respectively to see how large the segments would appear in practice. Five segments seemed rather small. While four segments high seems to work best in practice. Increasing the number of ribs to form multiple gores will increase the dome's weight. 3.2m x Pi = 10m = domes circumference. C/16= height of segments.= 62cm.[Or about 2' high.]  16 segments = 62cm wide.

So the base ring would have equal segment heights and widths. The segment height will remain constant but the width will shrink with increasing height towards the dome's pole. The visual height of each ring of panels will appear to shrink due to perspective. Probably helping to maintain a nicely balanced panel appearance overall. Particularly when seen from a low viewpoint as will occur with my own observatory.

My hope is that the visually diminishing segments near the dome's pole will make it more difficult to determine the exact size and shape of the dome when seen from a distance. Each segment or facet should take on a different shade depending on its orientation to the light. Further confusing the eye and softening the shape by simple, geometric stealth.

Painting the dome [dirty] sage green should help to minimize its impact when contrasted against the mixed background trees. Each panel could even be painted a random variation on a theme of Sage. Perhaps  by adding a few drops of black or white to the paint pot at intervals. Perfectionists, longing for a snow white dome for thermal reasons, don't have to live with it! 

Not much physical progress on the build. Forum discussion surrounding roof design and construction, in particular, continues.

Click on any image for an enlargement.

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NOT building the Octagon! Pt.70 Options on how NOT to building a lighthouse.

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I had turned the roof profile boards square on to the house to try and convince my wife that the roof design would work. It did not convince her [at all] that I was on the right track. It was still "far too tall!" And "it looks like the graphics on an estate agent's website!" Whoops! 👎

So I left the boards to rock in the gusty wind and went off cycle shopping. You may well imagine my shock on my return. As I rode back along the main road I could clearly to see the profile boards soaring high above the ridge of the house in bright, August sunshine! Eeek!

It might as well have been a lighthouse judging by its sudden high visibility in the soft, green landscape. Without further ado I took the boards down. While amateur astronomy is certainly nothing to be ashamed of, there is absolutely no reason to raise bright beacons in the unspoilt countryside! Daytime, light pollution aside, advertising my hobby is not my greatest desire. While others happily raise white domes beside busy main roads I'd rather hide mine behind the tall, intervening hedges.

The latest roof design had placed the peak 12' [4m] above the raised platform forming the obs. floor. This was obviously a meter too high judging from the degree of clear visibility seen from the road  from right across the fields. I'd tried different angles to bring the lower struts more upright but the difference in overall height was not exactly convincing. Though I did have the desired telescope clearance.

We had the same problem when British TV changed to a much weaker satellite with a very tight footprint. For years we had enjoyed perfect reception, on all channels, with quite a modest dish. The only way to cope now was to put up a very much bigger dish. I bought a cheap, secondhand one from an abandoned building site. In stark white, it stood out like Joddrel Bank seen from the main road! The reception did not improve. So it was duly moved to the back garden. Where it fared no better.

The observatory build is on hold while I weigh all my options and discuss it with the wise woman.

A hemisphere would be the lowest and most compact geometric shape which would accommodate my long refractor. Provided it wasn't stark white its almost horizontal top should not be very visible at glancing incidence. At least not as visible as a white pyramid set against the backdrop of our typically dark green, deciduous garden trees!

This morning I set up a 12' tall pole lashed to the vertical telescope. Then took photographs and studied the visibility of different heights from the road using my binoculars. Provided I do not exceed 12' above obs. floor level then the peak of the roof is largely hidden by an overgrown elder tree near my southern boundary. These trees do not usually grow much bigger than this specimen but there is always hope.

Logic suggests that a taller roof, painted bright white for thermal reasons, would be most visible. Particularly in winter when the trees have lost their leaves. Something much less low key begins to fade into the background. With camouflage netting and paint stippling in green and brown [arguably]  the least visible. And arguably the most silly option.

Painting the obs. roof the same low key colour as the house roof offers one solution. The roofs would visibly blend into each other. Greys are also good for low impact. A multi-sided or faceted surface could be painted in slightly different shades to break up the solidity and general outline. With suitable software it is possible to keep changing a [roof or dome] shape's colour with the click of a button. I must have tried every option except desert camouflage. Green is surprisingly hard to get right. It needs to be "dirty" green and preferably rather dark. Bright "grass" green looks awful IMO because it is so artificial!

The problem is one of contrast and expectation. When they put up truly vast, freshly galvanized, farm silos they look shockingly bright but soon fade to pale, silvery grey with lots of variation. You see an older silo and think nothing of it. Now paint it anything other than silver and your attention is immediately drawn to it. Arched corrugated iron is usually offered in dark green. The corrugations change the light and break up the outline and appearance. These buildings usually pass unnoticed in a green, rural environment.

The Danish countryside is full of half-timbered [and often thatched] houses. White and yellow ocher are the favourite wall colours. With timber framing in all sorts of colours. The roofs are grey brown and pass unnoticed. The countless wind turbines have a clever, light grey, paint job which constantly changes in changing light. Parts of the same windmill can look stark white and jet black at the same time as clouds roll over in sunshine. Almost white is the common appearance seen from any distance in bright sunshine. It is hard to ignore them but at least they are not pink, purple or black!

Good grief! The Head Gardener has decided She wants a sage green, geodesic dome! Gulp! 😨

However, the sudden demand for a geodesic seems to be a basic desire for texture rather than a "HUGE smooth and featureless, half ball." Basically, it just needs that something extra to play with the light. This could be achieved with facets, gores or even thin, pretend tiles. The main problem with any added extra "texture" is weight. No matter how thin and light the materials used, "fish scales" would soon add up. Facets, of any kind would break up the outline and each take on a different hue to soften the overall effect. Such facets are basic covering and need not add weight.

After a few discussions, back and forth, I think we've settled on faceted gores. Instead of a smooth "umbrella" effect each gore will be bent in a series of steps. Instead of small steps, like horizontal planks, the panels will be taller. Modesty prevents me calling it a jewel.

Finding an example, online, just to share an image, proved all but impossible! The nearest I came to it was a 'wire' model prior to the propriety image handling software smoothing the "ugly" framework into a perfectly smooth ball. The exact opposite of the effect I have been asked to achieve!

Meanwhile I have had a thorough soaking in observatory builder's websites and learned some new tricks. Not least was not using bare, shiny aluminium! The slightest kink, bend or distortion, from absolute geometric perfection, is magnified a thousandfold by the reflective surface! My main problem is sealing such a multi-faceted structure without using GRP. [Sage] Paint and [Sage] paint alone must suffice.

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Building the Octagon: Pt.69 More roof mock-ups.

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A forum member has kindly suggested suitable proportions for a bent, octagonal cone. He suggested I make up a template to check the clearance of the telescope. Since I had a few lengths of plastic conduit tube I used those.

 The first image shows the rather bendy conduit propped up in a 5' + 5' arrangement. This provided adequate clearance when the telescope was pointing high above.

The central prop is 2.3m high and is there to provide stability of the mock-up in an occasionally  gusty wind.

The second image is from a lower viewpoint and the struts have been 'straightened' simply by drawing over the image in red. I think you will agree that the upright "walls" are too high at 5'.

In the third image the "walls" have been reduced to 4' high. The roof struts have been extended to simulate slightly raised height to compensate for the loss of headroom. Overall height of the roof peak is now about 2.4m.

It is fascinating to move the telescope around to check for clearance with the 'virtual' dome.

And now with 4" boards to provide the vital, inward slopes which dictate the roof's geometry.  My 'cheating' using upright conduit to simulate the lower roof was changing everything which mattered.

As the inward tilt on the lower panels increases, the length of the upper panels decreases and the overall height increases.

I drilled some boards at 4" intervals to allow quick changes of length. Then  clamped them to the tops of the octagon support posts. In practice they should be outboard of the octagon. So I had better find a way of providing this overhang to get any real idea of the final appearance and clearance from the telescope inside. It isn't as simple as running a long board across the entire width of the octagon. The mounting and pier get in the way.

I can't believe how blind I was to the errors introduced by using upright lower panels. It was simply too easy to drill holes and stick the conduit into the tops of the octagon posts. From that point on it was all downhill. The geometry was completely wrong unless I overlaid the uprights with suitable angled conduit. I didn't and it made a mockery of everything I tried in the way of strut lengths. The 4" boards are rather heavy and really catch today's 20mph+ winds. So 2"x1" or similar battens would be better.

And now the latest iteration with overhang. I now have 5'+5' boards but connected outboard of the octagon by about 6" per side. With a gale blowing up there it doesn't feel very safe stretching high above my head on a stepladder to loosen the G-cramps at the bends.

So I have to lower each side in turn to make adjustments to angles and lengths. Then put them back up before moving on to the other side. There is barely enough clearance at around the 'bend' between upper and lower sections. Loads of clearance overhead. I want to try reducing the angles from the present 58° on the lower boards. This will lower the peak and provide more clearance around the bend.

It finally feels as if I am getting somewhere on the roof geometry. I could even shorten the upper boards now to flatten the top section. The peak is still too tall at over 12' above the obs. floor.

And last, but not least, 70° lower walls with 5' & 5' boards for a flatter 'roof.' My wife hates it!


Wet paint! What the latest shape would look like painted solid white and the building clad in weathered grooved ply.

Click on any image for an enlargement.

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Building the octagon Pt.68 Domes or Cones? Plywood or metal?

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The weight of an observatory roof or dome depends on its shape, area and the choice of covering material. It is possible to make some rough calculations by using the information and online calculators without leaving your computer chair.  

Plywood Weight | ThePlywood.com

Cone Calculator

Duratool aluminium weights:  337967.qxd - 359285.pdf

The plywood calculator above suggests that 4mm Birch plywood weighs 2kg or 5lbs per m².

Some allowance must be made for variation in wood density, glue weight and moisture level.

According to the online calculator above a cone of 1.6m radius and 2m height has a slant or lateral surface area of 13m². You can't have the same height of cone as a hemisphere because it would cut into the hemisphere. The hemisphere of 1.5m radius is the minimum swept volume to clear the telescope. A straight-sided cone to slip over that dome and reach the equator would need to be larger in diameter and /or taller.

So 13m² x 2kg = 24kg or ~60lbs. This is for the plywood covering alone. A real observatory is expected to survive long term, outdoors in storms, snow load, etc. so badly needs its supporting timber framework. This framework could easily dwarf the weight of the covering depending on materials, number of braces, etc..

Beware of including the Base area in your cone area calculations unless you plan to cover the base too. Some online calculators offer the Base area, Lateral/Slant area and Total area. Keep this in mind.

Let's try using 1.5mm aluminium instead of 4mm plywood: 1.5mm sheet aluminium weighs 4kg m².

That's a doubling in weight over 4mm plywood! Though aluminium might be stronger, longer lasting and far more waterproof than plywood. Aluminium might be easier to support using smaller aluminium cross sections. Plywood usually has to be coated for long term weather protection. Paint and GRP can add considerable weight.

Historically, many observatory roofs or domes were sheet copper covered over wood planking.

1.5mm Copper sheet weighs 13.5kg or 30lbs per m². That's 3.5 times that of aluminium sheet of the same thickness. Now imagine the weight of all that supporting planking! It's no wonder they don't build aircraft this way! But then, they might have used thinner copper cladding for this purpose.

A 1.5m radius hemisphere has a surface area of 14m². Perhaps our original cone was rather undersized to fit over a hemisphere? But both would still be of a similar weight to each other.

The right, circular cone to fit over a hemisphere of 10' diameter is 15' wide and 7' tall.
That's 4.6m wide x 2.13m high. Running those figures through the cone calculator increases our slant surface area to 22m².   That's quite an increase on 13m² ! Now we are up to 44kg or 90lbs!

Reducing the bottom diameter of the straight cone to 12' means a height increase to 9'.  This is for a cone which touches the hemisphere. So the cone would need to be larger, both ways, to make room for supporting rafters and braces. The only sensible answer, is to bend the sloping walls of the octagonal "cone" to wrap it more tightly around the matching hemisphere. 

A forum member has kindly suggested suitable dimensions for a 'bent' conical roof. I will now have to build a simple, full sized template to check clearance for the telescope in all positions.

Yesterday [Saturday] I fixed guttering along the shed roof adjacent to the observatory. This will prevent rain soaking the ground between them and stop splashing up against the walls of both buildings. Without access to sun and wind there was little chance for this area to dry out between showers.

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Alternative observatory 'roof' designs.

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After much searching online for images of  different observatory style I finally found rich a seam under "Victorian observatories."

William Brydone Jack Observatory

A most attractive raised observatory set centrally within a pair of attached buildings. The straight-sided octagonal roof matches the tall building on which it is supported. New Brunswick, Canada. This was Canada's first astronomical observatory. It contains a classical, Mertz 6" refractor.

Observatory Tour

File:Observatory at Horodnic, containing telescope - panoramio.jpg - Wikimedia Commons

 Astro Travels: Telescopes

Another fascinating design built on top of a very pretty, hexagonal building strongly suggestive of traditional thatched buildings. Perhaps a windmill? The decorative, scallop flashing seems to have arrived or been removed at some point between the two photos being taken.

 The Athenaeum Astronomy Association :: Gallery - The Athenaeum observatory

  

Athenaeum Observatory - Go Stargazing

Mobberley - bse_athenaeum_observatory.pdf

And finally, the gorgeous, Athenaeum Observatory seen from the air. This overhead image is not present in the Association's, otherwise-excellent, gallery. Note the similarity to the shape I have been trying to achieve in a bent, octagonal cone. Conservation of space and materials, with close adherence to the contained hemisphere in a beautiful design. A "flip-top lid," allows viewing at the zenith. Presumably the roof covering is wonderfully verdigrised, copper cladding. Of course, they weren't foolishly worrying about the visual appearance, when seen from below, as I have.

John Tebbutt in NSW, Australia built two observatories on his Windsor estate with non/hemispherical roofs in the mid to late 1800s.  One still contains Tebbutt's original Grubb 8" refractor on its heavy mounting.  There are numerous original and later images online if you search for "Tebbutt observatory." This link has a gallery of images but there are many others.

Peninsula House, Tebbutt's Observatory | NSW Environment & Heritage

  Astronomer John Tebbutt’s estate is on the market for the first time in 170 years - realestate.com.au

 https://www.realestate.com.au/property-house-nsw-windsor-124385298

Depending on which newspaper carries the sales story there are further images of Tebbutt and the Grubb instrument. Tebbutt's grandson has turned the observatories into a museum but has the estate for sale. John Tebbutt died in 1916 and appears on some Australian currency.

  

All images shown here are borrowed for non-commercial, educational, [fair use] purposes. Hopefully to provide more visitors to their original websites and to enjoy their facilities. Anyone objecting to their images appearing here should get in touch for their immediate removal. 

Click on any image for an enlargement. 

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Building the Octagon Pt.67 Quart "circus tent" in a pint pot.

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Tuesday: Went around painting more surfaces with the Safe-Way, rot protection, mineral juice. Including all the boards on the veranda. Was tickled by tiny 'storm' flies and tiny 'money' spiders flying in on strands of web. The decorative dragonflies were obviously not keeping up with their predatory duties.

Took down the pretend dome of plastic conduit and measured up the telescope and mounting. Just to prove, beyond all reasonable doubt, that you can't put a quart of telescope into a pint pot of dome.

So? Which part of: "Your pier's too tall" don't you understand, Chris? 😉

Answer: "I may be in limbo but I'm [far] too old to become a limbo dancer."

The difference between man and beast is that only man would try and put a large telescope in a dome of half the necessary size. 

Now, that's, what I call a lot of offset!
43cm or 17" to be exact.
Star diagonal floor clearance is 70cm or 27".

I think the realization is dawning on me that there is a folded refractor in my stars. Well, in the shed, actually. It's that, or make a very tall, dome bearing ring. Failing that, it means taking the chainsaw to the pier!

Now, for those waiting with bated breath for the next exciting episode of "Badly Made Models" I give you Pt.4 "The Taller Version." As I have already "given up the day job" I have little to fear from criticism of my artistry or construction skills. This is just a scale mock-up to see how form affects function as well as appearance.

The red circle represents the "best fit" hemisphere which will go inside this small scale suggestion for a rotating roof form. Though, for accuracy, one should make allowances for the depth of any "woodwork". So all construction materials must lie outside this circle. The red dome really is the minimum allowable dimension. Nothing must "stick out" inside the dome or the moving telescope will surely find it! Note how the ring of taller triangles visibly shrinks in comparison with the lower ring of trapeziums. Yet, seen from above, the "circus tent" looks distinctly "pointy." You may rest assured that the traditional red and white [or yellow] stripes will not be a feature of the full-sized version. Now I just need to add a ridge and I shall have a bi-pitched, octagonal observatory to be proud of. Well, that's the theory.

Wednesday: Spent time clearing up the building site and surrounds. The smaller timber off-cuts had been piling up without any real plans for organization. Stones and even oversized gravel had become redundant now that the site was level with the rest of the garden. Not to mention the overshadowing birch trees had finally gone. The sunken site was completely unusable for foot traffic before we barrowed in the 20 tons of self-compacting gravel. Leveling absolutely transformed the site into a useful space.

As did bringing in the finer gravel for a clean and comfortable walking surface. Not dragging clingy sand all over the place was a huge bonus. Previously, I could clearly see my regular walking routes between the site and other places to collect tools and materials. The sand was oddly brown and very noticeable against the darker soil and lawn grass.
 

Click on any image for an enlargement.

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