Construction of the Asymmetric Joukowski Airfoil through Karman-Trefftz Transformation, for n = 2, using GeoGebra 5.0

Detalhes bibliográficos
Autor(a) principal: Marinho, João Jefferson Faria
Data de Publicação: 2020
Outros Autores: Santos, Raphael Francisco Gomes dos, Martino, Luciana Santos da Silva
Tipo de documento: Artigo
Idioma: por
Título da fonte: Remat (Bento Gonçalves)
Texto Completo: https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/3895
Resumo: The Conform Transformation is a mathematical tool that allows the construction of complex geometries from simpler geometries. The Joukowski airfoil exemplifies this statement, however, obtaining it by conventional mathematical means is complex, making it necessary to use computational resources. This article demonstrates a technique whose purpose is to facilitate the understanding of the Joukowski Transformation, which consists of mapping a circumference in the asymmetric Joukowski airfoil using GeoGebra. The Joukowski Transformation was obtained through the Karman-Trefftz Transformation, for n = 2, using compositions of complex functions. The simulations were performed using the GeoGebra 5.0 software, which made it possible to construct and obtain mathematical equations, on the real plane, of the geometric figures involved in the transformations until obtaining the asymmetric Joukowski airfoil. The results of the simulation were satisfactory, such that the equations of the geometric shapes until the construction of the airfoil were successfully obtained.
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spelling Construction of the Asymmetric Joukowski Airfoil through Karman-Trefftz Transformation, for n = 2, using GeoGebra 5.0Construção do Aerofólio de Joukowski Assimétrico por meio da Transformação de Karman-Trefftz, para n=2, utilizando o GeoGebra 5.0Joukowski TransformationKarman-Trefftz TransformationAsymmetric Joukowski AirfoilGeoGebraTransformação de JoukowskiTransformação de Karman-TrefftzAerofólio de Joukowski AssimétricoGeoGebraThe Conform Transformation is a mathematical tool that allows the construction of complex geometries from simpler geometries. The Joukowski airfoil exemplifies this statement, however, obtaining it by conventional mathematical means is complex, making it necessary to use computational resources. This article demonstrates a technique whose purpose is to facilitate the understanding of the Joukowski Transformation, which consists of mapping a circumference in the asymmetric Joukowski airfoil using GeoGebra. The Joukowski Transformation was obtained through the Karman-Trefftz Transformation, for n = 2, using compositions of complex functions. The simulations were performed using the GeoGebra 5.0 software, which made it possible to construct and obtain mathematical equations, on the real plane, of the geometric figures involved in the transformations until obtaining the asymmetric Joukowski airfoil. The results of the simulation were satisfactory, such that the equations of the geometric shapes until the construction of the airfoil were successfully obtained.A Transformação Conforme é uma ferramenta matemática que possibilita a construção de geometrias complexas a partir de geometrias mais simples. O aerofólio de Joukowski exemplifica essa afirmação, entretanto, a sua obtenção pelos meios matemáticos convencionais é complexa, tornando-se necessária a utilização de recursos computacionais. Neste trabalho é demonstrada uma técnica cujo propósito é facilitar o entendimento da Transformação de Joukowski, que consiste em mapear uma circunferência no aerofólio de Joukowski assimétrico com o uso do GeoGebra. A Transformação de Joukowski foi obtida por meio da Transformação de Karman-Trefftz, para n=2, fazendo uso de composições de funções complexas. As simulações foram realizadas utilizando o software GeoGebra 5.0, que possibilitou a construção e obtenção das equações matemáticas, no plano real, das figuras geométricas envolvidas nas transformações até a obtenção do aerofólio de Joukowski assimétrico. Os resultados da simulação mostraram-se satisfatórios, de forma que as equações das formas geométricas até a construção do aerofólio foram obtidas com êxito.Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul2020-07-24info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArtigos; Avaliado pelos paresapplication/pdfhttps://periodicos.ifrs.edu.br/index.php/REMAT/article/view/389510.35819/remat2020v6i2id3895REMAT: Revista Eletrônica da Matemática; Vol. 6 No. 2 (2020); e4001REMAT: Revista Eletrônica da Matemática; Vol. 6 Núm. 2 (2020); e4001REMAT: Revista Eletrônica da Matemática; v. 6 n. 2 (2020); e40012447-2689reponame:Remat (Bento Gonçalves)instname:Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS)instacron:IFRSporhttps://periodicos.ifrs.edu.br/index.php/REMAT/article/view/3895/2687Copyright (c) 2020 REMAT: Revista Eletrônica da Matemáticahttps://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessMarinho, João Jefferson FariaSantos, Raphael Francisco Gomes dosMartino, Luciana Santos da Silva2022-12-28T16:05:32Zoai:ojs2.periodicos.ifrs.edu.br:article/3895Revistahttp://periodicos.ifrs.edu.br/index.php/REMATPUBhttps://periodicos.ifrs.edu.br/index.php/REMAT/oai||greice.andreis@caxias.ifrs.edu.br2447-26892447-2689opendoar:2022-12-28T16:05:32Remat (Bento Gonçalves) - Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS)false
dc.title.none.fl_str_mv Construction of the Asymmetric Joukowski Airfoil through Karman-Trefftz Transformation, for n = 2, using GeoGebra 5.0
Construção do Aerofólio de Joukowski Assimétrico por meio da Transformação de Karman-Trefftz, para n=2, utilizando o GeoGebra 5.0
title Construction of the Asymmetric Joukowski Airfoil through Karman-Trefftz Transformation, for n = 2, using GeoGebra 5.0
spellingShingle Construction of the Asymmetric Joukowski Airfoil through Karman-Trefftz Transformation, for n = 2, using GeoGebra 5.0
Marinho, João Jefferson Faria
Joukowski Transformation
Karman-Trefftz Transformation
Asymmetric Joukowski Airfoil
GeoGebra
Transformação de Joukowski
Transformação de Karman-Trefftz
Aerofólio de Joukowski Assimétrico
GeoGebra
title_short Construction of the Asymmetric Joukowski Airfoil through Karman-Trefftz Transformation, for n = 2, using GeoGebra 5.0
title_full Construction of the Asymmetric Joukowski Airfoil through Karman-Trefftz Transformation, for n = 2, using GeoGebra 5.0
title_fullStr Construction of the Asymmetric Joukowski Airfoil through Karman-Trefftz Transformation, for n = 2, using GeoGebra 5.0
title_full_unstemmed Construction of the Asymmetric Joukowski Airfoil through Karman-Trefftz Transformation, for n = 2, using GeoGebra 5.0
title_sort Construction of the Asymmetric Joukowski Airfoil through Karman-Trefftz Transformation, for n = 2, using GeoGebra 5.0
author Marinho, João Jefferson Faria
author_facet Marinho, João Jefferson Faria
Santos, Raphael Francisco Gomes dos
Martino, Luciana Santos da Silva
author_role author
author2 Santos, Raphael Francisco Gomes dos
Martino, Luciana Santos da Silva
author2_role author
author
dc.contributor.author.fl_str_mv Marinho, João Jefferson Faria
Santos, Raphael Francisco Gomes dos
Martino, Luciana Santos da Silva
dc.subject.por.fl_str_mv Joukowski Transformation
Karman-Trefftz Transformation
Asymmetric Joukowski Airfoil
GeoGebra
Transformação de Joukowski
Transformação de Karman-Trefftz
Aerofólio de Joukowski Assimétrico
GeoGebra
topic Joukowski Transformation
Karman-Trefftz Transformation
Asymmetric Joukowski Airfoil
GeoGebra
Transformação de Joukowski
Transformação de Karman-Trefftz
Aerofólio de Joukowski Assimétrico
GeoGebra
description The Conform Transformation is a mathematical tool that allows the construction of complex geometries from simpler geometries. The Joukowski airfoil exemplifies this statement, however, obtaining it by conventional mathematical means is complex, making it necessary to use computational resources. This article demonstrates a technique whose purpose is to facilitate the understanding of the Joukowski Transformation, which consists of mapping a circumference in the asymmetric Joukowski airfoil using GeoGebra. The Joukowski Transformation was obtained through the Karman-Trefftz Transformation, for n = 2, using compositions of complex functions. The simulations were performed using the GeoGebra 5.0 software, which made it possible to construct and obtain mathematical equations, on the real plane, of the geometric figures involved in the transformations until obtaining the asymmetric Joukowski airfoil. The results of the simulation were satisfactory, such that the equations of the geometric shapes until the construction of the airfoil were successfully obtained.
publishDate 2020
dc.date.none.fl_str_mv 2020-07-24
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Artigos; Avaliado pelos pares
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/3895
10.35819/remat2020v6i2id3895
url https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/3895
identifier_str_mv 10.35819/remat2020v6i2id3895
dc.language.iso.fl_str_mv por
language por
dc.relation.none.fl_str_mv https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/3895/2687
dc.rights.driver.fl_str_mv Copyright (c) 2020 REMAT: Revista Eletrônica da Matemática
https://creativecommons.org/licenses/by/4.0
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Copyright (c) 2020 REMAT: Revista Eletrônica da Matemática
https://creativecommons.org/licenses/by/4.0
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul
publisher.none.fl_str_mv Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul
dc.source.none.fl_str_mv REMAT: Revista Eletrônica da Matemática; Vol. 6 No. 2 (2020); e4001
REMAT: Revista Eletrônica da Matemática; Vol. 6 Núm. 2 (2020); e4001
REMAT: Revista Eletrônica da Matemática; v. 6 n. 2 (2020); e4001
2447-2689
reponame:Remat (Bento Gonçalves)
instname:Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS)
instacron:IFRS
instname_str Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS)
instacron_str IFRS
institution IFRS
reponame_str Remat (Bento Gonçalves)
collection Remat (Bento Gonçalves)
repository.name.fl_str_mv Remat (Bento Gonçalves) - Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS)
repository.mail.fl_str_mv ||greice.andreis@caxias.ifrs.edu.br
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