Elliptical dome

An elliptical dome, or an oval dome, is a dome whose bottom cross-section takes the form of an ellipse.[1] Technically, an ellipsoidal dome has a circular cross-section, so is not quite the same.

An elliptical dome at the San Domenico, Modena, in Modena, Italy

While the cupola can take different geometries, when the ceiling's cross-section takes the form of an ellipse, and due to the reflecting properties of an ellipse, any two persons standing at a focus of the floor's ellipse can have one whisper, and the other hears; this is a whispering gallery.

The largest elliptical dome in the world is at the Sanctuary of Vicoforte in Vicoforte, Italy.[2][3][4]

In architecture

A blue circle, graphed with a red ellipse. An elliptical dome has an elliptical base, and an ellipsoidal dome has a circular base.

An ellipse, the "reflecting," "whispering gallery" property of the foci F and F' illustrated: The distance from F to F' may be great, but a whisperer at F can be heard, as F'.

Both -a and a are points of the x-axis and -b and b are points on the y-axis

Elliptical domes have many applications in architecture; and are useful in covering rectangular spaces. The oblate, or horizontal elliptical dome is useful when there is a need to limit height of the space that would result from a spherical dome. As the mathematical description of an elliptical dome is more complex than that of spherical dome, design care is needed.[5]

In a geodesic dome with a circular base, the triangular elements align so their edges form great circles. Although not geodesic, a new, elliptical design was patented in 1989; it uses hexagons and pentagons to form a dome with a cross section that is elliptical. Due to its mathematical derivation, this design is called "geotangent".[6]

World examples

Elliptical domes come up in the design of all of the following:

• A number of mosques in Cairo, Egypt,[5]
• Part of St. Peter's Basilica, in Rome, Italy[7]
• The Basilica of St. Lawrence, Asheville, in Ashville, North Carolina,
• The Church of Saint Roch, Žižkov, in Prague, Czech Republic,
• The Four Domes Pavilion, in Wroclaw, Poland,
• The Indiana Theatre, in Indiana, city of Indianapolis,
• The Joe and Rika Mansueto Library, at the University of Chicago,
• The Kanteerava Indoor Stadium, in Bangalore, India,[8]
• The Mayflower Hotel, in Washington, DC,
• The Mosque–Cathedral of Córdoba, in Andalusia,
• The Palau Nacional, in Barcelona, Spain,
• The Pisa Cathedral, in Pisa, Italy,
• The Rose Hill Mansion, Bluffton, in Bluffton, South Carolina,
• The San Filippo Neri, in Turin, region of Piedmont, Italy,
• The Sant'Andrea in Via Flaminia, in Rome, Italy,
• The Santa Caterina, Casale Monferrato, in Casale Monferrato, Province of Alessandria, region of Piedmont, Italy,
• The Seville Cathedral, Spain,
• The Skyspace Lech, Tannegg/Oberlech in Vorarlberg, the westernmost federal state of Austria,
• The State Savings Bank Building, in City of Sydney, Australia,
• The Temple Sinai, in Oakland, California,
• The Sanctuary of Vicoforte, in Italy.

See also

• Pendentive
• Beehive house
• Beehive tomb
• Catenary arch
• Clochán
• Ellipsoid
• Onion dome
• Parabolic arch

References

1. Arun, G (2006). "Behaviour of Masonry Vaults and Domes: Geometrical Considerations" (PDF). Structural Analysis of Historical Constructions, New Delhi.
2. "Visiting the largest elliptical dome in the world, in Vicoforte". ItalyRiveirAlps. Retrieved 2020-12-04.
3. Chiorino, Mario Alberto. "Modeling Strategies for the World's Largest Elliptical Dome at Vicoforte". International Journal of Architectural Heritage.
4. Aoki, Takayoshi. "Structural characteristics of the elliptical masonrydome of the sanctuary of Vicoforte".
5. Elkhateeb, Ahmed Ali. "Domes in the Islamic Architecture of Cairo City: A Mathematical Approach" (PDF). King Abdulaziz University Department of Architecture Faculty of Environmental Design.
6. "Polyhedral structures that approximate an ellipsoid".
7. "The Engineering Behind Saint Peter's Basilica".
8. Kobielak, Sylwester (November 27, 2016). "Oval concrete domes".

External links and references

Creating elliptical domes

• Elliptical domes site
• Creating an elliptical dome
• Another reference, on creating ellitpical domes

Calculations

• Site for calculating figures related to elliptical domes
• Another site for calculations
• Dome calculator

More general references

• Buckling of Externally Pressurized Prolate Ellipsoidal Domes
• An article addressing many topics, including elliptical domes
• Use of elliptical domes, notably in Islamic architecture