My next thought, In stead of 2-3'stage pipes,'since your ready doing math and building a billion cones, why not make a 4-6 stage pipe that allow for smoother transition between segments?
There are cone building programs out there available for a moderate amount of money and a few which are basic but free and work similar to what you're talking about.
The best possible solution is a gradual "swell" out from the exhaust port to the center section of the pipe. Actually, stamped is the absolute smoothest transition offering the least resistance. While it is true that supersonic sound waves don't see turns and edges as long as the pipe crosssection is round, temperature gradients and flow DO see edges, turns, bumps, and pretty much all of the other physical things related to pipe building. The perfect shape would be perfectly smooth transition....obviously that not possible by hand without some REALLY heavy tooling so the second smoothest design would be more than three segments. The problem is, complexity is a cube of the square of segments. Theoretically, once you've done it once, you could do it 500 times to build a pipe out of 501 segments but the error over the length of each of the joints is exponential as you make more segments between two points (you know D1 and D2 and you only need one cone cut into corresponding segments to reach D2 from D1). If you want to make 40 cones between D1 and D2 the odds of missing D2 becomes much larger...
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