Elliptical dome

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An elliptical dome at the San Domenico, Modena, in Modena, Italy Modena San Domenico cupola ellittica.JPG
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.

Contents

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

See also

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History of early modern period domes

Domes built in the 16th, 17th, and 18th centuries relied primarily on empirical techniques and oral traditions rather than the architectural treatises of the time, but the study of dome structures changed radically due to developments in mathematics and the study of statics. Analytical approaches were developed and the ideal shape for a dome was debated, but these approaches were often considered too theoretical to be used in construction.

Santa Caterina, Casale Monferrato Roman Catholic church in Casale Monferrato, Italy

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Ellipsoidal dome Has a bottom cross-section which is a circle, but has a cupola whose curve is an ellipse

An ellipsoidal dome is a dome, which has a bottom cross-section which is a circle, but has a cupola whose curve is an ellipse.

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. 25 April 2016. Retrieved 2020-12-04.
  3. Chiorino, Mario Alberto (2008). "Modeling Strategies for the World's Largest Elliptical Dome at Vicoforte". International Journal of Architectural Heritage. 2 (3): 274–303. doi:10.1080/15583050802063618. S2CID   109078429.
  4. Aoki, Takayoshi. "Structural characteristics of the elliptical masonrydome of the sanctuary of Vicoforte".
  5. 1 2 Elkhateeb, Ahmed Ali (2012). "Domes in the Islamic Architecture of Cairo City: A Mathematical Approach" (PDF). Nexus Network Journal. 14: 151–176. doi:10.1007/s00004-011-0103-3. S2CID   119996869.
  6. "Polyhedral structures that approximate an ellipsoid".
  7. "The Engineering Behind Saint Peter's Basilica".
  8. Kobielak, Sylwester (November 27, 2016). "Oval concrete domes".

Creating elliptical domes

Calculations

More general references