Building a 3-frequecy icosahedral geosdesic dome
The purpose of this page is to guide a beginner in geodesic domes as to how to go about building a 3V icosa geodesic dome. This has grown out of my correspondence with a young engineer who wanted to go about doing this.
Geodesic domes are a sub class of tensgrity structures. Tensgrity structures need not be domal in charter - they can be of any shape. Many of the beautiful tensgrity structures are towers or needles. Geodesic domes need not be a portion of a sphere or have a circular cross section. They could be portions of ovals with or without a circular floor plan. Some of the best geodesic domes are combinations of two domes with very different radii.
To build large radius geodesic domes with conventional building material, it is convenient to break long struts into shorter struts. This is a process called frequency sub-division and there are many ways to achieve the frequency sub-division.
- 1V If the strut is left as it is, then the dome is of one frequency written as 1V or 1v.
- 2V If the strut is sub-divided into two struts, then the dome has two frequency written as 2V or 2v. Such a dome is visibly jerky.
- 3V If the strut is sub-divided into three struts, then the dome has three frequency written as 3V or 3v. Such a dome is visibly smooth.
- Higher frequencies. Struts get sub-divided into higher frequencies with some domes being 16 V or even higher. But increasingly those are domes built by professional builders.
Most Commonly built Dome
Given the huge possible variety of Geodesic domes that can be built, it will come as a surprise that most domes that get built are 3V ICOSA domes. This page guides you as to how to do that.
Fuller Kruschke Domes
Buckminister Fuller is well known as the inventor of Geodesic Domes. The version of the Geodesic Dome that the public most often sees is the 3f icosahedron. ICOSA in Greek means twenty. Hedron in Greek means face of a geometrical solid. Thus an icosahedron is a twenty faced geometrical solid. Thus an icosahedron is a twenty faced geometrical solid. An icosahedron is also a regular platonic solid. A regular solid has identical edges, angles and verticies. He published his design in his book Dome Cookbook of Geodesic Geometry in 1972. That book is out of print at present and copies are hard to find.
A 3 frequency, 3/8 icosahedron as the geodesic dome is the most common geodesic dome that is made. Vigyan Ashram domes are also the same. A 10 meter radius, 3 frequency icosa dome requires very large struts and the area of the largest triangle is huge. Both could be a problem when you practically build such a dome. By contrast, a 4 frequency icosahedron cuts at the equator flat and is a half dome. Compare the strut sizes (average length and longest length) of the two structures. Of course the four frequency dome will consume about 50 % extra material in both struts and hubs but will be far more safe.
The best three sites to consult as you work through your project are given below:
- A Dome Calculator. http://www.desertdomes.com/domecalc.html. This site gives you most of the calculations that you will need to make. However, when you make a 3 frequency icosa dome, its base is not straight. The deviation from straightness, is not very large and most manufacturer of smaller domes,pretend that it does not exist. That is also what the Dome Calculator does. Google for Desert Domes / Burning Man to see pictures of such domes.
- Domerama : http://www.domerama.com/ This site has more comprehensive set of dome calculators. In the initial stages, the process of fiddling with a 3 frequency icosa to produce a flat base was not well known. Now, one such method, called Kursche, is readily available on many sites including Domerama. It has 4 struts instead of 3 struts that are there in a normal 3 frequency icosa.
- The most advanced site that you might want to consult is called Simply Different http://simplydifferently.org/. It deals with all sorts of ecological structures, including domes. Go here for domes http://simplydifferently.org/Geodesic_Dome_Notes. It has another method of producing flat bases in odd frequencies icosahedrons. It has also another algorithm dealing with optimising the number of struts at higher frequencies so that variability in size is also reduced. Compare the four frequency optimised strut lengths with those in Desert Dome.
Geodesic Dome Construction
There are two main methods of constructing simple Geodesic domes that will interest students.
One is called strut and hub method where struts in form of angle iron (like Vigyan Ashram uses) or tubular pipes (as you want to do) are used along with hubs. Note that the Geodesic Dome theory has no use for a hub. It just assumes that you connect the struts in some manner. How you do it is your headache. The strut and hub method does leaves spaces between the struts and you need to fill them to have a usable structure. Vigyan Ashram uses ferro-concrete to do that job but straw bales have also been used.
The second main method is using triangular panels. In USA, many dome manufacturer use plywood panels whose sides are fabricated out of wooden logs that are called 2 by 4 . That means that the log is two inches by four inches wide. The plywood is backed with insulation, including thermocole, paper-crete etc. Here is one picture. Many more can be seen here.
Construction of 3 frequency icosa dome with pipes or tubes
While all sort of MS and Galvansied tubes are available in USA, the most common types of tube/pipe that is used for dome construction is called EMT. EMT stands for Electro Mechanical Tubes and are what we call conduit pipes in India. These pipes are used to carry concealed wiring. Indian conduits used are much weaker than the USA counter parts.
One of best set of resources on constructing a dome from such tubes is the site of Jack Booted liberal :
- Part 1 :http://jackbootedliberal.com/2010/05/building-a-4v-geodesic-dome/
- Part 2 :http://jackbootedliberal.com/2010/05/building-a-4v-emt-geodesic-dome-part-2/
After you have gone through the site, you can read more general instructions here at Domerama. If there doubts after reading both, I may be able to resolve them. If you want to see Indian students assembling a geodesic dome see this site of mine and Vigyan Ashram.
I will soon give you a link to literally hundreds of ways in which people fabricate hubs. But first you need to understand that hubs have to connect either five or six struts at any one time. In a typical dome,the number of hubs that connect five struts are far fewer than those that connect six struts. Still two types of hubs need to be fabricated.
Second hubs have two types of angles. They are inter strut angles (assuming that all struts are in the same plane). In a hub that has five struts, the inter strut angle in not 72 degrees. It is really a little lower than 71 degrees. Struts are in different planes and therefore there are dihedral angles between them. These are different for each pair of struts depending upon where the hub is placed.
The ball and socket joint that you have thought above will automatically align the strut to its correct dihedral angle. But the hub will not correct the inter strut angle and some distorting stress will be introduced in the design. Almost all designs of hubs ignore this distortion.
Link to different types of hubs: http://www.domerama.com/dome-basics/geodesic-dome-hub-connectors/ This is very comprehensive and very pictorial.
The first hub connector depicted there Steel Pipe and PVC Hub Connectors, is the most common way to join EMT tubes in domes. Its cheap costing about half length of one strut plus a number of high tensile nuts and bolts. Some 16 or 17 hubs downward is the ball and socket hub that you are interested in. Its made by Domekit.cc. You can see the details here. (Note that the main page of Domekit.cc will frustrate you. You must follow the link I have given.) You can see in the picture that there is one blue colored hub for five strut hubs and a white hub for a six strut hub. These appear to be made out of plastic and will be weaker than metal hubs that Vigyan Ashram makes or the first type of connectors shown on Domerama page.
Strength of the Domes
It is but natural to be wanting to know the strength of a dome. For a long time , there was no answer to this question except for a in-your-face assertion that domes are the strongest structures possible. Now that computing power is cheap and Finite Element Analysis (see also http://www.asme.org/products/courses/tools-and-methods-of-finite-element-analysis) programs very common , some engineers have tried to apply them to domes.
One student, Marek Kubik, has applied FEA to the type of Domes that Vigyan Ashram manufactures. His results are here. I should add that I do not agree with the entire approach or its results.
Another, more professional approach to a 3 frequency icosa made of EMT of known specifications, is here . While I do disagree with the approach and the findings, some things are worth noting. First his analysis shows that hubs are the weakest points in a system of struts and hubs. Hubs that he has used in his analysis break down at loads that are one eight of the loads that struts break down. Hubs breakdown at a force of 6kN while struts breakdown between 47 kN to 55 kN.
Because the tool, FEA, as it exists today, is faulty to use on a dome, it probably underestimates the strut breakdown strength by a factor of 6 to 8. The reasons why I hold the tool to be faulty are too long and complicated to be gone here but let me give you a simple reason. Probably early in your engineering studies you have would have read about the essential difference between a machine and a structure. In a machine, parts move relative to one another. In a structure, the parts are rigid and do not move in regard to each other. Geodesic domes are always moving in regard to each strut and are properly analysed as a machine and not as a rigid structure.