9/11 conspiracy and the math of the Twin Tower collapses

(Note: this post follows my earlier and unsuccessful attempt to do the math testing whether the World Trade Centers collapsed at near free-fall rates just because of the force of the collapsing upper stories - as opposed to controlled demolition. John C. started emailing me his much better work on this. I'm basically just being a stenographer - someone could probably hold my hand and guide me through the math, but I prefer to just get this out on the Internet for anyone's use.)


John's first email analysis:





Some assumptions that are implicit to the analysis that I did and the effects of those assumptions are as follow:

- The analysis assumes that there is no material deformation of the structure. At first glance this would appear to be enough to cause my method to be invalid (after all there is a fair amount of material deformation), but I thought about it and if material deformation does take place then the analysis is invalid but the structure has already started to fail so I don't think it is that much of a restriction.

- The analysis assumes that the impact will be evenly distributed over the surface which it probably will not be. This would act to increase the dynamic stress.

- The analysis ignores the elastic compression in the tower. Since the height was so large this would probably be significant. By ignoring it the analysis that I have done here is conservative.

- I assumed that the steel structure was the same above the impact as it was at the impact. This is probably not the case (the supports were tapered) and again this would make our estimate conservative.

- I have also ignored the deformation and heat problems due to the jet striking the building. This would be very significant in the first floor or two but would be less significant as we go further down in the building.

- I should also note that after the first floor or two my analysis again goes out the window. First, you no longer have a solid (or even semi solid) object causing the impact but something like a wave of rubble. Also, as each floor falls you start to pick up kinetic energy. If the floor fails then it did not absorb all the potential energy. This leftover energy will be in the form of kinetic and at the next level you get potential and kinetic. I ignored the kinetic. What the net result of these two factors would be I haven't a clue, but I suspect that the kinetic energy would be such that it would eventually dominate the equation. Thus my analysis could show how it would start and then it is driven by the extra kinetic energy picked up as each floor collapsed.


As I said in my previous e-mail I guessed at a lot of values and came up with a crude estimate of 40 times the static load (actually it was 36). While this is a far cry from my initial guess of 2,000 (what is a factor of 50 between friends) It is still very significant.

However I wanted a better estimate and thus I went into it a little more this morning and it turns out that a lot of my assumptions (i.e. the area of steel, the height of each floor) don't matter. The important assumption is how much each floor weighs and I assumed that it was 1.5 times the weight of the steel. For the weight of the steel I used the density of steel x area of steel x height of the floor. If you don't like my 1.5 factor you can easily replace it with one of your own.

I find it hard to talk about math in an e-mail so I am attaching some scans of my work. If this is going to be put on the net you should probably go over it fairly well to check my assumptions, my equation manipulation and calculations (Editorial note: John is giving me way too much credit). My final answer is 32. Thus the dynamic load is 32 times the static load. I don't know about the WTC but for most structures a safety factor of 2 or 4 is used. I heard Dr. Thomas Eagar give a guess of a safety factor of 5. So my analysis is still 6 times this!!!

I will note that I am a mechanical engineer, not a civil one and someone with an advanced degree in structural mechanics could probably pick some holes in my analysis, but with the stipulations above I believe it is pretty sound.

John
PS I will probably be sending you e-mails with little comments on them as I think of things. For example I ignored the structural aspects of the building. For example there are areas on the floor that are designed to take only the load of the floor so even a static load of 10 times the expected load would cause failure - let alone the dynamic load!!!

-----------
John's second email:

Hi Brian:

I was going over my calculations trying to get better estimates and I realized a couple of things.

1) My h is too small (I used 3 meters but a better guess would probably be 3.7.

2) I underestimated my floor weight. I have a couple of references that say that each floor was about 4,500 t. I have no idea how they come up with this figure - it seems too high to me but the people who give it probably know more than me.

Anyway, I was looking for references and I came across this one. You have probably already read it but I found it interesting:

http://www.tam.uiuc.edu/news/200109wtc/

They used a similar approach to what I did (except they seem to have rolled up E, A and L into a single constant - probably a good idea which would save you integrating but I didn't have all the information to allow me to do it). However what I found interesting was their first estimate was a ration of dynamic load to static load of 31!!! So I think my rough value of 31.5 is actually pretty good (even though I have errors in my analysis it would appear that my errors cancelled out). In engineering sometimes it pays to be lucky instead of smart!!

Best,
John

The Gronholm Method

In high school I had the oh-so-deep realization that artists took pop cultural fluff and turned it into high art. In my case it stemmed from seeing Norman Mailer transform your standard pulp war fiction into The Naked and The Dead, although it should have been obvious to me a lot earlier, say with Shakespeare.

Anyway, it's been done again with The Gronholm Method ("El Metodo"). This movie takes the Apprentice/Survivor concept from pop entertainment to art - an extremely well done depiction of people united in being pit against each other. It was striking to see this movie just shortly after watching "Crash" on DVD - Crash is okay, but this is a lot better. See it if you get the chance.

(For some reason, it also reminds me of a similar film for paranoid sci-fi fans, Cube.)

A partisan attack on Sierra Club, from the left

Sierra Club is picking up all kinds of flack for endorsing Republican Senator Lincoln Chafee. Chafee's had a few bad votes, like every other politician, but overall has been a good environmentalist.

Firedoglake, Kos, and Atrios have all been after Sierra Club, but to the extent they criticize SC for supporting someone who voted in Bill Frist as Senate Majority Leader, they're attacking it for not being a wholly-owned subsidiary of the Democratic party, which is a ridiculous basis for the attack. (Might also be worth remembering that Frist's Republican competitors for his job were even worse than him.)

Two other points worth mentioning: while Sierra Club is non-partisan, it's no secret that its membership and likely its leadership skews somewhat to the left. When SC endorses a Republican, they're overcoming a bias, so the accusations flung against them ring hollow. Second, if you read this comment thread, it's pretty clear that the people who actually know something about Chafee are much more sympathetic to the endorsement than the fire-breathers. More evidence suggesting the fire-breathers and the bloggers got it wrong.

Bush's second speech this August

For context, you might want to read the Bush's first speech on August 16th of this year.

Official White House Transcript

August 21, 2006

Speech by President Bush giving 48 hours to Iranian dictator Ahmadinejad to step down and end radiological threats from Iran


Good evening.

When I spoke to you last, five days ago, I announced that American forces had taken the decisive step to end the nuclear bomb threat from Iran. Our forces successfully destroyed the machinery that we know to be designed for nuclear weapons, not nuclear power. To save American lives and Iranian lives too, American forces used a fission-enhanced penetration weapon to destroy the Natanz gas centrifuge. Fission-enhanced penetration should not be considered nuclear bombing, as has been made quite clear.

Our necessary action made the mistake of the Iranian dictator equally clear. "President" Ahmadinejad brought this situation on his country by his dangerous pursuit of a new Holocaust, a nuclear Holocaust. We stopped him. History will be clear - we did the right thing.

Yesterday, President Ahmadinejad compounded his mistake. The crowds he spoke to in Tehran were brought there using a combination of force, hysteria, and lies. Whatever misleading images have been shown by the media, the Iranian people as a whole know that we want to help them, they love freedom, and they oppose their dictator.

Just a small, fanatical few support the dictator mullahs, but these few people control all the power. Fanning the hysteria, maybe even believing it himself, Ahmadinejad accuses us of attacking them with nuclear bombs. That is a lie. We did not use nuclear bombs; we used one fission-enhanced weapon. We did not start this confrontation; as stated before, our evidence leaves no doubt that Iran planned to distribute nuclear bombs to terrorists. Self-defense is not an attack.

Ahmadinejad then took a fatal step - he said in retaliation for raining "nuclear fire" on his own people, Iran will "soon" explode a radiological bomb at an American government or military facility within a major US city. The "nuclear fire" is a lie; we did not use a nuclear bomb, and all the military facilities that we hit were carefully targeted to minimize civilian casualties. Iran's dictators have no right to retaliate against something we had to do in self-defense.

While we have eliminated the greatest threat, Iranian nuclear bombs, a severe threat has now arisen from this planned "dirty bomb" attack. We have to take direct action to counter this new threat. To those who disagreed with our decision for pre-emptive self-defense in Iran, the need for self-defense should now be clear. Hindsight is not wisdom, but foresight about an open threat to our cities is simply obvious. We must remove Ahmadinejad and eliminate the threat he poses.

President Ahmadinejad has 48 hours to resign. A man this dangerous can no longer rule the country. Iran's subsequent leader must, in the same time period, renounce any plan to subject the United States to radiological attack, and open all nuclear facilities to UN inspection and inventory. If this deadline is missed, Operation Persian Freedom will begin.

We have made it clear to the Iranian people that our problem is not with them, but with the dictators who stole their country. Their freedom and sovereignty will be returned to them from the dictator mullahs who robbed them.

This dangerous world requires both courage and hope. I know our brave American soldiers have both courage and hope; I know the brave American people do as well. Moving forward today, we save Iran and save our own country.

May God bless America's work, and may God bless us all.

How they'll spin it, coming this August

My crystal ball showed me this speech by President Bush this upcoming August. More information on the factual background is here.

Be prepared.


Official White House Transcript

August 16, 2006

Speech by President Bush authorizing use of fission-enhanced penetration weapon to end Iran's nuclear bomb-making


Good evening.

Earlier today, I took the step that we have delayed as long as humanly possible, and authorized military action to end Iran's dangerous and illegal nuclear bomb-making program. Our brave fighting men and women have begun military operations, and all reports show that we have been successful in our efforts.

The dictator mullahs of Iran have denied they are creating nuclear bombs, but their lies can no longer be tolerated or excused. We simply cannot wait any longer. Every day that they continue purifying weapons-grade uranium brings us closer to the day when a terrorist nuclear bomb will explode in America, in Israel, and elsewhere in the West, causing countless civilian casualties. And these faceless terrorists would have not one nuclear bomb, but dozen or more, giving small groups of heartless fanatics the capacity to wage a world war. We have to stop them.

This danger to the world is not a risk, it is a certainty. The documentary evidence that the Secretary of State will present to the UN Security Council tomorrow will prove that Iranian mullahs planned to develop and distribute nuclear bombs to terrorists. We had to act, and we had to act now.

Iran's dictatorial leaders, together with some sincere-but-misguided Americans, accuse us of planning this operation for months. While we have to make advance plans, we never wanted to go forward with it. The Iranian dictators left the world without a choice.

The dictators and their misguided supporters here also accused us of planning to use nuclear bombs against Iran. Now we all have seen pictures of the devastation caused by gigantic nuclear bombs, both in tests and in the horrible, and necessary, bombing of Hiroshima that ended the Second World War. This is unthinkable - we would not use nuclear bombs such as these, and we have not done so.

The term "nuclear bomb" should appropriately belong to these massive, city-destroying weapons. To stop Iran's effort to make many such nuclear bombs, we have used something else. Typical convential weapons cannot reach the heart of Iran's weaponry program, the uranium gas centrifuges of Natanz, buried under seventy-five feet of shielding. If we were to shut down Iran's program with typical weaponry, we would have had to attack hundreds of "softer" targets, where the mullahs have made human shield hostages of their civiliam population. Or we would have had to launch risky ground operations in Natanze, causing the unnecessary deaths of American servicemen and women. Others may support the unnecessary death of American warriors defending our country, but I cannot.

The fission-enhanced penetration weapon that earlier today, breached and destroyed the Natanz nuclear bomb program, should not be considered a nuclear bomb itself. It is a destroyer of nuclear bombs and a saver of human life. The enhanced weapon does not have the destructive size or destructive intent of real nuclear bombs, and belongs in a separate class for military operations. The weapon, modified to maximize bunker-busting with very little radiation, was a success. We believe that any radiation now escaping from Natanz is from the destroyed uranium centrifuge operation, and the mullahs can only blame themselves for that problem.

With the Natanz operation destroyed, we have had to attack far fewer targets elsewhere in Iran. We believe that few if any civilians were harmed.

While it is unfortunate that we had to take this step, America and the world is better off for us having done so.

There is little chance that the Iranian dictatorship will learn from this mistake, but we know the Iranian people will see how the mullahs betrayed them and forced this attack. We extend our hand in friendship to the Iranian people, and we will gladly help them in their legitimate wish to be free.

We are all safer now, thanks to the bravery of our men and women in uniform. Our prayers are with them as they return, and we know all good-thinking people will support our troops in their own prayers.

May all our efforts for peace be rewarded, and may God bless America.

Bob Carter won't bet over global warming

Following Tim Lambert's post on Bob Carter, I emailed Professor Carter to see if he would bet me over global warming, offering 2:1 odds that temperatures will increase in 10 years.

He politely emailed me back, saying that because temperature change is a random walk, he won't bet me. I've replied to say that doesn't make sense.

Either he doesn't believe temperature changes are random, or he should bet me.

Adjusting Kyoto requirements for low-population-density nations

I'm too cheap to pay and read the whole article, but New Scientist is highlighting proposals to adjust carbon emission requirements from countries with low population densities:

Their rationale is that large countries have more natural vegetation to absorb pollution, and more fields and forests to provide natural resources for the world. So they should be entitled to a larger ecological footprint than small, densely populated countries.

I welcome the concept of introducing equity and fairness into the Kyoto targets, but I think my idea of allocating per-capita emissions worldwide would accomplish the same purpose. The per-capita emissions, allocated worldwide and then aggregated for each nation, should be net emissions, so low-density countries will have the opportunity to use their forests etc. as a sink to reduce their emissions. Reduce emissions enough, and then the low density nation can sell part of its emission quota to other nations.

The presence of carbon sinks in low-density nations is/should be a double-edged sword, though. If a nation screws with its carbon sink, say by cutting down the trees, then it has added to the net emissions from the country. That should be part of the climate management picture.

Ghosts of Rwanda

The PBS documentary Ghosts of Rwanda does an excellent and gut-wrenching job of describing the genocide in Rwanda in 1994, and how little the outside world did to prevent it. The movie is very hard to watch, but worth watching. While film-makers never overtly express an opinion as to who tried to help and who stood in the way on the international scene, we can draw some conclusions. Two people I've generally liked, Kofi Annan and Richard Clarke, don't come off well. Annan, head of UN Peacekeeping at the time, blocked numerous attempts by the hard-charging Canadian general managing UN forces there from taking more active steps to stop the slaughter. Clarke blocked Madeleine Albright's attempt to be slightly more active, and he refused to be interviewed for the show as well, which sounds like an admission of guilt to me. As an American documentary, it appropriately focuses on American inaction, but other countries, especially Belgium, have plenty to answer for as well. I hope that's happening.

I also wanted to recognize the heroism of an unarmed Segalese officer, Captain Mbaye, detailed to the UN team. He used nothing more than charm to negotiate his way through numerous roadblocks manned by crazed murderers, and conducted a completely unauthorized human smuggling operation that saved hundreds of people, while world leaders did nothing. Random mortar fire killed him in the last days of the genocide. More information is here. How he did it and even what he did remains mysterious. He deserves his own movie.

Declassifying versus leaking depends on intent

Juliette Kayyem and Jane Hamsher both pushed the ball forward on whether Bush's apparent command to reveal classified information was legal. Kayyem points out that declassification has to be in the public interest, and the reference to public interest makes it illogical to assume the "declassification" could be for a single member of the public, Judith Miller. Hamsher highlights the apparent lack of documentation that information was declassified. An update to her post points out that the information was apparently deemed classified afterwards.

While some legal experts say the President has the authority to declassify information at will, that doesn't mean Bush actually declassified the information. For reasons of his own (say, to smear someone without leaving his fingerprints on the smear), Bush may have kept the information classified, but commanded that it be leaked. The apparent fact that it was classified afterwards suggests this is what happened. That would make the disclosure illegal.

The twist I take on Kayyem's post is that if information is declassified to the point where a member of the public (Judith Miller) can have it, then it's completely declassified. Because it apparently was classified afterwards, then Bush didn't declassify it - he illegally leaked.

The only legal way out I can see for Bush is to claim he declassified the information and then at some point after the authorization, but before reporters starting asking for it, he or someone else reclassified it. To use this escape route, they need to claim it and prove it - where's the documentation for the reclassification? And it creates even more political problems for them of using governmental secrets for political advantage, and making Clintonian excuses as to why they didn't break the law. Except in Bush's case, it concerns national security.

March 2006 Iraq casualties

(Sorry, missed doing the February report.)

Avg. daily military fatality rate (nearly all of them Americans): 1.06. February was 2.07, January 2.06, and March 2005 was 1.26. Overall average to date is 2.3, down .03 from January. Total US dead as of today: 2343.

Iraqi monthly military/police fatalities: 193. February was 158, January was 189 and March 2005 was 176. Total dead: 4397.

Iraqi monthly civilian fatalities: 901. February was 688, January was 579, and March 2005 was 240. Note that the civilian numbers may be less accurate than others, but could still be useful in determining trends.

Comments: The American death rate has dropped somewhat in the last few months. That doesn't seem to have changed public pessimism - Americans appear to be tired of seeing hundreds of American dead annually as we enter the fourth year of the war.

Either the Iraqi civilian body count is low, or media overplayed the civil strife that resulted from blowing up the Shiite shrine towards the end of February. I recall seeing reports about thousands of deaths in sectarian violence.

9/11 Conspiracy post in progress, and it's not working

One of the many reasons offered to back the claim that 9/11 was a conspiracy is that the buildings fell at or near to a free-fall speed. I suspect the answer is here:

"The buildings did fall quickly - almost (but not exactly) at the same speed as if there was no resistance. Shouldn't the floors below have slowed it down? The huge dynamic loads due to the very large momentum of the upper floors falling were so great that they smashed through the lower floors very quickly. The columns were not designed to carry these huge loads and they provided little resistance."

It would be better to do this mathematically, though.

So we've got:

"A kilogram force,
for instance, is the force exerted by gravity on a mass of 1 kg.

1 kgf = (1 kg)(9.8 m/s^2) = 9.8 Newtons"

And kinetic energy from a falling object:

KE = (mass x velocity2)/2 or 1/2 mv2 (KE measured in joules)

And:

newtons multiplied by meters equal joules

So if I divide the KE by the distance the object has fallen in meters, I should get the dynamic load in newtons exerted by the object on the thing it hit, which I could then compare the static load exerted by the object on the support? Seems like it should work, but what do I know.

So using simplified numbers, let's pretend that stories 99-110 of the World Trade Center weighed 1 kilogram (don't like that? okay, we're just discussing failure of a tiny vertical cross section weighing a total of one kilo). A plane hits floor 98, impact blows away fire insulation, fire weakens (doesn't melt) steel, steel buckles, floor collapses, and now floors 98-110 collapse and fall 3 meters to floor 97. Floor 98 collapsed when its strength diminished below the force exerted by 1 kilo, or 9.8 newtons. What's the force that will be exerted by slightly over 1 kilo after a 3 meter fall?

I need to know the velocity, dammit. Now I'm tired of this. Found a calculator, here. It says the KE is 29.4 joules. Divide by 3 and you get 9.8 newtons. Dammit again, I'm defeated by the conservation of energy - I must be just measuring transfer between potential energy and kinetic energy. So how do you derive and compare static versus dynamic loads?

UPDATE: People in the comments are doing a much better job with this than I did.