More Supersonics

Kevin Murphy has some thoughts about supersonics, based on my previous post. He’s skeptical.

Given that he’s not stooped to calling me a scientific lightweight, and incapable of understanding mathematics, that’s fine, but he doesn’t really understand the whole picture, which is understandable since I haven’t really presented it. This is a matter of some frustration to me, but one that I can do little about until I can persuade the company involved to put up information on the web, so that it can be critiqued and reviewed.

Regardless, I’ll try to respond to his comments as best I can under the circumstances (which include limited time on my part).

…even if you have the same drag coefficient at supersonic as you do at subsonic — your drag, and thus fuel consumption, will increase substantially.

The key clause here is “if you have the same drag coefficient at supersonic.” At least for the wing, it’s actually possible to do better, at least in terms of induced drag (an effect of the end of the wing, which makes it greater than two-dimensional) which is actually improved at higher speeds. The notion, right or wrong, postulates that supersonic L/D for aircraft designed under this theory will be similar to that of subsonic aircraft, so it offers the potential (if not promise) of airfares comparable to subsonic fares for the same routes.

With regard to his comments on angle of attack, they’re not relevant, because any angle of attack that is non-zero will dramatically increase wave drag and induce shock waves. The aircraft’s nominal design condition is zero AOA. Takeoff and time to cruise aren’t an issue, either (as isn’t the engine) because we can get rid of the extreme sweep that has always been associated with supersonic aircraft (a design strategem that was always a kludge to come up with a way of minimizing wave drag without solving the fundamental problem).

Something like the SR-71 engines are a likely solution, in terms of the inlet, but that’s not a problem because they’ll be optimized for fuel economy at cruise speed (which will constitute most of their operating time), not takeoff/landing. Also, we’re not proposing anything as fast as the Blackbird–Mach 2.4 will probably be adequate.

But here is really the crux of the issue.

The claim is that with enough leading edge sharpness and the proper contouring behind, you can fly supersonically without shockwaves, except circulation (flow around the airfoil) which produces lift elimates the shockless effect. Why would this be? Well, without lift on a sharp symmetric airfoil the stagnation point would the the leading edge. If you add circulation, perhaps you move the stagnation point so that it is no longer on the leading edge. Could this be the problem? The flow splits at the stagnation point (that’s where it stops), and if it isn’t sharp where it splits, you get a shockwave? If that is the case, well, we’re screwed. No amount of adding in balancing circulation downstream will matter, and adding it to the flow over the wing to cancel it out will mean an end to the lift from the wing. Now you could make an unsymmetrical airfoil such that at the cruise condition the stagnation point is on the sharp point of the airfoil, but you’d have shockwave drag getting to that point (or if you had to fly off design point.)

The proposal is not to build a symmetric airfoil. Stagnation points really aren’t relevant.

Imagine a Busemann biplane, which is really a DeLaval nozzle inside two wings. The top of the upper wing is flat, as is the bottom of the lower wing. That allows the airflow to move past without shock. The ramping occurs within the two wings. Now, Busemann showed that this will have a shock-free flow, but because of the symmetry, it has no lift. Now imagine that the lower wing is dynamic–it’s actually a supersonic airflow coming from a non-shocking duct, with a flat lower surface. The lower surface of the “biplane” (after a short ramp) is a stream of higher-energy air (to satisfy Crocco), that mixes the total flow to provide the anti-circulation to balance the wing circulation.

The idea is to provide that balance to eliminate the need for the highly entropic downstream vortices, that require far more energy than that required to simply provide that balance. It spreads the residual shocks over a much larger footprint, reducing almost to insignificance the PSF on the ground, and essentially eliminates the wave drag.

Bottom line: if this works (and I don’t claim that it will–only that it’s not obvious to me that it won’t), this means wide-body supersonic aircraft, at non-ozone-eating altitudes, at ticket prices comparable to subsonic ones. It means obsolescing the current subsonic fleet in the same way that prop-driven airplanes were put out of business by jets, other than niches.

I think that it’s worth spending a tiny fraction (how about a percent of one year’s budget?) of the billion-plus dollars that NASA wasted on the High-Speed Research program, but NASA didn’t agree in the late nineties, even when Congress specifically appropriated it.