Funmurphys: the Blog

A Favorite Topic

Aerodynamics. I know everybody loves the subject. OK, it put food on my table for a long time and I have to admit that after a few years away I grow nostalgic. I came across a a post that was a followup to an argument in the comments at Transterrestial Musings about shockwaves, which led me to an article by Rand Simberg at TechCentralStation about a company that was trying to develop vehicles that could fly supersonically without shockwaves.

Let's say you eliminate or reduce the shockwaves associated with supersonic flight to the point that noise isn't an issue. Drag is still the enemy (drag is always the enemy to an aerodynamicist). And by that I mean, even if you have the same drag coefficient at supersonic as you do at subsonic -- your drag, and thus fuel consumption, will increase substantially. Drag increases as the square of the velocity, so if you go twice as fast, the drag is four times higher. Your increased velocity isn't enough to offset this, but it does help; in this case, assuming an engine (not necessarily the same one) with the same efficiency at the higher speed as the lower speed, the fuel consumption per mile will be double at twice the speed.

Next up is the concern Rand raises about high flight. I'm not convinced this goes away. Not only does drag go up as the square of the velocity; so does lift. So what you say? The problem is that for maximum range, you want to fly at your max L/D or lift over drag. But at cruise, lift is fixed -- it's the weight of the airplane. At a given velocity, you'll fly at an angle of attack based on your weight since lift is also a function of angle of attack. And your L/D is a function of angle of attack - and generally, your max L/D is going to occur at a high angle of attack, close to the onset of stall. So for range, you want the smallest wing possible - so you can cruise at your max L/D. The only way to control angle of attack for a constant velocity, constant weight is to control altitude - the higher the altitude, the higher the angle of attack. This is why planes perform step climbs during their flights - as they burn fuel and lose weight, they have to climb to keep their angle of attack, and thus their L/D, up. (Ideally you'd climb constantly, but air traffic control doesn't allow this.) So all things being equal, if you're flying twice as fast, you want a wing with a quarter of the area. But you also have to be able to fly low and slow, since that's where you start out. So you if you fly twice as fast at cruise, you have to either develop high lift devices (e.g. flaps) that are four times more effective (not likely), or you have to have more wing than is optimum for cruise and fly higher to compensate (and you probably still won't be as good as subsonic transport). When you throw in that the kind of design that will not create shockwaves will have poor subsonic performance, I'm understating the case. So yes, if you didn't have to worry about takeoff and climb to cruise, you could put on a smaller wing (or whatever you call your lift device) and fly lower.

While you might be able to have a more conventional engine placement, I'm not sure what kind of engines you're going to use. Given that there are no shocks, or only weak ones, will you need scramjets - engines that work with supersonic airflow? Or will you somehow slow the airflow to subsonic for the engines without shocks? The SR-71, which flies the kind of speed profiles we're talking about uses a hybrid turbojet/ramjet engine. Will something similar be needed? I know the design is pretty old, but those engines gulp fuel at low speeds.

In the comments, one of Rand's critics claimed Newton's Laws cause shocks, which led into a long digression over the rocket thrust equation. Let me just note the proper equations are Navier-Stokes, and no I'm not going to discuss them much here beyond noting that my fellow students and I were impressed by my fluid dynamics professor who could write the darn things out from memory - including various coordinate systems and assumptions (inviscid, incompressible, etc.) It may well be that you can formulate designs and circumstances where you don't get shockwaves in supersonic flight; I just don't know how real they are.

What is interesting to me was the connection of the shockwave to circulation. Let's take a step back. Current theory (and practice) tells us that if you have a blunt leading edge, you get a strong shock in front of the leading edge with high drag. If you have a sharp leading edge, you get a weak attached oblique shock with much lower drag. 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.)

In a nutshell, I don't think it will work, and even if it does, you still have to be able to mass produce it. But that's the fun of engineering -- solving difficult problems, especially the ones you don't see the answer to when you start.

Will this revolutionize air transport? Well, Rand is clearly right that it will have a better chance than what's come before, but I don't know if that will be enough. Unless you increase engine efficiency, you'll have twice the fuel consumption at cruise and fly higher than currently. So the question is, is there a large enough market of people willing to pay higher prices for faster flights? And that may be the largest uncertainty; you won't know the answer until you've actually built the planes and put them into operation.

UPDATE: Rand has posted a response that provides more information. Some of my thoughts are obsolete at this point.