Appendix B: Collapse of the towers – the application of some basic physics.
I have seen and read through quite a number of attempts to challenge the official theory of progressive collapse for the Twin Towers and for Building 7 by appealing to violations of the laws of physics. This may seem odd to those who are not trained as scientists, yet it is perhaps the most logical starting point for anyone who has been. Why? Because, showing any breach of the fundamental laws of physics would be quite sufficient to render all other evidence unnecessary. In this instance then, physics appears tantalisingly to offer the possibility of irrefutable proof one way or the other, which, with so little direct forensic evidence having been preserved, no other analysis can. For whatever the reliability of the witnesses, and regardless of all other distractions and deceptions that must be negotiated, the physics can NEVER be wrong.
Taking this approach then, some have presented the case that following the law of conservation of momentum, the collapse rate would have to be significantly below free-fall speed. This is a relevant and interesting argument, but one that, due to various unknowns about the collapse mechanism, is actually quite difficult to demonstrate conclusively without recourse to computer simulations. So having acknowledged this I have decided to leave the question there for others to consider.
The law of the conservation of energy, however, offers a more straightforward route. For those who don’t remember the law then let me briefly summarise it as follows: it says in a nutshell that energy can never be created or destroyed. And just like many of the laws of physics, it is really a profoundly simple rule. That is, it is simple to understand, but, and more importantly, it also simplifying.
It means that we only need to think about two things: the situation before and the situation afterwards. Whatever happened during the collapse is not at all important, just so long as we know how much energy we had to begin with and how much energy we would have needed to break everything to pieces. Well given this fact, it’s possible to make some useful estimates and indeed many have already done so.
They have calculated the initial “available energy”, which is easy enough because this must have been almost entirely the gravitational potential energy of the building, which is something anyone with a GCSE in the subject ought to be able to estimate. So everyone agrees on this part, more or less, accepting a figure of around a thousand billion Joules, which I’ve seen compared to “about 1% of energy released by a small nuclear bomb”. Sounds a lot when put like that. So that’s what we have at the start.
Now we need to estimate the amounts of energy that must have been involved in tearing the whole structure apart, into such small pieces that most of it was easily loaded onto trucks. We’ll need to include the energy required to blast some of the debris horizontally, and perhaps more significantly, we also need to add in the energy needed to pulverise huge quantities of the concrete into those large clouds of fine dust that settled across New York.
There are indeed already estimates for all of this, and much more besides, and those who have sat down and done the sums have frequently claimed to find an energy deficit. They find much more energy was needed than was ever available. They say that gravity alone just wasn’t sufficient to cause such total destruction. But these kinds of analysis are complicated, especially if we are seeking real precision rather than ball-park estimates. Having said that such an approach is far less complicated that NISTs use of finite element analysis. Here is certainly one way that a fully independent scientific investigation, run in tandem with a fully independent commission, might be able to settle the question one way or the other.
Now, back to the matter in hand. The molten steel. In order to melt steel from room temperature you have to add heat – lots and lots of heat. Well, actually that isn’t strictly true. And we’ll need to be careful about our terms. So let’s leave “heat” aside for a moment. Stating matters a little more scientifically then, we should talk instead about the “internal energy”. In layman’s language “raising the internal energy” is the same as “raising the heat”, it either makes the thing hotter or it melts it. But physicists prefer to use the term “internal energy” rather than “heat” because they need to distinguish between the different ways in which internal energy can be raised. “Heating”, then, in this more precise description, involves the transfer of energy from something hotter to something cooler. This is a one-way process, which occurs when you heat your saucepans on a hob, or leave your coffee to go cold.
You may have noticed that your pans don’t melt into the hob no matter how long you leave them, and that your coffee never cools down below room temperature. There is reason for this. We say that at some point the pan or the coffee has reached what is called “thermal equilibrium” with its surroundings. From this point on no further heat transfer can occur, because nothing can ever get hotter (reach a higher temperature) than the thing that’s heating it. To do so would violate the famous second law of thermodynamics and as the physicist Eddington once famously remarked:
“if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.”
Going back to the question of melting steel then, it’s certain that we would require fires hotter than the melting point of steel, which is about 1500C, whereas jet fuel doesn’t burn at temperatures nearly high enough. NIST in fact agree that the jet fuel and office fires in the towers could not have exceeded 2000F (about 1100C), and consequentially, they have never claimed that the original fires melted the steel. Indeed, according to their own report, the effect of the fires was only to cause weakening of the steel sufficient to initiate the collapse.1 So what do NIST make of the reports of molten steel…? Well, I’ll come back to that a little later, but first we must consider more of the physics.
Okay then, we’ve dealt with heating, but, as I mentioned earlier, there are other ways to raise the “internal energy” of a material. For instance, you might run an electric current through it, or instead you might apply forces to bend or compress or stretch it, perhaps over and over again. Stretching, bending, twisting and compressing and so on also causes materials to get hotter or potentially to melt, and these alternative ways of increasing internal energy are what physicists call generically “doing work”. So perhaps then we can account for the molten steel found in the ruins of the WTC by virtue of “work done” as it twisted and ripped apart. If we needed to consider every snapped rivet and twisted beam in isolation that would involve an incredibly complex analysis too, fortunately however there is a law of physics which rides to our rescue: it’s our old friend the theory of the conservation of energy.
I am about to present something known in the trade as “a back of the envelope calculation”. It is an attempt to provide an estimate for the addition temperature gain (beyond the 1100C of the fires) that could have occurred as the building smashed to pieces, but it will involve making certain approximations and assumptions, all of which I will endeavour to justify.
My prime assumption is as follows: that ALL of the available energy was ultimately absorbed by the steel alone, causing it to get hotter. This is a crazy assumption of course. It takes no account of energy absorbed by the concrete, making it hotter too. Of losses due to air resistance, which we should suppose might be considerable given that each floor would have to push the air out of the way like a plunger. It ignores the fact that since so much of the concrete was ground to dust, its own available gravitational energy would have been lost as it floated gently down to earth, taking with it whatever internal energy it might have gained from the process of being crushed. It ignores the fact that the ground itself must have absorbed a significant part of the energy as it gave way a little, and that some of that energy then caused tremors and therefore, though indirectly, rocked the other buildings in the close vicinity a little. For all these important reasons, my answer is likely to be a gross over-estimate of what was really possible, representing only the extreme upper limit on any true answer. But then remember that it’s only a back of the envelope estimation.
My next assumption is that the centre of mass of the building is exactly halfway up. In point of fact, the centre of mass must have been significantly below halfway because obviously the structure towards the bottom needed to be ever stronger to support the greater weight above. I also fail to take account of the fact that a significant part of the building’s mass lay in its foundations and the basements which had nowhere to fall. This means that I have again substantially over-estimated the available energy, forcing my final estimate to be an even higher upper limit. (Although, provided with full knowledge of the design of the building we could eliminate the biggest part of this second error.)
These then are the positives, if you like – factors which force the figure up – but there are also a few negatives. There is the additional weight of fixtures and fittings, of furnishings, and of the victims themselves. (Others, often far better qualified than myself, have attempted more accurate calculations with estimates on all of the above – they involve only modest adjustments). For our purposes then, it’s quite reasonable to say that these negatives are negligible, especially when offset against such enormous positives as all those listed above. As for the additional energy contained in the jet fuel (which is small when considered in the greater scheme), well this is irrelevant anyway since it has already been used to heat the steel. But it can only heat the steel to 1100C at most, whereas we are trying to account for temperatures above those generated by the fire. Right then, we can now do a very simply calculation. If all of the initial energy had somehow diffused evenly throughout the steel, how much would its temperature rise? Well, the answer is a mere 20C(with the relevant equation and figures given below).2
In other words, even if every last drop of energy went into heating the steel (which we presume is already 1100C – again a high estimate, with most the steel never reaching temperatures anywhere close to this upper limit) it would still need nineteen times more again to even reach melting point. Whilst we must remember that much more energy would again be required to melt any significant portion of it.3 In the case of the lower-level WTC7, this energy shortfall is exacerbated still further.
Being approximately half the height, and all other things remaining about equal, the estimate must also be halved, generating an average rise of 10C at the very most. So given these numbers, how can anyone seriously propose that the steel was melted as a consequence of the additional energy gain during collapse?4
Or let’s look at this all another way. Take a lump of steel (and mix in some concrete if you like) and drop it from the height of the twin towers. Will any of it melt when it hits the ground? And when cars or trains or even planes crash and get all crumpled up, and the kinetic energy converts into internal energy, do we ever expect to find even small puddles of molten metal? For such collisions generally occur at similar and at frequently higher speeds than the speed of the falling rubble.5 And the reason why cars, trains and planes don’t melt on impact is simply this: that small increases in internal energy require a whole lot of mechanical “work” input. It is for a similar reason we don’t try to boil water by shaking it around in a vacuum flask, a handy method for a stranded hiker. It is theoretically possible to heat water by elbow-grease alone, indeed the water temperature will measurably rise, but if you’re planning to make a cup of tea then just don’t hold your breath.
Nevertheless, I have come across just such implausible explanations presented by a few of those who wish “to debunk” the case for demolition and explain away the molten metal. That said, the guys at NIST have taken better care to avoid such utterly improbable conclusions. Instead, when it comes to the question of the origin of molten steel they have provided the following answer:
“NIST investigators and experts from the American Society of Civil Engineers (ASCE) and the Structural Engineers Association of New York (SEONY)—who inspected the WTC steel at the WTC site and the salvage yards—found no evidence that would support the melting of steel in a jet-fuel ignited fire in the towers prior to collapse. The condition of the steel in the wreckage of the WTC towers (i.e., whether it was in a molten state or not) was irrelevant to the investigation of the collapse since it does not provide any conclusive information on the condition of the steel when the WTC towers were standing.”6
Now, please read that back again. I’m right, yeah? They’re saying they didn’t bother studying the steel in the wreckage “whether it was in a molten state or not” because it couldn’t provide any information on its condition prior to the collapse. That’s a strange admission isn’t it? I mean if you want to find out how anything broke then in general it helps if you look at the pieces afterwards. I admit though I’m no expert.
They also say this, which I find still harder to fathom:
“Under certain circumstances it is conceivable for some of the steel in the wreckage to have melted after the buildings collapsed. Any molten steel in the wreckage was more likely due to the high temperature resulting from long exposure to combustion within the pile than to short exposure to fires or explosions while the buildings were standing.”7
Now quite frankly, I wouldn’t let my first year students get away with such meaningless obfuscation! Higher temperatures due to longer exposure times – give me a break. As if exposure time makes all the difference, when hotness is limited, let us remind ourselves, such that nothing can EVER (no matter how long the exposure time) become hotter than that which is heating it. So a “long exposure” to what exactly? “To combustion within the pile”. Oh really – and just what could have been burning so ferociously down in the rubble that wasn’t already burning when the building was standing tall and supplied with oxygen all around? As I say, I’m no expert, but I’ve used a Bunsen burner now and again and it certainly won’t get hotter when you shut the air down.
If you find that none of these arguments are persuasive then I refer you instead to the approach of an American physics teacher by the name of David Chandler. When in August 2008, after a seven year delay, NIST released the draft version of their “Final Report on the Collapse of World Trade Center Building 7”, Chandler, who had managed to book a seat at the technical briefing, came prepared to challenge NIST’s findings. And rather than getting bogged down in the nitty-gritty of their complex computer analysis, he posed just one very simple question:
“Any number of competent measurements using a variety of methods indicate the northwest corner of WTC7 fell with an acceleration within a few percent of the acceleration due to gravity. Yet your report contradicts this, claiming [the building collapsed] forty percent slower than free-fall based on a single data point. How can such a publicly visible, easily measurable quantity be set aside?”
You can make your own judgement of their response to this ludicrously simple challenge by watching the video below:
When NIST released their “Final Report” just a few months later in November, and seemingly in direct response to this challenge made by Chandler and others, there was one very important revision to the updated version. It is revealed in the following graph which now formed part of the report:
So finally then, NIST are claiming that the collapse of WTC7 occurred in three separate phases, but what is most interesting is the phase they designated “Stage 2”. In the corresponding section of the graph there is a linear regression best fit to the data points, and the gradient of that closely fitting line is given as 32.196 ft/s2. For those of us more familiar with SI units that is equivalent to 9.8133 m/s2. In other words, NIST are actually conceding that WTC7 underwent free-fall collapse for some 2.25s (of their claimed 5.4 s collapse time).
David Chandler further discusses the implications of NIST’s revised version of events in a second video:
And in a third video he puts NIST’s admission of free-fall into a fuller context. Pointing out how their analysis relies on a computer model that has never been made publicly available, thus denying the opportunity for proper scrutiny and testing of their own findings by others with relevant expertise. Worse still, NIST has only ever released a selection of outcomes from their secret model. A selection that presumably best matches the results they wished to reproduce. All of which, as Chandler very eloquently explains, reveals how NIST’s hugely expensive investigation appears to have been nothing but a fraud and a cover-up:
1“In no instance did NIST report that steel in the WTC towers melted due to the fires. The melting point of steel is about 1,500 degrees Celsius (2,800 degrees Fahrenheit). Normal building fires and hydrocarbon (e.g., jet fuel) fires generate temperatures up to about 1,100 degrees Celsius (2,000 degrees Fahrenheit). NIST reported maximum upper layer air temperatures of about 1,000 degrees Celsius (1,800 degrees Fahrenheit) in the WTC towers (for example, see NCSTAR 1, Figure 6-36). However, when bare steel reaches temperatures of 1,000 degrees Celsius, it softens and its strength reduces to roughly 10 percent of its room temperature value.” from NIST’s Answers to Frequently Asked Questions (August 30, 2006).
2mass of building x g x height/2 = mass of steel x c x change in temperature
where mass of each tower = 500,000 tons, height of towers = 411m, mass of steel = 100,000 tons, and specific heat capacity of steel = 500 J/Kg/K (this value may vary between 400-600 depending on composition).
3the specific latent heat of fusion of steel is about 270,000 J/Kg. So to melt just 10 tons of the original 100,000, would require 2.7 billion Joules of energy, which is about a quarter percent of the total available (at a conservative estimate).
4You might argue that by assuming all the energy was evenly distributed I have greatly under-estimated what could have happened on a local scale. That some parts of the building would have been significantly more bent or twisted or otherwise deformed than other parts. That they could have got substantially hotter than the average. This is true, of course, but then we might very reasonably expect that it was those regions regions lower down in the building that would experienced the greatest forces and impacts. But since these are areas at the furthest distances away from the fires we would expect the steel in those areas to be cool – around room temperature – and therefore requiring substantially greater increases in internal energy to reach melting point. It should also be noted that the steel framework of the building would have acted like a giant heat sink continually conducting heat away to cooler regions and so continually distributing the internal energy more evenly throughout.
5The average kinetic energy per unit mass is commensurate and so we might reasonably expect similar effects.
6from NIST’s Answers to Frequently Asked Questions (August 30, 2006).