{"id":25,"date":"2018-02-12T21:24:41","date_gmt":"2018-02-12T20:24:41","guid":{"rendered":"https:\/\/blogs.futura-sciences.com\/lehning\/?p=25"},"modified":"2018-03-03T11:08:31","modified_gmt":"2018-03-03T10:08:31","slug":"porte-avions-altitude-clothoide","status":"publish","type":"post","link":"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/02\/12\/porte-avions-altitude-clothoide\/","title":{"rendered":"Un porte-avions en altitude et sa clotho\u00efde"},"content":{"rendered":"<p>La m\u00e9thode la plus rapide pour se rendre \u00e0 Namch\u00e9 Bazar, puis vers l\u2019Everest et d\u2019autres sommets himalayens, est de prendre l\u2019avion de Kathmandou \u00e0 Lukla, ville situ\u00e9e \u00e0 2900 m\u00e8tres d\u2019altitude, sur un piton rocheux. Il est possible ensuite de se rendre \u00e0 Namch\u00e9 Bazar en une ou deux \u00e9tapes \u00e0 pied.<\/p>\n<figure id=\"attachment_27\" aria-describedby=\"caption-attachment-27\" style=\"width: 300px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-27 size-medium\" src=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/PisteLukla1-300x199.jpg\" alt=\"\" width=\"300\" height=\"199\" srcset=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/PisteLukla1-300x199.jpg 300w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/PisteLukla1-768x510.jpg 768w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/PisteLukla1.jpg 787w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><figcaption id=\"caption-attachment-27\" class=\"wp-caption-text\">La piste de l&#8217;a\u00e9roport de Lukla. \u00a9 Herv\u00e9 Lehning<\/figcaption><\/figure>\n<p style=\"text-align: left\">L\u2019arriv\u00e9e sur l\u2019a\u00e9roport est impressionnante. De loin, la piste ressemble \u00e0 celle d\u2019un porte-avions perch\u00e9 en altitude. Le bout de piste est au sommet d\u2019une barre rocheuse de 700 m\u00e8tres de haut. Apr\u00e8s quelques dizaines de m\u00e8tres \u00e0 plat, elle s\u2019incline de 15\u00a0% pour redevenir horizontale au niveau du parking, apr\u00e8s 350 m\u00e8tres. La pente permet un atterrissage plus court. En observant la piste, on remarque qu\u2019elle s\u2019incurve progressivement. Quelle est la courbe emprunt\u00e9e entre les deux morceaux droits\u00a0?<\/p>\n<figure id=\"attachment_28\" aria-describedby=\"caption-attachment-28\" style=\"width: 300px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-28 size-medium\" src=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/AeroportLukla-02-300x113.png\" alt=\"\" width=\"300\" height=\"113\" srcset=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/AeroportLukla-02-300x113.png 300w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/AeroportLukla-02-768x288.png 768w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/AeroportLukla-02-1024x385.png 1024w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/AeroportLukla-02.png 1294w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><figcaption id=\"caption-attachment-28\" class=\"wp-caption-text\">Raccordement entre deux droites par un cercle.<\/figcaption><\/figure>\n<p>La premi\u00e8re partie permet la prise de contact avec le sol mais le freinage se fait essentiellement dans la partie en pente. Bien entendu, il n\u2019est pas question de raccorder brutalement les deux droites. On peut imaginer de le faire au moyen d\u2019un cercle de rayon R comme sur la figure ci-dessus. Dans ce cas, l\u2019avion serait soumis brutalement \u00e0 une acc\u00e9l\u00e9ration centrifuge \u00e9gale \u00e0 V<sup>2<\/sup>\u00a0\/\u00a0R o\u00f9 V est sa vitesse, ce qui aurait comme cons\u00e9quence de le d\u00e9stabiliser.<\/p>\n<h2>Une clotho\u00efde<\/h2>\n<p>Il est donc n\u00e9cessaire de raccorder les deux droites avec le cercle, exactement comme on le fait pour les voies de chemin de fer ou les \u00e9changeurs d&#8217;autoroutes. La courbe la plus souvent utilis\u00e9e pour cela est une clotho\u00efde, obtenue en faisant varier la courbure (l\u2019inverse du rayon) lin\u00e9airement entre 0 (pour la droite) et 1\u00a0\/\u00a0R (pour le cercle).<\/p>\n<figure id=\"attachment_31\" aria-describedby=\"caption-attachment-31\" style=\"width: 300px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-31 size-medium\" src=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/AeroportLukla-03-300x300.jpg\" alt=\"\" width=\"300\" height=\"300\" srcset=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/AeroportLukla-03-300x300.jpg 300w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/AeroportLukla-03-150x150.jpg 150w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/AeroportLukla-03-768x768.jpg 768w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/AeroportLukla-03-1024x1024.jpg 1024w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/AeroportLukla-03.jpg 1590w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><figcaption id=\"caption-attachment-31\" class=\"wp-caption-text\">Une clotho\u00efde<\/figcaption><\/figure>\n<!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"<p>La m\u00e9thode la plus rapide pour se rendre \u00e0 Namch\u00e9 Bazar, puis vers l\u2019Everest et d\u2019autres sommets himalayens, est de prendre l\u2019avion de Kathmandou \u00e0 Lukla, ville situ\u00e9e \u00e0 2900 m\u00e8tres d\u2019altitude, sur un piton rocheux. Il est possible ensuite de se rendre \u00e0 Namch\u00e9 Bazar en une ou deux \u00e9tapes \u00e0 pied. L\u2019arriv\u00e9e sur &hellip; <a href=\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/02\/12\/porte-avions-altitude-clothoide\/\" class=\"more-link\">Continuer la lecture de <span class=\"screen-reader-text\">Un porte-avions en altitude et sa clotho\u00efde<\/span>  <span class=\"meta-nav\">&rarr;<\/span><\/a><!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt --><\/p>\n","protected":false},"author":12,"featured_media":73,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[29,10],"tags":[24,23,22,26,25],"class_list":["post-25","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-maths-2","category-voyages","tag-aeroport","tag-avion","tag-courbe","tag-himalaya","tag-montagne"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Un porte-avions en altitude et sa clotho\u00efde, par Herv\u00e9 Lehning<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/02\/12\/porte-avions-altitude-clothoide\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Un porte-avions en altitude et sa clotho\u00efde, par Herv\u00e9 Lehning\" \/>\n<meta property=\"og:description\" content=\"La m\u00e9thode la plus rapide pour se rendre \u00e0 Namch\u00e9 Bazar, puis vers l\u2019Everest et d\u2019autres sommets himalayens, est de prendre l\u2019avion de Kathmandou \u00e0 Lukla, ville situ\u00e9e \u00e0 2900 m\u00e8tres d\u2019altitude, sur un piton rocheux. Il est possible ensuite de se rendre \u00e0 Namch\u00e9 Bazar en une ou deux \u00e9tapes \u00e0 pied. 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