2001-03-01|Sunatori's Angle for Golden Dome Shape

If a dome is a hemisphere (geodesic or otherwise), then extra load produces an outward stress at the opening, leading to a crack at the bottom. If a dome is close to a sphere, then extra load produces an inward stress at the opening, leading to a crash at the bottom. There may be a point where an outward force and an inward force cancel out, showing only a downward force by the gravity of the dome. Maybe domes like the former Expo '67 U.S. Pavilion and the Epcot Centre have this "Golden Dome Shape".
- angle of dome = pi radian (180 degrees)
  - bottom opening = diameter (regular dome)
  - outward stress > inward stress
- angle of dome < SA radian (SA*pi/180 degrees)
  - bottom opening << diameter (baseball dome)
  - outward stress > inward stress
- angle of dome = SA radian (SA*pi/180 degrees) "Sunatori Angle"
  - bottom opening < diameter (Golden Dome Shape)
  - outward stress = inward stress
- angle of dome > SA radian (SA*pi/180 degrees)
  - bottom opening << diameter
  - outward stress < inward stress
U.S. Patent 3 203 144 is limited to geodesic domes only (Special Theory of Domes). I am wondering how the exact angle of dome to achieve
- outward stress = inward stress
could be calculated, assuming a cut hollow sphere with a uniform distribution of mass along the surface. Such "Sunatori Angle" would be considered a part of a more universal solution, i.e., The General Theory of Domes.

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"Sunatori, Go Simon" <GS.Sunatori@HyperInfo.CA>

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