Thursday, July 12, 2012

How to Make a Geodesic Dome: Eliminate Heating Bills and Homelessness Panic Attacks

If you can't, or don't want to, pay crippling heating bills or if you suffer from visions of imminent destitution and homelessness, build yourself a geodesic dome home in your bedroom, heat it with a lightbulb . . . and flee with your dome when the bank repossesses your house!


recent photos of life in the dome: MONEY or CURRENCY click here

Above, dome nearly completed, without glass and perspex windows (its summer!)

 Above photo, interior of dome, nearly completed

Above photo, interior of dome, nearly completed.  
However, most governments and legislators would prefer people of low income to live here . . .

In 'charming' town planning projects that give the local medeival architecture a real boost to their image, eh hem . . . Spot Ales' medieval fort and, significantly, old prison, it's a job to find it, but if you squint hard enough. . .

 Anyway, enough of sad and unsightly things, let's move onto to more hopeful vistas . . .

The first step in building a geodesic dome home is to fully understand and visualise the geometry of the structure beforehand.

To do this it is essential to build a small model version that you can refer back to whenever you get confused or stuck. It's possible to build a dome without first doing a model, but you're more likely to get in a fix, which wastes time and money.

To make a 50cm diameter cardboard model you'll need a pencil, a compass, a ruler, 15 sheets of A4 lightweight photocopy card in one colour, and 5 sheets of the same card in another colour, one large piece of thick cardboard for the base (from a big cardboard box will do), glue, at least twenty very small boston clips, thumbtacks and probably some other stuff too, we'll see as we go along. The two fluffy assistants are optional.

I found a useful video on YouTube showing how to 'construct a geodesic dome' out of cardboard. The instructions are for children so even a maths moron such as myself could follow them! The dome is composed of 10 equilateral triangles that join together 6 pentagons, each pentagon being composed of 5 isosceles triangles.

In all, the dome requires a total of 40 triangles, 30 of them isosceles and 10 of them equilateral. In order to attain the dome diameter of 50cm the 3 sides of the equilateral triangles must be 15cm45 long precisely (to be called length A). The isosceles triangles must have one side measuring, again, 15cm45 and the two other sides measuring 13cm66 (to be called length B).

Being the congenital maths moron I am, it was impossible for me to calculate how to draw two triangles together (to save paper), centering them correctly on a sheet of photocopy paper. So I drew one, photocopied it, cut them both out, then stuck them together on a sheet of paper. In this way I had the template for two triangles neatly fitted together and centered on the A4 paper.  I then made 5 photocopies of the template below so as to get 10 equilateral triangles in lightweight yellow card.

To make an equilateral triangle, use your ruler to draw a 15.45cm line at the bottom of your page. Set your compass to exactly 15.45cm. Putting the point at one end of the line, draw an arc approximately where the top point of the triangle should go. Switch the point of the compass to the other end of the line and draw another arc. Where the two arcs cross is the third point of the triangle. Use your ruler to draw the two other sides. To draw the glue tabs, draw a line 1cm parallel to all three sides around the entire outer edge of the triangle. Cut off its points, as in the triangles above, by drawing a straight line to slice off the points of the outer triangles so that the glue tabs can be stuck together without the ends overlapping. To draw the isosceles triangle draw the base line of the triangle again at a length of 15.45cm, but set the compass at 13.66cm instead so as to achieve the two shorter edges. I then made 15 photocopies of the template, this time in blue card, so as to get a total of 30 isosceles triangles.

Carefully cut out all your triangles and, using a book and a ruler, fold the glue tabs carefully along each of their lines.

Apply glue to the tabs and stick the five isosceles triangles together (sticking together the B sides) so as to form a pentagon, leaving the last two tabs unglued. When applying glue be sure to use a scrap piece of paper underneath so as to not get anything grubby. Stick the B sides together two by two. If you try to apply glue to all of the sides at the same time and then try to stick them all together simultaneously, the tabs where you applied the glue first will have dried. So just go edge by edge. Glue needs to be applied to both glue tabs being stuck together and not just one, to ensure a strong fix.

Assemble all six pentagons in the same way, leaving the last two edges open on each one. To be sure that the glue dries completely you may want to leave the next stage for the following day; otherwise, leaving it for a couple of hours should do it. Once dry, the final edges of the isosceles triangles can be glued together. As you pull the two sides against one another you'll see why it was necessary to allow the other sides to dry first, as now the pentagons will be raised into their three-dimensional volume, putting strong pressure on all sides. This is where you now need to attach the small boston clips to clamp the freshly glued sides together. I left them all overnight again, but if you're feeling brave, another couple of hours should do.

Here we have the six pentagons fully assembled on my scruffy old floor. As you can see, my fluffy assistant to the left seems satisfied with the work so far. I have placed the ten equilateral triangles next to the pentagons, ready for the next stage.

Now we need to make the base. Thinking I was very clever, I bought some fancy hard card instead of using the simple cardboard box card suggested in the video. The result was a fiendishly difficult challenge with a Stanley knife when it came to the cutting stage. It was all very scary and not at all appropriate for children . . . or for fluffy assistants for that matter. So use normal cardboard from a box as it's far easier to cut with no more than a pair of scissors. And it's free.

Cut out your piece of cardboard for the base, making it no smaller than 56cm squared. Find its center by drawing diagonal lines from each of its corners, creating a cross in the center. Here, one of my fluffy assistants is demonstrating how this can be done very easily with a builder's rule, useful as it's so big. A straight plank would also do the trick.

Here is the base with the cross revealing the center of the square. At this point you may wish to take a small break and give yourself a vigorous scratch for good measure.

Now we need to make a big compass out of a 35cm x 4cm strip of card. This card is thicker than the triangles but lighter than the base board. It needs to be quite thick and strong so as not to tear, but not too thick to put the nib of a pencil through it. Place the cardboard strip on another piece of cardboard as we are now going to push thumbtacks into it to create pencil holes. My assistant is helpfully indicating the spacing of these four holes. The one on the far left, let's call it the '0cm hole', will be the point where we pin this card compass into the center of the base. Now place a tack at precisely 16cm to the right of the first hole, then 25cm and finally at 27cm distant from the first hole. We have now created four holes at 0cm, 16cm, 25cm and 27cm.

Tacking the 0cm hole to the center of your cardboard base, use the holes at 16cm, 25cm and 27cm to draw three concentric circles. The fluffy tail is optional in this simple manoeuvre, but adds interest.

Here is the base with the three concentric circles drawn.

Cut out along the center circle to create an inner hole. Cut out along the outer circle to finish the now circular base. Sitting on the circle will prevent it from unexpectedly flying away . . .

Set the compass to 15.45cm precisely. To make it easier to set it perfectly I drew a line of the right length on a piece of paper, dug the point into one end of the line and carefully pulled the compass to the right length. Place the point of the compass on the circle inside the outer edge of your base and draw an arc further along the line of your circle. Then place the point where your arc crosses the line and draw another arc further along. Continue all around the circle till all the points of your decagon (ten-sided polygon) are drawn.

At this point you will discover if your compass is set precisely or not. If it isn't your last arc will be too far in or out. Cursing loudly at this juncture may help relieve tension. If it's not right, rub out the marks and start again. I actually ended up having an approximate decagon and just bodged along as I do, knowing that the length A sides of the triangles would make up for any incompetent fumbling around with the compass. Now use your ruler to draw straight lines from point to point, thus completing the drawing of the decagon. My assistant pointed out that my work was rather unprofessional.

She explained that putting one's nose up against the base and scrutinising it carefully was all it took to discover my sloppy work.

She even went so far as to call my other assistant over to prove her point

At this moment in the proceedings my assistants became suddenly overwhelmed by a frenzy of excitement. Perhaps my lack of professionalism had compromised their respect for the project.  All at once my ordered workshop had degenerated into a wrestling ring!

Determined to get things under control, I raised my voice and commanded, 'No no, you naughty assistants! Stop this monkey business at once!!!'

Fearing my authority had indeed been compromised I was forced to take radical measures. Reciting the affirmation 'I am strong and in control. I am respected' I grabbed them round their fluffy bellies and firmly transported them out of the room, shutting the door behind them! They were outraged, but I felt proud to have proved to myself and to the world at large that I was an impressive figure of authority, not to be messed with. I could now get on with laying out my card dome sections, base, boston clips, thumbtacks and glue without further ado.

Applying glue to both sides that needed to be stuck together, I glued the pentagons and equliateral triangles alternately round the base following the decagon I'd drawn previously, as neatly as possible. To keep everything in place it's essential to use the boston clips on the dome's edges and the thumbtacks around the base to hold everything in place and give the glue time to work.

Once the bottom layer was complete I applied liquid glue all around the join of the base to give it extra strength.

I added the final layer of equilateral triangles . . .

And using the hole in the base in order to access the final layer from underneath, I glued in the last pentagon. Et voila . . . the dome model was complete . . . as was my initiation into the mysterious world of geometry and mathematics!

 The most difficult part of building a dome being accomplished, I could now apply myself to the simple task of building the dome home itself. All that was needed was a comfy chair, a hot drink, and a handy assistant to take care of all the boring woodwork!

To make lifesize domes, you can use the model as a ratio guide.  In the video for making the model, the man gives the following mathematical formula for understanding the diameter and length ratios (not that I understand a word of it, mind).  This was the formula he gave (and that I still haven't figured out in my brain):
r = radius of dome
A = r x 0.61803 (base side)
B = r x 0.54653 (sides of isosceles)

Here is how we went about calculating the real dome:

The model is 50cm diameter, composed of 40 triangles of which 10 are equilateral and 30 are isosceles. 
Length A (of the equilaterals) is 15.45cm and length B (of the isosceles) is 13.66cm

Therefore, to make, for example, a 2m diameter dome, simply multiply all of the dimensions above by 4 (50cm x 4 = 2m).

So for a 2m diameter dome:
Length A = 61.8cm (15.45 x 4) 
Length B = 54.64cm (13.66cm x 4).

For the 3m dome that we built, simply multiply the model's dimensions by 6 (50cm x 6 = 3m).

Here it is in its skeletal form to help you visualise the following calculations,

The 3m diameter dome:
Length A = 92.7cm
Length B = 82cm
Now it is necessary to count all of the spokes, or wooden bars, of the dome (lengths A and B) so as to know how many to cut to support the forty triangles.

As there are 6 pentagons, each composed of 5 central (radial) spokes, this makes a total of 30 length B spokes of wood.  The 10 equilateral triangles, joining the pentagons together, are all composed of 3 length A spokes, which makes 30.  Don't forget to add the 5 additional length As at the base of the bottom pentagons. 

The door is best put in one of the hexagons (composed of an upper and lower equilateral and 2 isosceles to each side) rather than the pentagons, because the hexagons have horizontal tops and bottoms, good for putting in a rectangular door:  The pentagon is pointed at the top and a bit lower down, requiring one to stoop.  Therefore, from the above calculation of the number of total spokes, it is necessary to subtract the central spokes of a hexagon, that is, two length Bs and 4 length As

The 3m diameter dome:
Total number of length A (92.7cm) spokes/bars  = 35 (minus 4 for door = 31)
Total number of length B (82cm) spokes/bars = 30 (minus 2 for door = 28)

After trying out the dome without a base, as you'll see in the photos below, we decided that having a bit of extra height would be far more comfortable and spacious to live in.  It was worth the extra effort:
Our base consisted of: ( . . . . . . . . . )

The metallic bars, or braces, to join the spokes together into 'hubs' were each 10cm long with 4 screw holes.  We chose to join the wooden spokes with more or less the cheapest available, strong enough to do a nice job, but flexible enough to bend with pliers in those all-important bodge job moments.  I think the price in a DIY shop was about 3 euros for a pack of twenty five.  We bought four packs, giving us about 100 metal brackets in all.  We got in a fix and ran out at some point, so it's useful to buy a few extra just in case.

We bought the cheapest non-planed bars of wood, 3cm x 4cm thick in strips of 2 meters, to cut up into the lengths B and A.  In all we spent approximately 70 or 80 euros on the wooden understructure frame of spokes.  One day I will make these spokes out of locally harvested bamboo and join them using the ring hub method instead.  Meanwhile, we did actually happen to have a spare door hanging around, so that was one expense we were spared.  Planing the wood is boring and quite time consuming, so having a handy human assistant around to take care of this is advisable.

The metal braces are put in a vice (or some other mechanism to keep them still) after first being stuck together in a straight line with masking tape so as to prevent them slipping out of place when whacked . . .

Then they were whacked and bent in the middle at a 36° angle using a protractor as a guide.  After much head scratching we finally figured out that the angles of the dome would correspond to the angles of the base of the structure; that is, a ten-sided polygon which is called a decagon.  A circle is 360°, and divided by 10 = 36.

Here below are the metal braces each screwed into the wood using the two screwholes, leaving the other half of the bar jutting into the air.  All of the wooden bars must have metal braces attached to both ends.

Each hub is joined by a butterfly screw (well, that's what I call them, anyway)

Here is what the dome looked like, rapidly erected with no base . . .

. . . leaving the hexagonal door gaping saggily open and in desperate need of two vertical support lengths of wood for the rectangular door shape, plus short spokes supporting the middle of each length.  However, we had more ambitious projects afoot, so we didn't bother.

Nevertheless, the basic dome, covered as in the photo below, with decorative hand embroidered nomadic Indian fabrics and blankets, makes a very nice mini-yurt structure for keeping warm in the winter, or covered with a canvas for a outdoor tent.

But that's not what we wanted . . . so we took it all down and started again, this time with a base . . .

Oops . . . forgot to add the side bars of the rectangular base sections . . .

At this point having someone holding the model as a guide and telling the other person which order the lengths A and B go is vital if you don't want to spend all day and all night putting the wrong lengths in, dismantling everything, reconstructing it and so on.  It can even be helpful to mark, both on the model dome and the wooden spokes, if they are As or Bs.  Additional assistance of the fluffy ginger variety is optional.

A handy broom, however, is essential . . .

The first round is up, leaving a gap for the door, so everything's a bit wobbly and the broom is more appreciated than ever.

This floppy hexagonal gap for the door is a tricky number.  If you have a door ready made and fitted at this stage, it's best to put it in earlier rather than later.  In our case the door was still an unexpected but rapidly approaching crisis.

The last spokes go in . . .

Up and up . . .

And now, the door . . .

It is not going to be fixed into a solid wall so anything you can do to rigidify it could be helpful.  We attached planks to the base and top of the frame to reinforce it and attached the whole lot to the dome with 45° angled brackets as in the photo below.  It's tricky, fiddly and at times infuriating, so experts in bodge jobbing are more likely to win the day on this one.  At times the frame and even the whole dome needs yanking around till you get everything well balanced and grounded evenly on the floor:

After admiring the recycle crochet jumper I made for my assistant, you may wish to turn your attention to the piece of string attached to a hub with a bracket sticking up.  This is to measure and gauge the angle and lengths from the top four dome hubs to each side of the door that must be joined to it with four bars. Goodness knows what angle they may be, all depends on the size of the door in relation to the dome, its base, etc.  So forget about maths, get your string out, a handy pair of pliers and start wiggling the metal brackets on the door and the hubs into the right angle.

Once you have achieved this most difficult of tasks and furthermore attached the bars successfully in place, you may wish to invite your assistants in to check it out and test for areas of sloppy handiwork.  In our case we were most relieved to meet with the door inspector's approval.

Following which, sitting down with a hot cup of organic mint tea and admiring the view is a good way to spend the next few days of well earned rest.

notes re heating with 40 watt lightbulbs etc (from Money or Currency post)

NEVER use an open flame candle in your dome!

Unless you particularly like BONFIRES . . . special bonfires IN your house . . .

The same goes for electric lamps that should preferably be stuck down to whatever surface they are sitting on ... i put blue tack on their base so they don't fall over ... electric lamps are also a fire hazard if not placed carefully where they will not over-heat near inflammable surfaces such as fabrics and wood, of which there are plenty in a dome ...

A shielded heater can be created putting metal shields around a shelf of lamps ...  i use recycled oven shelves and panelling found thrown out in the street .. . and rarely use lamps more than 40 watts

So basically be VERY careful to avoid putting too hot a lightbulb too close to wood or fabrics, or anywhere where something inflamable can over heat and catch fires.

If one goes for the candle lantern option, then in a super insulated small space you need to evacuate the candle vapour with a chimney.

If worried about not enough air in your small space ... add air chimney at top of dome and an air vent in lower wall.

I didn't need it as this structure is not air tight and just opening the door during the day as you go in and out gives the air circulation you need.