Entry # 24 A breakthrough in the matter of “air-buoyant vacuum containers”.
While carefully cutting out pieces of Al-coated cardboard – part of my effort to build a demonstrable “cost-effective solar concentrator” based on the hex-rosette, I could not avoid getting bored and anxious with the intricacy of it. Unfortunately, though my ideas are big, my available means are small, and I only have 23 pages of the reflector-coated material to hand, where my design actually needs 21 : not much room for error, hence a build-up of anxiety and trembling boredom. Fiddling around with ruler and sharp pencils takes time, and unfortunately, my printer cannot handle the thick cardboard. And the shapes have to be accurate, and scored for easy bending, and all of it takes time. Have no fear, the thing will get built, but something had to be done about the boredom.
I went back to one of my perennial projects, the one I call my “Engineer's Holy Grail” – how to do what engineers have never done, namely build a material envelope-shape, like a balloon, blimp or Zeppelin, and make that so light and strong that once the air is pumped out, it will rise up, like a Montgolfier or helium/hydrogen filled balloon. It must collapse – you say, if it is light enough, and it can't be air-buoyant if it's strong enough to sustain a vacuum or near-vacuum.
When a serendipitous mind like mine starts to worry a problem, as a dog worries an old bone, something sometimes clicks, and this time, it did, and I hope the click will be heard around the world !
Consider old Plato's “icosahedron” - 20 equilats edge-joined together, which can be built as a lattice of 30 thin rods, joined together five rod-ends at a time. Weight and volume according to choice of material and scale. Now – erect scale-compatible octahedrons/octahedra so that one is face-butted to each equilat of your icosahedron – you will need 20 octahedra, and they will jut outwards every which way from the icosahedron. Now comes a surprise : the octahedra all face-butt together, and by their unbutted outer equilats, they define a well-known Archimedian solid, - twelve pentagons so surrounded by twenty equilats (joined by their corners) that the pentagons also only join by their points. In other words, an icosahedron now nests inside that archimedian solid, but does not float around, because there are ribs belonging to the face-butted equilats, between the inner and the outer solid-shapes. The only plane-shapes in all the complete space-lattice are equilats, and the only rods are rods of unit length – in the scale chosen !
The complete lattice has the surface of that particular archimedian solid, equal in area to 12 unit-side pentagons and 20 unit-side equilats. If that surface is hermetically covered with Mylar or some other thin, strong membrane, then when the inside air is exhausted, there will be a loss of weight, as dear old Archimedes himself proved, running through the streets of Syracuse in his birthday suit, shouting “EUREKA !”
If you don't believe it, look at the photo called “Engdotcom-hg”, which I have posted as a group-file in “IdeasII”.
Now if some prof-of-engineering will only prove me right, using his research budget and a supply of Ph,D students, my “click” will indeed be heard around the world !