Thursday, September 14, 2006 ... Deutsch/Español/Related posts from blogosphere

Preprint on falling Twin Towers

This looks almost like a physics preprint:

The result of the paper is that the author believes that the airplanes were not enough to make the Twin Towers collapse: the collapse was too fast, he essentially says. I don't believe this conclusion but still, there are some technical arguments that others might want to look at.

What do I think about the collapses?

Each tower collapsed roughly in 10 seconds which is comparable to the time of free fall from the same height. Recall that in 9 seconds, you fall by 5 x 9 x 9 = 400+ meters which is a bit less than 417 meters of the full height of the WTC towers.

I don't see anything wrong with the nearly free-fall model. For example, the 93rd floor of WTC1 (or 77th floor of WTC2) suddenly broke because of the high temperature melting the metalic structure. The remaining 10+ floors of WTC1 (or 20+ floors of WTC2) above the critical point - whose mass was 50,000 tons for WTC1 (or 100,000 tons for WTC2) started to fall freely, and they were hitting the lower floors one by one and taking the other floors with them. The new floors slow down the avalanche a little but not much because the falling part of the tower is much heavier.

If the momentum of falling 20 floors is suddenly shared by 21 floors (because another floor joins the avalanche), the velocity decreases by 5 percent only, and this percentage is decreasing as the collapsing portion of the tower relatively grows.

P.S. (off-topic): There is a new contribution to the heavily overpopulated family of anti-physics shitheads. His name is Gregg Easterbrook. Oh no, he's been fighting against extra dimensions for years. Fortunately, Gene seems to be correct and some people are able to see that Easterbrook's text is nonsense: DovBear, Ezra Klein. Still, most people are morons, and I chose not to link to them because they have enough links to each other.

Update - elastic model

I have asked many people what they think about it. An interesting response came from Yevgeny Kats - during our long chat about more serious physics. He figured out that my model - that is totally plastic - is actually making things slower than necessary; intuitively it is because I am losing kinetic energy which slows things down. He proposed a different, completely elastic model, as a zeroth approximation, and I offer you my quantitative version of it.

In this picture, the floors never join into a single object. When the (F+1)st floor reaches the Fth floor, the upper floor stops completely while the lower floor picks all of its speed. Imagine that you look at the (F+1)st floor before the elastic collision but you choose the Fth floor after the elastic collision.

In this picture, you can visually follow a floor that is freely falling, and whenever it reaches another floor, it gives it a signal to fall freely (from zero initial velocity). If I exchange the identification of the 2 floors during each elastic collision, the floor whose initial height is "h" will thus reach the ground after time
  • sqrt(2(H-h)/g) + sqrt(2h/g)
The first term counts the time needed for the first collapsed floor whose height is "H" to reach the floor "h": here, "H" is the total height of the building (or the airplane). The second term computes the time from the relevant elastic collision. It is easy to see that the maximum of the function above appears for
  • h = H/2
and the total time at this value is
  • 2 sqrt(H/g)
which is sqrt(2) times longer than the time of the free fall. For the WTC1 tower that was hit near the top, around 360 meters above the ground, the result is
  • 2 sqrt(360 / 9.8) = 12 seconds,
in agreement with observations. It is conceivable that a compromise between the plastic and elastic models could actually make this time even shorter.

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snail feedback (11) :

reader Leucipo said...

Interestingly, the question of a big free falling mass reaching a smaller free falling mass (or the contrary) is one of the discussions in Galileo "Two new sciences", aiming to deduce the well known, er, galilean equation of free fall.

reader DonQ said...

the 93rd floor of WTC1 (or 77th floor of WTC2) suddenly broke because of the high temperature melting the metalic structure.

What produced the high temperature (2750 deg. F) required to melt the steel structure?

Not jet fuel, which burns at max. of 1800 deg F... so what was it?

reader Luboš Motl said...

You don't have to melt the steel completely for the building to collapse. Already at 1500 deg F, the steel loses rigidity. Moreover, the core of the buildings probably collapsed first, a fraction of a second before the rest, and this core collapse was probably caused by a structural damage by the airplanes.

Your belief that a building cannot collapse unless the steel is melting completely is just a belief that is not supported by anything whatsoever - and most likely can be easily falsified. You believe these bizarre things only because you want to believe them but they have nothing to do with rational reasoning or arguments about these questions.

It is absolutely clear that there exists an upper bound on the temperature of fires and on the total energy deposited by the airplanes that still allows the buildings to survive permanently. This upper bound on the temperature is surely lower than the melting point of the steel, and the upper bound on the energy is arguably comparable to the energy of the airplane. The only question is how far it is, and 9/11 was an extraordinary and expensive experiment that gives us experimental data.

It is incredible that these buildings could be standing at all.

You have not made any reliable calculation of the critical temperatures, critical maximum energy, or anything like that to make any conclusions. What you're writing about the insufficiency are just your conspiracy beliefs.

Try to take a Boeing and smash it to your house. I am curious how it will survive.

reader yeslove said...

Most pysicists through history has been wrong, you try to cover up that fact by pointing out a few geniouses who saw the light in spite of the lies and misconceptions of their contemporaries and had to pay dearly to came up with something truly groundbreaking and new. At the time many of them were treated as outcasts or threathened with death. These few people are a minority and hardly representative of the physics community. Most of you are wrong and will be proven so by the next paradigmatic break-trough.

Why the venom?
Because I agree with you on the CO2 issue pertaining to GW and then find your childish momentum calculations in the wtc patched up with uninformed and grave insults against truthers.

Elastic collision huh? Did you ever look at a photo of the collapse and notice the clouds of pulverized concrete, rubble and steel-beams ejected within a radius at least double the towers. How many percent of each floors mass remained inside the perimeter and were able to transfer any momentum to the floors below?

Look at your flimsy example of 10 moving floors + one static reducing speed with only 5% and the ease with which I hit the keyboard and counter that the vertical core and perimeter steel beams on impact propagated the forces several floors below and describe the situation as 10 moving floors + 10 static now reducing speed with 50%. A claim equally false as your own.

Please check out Gordon Ross analysis of momentum transfer linked at this page together with criticism by Frank Greening and replies by Ross.

Or have a look at Steven Jones discovery of microscopic iron 'spherules' abundantly present in the dust (google it).

Not even NIST beleives in a pancake collapse.

I know more than you because I know I am a victim of my own propaganda and you dont.

But I like your GW attitude.

reader EricBaum said...

I just got interested in this, and I have a question. It seems to me the real question is WTC 7 for which
Jones says the free fall time for a rock from the roof was 6 seconds and that the building fell in 6.6 seconds. This is well within the elastic model result above if I understand it and is thus perhaps very hard to understand.

It seems to me the twin towers themselves do not provide as clear an example because both hypotheses, standard/plane and truther/thermite, agree (if I understand the competing models) that the girders are taken out at the level where the planes struck, (although they disagree on the cause for the girders being taken out there) which in either case is near the top of the building. So both sides agree that the fall from there down is due to pancaking, and since that is a big constant term added on to the time for fall, it obscures the test of the models. WTC 7 is a much clearer test case, and it is unclear to me whether any physical model that doesn't involve thermite or some such taking out the beams on or near the ground floor at the start can account for the fall times, assuming Jones is right in the figures he quotes.

If you can address this Lubos, I would be grateful.

reader Luboš Motl said...

Dear Eric, first, the plastic model is the slowest one and unrealistic for the collapse of any of these buildings.

The elastic model is faster - just 1.414 times slower than the free fall - but it is in no way an upper bound on the speed, either. The collapse started by the collision with the airplane *is* a sort of explosion, too. What matters is how quickly the heat spreads to melt the steel structure and how quickly the heat is generated so that the huge pressure from the hot air and exploding traces of fuel inside the floors are able to knock the floors beneath - and all these things may happen faster than the free fall in principle.

The very term "thermite" suggests that the discussion isn't serious physics. It's just one among many types of materials that may contribute. By saying "thermite", one assumes a particular answer, and a very contrived, special, ad hoc, preconceived one. It just makes no sense to talk with people who immediately say "thermite" and then look for ways to defend their first guess.

There were lots of things inside the floor that were burning and causing similar increase in pressure and temperature as a "thermite" but they were not thermites, like the plastic-wood furniture and other things. The truther "scientists" completely deny the existence of all these things because they disagree with their predecided answer. They deny the reality, they're paranoid idiots.

reader EricBaum said...

Lubos, your comments in response to mine are mostly just ad hominem attacks, which are not in the slightest convincing, just the contrary if anything they are evidence of the weakness of your position. Also you didn't at all respond to my question re WTC 7, the timing of the crash seems to have been well below what is achievable by the elastic calculation. Nobody has yet proposed a mechanism up to the challenge, as I understand it, without invoking explosives/thermite. Are you up to this challenge, or are you just going to continue ad hominem attacks as your new reasoning method? sqrt(2) free fall time is said to be 8.4 seconds, but the building is claimed to have fallen
in 6.6

PS-- I find it quite amusing that the book I am reading, Debunking 9/11 Debunking by David Ray Griffin, offers a very compelling and well reasoned argument that Kean and Hamilton, while giving a useful list of bad reasoning methods they say characterize conspiracy theories, actually fall prey to every flaw they so detail while in fact the Truthers do not at all display these flaws; and at the same time Griffin supports with the occasional offhand comment the theory of global warmism, while you Motl realize that the global warmists also fall prey to all these invalid reasoning methods such as ad hominem and denying bad data and such, but you simultaneously incorrectly apply these bad reasoning methods to the Truthers. The real situation is, the supporters of the standard Conspiracy theory (planes brought the buildings down), like the global warmists, resort a lot to invalid methods of reasoning, while the Truthers and the skeptics, at least the best ones, are much more open to evidence and correction-- so indeed it is true I am quite sure that Truthers and skeptics are highly correlated. This doesn't make the Truthers right, they have a high hurdle of a relatively poor prior likelihood caused by invoking additional unseen factors, thus a poor Occam factor, and also of invoking a Government conspiracy that might be involved as a priori unlikely. Nonetheless, I believe they have made some serious arguments that the weight of the evidence is so high as to overcome these factors, not only convincing a large fraction of the population but some smart people who have looked into it in serious ways, and ad hominem attacks are not going to convince anyone serious of the contrary.

reader Luboš Motl said...

I have already answered all your questions, asshole. You just don't want to read. The elastic model is in no way an ultimate upper bound on the speed; it's just a simple fucking oversimpified model. Any heat spreading through the metal and explosions driven by the hot air and burning things in the floor is guaranteed to speed up the collapse beyond the previous limit, including the limit of the purely elastic model.

reader EricBaum said...

You still haven't suggested a mechanism up to the task of bringing down WTC 7 in 6.6 seconds, merely argued there is no argument based on simple momentum transfer and conservation of energy capable of proving its impossible.

You also, btw, haven't addressed the question of how the buildings ever got hot enough to weaken steel.

But this hasn't prevented you from more ad hominem attacks

reader Luboš Motl said...

There is no simple way to calculate the the collapse time is exactly 6.6 seconds. It's a terribly complex physics-chemistry problem depending on stifness, combustibility, latent heat, expandability, and lots of other physical quantities descriibing lots of materials in the tower.

I have showed idealized pure-mechanics models as well as factors that may slow down and factors that may speed up the collapse. When one does the simulation properly, he will get the time that agrees with the observations.

You also, btw, haven't addressed the question of how the buildings ever got hot enough to weaken steel.

Fire weakens steal so that it can reshape or break. The profession of "blacksmithing" has been based on it for thousands of years, stupid asshole.

reader EricBaum said...

The claim is that office fires, nor jet fuel fires, especially oxygen starved fires, don't reach anywhere near the temperatures necessary to weaken steel, especially because steel is a great conductor of heat and there was vast quantities of steel interconnected in the buildings to carry the heat away, and the towers fell in under an hour.

Incidentally, this is presumably why no other steel structure buildings have ever fallen in a fire.
And also why smelting steel requires specially designed furnaces.

Why all the insults?

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