Humint Events Online: Scaling, Euler's Formula and My WTC Model

Saturday, December 30, 2006

Scaling, Euler's Formula and My WTC Model

IMPORTANT UPDATES-- see below

I described and took pictures of my 1:200 scale WTC tower model here.

I found that my model was extremely resistant to any sort of collapse.

If (admittedly a large "if") my model was an accurate representation of a WTC tower, my findings would strongly imply that the towers were blown up by demolition.

There were already many reasons to think the WTC was blown, but I built the model with hopes of creating a convincing physical case for demolition.

Importantly, I built the model in good faith. I didn't know what to expect, and if it had collapsed in a heap, I would have reported that. One reason to do experiments, after all, is TO LEARN.

The tower was built out of steel wire and was a 1/200th scale version of a WTC tower-- in terms of basic proportions. I knew it was not a perfect model and I never claimed it was a perfect representation of a WTC tower. I built it because I was interested in the collapse mechanics. In terms of scaling down, I tried to make things roughly proportional, such as weight and column strength.

I was in fact worried about scaling issues-- that idea that although the structural elements were proportionally smaller, that there would be a different degree of strength. But I wasn't sure how to control for that, and some limited research I did on scale models failed to reveal what I should be worried about.

So I proceeded with the model and you can see the results here.

Predictably, revealing my model here on my blog induced cries of derision from the usual suspects. What an idiot I was, what a moron I was, how sad I was, how pathetic I was, how sad if I passed my idiocy to my children, etc etc.

Unfortunately, there was very little in the way of productive criticism as to what was wrong with my model-- and in fact that was what I was looking for.

Yesterday, I noticed a new comment saying how dumb I was, how I should have taken an engineering course, then mentioning the strength of an ant relative to a man.

Putting aside the gratuitous insults, the ant strength idea was something I could grab onto, and I did a little bit of reading on the strength of ants versus men. According to one site (that I can't locate right now), the apparent strength of ants has mostly do with the relationship between strength and the cross-sectional area of muscles.

So that wasn't very useful. But the same site also noted how a man scaled up to 100 feet would not be able to stand, because his bones could not stand the weight-- even if they were proportionally bigger.

Now that sounded like something relevant to my model.

So I did some reading on column load versus length, and found Euler's formula. Most relevant to my model:
Another bit of information that may be gleaned from this equation is the effect of length upon critical load. For a given size column, doubling the unsupported length quarters the allowable load.


What this would mean in simple terms is a column gets progressively weaker as its length increases, even if it is proportionally stronger.

Thus, let us say you have a two inch column of thickness 1 (Column A). It can support load X without buckling.

Now, let us say you have an eight inch column (Column B) of thickness 4.

What load can it take? According to Euler's formula, very approximately, F = K/L^2
Where F = load force, K is a constant and L is length. Basically load is proportional to the inverse of the length squared.

For the two columns, the constants should basically cancel out. For column A, F= K/1 and for column B, F= K/16-- simply in terms of length. A column 4 times longer than another column of the same thickness would hold only 1/16th the weight or load.

But column B is 4 times thicker, making it in essence 4 times stronger. So it could roughly hold 1/4th the weight or load. Thus, VERY SIMPLY, a column that increases in size proportionally in terms of thickness and length will hold less weight by the factor that it increases in length.

Getting to my model now. It was a 1/200 scale, meaning the columns were 200 times stronger to the analogous WTC columns if they were perfectly proportional in terms of size and strength.

And this would then explain the scaling effect quite well-- why my model was so resistant to collapse.

But were my columns proportional?

In fact, my columns were not perfectly proportional. They were 1.9 times smaller proportionally than a WTC outer column, in terms of cross-section. And I used less of them per outer wall (24) than the WTC (62). So that lowers their effective strength by 2.6 fold. Another important consideration was that I had only 1/5th the floors of the WTC (22 versus 110), thus making my columns proportionally 5 times longer than WTC columns (though this is somewhat counter-balanced by the about same degree of horizontal cross-bracing as the WTC outer columns. So we can lower this length factor somewhat-- say 2-fold. This means my shorter model columns were approximately 20-fold stronger than the WTC columns (200/(1.9 x 2.6 x 2)) taking these factors into consideration.

Other factors are that:
a) the WTC columns were box columns whereas my model columns were solid thin wires (and a larger cross-sectional area hollow column is significantly stronger than a solid column with a smaller cross-sectional area)
b) the outer wall columns in my model had over 100 times less steel per cross-section than an individual WTC outer column (0.9 mm round) at floor 80 (180 sq. mm proportionally versus roughly 18320 sq. mm)
c) the galvanized steel wire in my model was undoubtedly poorer quality than the steel used to make WTC columns.

I will factor in that 100-fold cross-section and calculate that my individual model columns were at least 5-fold weaker than the WTC columns!

SO-- in fact, my model WAS indeed significantly weaker than the WTC and STILL DIDN'T COLLAPSE.

AGAIN, I CHALLENGE ANYONE TO BUILD A SCALE WTC MODEL THAT COLLAPSES UNDER ITS OWN WEIGHT.

P.S. Made a mistake in calculating cross-section of steel in the model columns and significantly revised the conclusions to this post a couple of hours after posting.

UPDATE-- this section "b) the outer wall columns in my model had over 100 times less steel per cross-section than an individual WTC outer column (0.9 mm round) at floor 80 (180 sq. mm proportionally versus roughly 18320 sq. mm)" was wrong and thus my overall conclusions were very wrong.

I made a major error in calculations-- actually my model columns were 32400 sq. mm in proportional cross-section-- making them 1.8-fold stronger than WTC columns. This obviously changes the overall equation and means my model was roughly 34 times stronger proportionally than the WTC. Thus my model is not a good system for studying collapse mechanics.

UPDATE 2-- 1/1/07-- OOPS again. Realized I factored in the scale of the columns twice, and the first time going the wrong way-- so I need to take away a factor of 1.9. Also found another mistake, meaning I need to redo the overall calculations.

So, my model columns were 200X stronger than the WTC columns due to scale.

They were 1.8x stronger proportionally, in terms of cross-section of steel.
I had 2.6x fewer columns per wall and 5x few floors meaning the effective strength of the model columns was 5x weaker. Except my model columns had similar cross-bracing to the WTC, meaning we need to lower the 5x figure. Let's be generous and cut this in half to 2.5x.

Thus we have 200 times 1.8 divided by 2.6 divided by 2.5 = 55.

Meaning that VERY ROUGHLY the model columns were 55 times stronger proportionally than the WTC columns. In reality the model is probably less than this-- due to weaker steel and inferior column shape. But the bottom line is the model is far too strong proportionally, and needs to be redesigned.

The simplest way would be to redo the model design with even smaller wires than what I used.

13 Comments:

Anonymous Anonymous said...

Hi Spooked, your focus on collapse may be the wrong focus. The towers did all sorts of additional things like pulverize concrete and toast cars in the neighborhood.

I think you're letting the enemy's choice of words influence your model.

The towers didn't collapse... so why attempt to model a collapse? See if you can make 80% of your steel disappear and make the rubble pile only 1% of the height of your tower.

I agree with you, that the collapse story is impossible, but I don't quite see why you want to model what they claim happened, instead of what we observed. Set your goals higher: make your tower turn into a cancer-causing dust fountain that smoulders for months afterwards.

Fred

1:29 PM  
Anonymous Anonymous said...

"psst, larry. want to make a few bucks? i have an idea...."

"what a good idea! you're the man dick!"

1:45 PM  
Blogger spooked said...

Fred-- you're totally right-- but I just wanted to set basic goals. And mostly I wanted to get people to think about this!!!

2:00 PM  
Anonymous Anonymous said...

some of us know better than to address this issue even indirectly so i will just say that we are having quite the giggle at your expense over at the conspiracysmasher.blogspot.com

2:35 PM  
Anonymous Anonymous said...

Laffin' my ass off here, ol' Spook. Let's go thru some of the comments left on the Instapinch:

"One of the beauties of life is that whenever you feel that you’ve seen it all, that you’ve already encountered the stupidest human on the planet, someone comes along and proves you wrong."

"We can scale materials, but we can’t scale their physical properties. It’s easy to build a scale model 747 out of balsa wood, but a full sized 747 could not be made of balsa. Correspondingly, it’s easy to build a lame chicken wire tower in your apartment out of steel wire that is percentage wise many times stronger in that small model than it was in a real full scale world trade center. And it’s an especially nice touch of moonbat stupidity to not light it on fire, and not actually simulate the force of a fully fueled scale model hitting the tower, etc."

"That has to be the stupidest thing I have ever seen. Too bad he didn’t take all the time, money and effort it took to make that ‘model’ and use it to go to school and get an engineering degree."

"Everybody knows Big Foot jumped up and down on top of the WTC to knock them down. Why doesn’t this guy just accept it and move.on"

"I am now a notch above retarded for reading this. Thank you, can I have my minute back now?"

"Man this has to be the funniest shit I’ve ever seen in my life dude. This retard is a biomedical researcher? That’s fucking amazing."

"Seriously, though, this guy needs to get laid big time."

"Now all he needs to do, is dress up in an airplane suit and run at it at full speed….after setting himself on fire to simulate the jet engine fuel temperature"

"So apparently this tool thinks that it is possible to bend the top of a skyscraper over until it is hanging upside down along the rest of the building"

Yo haev NEVER let me down, man! Come on, though...I really really want to see that Lego Pentagon and see how you model that!

You wanted to get people thinking about it - well, they're thinking what a total complete ass-wipe fool this Spook buttbrain is! Well done!

5:00 PM  
Anonymous Anonymous said...

hi pinch!
hey go get your boss would you?
i'd like to ask him why a simple bird will damage an aluminum 767 wing but that same aluminum 767 wing can in turn go right thru several wtc massive hardened steel box columns!
hey pinch why did a supposed grey 767 look like a shadowy flat black ridiculous cardboard cut-out silhouette of a 767 even in the direct cloudless sky sunlight of 9/11/01 and how could that same ridiculous looking 767 fly without it's right wing?

5:19 PM  
Blogger Ningen said...

Fred raises a good point. It's hard not to use the word "collapse" because we are told the buildings fell and are trying to prove they could not have. I know you see the limits of the word, Spooked.

I think "annihilation" and "obliteration" are possible words to use - any others? "Pulverization" is another possibility -- it's not clear to me that steel was not also pulverized. Is "dustification" a word? And of course, Judy Wood's "blown to Kingdom come."

About the toasted cars, has there been any other explanations for how that could have happened? I got thrown off by the argument that the cars were towed to under that bridge, but that begs the question of how they got toasted in the first place.

5:21 PM  
Blogger Ningen said...

Pinch, one of your boys' comments was worth reading:

"Everybody knows Big Foot jumped up and down on top of the WTC to knock them down. Why doesn’t this guy just accept it and move.on"

Make Big Foot from outer space, invisible, and really, really big, and you've a more plausible explanation than NIST's fraudulent obstruction of justice report.

You can't prove such a Big Foot doesn't exist somewhere in the universe. You can prove that NIST is lying, and many people have.

Just to be clear, when I say NIST is obstructing justice, I mean as a corporate entity. Individual criminal liability remains to be assigned.

5:34 PM  
Anonymous Anonymous said...

Is this a comedy blog? If it is, you write some funny stuff - good work!

6:14 PM  
Anonymous Anonymous said...

hey go get your boss would you?
i'd like to ask him why a simple bird will damage an aluminum 767 wing but that same aluminum 767 wing can in turn go right thru several wtc massive hardened steel box columns!


It's amazing how close you can get to the scientific principles at wirk here, yet still completely miss it.

6:28 PM  
Anonymous Anonymous said...

It's amazing how close you can get to the scientific principles at wirk here, yet still completely miss it.

miss what? right. your brain is obviously wirking overtime yet you didn't see fit to elaborate?

Aircraft: B-727
Damage: Engine, radome, right wing
Wildlife Species: Snow geese

Aircraft: B-757-200
Damage: Both engines and wing
Wildlife Species: European starlings

Aircraft: B-747
Damage: Engines, cowling, wing, fuselage
Wildlife Species: Snow geese

birds are stronger than planes!

but planes are stronger than wtc!
----
how was this plane able to fly with a stub for a wing?

7:24 PM  
Blogger spooked said...

Yes, Pinch, treason and mass murder is freaking hilarious.

Only brainwashed tellytubbies believe the govt 9/11 story.

Like a bunch of your Bushbot friends are going to think rationally about the WTC demolition?

Gimme a break.

8:26 PM  
Anonymous Anonymous said...

Fred kicks ass and takes names...his writings simply cut through the bullshit, almost like listening to a Chomsky AK-Press album (sorry i like chomsky)...GO FRED GO!!!

7:14 PM  

Post a Comment

<< Home

Powered by Blogger