Architectural Characteristics of Different Configurations Based on New Geometric Determinations for the Conoid

The aim of this article is to orient the evolution of new architectural forms offering up-to-date scientific support. Unlike the volume, the expression for the lateral area of a regular conoid has not yet been obtained by means of direct integration or a differential geometry procedure. In this type...

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Detalhes bibliográficos
Autor: Cabeza Laínez, José María
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/130978
Acesso em linha:https://hdl.handle.net/11441/130978
https://doi.org/10.3390/buildings12010010
Access Level:acceso abierto
Palavra-chave:Conoid
Ellipse
Calculus of surface areas
Parametric design
Number psi
Cubature architecture
Design paradigms
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spelling Architectural Characteristics of Different Configurations Based on New Geometric Determinations for the ConoidCabeza Laínez, José MaríaConoidEllipseCalculus of surface areasParametric designNumber psiCubature architectureDesign paradigmsThe aim of this article is to orient the evolution of new architectural forms offering up-to-date scientific support. Unlike the volume, the expression for the lateral area of a regular conoid has not yet been obtained by means of direct integration or a differential geometry procedure. In this type of ruled surface, the fundamental expressions I and II, for other curved figures have proved not solvable thus far. As this form is frequently used in architectural engineering, the inability to determine its surface area represents a serious hindrance to solving several problems that arise in radiative transfer, lighting and construction, to cite just a few. To address such drawback, we conceived a new approach that, in principle, consists in dividing the surface into infinitesimal elliptic strips of which the area can be obtained in an approximate fashion. The length of the ellipse is expressed with certain accuracy by means of Ramanujan’s second formula. By integrating the so-found perimeter of the differential strips for the whole span of the conoid, an unexpected solution emerges through a newly found number that we call psi (ψ). In this complex process, projected shapes have been derived from an original closed form composed of two conoids and called Antisphera for its significant parallels with the sphere. The authors try to demonstrate that the properties of the new surfaces have relevant implications for technology, especially in building science and sustainability, under domains such as structures, radiation and acoustics. Fragments of the conoid have occasionally appeared in modern and contemporary architecture but this article discusses how its use had been discontinued, mainly due to the uncertainties that its construction posed. The new knowledge provided by the authors, including their own proposals, may help to revitalize and expand such interesting configurations in the search for a revolution of forms.MDPIHistoria, Teoría y Composición Arquitectónicas2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/130978https://doi.org/10.3390/buildings12010010reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésBuildings, 12 (1), 1-28.https://doi.org/10.3390/buildings12010010info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1309782026-06-17T12:51:07Z
dc.title.none.fl_str_mv Architectural Characteristics of Different Configurations Based on New Geometric Determinations for the Conoid
title Architectural Characteristics of Different Configurations Based on New Geometric Determinations for the Conoid
spellingShingle Architectural Characteristics of Different Configurations Based on New Geometric Determinations for the Conoid
Cabeza Laínez, José María
Conoid
Ellipse
Calculus of surface areas
Parametric design
Number psi
Cubature architecture
Design paradigms
title_short Architectural Characteristics of Different Configurations Based on New Geometric Determinations for the Conoid
title_full Architectural Characteristics of Different Configurations Based on New Geometric Determinations for the Conoid
title_fullStr Architectural Characteristics of Different Configurations Based on New Geometric Determinations for the Conoid
title_full_unstemmed Architectural Characteristics of Different Configurations Based on New Geometric Determinations for the Conoid
title_sort Architectural Characteristics of Different Configurations Based on New Geometric Determinations for the Conoid
dc.creator.none.fl_str_mv Cabeza Laínez, José María
author Cabeza Laínez, José María
author_facet Cabeza Laínez, José María
author_role author
dc.contributor.none.fl_str_mv Historia, Teoría y Composición Arquitectónicas
dc.subject.none.fl_str_mv Conoid
Ellipse
Calculus of surface areas
Parametric design
Number psi
Cubature architecture
Design paradigms
topic Conoid
Ellipse
Calculus of surface areas
Parametric design
Number psi
Cubature architecture
Design paradigms
description The aim of this article is to orient the evolution of new architectural forms offering up-to-date scientific support. Unlike the volume, the expression for the lateral area of a regular conoid has not yet been obtained by means of direct integration or a differential geometry procedure. In this type of ruled surface, the fundamental expressions I and II, for other curved figures have proved not solvable thus far. As this form is frequently used in architectural engineering, the inability to determine its surface area represents a serious hindrance to solving several problems that arise in radiative transfer, lighting and construction, to cite just a few. To address such drawback, we conceived a new approach that, in principle, consists in dividing the surface into infinitesimal elliptic strips of which the area can be obtained in an approximate fashion. The length of the ellipse is expressed with certain accuracy by means of Ramanujan’s second formula. By integrating the so-found perimeter of the differential strips for the whole span of the conoid, an unexpected solution emerges through a newly found number that we call psi (ψ). In this complex process, projected shapes have been derived from an original closed form composed of two conoids and called Antisphera for its significant parallels with the sphere. The authors try to demonstrate that the properties of the new surfaces have relevant implications for technology, especially in building science and sustainability, under domains such as structures, radiation and acoustics. Fragments of the conoid have occasionally appeared in modern and contemporary architecture but this article discusses how its use had been discontinued, mainly due to the uncertainties that its construction posed. The new knowledge provided by the authors, including their own proposals, may help to revitalize and expand such interesting configurations in the search for a revolution of forms.
publishDate 2022
dc.date.none.fl_str_mv 2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/130978
https://doi.org/10.3390/buildings12010010
url https://hdl.handle.net/11441/130978
https://doi.org/10.3390/buildings12010010
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Buildings, 12 (1), 1-28.
https://doi.org/10.3390/buildings12010010
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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