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# 9 EMBaero, I have million books

21 October 2007

Here is letter from an anonymous person.

I have about 25 of the most well-known textbooks on aerodynamics sitting in front of me, and they all state that the Oblique shock equation has two solutions (weak shock and strong shock). This equation is the first one to appear in the theory section of the Oblique shock article. It is impossible to take that equation and analytically solve for the shock angle based on a given corner angle and upstream Mach number. This is why every textbook contains oblique shock tables, where the results are tabulated since solving for the shock angle based on those two parameters requires a very complex, non-analytical iterative process. If you want to claim that you have invented some new solution, you have the burden of proof and have to post information about your solution before it will be allowed on Wikipodia. Adding a link to your compressible flow text is not good enough, and I want to see something along the lines of an AIAA journal article.

Response:

Dear Mr. EMBaero,

The fact that your books claim that there are only two solutions does not say much about these books. No single book or article shows only two solutions to oblique shock!

References that we have today show that there are three solutions. Should you check the NACA report 1135, you will find that the governing equation is a sixth-order polynomial equation. Mathematics teaches us that in this case there are six solutions. Due to symmetry, (my book explains this further) the six solutions are actually three pairs of two. You can see the ``impossible'' solution. You are also invited to use my utility to generate the oblique shock diagram of arbitrary specific heat ratio, (it takes only 0.5 sec per run).

Also, please read my comment to Mr. Beychok on my opinion of a (close) review committee.

Genick

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Genick Bar-Meir ||| www.potto.org