Principle behind the design:
Reversing the perspective: First and foremost, the conceptual approach is reversed. It is not that “the components of a geodesic structure form a natural parabola,” but rather that we “identify” a geodesic structure on the surface of a pre-defined parabola.
Approximation of the surface: The fundamental principle of the Geodesic Parabolic Dish Antenna is to approximate a parabolic surface using multiple planes. This is the same principle used in any antenna where mesh is attached to a frame.
Definition of a plane: A plane is uniquely defined by three points, not four. Using four points would result in two intersecting planes.
Triangular composition: Consequently, the parabolic surface is composed of a collection of triangles.
Structural efficiency: While the edges of these triangles form the structural ribs, it is highly advantageous if the shared edge of two adjacent triangles can be formed by a single rib. Please note that in a typical Geodesic Dome, the edges of adjacent triangles are often separate components.
Choice of material (Flat bars): To form a triangle, three ribs must intersect. Considering the connection and the thickness at these intersections, using flat bars is the optimal choice.
Constraint of geodesics: A flat bar, which can only bend in the direction of its thickness, must follow a “geodesic line” to conform to a parabolic surface.
The design process: My design begins by “identifying” geodesic lines on the parabolic surface, initially positioned at 120-degree intervals.
Engineering advantages: At the intersection of flat bars along these geodesic lines, the surfaces of the bars meet at a perpendicular orientation. This allows the faces of the flat bars to fit tightly together, which is a significant manufacturing advantage.
Unique determination of length: Once the vertices of the triangular segments (the intersection points of the flat bars) are identified on the parabolic surface, the lengths of the triangle’s sides are uniquely determined.
Formation of the parabola: By joining the flat bars according to these uniquely determined triangular dimensions, the intended surface—the parabola—is naturally and uniquely formed.
References: For a better understanding of geodesic lines, I recommend this video: The Nature of Geodesics (https://www.youtube.com/watch?v=m6WY6VtPYrk).
Further reading: Additionally, I encourage you to read all the references listed in my Design Chart.
I hope this explanation helps your understanding.
Regards.
Yoshi Takeyasu
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