Sketch of concepts used in the vertical ellipsoid dome calculator

A sketch of the concepts behind the Vertical Ellipsoid Dome Calculator. We can describe short, over-the-center oblate ellipsoids to tall, nearly complete prolate ellipsoids.

Dave South

Inflatable shapes are the basic components of Monolithic Dome design. If it inflates, it can be constructed … probably. There are two primary shapes that dominate dome design — the sphere and half-ellipsoid. However, these are not the whole design palette. Sometimes we need to go beyond the basics. or in this case, beyond half of the ellipsoid.

The vertical ellipsoid has a round base and an elliptical cross-section. In other words, it looks like a circle when viewed from above and an ellipse when viewed from any side. Unlike the half-ellipsoid calculator, we can specify any portion of the ellipsoid. Maybe we just want the top, a little more than half, or almost a whole ellipsoid — short or tall, narrow or wide.

This is what the Vertical Ellipsoid Dome Calculator is for. It gives complete control of the overall ellipsoid shape and where that shape intersects the ground. The underlying code for this calculator is shared with the half-ellipsoid calculator. They both iterate over 36,000 slices of the shape to find the surface area and the result is more accurate than our old calculator — about eight to nine significant digits instead of three to four.

The Palapa Pineapple dome home in Belize

The Palapa Pineapple in Belize is a four-story prolate ellipsoid dome home with an open first floor, living space in the next three levels, and then a rooftop covered deck. The shape worked best for the land and the needs of the homeowners.

Dave & Mary Spellings

So when should you use it?

For messing around with basic dome designs the spherical or ellipsoid calculator is easier and more approachable. Start there. Need a large commercial structure, use the spherical calculator. Want to build a home in a single dome, try the ellipsoid calculator. But while you work on your dream building, you might run into ideas that go beyond just the dome.

For example, Dave and Mary Spellings wanted a dome home in Belize. They wanted a 360-degree ocean view and a home that stood out. The basic designs wouldn’t cut it. Eventually, they settled on a pineapple shape. Now we are into vertical ellipsoid territory. The basic shape is a prolate ellipsoid, four stories tall topped with an open observation deck and a beautiful view of the ocean.

What about a ufo-like design or a home that “tucks” into a hillside? Maybe a specialty dome as part of a multiple dome complex? How about a hobbit home design that’s buried and looks like something straight from the shire? And then there are custom, interconnected domes. We need estimates of multiple domes before we start designing the connections.

All these designs require more advanced calculations. So while we may not use the vertical ellipsoid calculator for every dome, when it’s needed, it’s invaluable. Give it a try.