Charles Austin — who’s sadly given up blogging again — claimed that walking and running the same distance burned the same number of calories, running just did it faster. Well, both Charles and Bruce were wrong, because baby we were born to walk. Unlike other creatures, people burn far more calories running than walking. And running is especially hard on the knees and quads. I could have told you that, but the article does it so much more scientifically.

Good news on the energy front. Australian researches say they’ve found a way to split water and thus provide hydrogen using titanium coated ceramics. It would require a shift over to a hydrogen based energy system, but say good bye to pollution, carbon dioxide, and oil embargoes. I hope it pans out, but as always with revolutionary breakthroughs, caution is advised.

I’m back in school again, roughly 22 years after clutching my precious leather-bound diploma at Stanford University in June 1982. I have enrolled in a Master’s program at the local university. With a full-time job, a full-time wife, and three little children I thought it would be best to take only one course at a time. So I’m on the five-year plan for a Master’s Degree.

Some things have NOT changed about college since Kevin and Sean and I were on The Farm with John Elway. College students look and behave exactly the same. They still carry backpacks, ride bicycles (except Kevin), stand in line during registration, wear scruffy clothes, and sit in the sun while trying to do their homework. They still sit in lectures and take notes.

What HAS changed is the delivery of material, thanks to PowerPoint and the Internet. I remember sitting in the Physics Tank (Bloch Hall, demolished in 1997) taking notes, madly trying to keep up with the professor writing on the board, and hoping I had copied all the essential formulas before he went on to a new greenboard. I even had one of those nifty four-color pre-med pens! Now my instructor posts the lecture notes on the class web site the day before class, so we can print them out and make any additional notes in the margins while he lectures. This is a big improvement since I don’t have to watch helplessly as my hasty handwriting gets more and more illegible trying to keep up. I know that I’ve gotten all the important material, that I have all the correct parameters to the Clausius-Clapeyron equation. The downside is that it puts us students into more of a passive mode during class, and it’s all too easy to zone out especially if Graham has kept me up the night before.

I am taking Dynamic Meteorology, one of the core courses leading to a Master’s Degree in Atmospheric Science. At the first class our professor showed us a spectacular animation of the earth’s general circulation over several months. One could clearly see great gobs of moisture tearing off the North Pacific and slamming into the Alaskan panhandle and British Columbia. Yee-hah!

Maybe someday I’ll post a little primer on global warming. 😉 

Rand answered my earlier musings. What he’s let on so far (I appreciate that he can’t tell everything he knows) is intriguing. If you take the wing of the Busemann biplane, which is a theoretical model going back to the thirties (twenties?– I took my Liepmann and Roshko home last night and left it there), at zero alpha and at discrete Mach numbers controlled by the geometry it has no wave drag as the shockwaves are completely contained within the two wings. Sadly, it also generates no lift at this condition because of symmetry. I don’t have a picture, but essentially the airfoils are very roughly triangular with the upper one flat on the top and the lower one flat on the bottom, so a chordwise view looks like a 2-D converging-diverging nozzle – or a De Laval nozzle. Interestingly, this nozzle is used mainly to accelerate subsonic to supersonic flow, or to achieve constant flow rates despite fluctuations in back-pressure (pressure downstream of the exit), or as rocket engine nozzles. Here though, the flow is already supersonic before entering.

In the Busemann biplane, the airflow is compressed beneath the upper wing and thus has higher pressures on the bottom that the top, which is lift. The bottom wing would operate in the exact same way, only upside down which leads to no net lift. The secret of lift at zero alpha is then to replace most of the lower wing with a jet of air with higher energy than ambient. While the lower wing would provide a small amount of negative lift, the upper wing due to its much larger area and much greater compression would provide far more positive lift. The question is, will this jet eliminate the shocks from the upper wing in the same way a correctly sized solid lower wing would? I don’t know — and even if theory tells you it’s possible, that doesn’t mean you could actually achieve such a state with real equipment in real life (which Rand is clear about himself).

One of the interesting things is that the wing would operate at a fixed Mach number without shocks. Since you couldn’t vary the angle of attack, the only control of lift at cruise is altitude. Thus you’d fly a particular altitude for a particular weight — once you got to your cruise Mach, the plane would either float up or down until it reached the altitude that its lift equaled its weight. Then it would float steadily upwards during cruise as it burned fuel.

Even if such a wing did work, life isn’t all roses. You have the structural issues of making the wing, especially the lower one which will have to be small, hollow for this high energy air to flow through and out of, and strong enough to take the loads. And you still have the whole rest of the plane. What do you do about the shockwave the nose of the aircraft generates? I know it can be mitigated by high fineness ratio, but not eliminated. I suppose the nose shape could be such that the shock only went upward. If not, this shock also has implications for wing placement – the wing will most likely operate without shocks in a very narrow Mach range. Being the nose shock the Mach number will be lower than in front of it, and unless you can design this wing to also handle have a region through a shockwave, the wing will have to be completely behind the shock. There are also control surfaces to worry about. It’s fine to have your wing produce constant lift, but control surfaces have to be able to vary their forces and moments. You’d get shocks and wave drag off of them. You could use engine thrust vector control, but you’d need it in all three axes.

I think you still have a problem in getting to cruise. This wing wouldn’t be particularly good at subsonic flight, and I’m not sure you could put flaps in the wing without causing problems at cruise. Thrust vector control would help again here, but you sizing the wing for takeoff and climb versus cruise would be a problem. And because the wing design allows for zero wave drag only at certain supersonic Mach numbers, you’d still have to blast your way through the transonic drag wall at high angle of attack. My engineering judgement tells me that such a transport, when all said in done, will have more expensive acquisition and operating costs than current subsonic transports. High enough to outweigh the benefits of faster travel

So what I see is a fairly straightforward science problem — will this semi-solid Busemann biplane wing design eliminate wave drag — coupled with a host of engineering problems. And really, this is the sort of thing NASA should be all over. Start the funding off to assess the science problem first, and then if it looks feasible, start on the engineering problems. Solving engineering problems is what puts the joy into engineering.

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 eliminates 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.

I don’t know about you, but I didn’t realize that there was more to the European mission to mars than the Beagle 2 lander. So it came as a bit of shock to read about the exquisite picture the orbiter (dubbed Mars Express) was taking of Mars. Expect the unexpected, and more really cool pictures.