Advanced Dome Calculations
By: David South Jr.
October 24, 2006
Spherical Dome Calcs Reference
- Diameter
- Diameter of the base of the dome. (see diagram above)
- Height
- Height of dome from base to apex. (see diagram above)
- Stemwall
- Vertical wall equal in diameter to the base of the dome extending from the base down to the ground. For hemispheres -- where the height is equal to half the diameter -- the stemwall can usually be inflated as part of the Airform. For low-profile spheres, the stemwall will have to be built before inflating the Airform -- this is the Orion style dome (see Italy High School). For Orion style Monolithic Domes, you must make the Stemwall tall enough to accomodate a doorway -- usually 8 feet minimum. For Airform style Stemwalls, it can be any height. (see diagram above)
- Radius of Curvature
- The distance to the center of the sphere described by the dome. Spherical domes are part of a larger sphere. For a hemisphere, the radius of curvature is equal to the height and equal to the radius of the base. (see diagram above)
- Circumference
- Distance around the perimeter of the dome.
- Floor Area
- Area of the floor. The floor is defined as a circle equal to the diameter of the base of the dome.
- Surface Area
- Dome, Stemwall, and Total Surface Area describe the surface area of the dome and stemwall separately and then totals the two together.
- Volume
- Dome, Stemwall, and Total Volume describe the cubic volume contained by the dome and stemwall separately and then totals the two together.
- Level
- The level above the base of the dome to calculate radius and area. (see diagram above)
- Radius @ Level
- The horizontal radius at the 'Level' specified. (see diagram above)
- Area @ Level
- Area of the circle described by the Radius @ Level. (see diagram above)
Oblate Ellipsoid Dome Calcs Reference
- Diameter
- Diameter of the base of the dome. The semi-major axis (a) of the ellipsoid will be defined as half of the diameter. (see diagram above)
- Height
- Height of dome from base to apex. The semi-minor axis (b) of the ellipsoid will be defined as equal to the height. (see diagram above)
- Stemwall
- Vertical wall equal in diameter to the base of the dome extending from the base down to the ground. For half-ellipsoids -- where the height is equal to half the diameter -- the stemwall can usually be inflated as part of the Airform. These formulas are setup to only calculate half-ellipsoids. Orion style walls may be built if you choose, however, low profile spherical domes may be more appropriate. (see diagram above)
- Ellipticity
- The ratio between the a and b of the ellisoid shape where 1.0 is a sphere, 1.35 is a moderately elliptical dome, and 1.45 is a highly elliptical dome.
- Circumference
- Distance around the perimeter of the dome.
- Floor Area
- Area of the floor. The floor is defined as a circle equal to the diameter of the base of the dome.
- Surface Area
- Dome, Stemwall, and Total Surface Area describe the surface area of the dome and stemwall separately and then totals the two together.
- Volume
- Dome, Stemwall, and Total Volume describe the cubic volume contained by the dome and stemwall separately and then totals the two together.
- Level
- The level above the base of the dome to calculate radius and area. (see diagram above)
- Radius @ Level
- The horizontal radius at the 'Level' specified. (see diagram above)
- Area @ Level
- Area of the circle described by the Radius @ Level.
Prolate Ellipse
Description coming soon.
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