{"id":220,"date":"2015-04-14T23:36:43","date_gmt":"2015-04-15T04:36:43","guid":{"rendered":"http:\/\/charles-oneill.com\/blog\/?p=220"},"modified":"2015-04-14T23:41:58","modified_gmt":"2015-04-15T04:41:58","slug":"joukowski-transform","status":"publish","type":"post","link":"https:\/\/charles-oneill.com\/blog\/joukowski-transform\/","title":{"rendered":"Joukowski Transform"},"content":{"rendered":"<p>\\(\\) The Joukowski transform is a stunningly simple mathematical operation that converts a circle into an airfoil.<\/p>\n<p>$$w=z+\\frac{c^2}{z}$$<\/p>\n<p>The beauty of the transform is that ideal fluid flow past a circle is described by a classic and well known set of terms.<\/p>\n<p><a href=\"http:\/\/charles-oneill.com\/blog\/wp-content\/uploads\/2015\/04\/joukowski.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-221\" src=\"http:\/\/charles-oneill.com\/blog\/wp-content\/uploads\/2015\/04\/joukowski-300x233.png\" alt=\"joukowski\" width=\"300\" height=\"233\" srcset=\"https:\/\/charles-oneill.com\/blog\/wp-content\/uploads\/2015\/04\/joukowski-300x233.png 300w, https:\/\/charles-oneill.com\/blog\/wp-content\/uploads\/2015\/04\/joukowski-1024x797.png 1024w, https:\/\/charles-oneill.com\/blog\/wp-content\/uploads\/2015\/04\/joukowski-800x623.png 800w, https:\/\/charles-oneill.com\/blog\/wp-content\/uploads\/2015\/04\/joukowski.png 1037w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><a href=\"http:\/\/charles-oneill.com\/blog\/wp-content\/uploads\/2015\/04\/cylinderflow.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-225\" src=\"http:\/\/charles-oneill.com\/blog\/wp-content\/uploads\/2015\/04\/cylinderflow-300x232.png\" alt=\"cylinderflow\" width=\"300\" height=\"232\" srcset=\"https:\/\/charles-oneill.com\/blog\/wp-content\/uploads\/2015\/04\/cylinderflow-300x232.png 300w, https:\/\/charles-oneill.com\/blog\/wp-content\/uploads\/2015\/04\/cylinderflow-1024x792.png 1024w, https:\/\/charles-oneill.com\/blog\/wp-content\/uploads\/2015\/04\/cylinderflow-800x619.png 800w, https:\/\/charles-oneill.com\/blog\/wp-content\/uploads\/2015\/04\/cylinderflow.png 1033w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>I made a small visualization program that allows experimentation with a Joukowski airfoil in an ideal fluid flow environment. This is meant to illustrate conformal mapping to my GES 554 class and airfoil theory to AEM 614.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Joukowski transform is a stunningly simple mathematical operation that converts a circle into an airfoil. $$w=z+\\frac{c^2}{z}$$ The beauty of the transform is that ideal fluid flow past a circle is described by a classic and well known set of terms. I made a small visualization program that allows experimentation with a Joukowski airfoil in [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[154,153,155],"_links":{"self":[{"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/posts\/220"}],"collection":[{"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/comments?post=220"}],"version-history":[{"count":3,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/posts\/220\/revisions"}],"predecessor-version":[{"id":226,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/posts\/220\/revisions\/226"}],"wp:attachment":[{"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/media?parent=220"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/categories?post=220"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/tags?post=220"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}