Elliptical dome

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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.[1] 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.[2][3][4]

In architecture[edit]

A blue circle, graphed with a red ellipse
A blue circle, graphed with a red ellipse. An elliptical dome has an elliptical base, and an ellipsoidal dome has a circular base.
Wispering gallery property of ellipses
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[edit]

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

See also[edit]

References[edit]

  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. ^ a b 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[edit]

Creating elliptical domes[edit]

Calculations[edit]

More general references[edit]