John Jacoby's patent: spherical dome from great circles
Gerry Toomey
Taff, Dick, Katrina & others,
I'd like to revisit a discussion thread from May 19 & 20, 2011 having to do with a newly issued patent.
The subdivision method Taff referred to, class I method 2 outlined in Domebook 2, uses the equilateral face of an icosahedron as its starting point. The "edges" (rims?) of the spherical version of that triangle all have arc lengths of 63.435 degrees. John Jacoby's "spherical dome" subdivision method, brought to our attention by Dick (U.S. patent no. US 7,900,405 B1, issued March 8, 2011), is completely different. It's based on a spherical isosceles triangle with arc lengths 90, 90 and 60 degrees.
With Jacoby's 3-way grid, each trio of great circles does indeed intersect at a single point. I modeled his method in Excel and Antiview using a dome with 5 rows of triangles (4 main rows plus a skirt to flatten the base) as the example. The result shows a set of smooth lines. The model also shows clearly that, unlike class I, method 2, the edges of the principal polyhedron triangle (PPT) are not divided into equal arcs. Rather, from the six-way dome apex to the dome base, the arcs get progressively smaller.
This new great-circle subdivision method merits attention. It has much in common with the Richter/Temcor lesser-circle breakdown, though it doesn't appear to be nearly as flexible for construction purpses. It isn't suitable as a planar geodesic dome in which you connect individual strait struts at each node. This is because the inventory of arc lengths and chord lengths is huge, even for a low-frequency dome. Jacoby's method, though, as mentioned in the patent document, is suitable for a spherical dome in which the members are curved. As with Temcor's design, it will work best for a very-low-profile structure like the Antarctica dome. You would criss-cross long strips of flexible material -- one on the inside, one on the outside, and one in the middle. These could be connected together with bolts or some other fastener. In the case of the 5-row dome in the attached diagram, you would need 28 strips of six lengths, including the base tension ring. If you wanted to add the refinement of taking into account the thicknesses of the strips, then you would have 16 discrete lengths.
I can readily imagine Jacoby's method being used successfully for a small backyard greenhouse or for the top -- a spherical cap -- of a cylindrical tank. The trick is to find a way to cover the spherical (rather than flat-faced) grid. Maybe shrinkwrap plastic, molded pvc panels, ferrocement/shotcrete???
In any case, as far as I can tell through Excel modeling, the key idea Jacoby outlines in his patent document, namely that you can use great circles to create spherical triangular grids with various spacings between the circles, is geometrically valid.
I'm also attaching an image of an icosahedral geodesic sphere (planar version) generated by the intersection of 31 great circles. Again, this was mathematically modeled in Excel, and I used Antiview to generate the images. As you will see, it divides nicely into hemispheres.
- Gerry in Quebec
On May 19 2011, 3:50 pm, Dick Fischbeck <dick.fischb...@gmail.com> wrote:
> http://www.google.com/patents?id=DREuAQAAEBAJ
>
> in three spherically concentric layers to cross at the vertices of
> contiguous spherical triangles
On May 20 2011, 7:15 pm, TaffGoch <taffg...@gmail.com> wrote:
> If they are truly great circles, then all of the intersections won't pass
> through the same point, to produce a common vertex (any two circles will
> provide a vertex, but the third great circle won't pass through that point.)
>
> If it was this simple, Bucky wouldn't have had to do all that work! His
> compensation for the non-coincidence was to take the centerpoint of the
> small triangle "window" created by the three approximately-intersecting
> great circles. This is discussed in Domebook2, under the description of
> "class-I," "method 2" (on page 107, in my edition.)
>
> Amazing what you can get a patent for....
>
> -Taff
On May 20 2011, 8:01 pm, "dick.fischb...@gmail.com" <dick.fischb...@gmail.com> wrote:
> I don't think the uspto cares if something is true. they just check to
> see if it was claimed before!
Gerry Toomey
JACOBY
Dick Fischbeck
Dick Fischbeck
Dick Fischbeck
Dick Fischbeck
Hello, Dick.Thanks for the info and comments. I will look into them.It is funny, Dick. I had my dome concept years ago. I finally decided to go for a patent, but not for the dome’s sake, but to see if I could get a patent pro-se. I got the patent and was amazed that I did it all myself. I am proud of my dome, but I am also proud of getting my own patent.Dick, my dome concept was important to me. In order for it to work, the members would have to be bent about their minor axes. The only way that would work was if their centerlines followed concentric circles. Voila, I did it. I have a model, which I built. I can send you a picture, if you want.Where are you located?I will check out the Supine.Thanks for contacting me.Sincerely,