The Double Bubble Comment Rescue/Response

In my recent Tuesday Tech Links, DavidTC was asking about the Double Bubble airliner and why the two overlapping circles was better than an ellipse?  This is an excellent question and one that deserves something of an in-depth reply.  One of the reasons this is an excellent question is because we already have two very well known airliners that have non-circular cross sectional hull shapes: the Boeing 747 and the Airbus A380 (links go to a Google image search for the hull cross sections).

So it is possible to build an airliner with a non circular hull.  The 747 has a circular main hull and a semi-circular upper deck, while the A380 has an elliptical hull.  The reason such hull shapes were chosen has less to do with engineering and more to do with the economics of the aircraft, i.e. the extra structure needed to make those shapes work well was acceptable in order to gain the extra passenger capacity they would allow for on a large, long range aircraft.  The fact that both aircraft are high capacity, long range airliners is a big part of the reason those hull shapes are economical.

On a short range hauler, especially one that will be carrying primarily passengers and little freight, they make less economic sense.

Now how does the Double Bubble work?  Imagine a cylindrical pressure vessel, a scuba tank, for instance.  Let’s ignore for the moment the ends of the tank and just focus on the cylindrical part.  Once the tank is filled and pressurized, the force of the internal pressure will act equally in all directions upon the inner wall of the tank.  This will add some stress to the tank wall, as well as giving the tank an added bit of stiffness.

The force of the internal pressure is equal in all directions.

The force of the internal pressure is equal in all directions.

The force acting equally in all directions is important.  Those arrows in the above image represent the force vectors resulting from the internal pressure.  If we overlay a second pressure vessel, like so:

Two tanks overlaid to form the double bubble. Black background so things are bit easier to see.

Two tanks overlaid to form the double bubble. Black background so things are bit easier to see.

Notice how, in the area of overlap, the arrows are equal in size, but opposite in direction?  That means that they will cancel out.  To further this point, let’s say that the tank walls intersected neatly and the internal pressure was equal in both lobes and the middle section,  If this could magically be so, the internal walls would not feel the pressure, since it would be equal on both sides.  The force vectors would be zero.  If this is the case, those walls are not adding much to the structure of the whole, so we can delete them and get this:

Double Bubble Pressure Hull

The conjoined pressure

Of course we still have that join to deal with, and we must, because sharp corners are structurally bad (internal stress concentrates in corners, and the sharper the corner, the higher the concentration), so we cheat a bit and give the join a small radius of its own (a fillet) and then beef up the structure at that location enough to make it safe.

So why not an ellipse on it’s side?  One word answer – Windows.

If there is one thing aerospace structural engineers hate more than anything it is windows.  They hate them enough that a plane like this makes them downright giddy, and not because OLEDs are cool.  Windows killed the Comet.  Windows are a hole in the structure of the aircraft that can not carry any load through the glass, so the window has to be designed so the load is carried around it, which means extra structure, and load paths that are even more complex than they already are.  Seriously, if they could have OLED panels with camera links that were perfect, cockpits would not have windows.

So let’s look at an ellipse that is the same height as the double bubble hull above.

An elliptical hull that is the same height and width as the double bubble.

An elliptical hull that is the same height and width as the double bubble.

Notice where the windows would be, and how tight that is.  That’s gonna give you either very tiny windows, or very curved ones, and the structural engineers already hate you enough.  Of course, if we change the ellipse to have an equivalent curvature for the windows, we get this.

Ellipse Correct Curvature

An elliptical hull with the same width and the correct curvature for the windows.

Well, damnit, at this point I’m not saving enough volume and weight to make this attractive.  How about one more configuration, a stretched circle.

Not really stretched, just two semi-circles connected at the horizontal tangent.

Not really stretched, just two semi-circles connected at the horizontal tangent.

Right width, height, and curvature, and just a little bit of extra volume, but the loads through those flat sections are gonna be a mess because this is a pressure vessel.  We’d have to beef them up quite a bit, much more than the join has to be beefed up.  Now, if this was wide enough that it could serve as a lifting body, such that I could significantly reduce my wing area, this might very well be a winner, but I can get aerodynamic benefits just by adding lightweight aerodynamic fairings, so justifying the extra structure is a hard sell.

Other benefits of the design can be seen in the tail (the brochure is here, it should open in another window).  There is actually a lot going on here.  An airliner like this would compete with other short haul aircraft, like the 737 or A320.  One of the problems we have with those two aircraft is that it’s getting really hard to sling better engines under the wing because the engine nacelles are darn near scraping the ground as it is.  Current ground clearance is somewhere between 12″-18″, depending on the engine.  The full travel((how far they can compress vertically)) on the landing gear struts is just shy of that, so a hard landing can also mean a nacelle strike if the wing flexes too much, which will take that plane out of service for a while.  Tucking the engines in the back not only keeps your wings clear (reducing drag, improving lift), but also eliminates that concern and lets you have shorter gear if you want.

Looking at the tail some more, notice how it’s a double T-tail, instead of a normal empennage?  I’ve mentioned before about how T-tails are structurally expensive, so you have to have a good reason to use one.  Well a twin T-tail is a whole let less structurally expensive.  Still a bit more than a normal empennage, but still cheap enough that if you have a good trade-off, it can be worth it.  The T-tail, along with the furrow in the aft part of the hull fairing, act to form a channel that can help smooth out turbulent airflow as it enters the turbine intakes, which can simplify inlet design, reducing weight and cost, and improving efficiency.  One of the big reasons is air entering a turbofan can not be supersonic, and even though airliners do not travel at supersonic speeds, air travelling around the aircraft can locally become supersonic.  Shocks are really hard on turbine blades, so preventing them from forming near those blades is important.  If you can use a significant length of the fuselage as an inlet to shape and slow the flow, you make your life easier.  In the same flow stream, you can use the wake flow of the body to support the jet exhaust, improving it’s efficiency.

So final question, if the tradeoffs are good, why hasn’t this design been done before?  Well, it has, but in vertical arrangements (see Super Guppy and C-97), so it’s not exactly new, but the horizontal arrangement is now attractive thanks to materials like Carbon Fiber, which can form a strong join without adding too much weight.

Like I said, it’s all about tradeoffs.

 

 

Image by geckzilla


Associate Editor

A Navy Turbine Tech who learned to spin wrenches on old cars, Oscar has since been trained as an Engineer & Software Developer & now writes tools for other engineers. When not in his shop or at work, he can be found spending time with his family, gardening, hiking, kayaking, gaming, or whatever strikes his fancy & fits in the budget. ...more →

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27 thoughts on “The Double Bubble Comment Rescue/Response

  1. Articles like this often don’t get huge commentary on them because there is typically isn’t much for a commentariat to say in response. But don’t let that lack lead you to believe this sort of thing isn’t read and appreciated on its merits.

    The best thing the blogosphere can offer is things written by experts for the educated layman. We could all use much more of that around in every topic. Its like what Vox proported to try to do but couldn’t, because Vox is written by the same class of non-expert journalist type that already wrote for newspapers, not by people actually knowledgeable enough to really explain something on a particular topic.

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  2. My question is: just making a single bigger cylinder with a bigger diameter (whether circular or elliptical) is a volume vs surface area issue, correct?

    Or is the biggest advantage maximizing the diameter of the centerline with less ‘wasted’ space?

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    • It’s all about maximizing centerline, since that is were the people sit. If I can nearly double the passenger capacity without having to double wing and engine sizing, I potentially have a huge market advantage.

      The importance of how much passenger windows drives design can not be overstated. If It was all about packing bodies in the hull, we could extend environmental controls to the lower cargo deck and pack a bunch of passengers in there as well.

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    • “is the biggest advantage maximizing the diameter of the centerline with less ‘wasted’ space?”

      Yeah, that’s it. Cargo is more often wide and flat than it is square, so you care less about overall cross-section area than you do about the maximum width (or height) that can fit inside the aircraft.

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    • Yes, same concept, but reverse direction. Airliners are higher internal pressure, so the hull is in tension. Subs have higher external pressure, putting the hull under compression. The structural design is different between the two, but both are taking advantage of the environmental stress to help stiffen the structure.

      Also, notice how subs don’t have any fecking windows. Seriously, windows drive structures guys nuts.

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  3. Oh! One final thing that affects all of this – regulations!

    The FAA does not tell aerospace companies how to build airplanes. Boeing can slap together whatever design it thinks will fly and sell well, but it has to meet the FAA regs, which are all about keeping the airplane flying in one piece and getting passengers & crew safely to the ground. Designs that are uncommon are not only challenging for the engineers designing them, but also challenging for FAA regulators to evaluate. Ergo, uncommon designs have an additional expense of being harder to get certified.

    Everyone and their dog in the aerospace business knows how to evaluate a cylindrical hull such that it will meet FAA regs. Same with elliptical hulls, and even Double Bubbles (since they’ve been done in the past in vertical arrangements). Something like the stretched cylinder, however, is very uncommon and will present a challenge getting it certified. So even if the structure was easy to evaluate, the cost of the regulatory process might bust the design before it ever got off the drawing board.

    I saw lots of really cool airliner designs discarded for this exact reason. Boeing and Airbus are nothing if not conservative when it comes to design. That conservativeness is actually one of the reasons the 787 did not do as well as it should have.

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  4. I think the issue is more subtle than corners causing a stress concentration. As you point out, you can smooth out the curve and avoid that issue. It’s a question of the skin being in bending rather than pure tension.

    A sphere, when pressurized inside, is put in tension all over. The same thing happens for an oval or for an ellipse; while those shapes have variation in the state of tension due to the changes in curvature, it’s still all-out, only stretching the skin.

    The problem with the double-bubble arrangement is that the reentrant-curve “pucker” between the circles is going to want to open up–the pressure will try to flatten it out. This puts the interior surface at that location into compression, rather than tension; so now you need to worry about your ribs buckling (something that doesn’t happen with non-reentrant curves) as well as the fact that you have a larger stress gradient between outside and inside (which has implications for fatigue life).

    Boeing’s Blended Wing Body concept is using an elliptical pressure vessel.

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    • Exactly, and one reason the horizontal arrangement hasn’t really been done (trust me, I know how much those wings can flex, and I don’t care how stiff the wing box is, flexing wings will cause a body to flex the same way). I think being able to build more with materials like carbon fiber alleviates some of those concerns, especially fatigue (assuming the engineers design structural components like they are made out of carbon fiber, rather than treating it like black aluminum, which is one reason a certain high profile design is struggling with weight issues).

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    • Boeing’s Blended Wing Body concept is using an elliptical pressure vessel.

      And I can’t tell you how anxious people are about the windows, or rather, that if it doesn’t have enough windows, no one will want to fly in it, and no, you can’t actually let people sit out near the wing tips so they can have a window seat.

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