Engineering:Elliptical dome

Short description: Dome who bottom cross section takes the form of an ellipse

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

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

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.

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.

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".

World examples

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

• A number of mosques in Cairo, Egypt,
• Part of St. Peter's Basilica, in Rome, Italy
• The Basilica of St. Lawrence, Asheville, in Asheville, 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,
• 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

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