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George Cayley (1773-1854) 91 TEORÍAS PIONERAS SOBRE LA ESTABILIDAD LONGITUDINAL DE LOS AVIONES “ANÁLISIS CRÍTICO-HISTÓRICO DE LAS TEORÍAS PIONERAS SOBRE LA DE LOS AVIONES”. (1799-1913) Presentada por: José Pedro Magraner Rullán. Dirigida por: Rodrigo Martínez-Val Peñalosa. Dirigida por: Francisco Payri González. Univèrsitat Politècnica de València Julio de 2017 1 TEORÍAS PIONERAS SOBRE LA ESTABILIDAD LONGITUDINAL DE LOS AVIONES 2 TEORÍAS PIONERAS SOBRE LA ESTABILIDAD LONGITUDINAL DE LOS AVIONES Resumen El presente trabajo consiste en una investigación sobre las primeras teorías físico- matemáticas aplicadas al estudio del vuelo artificial con aeroplanos, y particularmente el tratamiento del problema de la estabilidad longitudinal. Se analizan las aportaciones mínimamente analítico-formales de G. Cayley, A. Pénaud, O. Lilienthal, A. Zahm y los hermanos W. & O. Wright. Se estudian también las publicaciones matemáticamente más sólidas de N. E. Zhukowsky, H. G. Bryan, F. Ferber, F. W. Lanchester, R. Soreau, P. Painlevé, G. de Bothezat y T. Von Kármán & E. Trefftz. Se incluye también el estudio de la aportación eminentemente divulgativa de E. A. Duchêne. El período analizado abarca desde 1799 hasta 1913. Abstract The present work consists of an investigation on the first physical-mathematical theories applied to the study of the artificial flight with airplanes, and in particular the treatment of the problem of longitudinal stability. The minimally analytical-formal contributions of G. Cayley, A. Pénaud, O. Lilienthal, A. Zahm and the W. & O. Wright brothers are analyzed. The mathematically stronger publications of N. E. Zhukowsky, H. Bryan, F. Ferber, F. W. Lanchester, R. Soreau, P. Painlevé, G. de Bothezat and T. Von Kármán & E. Trefftz, are also studied. Also included is the study of the eminently informative contribution of E. A. Duchêne. The period analyzed covers from 1799 to 1913. Resum El present treball consisteix en una investigació sobre les primeres teories físico- matemàtiques aplicades a l'estudi del vol artificial amb aeroplans, i particularment el tractament del problema de l'estabilitat longitudinal. S'analitzen les aportacions mínimament analítico-formals de G. Cayley, A. Pénaud, O. Lilienthal, A. Zahm i els germans W. & O. Wright. S'estudien també les publicacions matemàticament més sòlides de N.E. Zhukowsky, H.G. Bryan, F. Ferber, F.W. Lanchester, R.Soreau, P. Painlevé, G. de Bothezat y T. Von Kárman & E. Trefftz. S'inclou també l'estudi de l'aportació eminentment divulgativa d' E.A. Duchêne. El periode analitzat abarca des de 1799 fins 1913. 3 TEORÍAS PIONERAS SOBRE LA ESTABILIDAD LONGITUDINAL DE LOS AVIONES 4 TEORÍAS PIONERAS SOBRE LA ESTABILIDAD LONGITUDINAL DE LOS AVIONES A MIS ALUMNAS Y ALUMNOS. 5 TEORÍAS PIONERAS SOBRE LA ESTABILIDAD LONGITUDINAL DE LOS AVIONES 6 TEORÍAS PIONERAS SOBRE LA ESTABILIDAD LONGITUDINAL DE LOS AVIONES “Ex Umbris et Imaginibus in Veritatem” John Henry Newman. 7 TEORÍAS PIONERAS SOBRE LA ESTABILIDAD LONGITUDINAL DE LOS AVIONES 8 TEORÍAS PIONERAS SOBRE LA ESTABILIDAD LONGITUDINAL DE LOS AVIONES En primer lugar deseo expresar mi agradecimiento al Prof. Rodrigo Martínez-Val, de la Universidad Politécnica de Madrid y al Prof. Francisco Payri, de la Universitat Politècnica de València, por haber aceptado dirigir este trabajo. Sin su benévola aceptación, su comprensión y su ocasionalmente compulsiva insistencia, no habría sido posible culminarla. Debo agradecer también, al Prof. José María Desantes las facilidades que el DMMT me ha proporcionado, en muy diversos aspectos. El Prof. Antonio Torregrosa ha gestionado con eficacia la obtención de una bibliografía que, dado el carácter de la presente tesis, era imprescindible y frecuentemente de dificultosa localización. El DMMT ha proporcionado también traductores1 de ruso y alemán cuando ha sido necesario. Agradezco a los evaluadores externos Prof. Damián Rivas Rivas, de la Universidad de Sevilla, Dr. Jaime Cabezas Carrasco, del Instituto Nacional de Técnica Aeroespacial “Esteban Terradas”, y al Prof. Pablo Fajardo Peña, de la Universidad Carlos III sus observaciones; todas ellas han sido tenidas en cuenta en la medida que nos ha resultado posible. Estoy en deuda también con los evaluadores internos, Dr. Pedro Martí Gómez- Aldaraví y Dr. Marcos Carreres Talens, que han tenido la amabilidad de criticar diversos capítulos de la tesis, aportando valiosas sugerencias; no podría dejar de mencionar tampoco las que la Prof. Xandra Margot y el Prof. Andrés Tiseira me han proporcionado con sus consejos, así como el valioso trabajo que Pedro Quintero ha aportado. De muchas otras personas del Departamento de Máquinas y Motores Térmicos, en sus distintas dependencias, soy deudor. Su número es muy elevado y explica -aunque no la justifique- la ausencia de mención nominal. En esa misma línea, siento también la necesidad de agradecer a las alumnas y a los alumnos de la asignatura “Mecánica de Vuelo” las sugerencias –entre otras cosas también valiosas- que me han proporcionado a lo largo de 8 años de docencia en la UPV. Finalmente, agradezco también a mi familia el apoyo (y la paciencia) que han derrochado durante el tiempo en que he estado inmerso en la confección de este trabajo. PS: no sería razonable omitir la mención de Stephen Wolfram. Gracias a “Mathematica ®” ha sido posible realizar este trabajo con una fiabilidad cuyos fallos son atribuibles únicamente al autor de la tesis. 1 En el cuerpo de la Tesis se otorgan, nominal y oportunamente, los créditos debidos a los traductores. 9 TEORÍAS PIONERAS SOBRE LA ESTABILIDAD LONGITUDINAL DE LOS AVIONES 10 TEORÍAS PIONERAS SOBRE LA ESTABILIDAD LONGITUDINAL DE LOS AVIONES INDICE Índice General……………………………………………………………..…11 Lista de Tablas ……………………………………………………………….21 Lista de Figuras ……………………………………………………………… 23 Nomenclatura………………………………………………………………… 33 Capítulo 1 39 Introducción. 1.1 Generalidades 1.2 Un problema de Aerodinámica. 1.3 Estabilidad Estática 1.4 Estabilidad Dinámica 1.5 Nota sobre las características del presente trabajo. Bibliografía. Capítulo 2 49 Teorías aerodinámicas a finales del siglo XIX, en los temas relacionados con el estudio de la estabilidad de aviones. 2.1 Introducción. Placa plana sometida a una corriente de aire. 2.2 La denominada “Resistencia Aerodinámica Específica del Aire” 2.3 La Resistencia aerodinámica de una placa plana con incidencia variable. 11 TEORÍAS PIONERAS SOBRE LA ESTABILIDAD LONGITUDINAL DE LOS AVIONES 2.4 Relación entre la función f y los coeficientes aerodinámicos asimilables a los clásicos CL y CD 2.5 La posición del centro de presión xCP . Perfiles planos y perfiles con curvatura. 2.5.1 Posición del centro de presión de una placa plana. 2.5.2 Centro de presión de superficies curvas. 2.6 Inicio de la teoría matemática de perfiles bidimensionales. 2.7 Conclusiones. 2.8 Anexo I. Centro Aerodinámico y Centro de presión. 2.9 Anexo II. La Ley de Avanzini. Bibliografía. Capítulo 3 George Cayley (1773-1854) 91 3.1 Nota biográfica. 3.2 Documentos de referencia objeto de estudio. 3.3 Descripción del contenido. 3.3.1 “On Aerial Navigation”, Parte I. 3.3.2 “On Aerial Navigation”, Parte II. 3.4 El timón horizontal móvil. 3.5 Sobre el Modelo de Planeador de 1804. 3.6 Sobre el Modelo de Planeador de 1808. 3.7 Sobre el Modelo de Planeador de 1818. 3.8 Sobre el Modelo de Planeador de 1849 (1853). 3.9 Sobre “The Governable Parachute” (1852) 3.10 Conclusiones Bibliografía Capítulo 4 Alphonse Pénaud (1850-1880) 109 4.1 Nota Biográfica. 4.2 Documentos de Referencia. 4.3 Descripción de contenido. El estabilizador automático. 4.3.1 Otros proyectos. 4.4 Conclusiones. 4.5 Anexo I. La mecánica de vuelo estacionaria de A. Pénaud. Bibliografía 12 TEORÍAS PIONERAS SOBRE LA ESTABILIDAD LONGITUDINAL DE LOS AVIONES Capítulo 5 Otto Lilienthal (1848-1896) 125 5.1 Nota biográfica 5.2 Documento de referencia objeto de estudio. 5.3 Descripción del contenido. 5.3.1 Las Gráficas Polares de la Fuerza Aerodinámica. 5.3.2 La Posición del Centro de Presión. 5.3.3 Control del Momento de Cabeceo. 5.4 Conclusiones. Bibliografía. Capítulo 6 Nicolai Egorovitch Zhukowsky (1847-1921) 137 6.1 Nota Biográfica. 6.2 Documentos de referencia. 6.3 Descripción de contenido. 6.3.1 “Sobre el vuelo de planeo de las aves”. (1891) 6.3.2 “Sobre el ángulo óptimo de vuelo de un aeroplano”. (1897) 6.3.3 “Sobre la Caída en el Aire de Cuerpos Ligeros Alargados con Giro Alrededor de su Eje Longitudinal”. (1906) 6.3.4 “Descripción elemental de la Dinámica de los Aeroplanos”. (1913) 6.4 Estabilidad angular en cabeceo. 6.5 Conclusiones Bibliografía Capítulo 7 A. F. Zahm (1862-1954) 167 7.1 Nota Biográfica. 7.2 Documento de referencia. 7.3 Descripción de contenido. 7.4 Conclusiones Bibliografía 13 TEORÍAS PIONERAS SOBRE LA ESTABILIDAD LONGITUDINAL DE LOS AVIONES Capítulo 8 W. Wright (1867-1912) & O. Wright (1871-1948) 173 8.1 Nota Biográfica. 8.2 Documento de referencia. 8.3 Descripción del Contenido. 8.4 Conclusiones Bibliografía Capítulo 9 H. G. Bryan (1864-1928) & W. E. Williams (1881-1962) 183 9.1 Nota Biográfica. 9.2 Documento de Referencia 9.3 Descripción de contenido. 9.3.1 Polinomio Característico del Sistema Lineal. 9.3.2 Derivadas Aerodinámicas. 9.3.3 Condición Fundamental de Estabilidad. 9.3.4 Cálculo de las Derivadas Aerodinámicas. 9.3.5 Hipótesis Aerodinámicas. 9.3.6 Formulación genérica de las Derivadas Aerodinámicas. 9.3.7 Aplicaciones numéricas a casos particulares. 9.3.7.1 Análisis de la estabilidad aplicado a una sola lámina sustentadora. 9.3.7.2 Planeadores formados por dos planos. 9.3.8 Efecto del Momento de Inercia sobre la estabilidad. 9.3.9 Carácter de las oscilaciones alrededor del equilibrio. 9.4 Conclusiones. 9.5 Resumen Crítico Bibliografía Capítulo 10 Ferdinand Ferber (1862-1909) 211 10.1 Nota Biográfica. 10.2 Documento de referencia. 10.3 Descripción de contenido. 14 TEORÍAS PIONERAS SOBRE LA ESTABILIDAD LONGITUDINAL DE LOS AVIONES 10.3.1 Ley de equivalencia de las superficies.
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