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Re: four winged Archaeopteryx

What I should probably have said was something like "expecting a
immobile tail surface to work for bird flight is a very strong claim"; a
fixed frond tail would have uniform drag and be a uniform contribution
to flight stability.

I understand what you are getting at, but that is only true if the tail itself is kept in a uniform position and the angle of the body is also kept uniform. In fact, because the airflow from the wings would interact flows around the tail, the wings would technically have to be static as well (though that is a more minor consideration). The tail feathers could have limited (or absent) mobility at the feather base, and yet the tail would still be adjustable because the tail can move at its base. Certainly, adjusting angle of attack of the tail would be relatively simple and well within known anatomical limits.

So you either have an Archie that can't fly with lost feathers/feather
damage to the tail, maybe can't turn without heroic effort, and is in
serious trouble with gusty winds (or anything else which applies an
assymetric airflow to the tail), or you've got an Archie with some
ability to adjust the tail surface to cope with conditions.

Modern birds have only limited motion at the feather base of most of their remiges. The primaries have fine control, but the secondaries and tertiaries are mostly mobile by virtue of attachment to a mobile lever arm (ie. the ulna and humerus). Since Archaeopteryx could most likely alter its tail position to some degree, it would easily account for changes in airflow over its tail along roughly analogous lines. Even if it could not move its tail (highly improbable), Archaeopteryx would not be prevented from turning, or from flying with feather damage to the tail. In both cases, the wings (being the primary lift surfaces) would adjust accordingly. The total forces associated with the wings would have exceeded those of the tail.

There are, in fact, examples of extant bird species that deal with a problem similar to a rigid, feathered tail: both quetzals and peacocks (or rather, the males of each) have long trains of feathers grown from the back. Because the trains are not actually part of the tail, they do not have the same mobility as retrices. Peacocks can lift their train for display, but have little fine control of their display feathers in flight. In both cases, while the display feathers certainly have aerodynamic costs, the birds can compensate quite well. In the case of Archaeopteryx, the tail would actually be aerodynamically useful, so Archaeopteryx would have been in better shape than a modern Quetzal, even if it had no tail mobility (which, again, I doubt was the case).