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Most large aircraft have a similar design for their trimmable horizontal stabilizer: they connect to the tail cone on a flattened area which allows them to be rotated within some range:

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From left to right: A319 (source), A320 (source, B787 (source)

But the THS of the A330 is different, it looks like a frog eye... What is the purpose of this flexible wall?

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Source

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It is a seal- to prevent entry of air into the stabilizer mounting area. For aircraft with trimmable horizontal stabilizers (THS), there is an opening to the rear of the aft bulkhead to allow for the movement of the THS. It can be seen in the following image for Boeing 787.

787 Aft fusealge

Boeing 787 aft fuselage structure; image from aero-news.net

Now, as the opening will be there while the THS moves, a seal has to be present to prevent entry of air (and FoD etc.). Boeing went ahead and put a hinge aperture sealing plate over that area, with only a small opening where the actuated area of the THS moves, with the seal inside the structure, as can be seen below.

777 THS

777 THS area; image from deicinginnovations.com

Without cover, the are will look something like this:

THS-1

Trimmable horizontal stabilizer region without cover, ; image from skysoftairlines.blogspot.in

Airbus, on the other hand went ahead and put a tailplane sealing plate outside the opening. This was used in the A330 and initial versions of A340 (which shared the fuselage with A330), before Airbus changed its mind and made the THS region similar to the other aircraft in A340-500 and -600 versions, where the horizontal stabilizer was redesigned.

Also, see these (1 & 2) patents and this discussion.

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This structure prevents air from flowing between stabiliser and fuselage, which helps to increase tail effectivity. In this particular case the A330 has a wider trim angle range which produces more vertical travel of the root of the stabiliser which in turn requires a more elaborate seal.

As any other part of the outer shape of an aircraft, the intersection between fuselage and horizontal tail is optimised for performance and construction cost. Where the compromise between both is struck depends on the trim angle range, the manufacturer's philosophy and its culture.

If you look at the tail from above, you will see that the fuselage is coke-bottled there in order to smooth out the cross section distribution over length, like it is done on supersonic fighters. This produces a flat surface on the side just where the biggest thickness of the horizontal tail sits. Unfortunately, this is not where the largest vertical travel of the root of the tail surface happens; this is either at the leading edge (for highly swept tails) or at the trailing edge.

For the ERJ-170, this flat surface is sufficient to cover the travel of the stabiliser nose, but for the A330 a wider range of trim angles is required. This might be because Airbus wanted a wider cg range or because the flaps produce a higher pitching moment change.

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