Talk:Joukowsky transform

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This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 09:56, 10 November 2007 (UTC)[reply]

karman-trefftz image

The second plot does not do a great job of differentiating between the two transforms. With the high line thickness, the tail of the second airfoil looks just as cusped as the first airfoil. Maybe thinner lines or a more appropriate parameter choice would illustrate this difference more clearly? —Preceding unsigned comment added by 24.28.82.87 (talk) 22:04, 15 April 2009 (UTC)[reply]

History & Usage

Can someone provide some history of when this mathematics was developed, both the pure and the applied, and by whom (if not developed by the namesake). Also, some explanation of whether these create 'optimal' airfoils for various relative air speeds / viscosity etc. —Preceding unsigned comment added by 1.152.18.227 (talk) 16:26, 16 April 2011 (UTC)[reply]

Article name

Why is this article called "Joukowsky transform" when that is just one specific case of the more general Karman-Trefftz transform? ~Anachronist (talk) 02:11, 7 July 2020 (UTC)[reply]

The Joukowski transform (and the concept of the Joukowski airfoil) are sufficiently well known and notable that a Wikipedia article is justified. Whether the K-T transform is sufficiently well known and notable to justify its own article is debatable. If we had a separate article devoted to the K-T transform it is likely there would be pressure to merge the two into one article about design of airfoil sections using conformal transforms; then there would be a question about what that article should be titled.

I regard the current article as a good and sufficiently comprehensive article about the J. transform, but the coverage of the K-T transform is not quite so comprehensive. For example, we have our article on the Kutta condition to explain how the circulation is determined for a J. airfoil with a sharp trailing edge. We don’t have any coverage of determining the circulation for a K-T airfoil. Do you know how von Karman and Trefftz recommended how circulation should be determined?

My summary of the situation is that this article would work if it was titled K-T transform, but this transform is not so well-known as the J. transform so it is better that the present title be retained. There is (or should be) a redirect so that any reader searching for the K-T transform will be taken to this article. Dolphin (t) 22:46, 7 July 2020 (UTC)[reply]

Would anyone mind if we scale the result of the Joukowsky map by half, so the circle is mapped to the interval [-1, 1]?

I’m not so sure about airfoils, but in other areas of mathematics the convention of using a [-1, 1] interval is much more common than a [-2, 2] interval, i.e. a map $z\mapsto {\tfrac {1}{2}}(z+z^{-1})$ . If we want to talk about the relation to the cosine function, orthogonal polynomials, Bernstein ellipses, etc., this is much more natural. Here’s one example of a source using this convention, https://www.tandfonline.com/doi/pdf/10.1080/00029890.2019.1528814 –jacobolus (t) 03:24, 2 December 2022 (UTC)[reply]