It's funny... you're showing some 3D CFD visualization of a shock cone produced by a supersonic transport, yet you claim that 2D compressible flow equations would be able to approximate this 3D compressible flow problem well enough? Whatever... I'm not going to argue this with you or anyone else. There's a reason why you need CFD to "solve" complex 3D compressible flow problems like the one above. You've pretty proven my point. In absence of a supersonic wind tunnel, you need CFD. Applying hand calculations to these sorts of real-world problems is a practice in futility. You can gain a decent understanding of real-world 3D compressible flow by studying 2D compressible flow, but you don't apply 2D equations to 3D problems. You apply 2D equations to 2D problems.

oooh, pretty colors.

I think you are misunderstanding me. I'm not doubting the importance of 3D models, wind tunnels and CFD in engineering at all. But the thing is, nobody on this board really expected that type of accuracy. If you want a rough estimate of an aircraft speed performance, the planform (A 2D section of a 3D shape) is what you look at first, and in all likelihood is what engineers specify first, at least roughly. If all you're concerned about is the nose shock, what follows later isn't really all that relevant for 3D or 2D, and like I said earlier, you can take a 2D equation for the shock and INTEGRATE it to create a 3D solution. This will be fairly accurate for what they were trying to do here when comparing the F-22 to the F-35, much more so than integrating 2D lift equations over a wing, but that is an entirely separate effect. Of course, you'll need 3D analysis and area-ruling in the end, but that doesn't mean that looking at the planform won't give you a good idea of an aircraft design/max speed. That's all I was trying to say, sorry if that wasn't clear.

Just a little napkin analysis, thats all. One of my old profs said a good engineer should be able to get a rough answer using only a napkin, pencil, the basic equations in your head, and intelligent assumptions. Doesnt build airplanes, but it gets answers.

Teach less, learn more. That's all I've got to say. Not many people are qualified to be giving lessons in supersonic aerodynamics (including myself), so forgive me if I warn others about the oversimplifications inherent in your analyses.

Well, dwightlooi has evidence to back up his assumptions. Do you call that schilieren photo a fluke?

What is the Schlieren photograph proving exactly?

It shows the shock formations, which can be used to prove theories. Yes, I could pull out my Texas A&M supersonic wind tunnel lab report too, but what does that prove? One last thing....only a qualified individual should be telling people that their practices are incorrect.

As for telling someone their practices are incorrect, I'm qualified enough to do that in this particular case.

If it were as simple as he's making it out to be with his drawings, there wouldn't be a need for shock-capturing CFD algorithms, flux limiters, advanced meshing techniques... the list goes on.

By the way, you can see just how imperfect those shocks are in the Schlieren photograph of the F/A-18. Accurately modeling those shocks in CFD simulations wasn't even possible until 2nd-order accurate flux limiting schemes were developed and applied to the Navier-Stokes equations.

When someone starts calculating Mach numbers to the 3rd decimal place in this sort of situation, I call foul.

Notice the F/A-18 photo says ~ M 1.4. And that's +/- 0.X?? What is X? 0.05? 0.1? What? What's the measurement error inherent in measuring the angles from that photo itself?

If my point isn't clear yet, it never will be. I've explained my "pet peeves" well enough. It's not like they're invalid pet peeves. Or are they? You tell me.

R1 just out of curiosity, who do you work for? It occured to me that with your knowledge and drive for perfection you must work for one of the major companies. I'm curious to know what projects you've worked on that you can discuss. Thanks.