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Difficult Problems

There are some problems that do not get discussed in most textbooks of aerodynamics because the space required to describe the solution is judged by the authors and editors to be excessive for the value received. In many cases, this is because the solutions require numerical techniques such as root finding, numerical integration or solution of linear systems. However, these questions do arise and the practising aeronautical engineer occasionally needs the solution. Since the standard textbooks are of little help, a lot of time can be expended in the search for an answer, even though the problem has been solved over and over again by others. Maybe this page will help.

The PDAS CD-ROM has a suite of numerical procedures that may be used for the solution of these problems. The source code for the numerical package may be downloaded from this site (Plain text, 16KB).

The following pages contain mathematical expressions and charts. Beginning now (Oct 2002), I am going to serve all such pages in XHTML with MathML encoding of the mathematical expressions. You may have trouble seeing the math if your browser is not XML and MathML enabled. If you use Firefox and install the proper fonts, you should be OK. If we all complain enough, the next versions of Opera and Internet Explorer should have this capability. And before long, I plan to put the charts in SVG. I am not doing this to make it hard on you, but so we can all have better web pages containing scientific and engineering information. The technique of using images for math and charts is tedious and error-prone and leads to pages that require a long time to load. With XHTML-MathML-SVG, we can have web pages that look like journal articles and the only external images that need to be loaded will be photographs.

Note added February, 2013: I hope I live long enough to see this, but I wouldn't take any bets. As a short-term (hah!!) work-around, these pages are also available in Portable Document Format (PDF).

- Go to the list of difficult problems.
- Go to the download page for Difficult Problems.

If you have comments about MathML or SVG, send them to me at pdaerowebmaster AT gmail DOT com.

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