my first introduction to geodesic domes was in my teenage years. i was reading a book by fiction author Kim Stanley Robinson called "Antarctica" and came to a part in it that seemed to take a ton of unnecessary time to describe the idea of what a geodesic dome was and why the hell they would built one in a frozen wasteland like antarctica. it provoked me to think about the concept for a moment and then that moment was gone. i forgot all about the domes for years and years until this blog post.
so what exactly is a geodesic dome? let's find out.
A geodesic dome is a hemispherical thin-shell structure (lattice-shell) based on a geodesic polyhedron. The triangular elements of the dome are structurally rigid and distribute the structural stress throughout the structure.
by that definition, i can think back even further and remember perhaps the first geodesic dome that i ever (unwittingly) encountered. it was that old-style school yard climbing structure.. never was sure what it was called.. a jungle gym maybe ? it look's like this:
so what's the deal with these things.. they have them on playgrounds for kids and they have them at the bottom of the world in a the most hostile wasteland on earth. but why?
it turns out that part earlier about "triangular elements distributing stress" is the geodesic's true super power. it allows the domes to be able to withstand very heavy loads for their size, making them perhaps one of the strongest and safest man-made structures to exist even today. you'll find a geodesic dome equally at home in the wastes of Antarctica as in your neighborhood playgrounds for one reason.. they are very, very strong and by extension.. very, very safe.
but again, why? why are they so strong and safe exactly? what's the difference between a bunch of rectangles and a bunch of triangles ? is there really that much more strength by losing one side of a rectangle? let's find out.
first discovered (invented?) by: R. Buckminster Fuller (1895-1983) in 1954. "Bucky" was an American architect, systems theorist, author, designer, geometrician, cartographer, philosopher, inventor and futurist. the geodesic dome design was envisioned as "sacred geometry," a structure made to utilize the inherent strength of arch shapes and also have a triangular rigidity which makes them very strong and resistant to falling or crushing.
it is said that while Bucky was coming up with the geometry of the geodesic domes he first drew inspiration from nature. R. Buckminster Fuller noticed that the shell of a soap bubble is very light and brittle, however still very strong as long as it is in that shape. in comparison: a box is made of relatively heavier and stronger material but will succumbs to distortion easily in the face of compressive forces.
this is because triangles are the strongest of all shapes known to man. when many triangles are connected to form a dome it translates in to a very strong self-supporting structure (the best kind of structures, in my opinion). this strength eliminates the need for supports and occurs naturally as a result of triangles distributing strength evenly across it's frame. another advantage is that the dome's strength actually increases as the size of the structure increases.. meaning that the bigger it is the stronger it gets.
on the other hand, we have the rectangular or box-like structures we see, rely on and live in everyday. it has always seemed to me like us human beings are somehow oddly compelled to build and replicate these 4 sided shapes. it appears like everything we build, craft or own is thoughtfully designed for and intended to be used with other rectangles. the only exception i've noticed is the old analog clocks that used to hang on the walls in grade school, but even those were hung with a small wooden frame around them to mount them securely there. it's an old paradigm, but, i digress..
back to fun with shapes time.. the reason the triangle is stronger than the rectangle is because the rectangle distributes loads at right angles which makes them considerably weaker. on the other hand are triangles which distribute the structural stress throughout the sides making them unique in a sense. the angle between two sides of the triangle is based on the length of the opposite side of the triangle.
remember high school geometry? that's okay, neither do i! there was something called the pythagorean theorm or a² + b² = c². this old proof describes the mathematical reasons why an equilateral triangle is the strongest 2d shape that we know of. i won't bore you with a blatant copy & paste job explaining why i don't understand math so just go and check out wikipedia if you are so inclined.
ok, so now we've arrived at the point in this blog where paper beats rock and triangle beats rectangle. still with me? good. the perfect geodesic dome would be constructed with the consideration that all of the triangles which make up it's frame should be as close to equilateral triangles as possible. in this way the stresses will be approximately the same on all the struts, so that there is very little wasted strength. you can use something like this handy dome calculator to determine the radius and the lengths of the struts.
in general there are two geometric shapes that are most commonly used when constructing a geodesic dome. they are the Tetrahedron (a polyhedron with four triangular faces, six straight edges, and four vertex corners.) and the Octahedron (a polyhedron with eight faces, twelve edges, and six vertices). often when designing a dome you will start with a tetrahedron or octahedron, subdivide the triangles and push the vertices out to the surface to make successively better approximations to a sphere.
there are some drawbacks however. one problem to be aware of is that if you plan to use a tetrahedron as a sphere rather than a dome your design will have no natural "equator" when its triangles are divided into an even number of sub-triangles. another problem is that the more subdivisions are required the more different length struts are required.
for example: a icosahedron-based dome (a polyhedron with 20 faces), for the 1V, 2V and 3V designs require 1, 2 and 3 different strut lengths, respectively. the struts are the pieces which make up the 3-sides of the triangle shaped pieces which compose the dome
the reason you want to have struts of the same length is because during construction it's much easier to have a number of spares in case there is damage. another good reason is because it's easier to quickly create a stack of struts to use when you only need to measure and cut a few different lengths.
well, that's it. you have now been imparted the knowledge, the power and the sacred geometry of the geodesic dome (a trinity of sorts). but (as uncle ben says) with great power, comes great responsibility! build safely out there folks.