Comparisons between the A340 and 747-200 wing: sweep angle and span

Question

Here is a picture of the wings of the A340 (launched in the late 1980s) and the Boeing 747-200/400 (launched in the early 1970s / 80s) superimposed upon each other (source: https://www.amazon.com/Evolution-Airliner-Ray-Whitford/dp/186126870X).

I was hoping to use this image to inquire about technological improvements in wing design between 1970 and 1990. The reason for the comparison between these two airliners in particular is that they seem as close to a "fair" comparison that can be made between airliners over very different time periods, specifically because they're designed to carry relatively the same amount of people.

Specifically, there were two facts about the wing planform that I wanted to ask about.

1. Greater aspect ratio. The A340 has a much greater aspect ratio because it has the same span but much lower total wing area. This improved the L/D ratio by reducing induced drag. What allowed engineers to use a higher aspect ratio wing for the A340? I.e., could the engineers at Boeing in the late-1960s have designed a plane with the same aspect ratio as the A340 if they wanted to (in which case, the higher aspect ratio on the A340 was a design choice, and not a result of any improvement in techniques, methods, materials etc.).

2. Less wing sweep. Wing sweep is desirable because it lets you fly faster without incurring extremely large drag penalties (increases critical mach number), but it does so at the expense of lift. Therefore, if you can get away with a lower sweep angle for a given speed, that's something that would be good for fuel efficiency. How were engineers able to get away with reducing the wing sweep of the A340 while having it fly at generally speaking, the same cruise speed as the Boeing 747?

Thanks so much!

Answer 1

Both less wing sweep and increased aspect ratio are accommodated by the progress in application of rear loading supercritical wing profiles in the couple of decades between design of the two types.

Pic above is from Torenbeek, earlier used in this answer, and depicts the increased thickness of the supercritical profile - which enables higher aspect ratio. But the main difference is actually the higher allowed Mach over the wing => less wing sweep required => way less constructive and aerodynamic problems.

Aspect Ratio is $b^2/S$. Start sweeping the angle of any given wing and the span reduces, so there is a feed-forward loop in the two parameters considered in the question.

Answer 2

When development of the A330 / A340 started, those designs were internally called TA9 and TA11, TA standing for Twin Aisle. A study (sorry, no link, this was before the WWW) by Airbus Bremen showed marginal advantages for a high aspect ratio wing but a wing of lower aspect ratio was chosen eventually. Why? It offered more internal volume for fuel and a simpler flap mechanism.

Still, the new wing has a higher aspect ratio compared to earlier airliners simply because less fuel needs to be carried along with the low specific fuel consumption of modern high-bypass turbofans, even for a record-setting long range flight from Paris to New Zealand.

Answer 3

Even if the MTOWs are similar, the comparison might be anyway a bit unfair because the wing of the A340 was developed for the A330 as well, so most probably some additional compromises were imposed during its design.

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First of all a short clarification in terms:

• induced drag is proportional to wingspan, not aspect ratio.
• induced drag coefficient is proportional to aspect ratio.

In fact, $C_{D_i}$ is normally expressed as:

$C_{D_i}= \frac{C²_L}{\pi AR e}$

But the relevant drag term is:

$D_i = qS \cdot C_{D_i} = qS \frac{C²_l}{\pi eAR} = qS \frac{L²/q²S²}{\pi eAR}=\frac{L²/qS}{\pi eb²/S}=\frac{L²}{q \pi e b²}=\frac{W²}{q \pi e b²}$

Where $W$ is the weight, $b$ the wingspan, $e$ the Oswald coefficient and $q=½ \rho V²$.

So induced drag is proportional to the wingspan $b²$. That means that being $b$ the same between B747 and A340, then $D_i$ is also the same for both of them (obviously if $W$ and $e$ are the same).

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So the real question now actually becomes what drives the choice of $b$ (and not $AR$) during design phase? Looking at the previous equation of $D_i$, one can see that it increases with the weight and decreases with the speed. That means that $D_i$ is maximum when the weight is big and the speed is small i.e. at takeoff. And indeed, normally for a jetliner the requirement on the OEI climb at take off is the sizing requirement for $b$. That's also why an airplane usually gets a wider wing as soon as the weight increases due to some update.

So, having sized the wingspan, once that also the value of $S$ is chosen satisfying all the necessary requirements, the $AR$ that pops out is the one that is needed. But this triggers then the next question.

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Why has the B747 a bigger wing surface than the A340? Generally speaking, a bigger surface is never good for something flying because it implies bigger drag. But a wing with a bigger $S$ does not generate only more drag but more lift as well. And, again, a lot of lift is needed at takeoff... especially if the available engine(s) is not pushing that much, as was the case for the B747: the original Pratt & Whitney JT9D delivered some 200kN thrust, it was the very first commercial turbofan and it was the non plus ultra of those times. A modern Rolls-Royce Trent 900 as seen on the A380 can easily push almost twice as much. So for the original B747 a big wing surface was needed to compensate for the lack of thrust and meet anyway the takeoff requirements. This is also demonstrated by the very complicated slats and flaps used on its wing. And, last but not least, bigger wing gives also more volume for fuel, which is something that the original JT9D for sure needed.

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Last topic: what about wing sweep? Here the choice is a bit more complicated because sweep angle is mutually influenced by airfoil, taper ratio, twist and possibly other aerodynamic criteria.

Sweep is mainly used to increase (increase in this case is good) the critical Mach number but it also improves lateral stability and shifts the CG forward improving pitch stability as well. All this happens at the expense of an higher structural weight and possibly pitch-up problems if combined with an high AR (so one of the two should be low).

An higher sweep allow the use of a somewhat thicker airfoil giving a more efficient wing structure, partially compensating for the higher weight due to the sweep itself. And thicker airfoils also allow more fuel volume.

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As usual in the aerospace world, it is a matter of compromises among contrasting requirements.