Not quite. As you increase the AoA, the angle between the "waterline" (direction the nose is pointed) and the true "velocity vector" increases. This means that the whole airplane is plowing thru the air at an increased angle, thereby increasing the parasitic drag of the fuselage & horizontal stabilizer as well.
Nonetheless, this component is usually folded into the "induced drag", since it simplifies the understanding of effects for the pilot into "them factors that are affected by AoA vs. them factors that ain't".
Right. This is why the whole concept of "induced drag" as a separate quantity is a little bit silly to begin with -- the induced drag gets mixed up with regular parasitic drag no matter how you look at it. But that's the way the assumptions and the terminology work. It's not a terrible approximation, provided you only vary your pitch a couple of degrees, and your wings are relatively large compared to the fuselage bluff area.
I've heard Lear also claim that Ground Effect would prevent the plane from flying that fast & that low. This is, of course, silly.
John Lear (the son of the inventor, not the inventor) has claimed all kinds of crazy things. I dislike making fun of the incompetent. Suffice to say that most people can figure out things like this on their own.
And I would again argue that, aside from the initiating event, "buckling" is a mostly irrelevant failure mode during the crush down of the towers. In order to get any column to buckle, you have to (to a variable degree) constrain its ends and maintain the compressive forces approximately aligned with the axis of the beam. During the crush down, neither one of these conditions were met. In addition, if those (comparatively) thin walled, 14" box columns & I beams did buckle, they would absolutely have retained kinks in them after the process.
The proof of that buckling was not a dominant process is the lack of kinked columns in the rubble.
Which leads to the actual failure modes during the buildings' collapse: the fracture of bolts & welds that joined the columns to their cross bracings.
And, with this as the failure mode, then I have to say that the building did NOT get significantly stronger in the lower floors, because the actual parts that failed, the bolts & welds, did not get stronger.
Nope, I disagree with this. There are a lot of possible failure mechanisms, and different choices at different times in the collapse -- for instance, long after initiation, the debris pile is moving so fast that you're essentially shearing away ALL supports and simply pushing columns to the side, not really loading them at all. This is seen in the surviving core remnants of both Towers. But early, and in many cases, I am reasonably sure that buckling is the correct mechanism.
First, in terms of the failure theory, you are correct that actual vertical loading to failure is unlikely. But there is more than one way to buckle. The other one is to apply an eccentric load, essentially adding moment to the columns. Think of buckling where the top is unrestrained, or a free-ended beam rather than a true column.
Second, regarding the debris evidence, some buckling will be elastic. You do not necessarily need to find kinks in the recovered columns. The actual permanent displacement, if any, may be quite small. Additionally, as NIST reported, even though a lot of the structural members
looked straight after the collapse, they weren't. NIST had trouble finding even a single one that was true after the collapse.
Third, regarding fracture, there is no solid cross-bracing between perimeter and core except in select areas, and the perimeter can fail as a unit. The perimeter, therefore, is highly likely to buckle. The core, well, it's more solidly framed so there I would agree fracture and shearing of seats followed by instability is the dominant mechanism.
Fourth, regarding weld strength, this does indeed increase with depth below the collapse initiation point. More bearing surface to support the welds. Thicker webs, wider columns, etc. This is all academic, however, since after the collapse really starts rolling, the structural strength is but a roundoff error; most of the delay comes from momentum transfer, not actual springiness in the lower structure.
Fracture is definitely a big part of the story. Hard to model, though.
I think that a Rapid Prototyping process might make the job reasonable. Fabbing 3 story segments at a shot, growing the part in the z axis. You could even produce the column stagger. The scale factor is the determined by the area capability of the prototyping system compared to the 207' side of the building.
[...] While I doubt that RP could generate the thin walled cross-sections of the columns, I don't think it'd hurt the model if they were oversized. Because, as I said before, I don't believe that their buckling was a significant failure mode.
I actually think it'd be fairly easy. The column stagger in the RP model would be different than the original structure, and the dimensions and material used would be different than a true scale reproduction, but the correct strength as a function of height would be a pretty simple polynomial -- no worse than fourth order. Nothing you couldn't build.
Of course, depending on what you wanted to prove, you wouldn't need the whole 110 stories anyway. If you got progressive collapse through 10 stories, that would probably be enough to prove the effect. That wouldn't allow a timing estimate of the total collapse, but it would let you study what it took to arrest progressive collapse.
This is third-show material, coming soon.
Good observations. Like I said repeatedly, these are not meant to be perfect models. They're simplified in numerous ways. That doesn't make them wrong, it just means you can take it a lot further if you want more resolution.
