Calculating the force of a turbidity flow.

[leftysergeant]

I keep running into twoofers who insist that the distance at which some of the perimeter columns of the towers landed supports a theory of demolition charges. To those of us with brains, it is obviously the result of all that pulverized material, that turbidity flow, if you will, shoving them outward.

Is there any way to calculate how much force the expanding debris would be applying to the perimeter columns per square inch and how far it should throw them from a given height?

(Bear in mind that, if you answer, you are responding to someone who is almost totally dyscalculic, so I might have to ask for a lot of clarifications.)

[BigAl]

I keep running into twoofers who insist that the distance at which some of the perimeter columns of the towers landed supports a theory of demolition charges. To those of us with brains, it is obviously the result of all that pulverized material, that turbidity flow, if you will, shoving them outward.

Is there any way to calculate how much force the expanding debris would be applying to the perimeter columns per square inch and how far it should throw them from a given height?

(Bear in mind that, if you answer, you are responding to someone who is almost totally dyscalculic, so I might have to ask for a lot of clarifications.)

Without being Twoofish about it, I also wonder what mechanisms can account for the horizontal velocity that was necessary to send large beams some distance from the building.

I wonder if the fire-induced collapse of the floors which pulled the external beams in, spring-loaded them and caused them to fly when the floor connection finally gave way.

[Myriad]

I believe the calculation leftysergeant is describing would be a complex and difficult one.

However, some of the general principles involved can be demonstrated with simple experiments. For instance:

Take half a strand of uncooked dry spaghetti. Place it vertically, with the bottom end fixed in place (or at least, on a rough surface where it's not likely to slide sideways). Press straight down on the top end of the strand until it breaks. Observe the motion of the resulting "debris." (If you can find it after the experiment. Try under the refrigerator.)

It doesn't require unusual sideways forces (such as floors pulling in) to cause sideways deflections of columns subjected to excessive axial loads and/or compromised horizontal bracing. That's a normal aspect of the phenomenon of buckling.

Respectfully,
Myriad

[leftysergeant]

Better analogy to what I am asking would be to form a box of lasagna noodles tacked together with spaghetti, then pour rice into the center of it and see where the lasagna goes.

All that debris falling onto the lower floors could not get down the inside, so it had to push outward, applying force to the perimeter columns in doing so.

How much force?

[Newtons Bit]

I am an old man now, and when I die and go to Heaven there are two matters on which I hope for enlightement. One is quantum electrodynamics and the other is the turbulent motion of fluids. And about the former I am rather more optimistic.
- Sir Horace Lamb
1932, Quoted in Computational Fluid Mechanics and Heat Transfer, by Anderson, Tannehill, and Pletcher, 1984.

[Wolrab]

Turdbidity flow is fairly easy to calculate. You just need some starting parameters such as: the amount of water released per flush, the direction the water takes upon flushing, the curve of the porcelain, the diameter of the drain, and, of course, the type of turd to be disposed of.
In the case of the truth movement, the sheer volume of excrement can overwhelm the toilet and cause a complete absence of turdbidity. Then it will just overflow onto the floor.

[newton3376]

I am an old man now, and when I die and go to Heaven there are two matters on which I hope for enlightement. One is quantum electrodynamics and the other is the turbulent motion of fluids. And about the former I am rather more optimistic.
- Sir Horace Lamb
1932, Quoted in Computational Fluid Mechanics and Heat Transfer, by Anderson, Tannehill, and Pletcher, 1984.

I was just going to ask.....

Isn't this a question that would need to be answered by fluid dynamics/mechanics?

That topic (like electromagnetics) can get really, really nasty mathematically....

[ellindsey]

I think a better question to ask would be why would pieces of debris flung far away be indicative of demolition charges at all? Controlled implosions do not fling large pieces of debris all over the place. The explosives used are small and precisely placed, doing just enough damage to sever key structural beams, and are not capable of flinging large parts of the building far away. The bizarre alternate theory involving thermite would also not result in large pieces of debris being hurled through the air, since thermite isn't an explosive at all. About the only demolition method which would result in perimeter columns being hurled far from the collapse site would be something involving some massive bomb placed in the center of the building, which would have been impossible to hide and would also have resulted in unmistakable effects such as every window in downtown NYC being shattered.

[leftysergeant]

To the rational among us, yes, it is obvious that there were no explosives used. I am just trying to find a way to explain in terms that a twoofer-sized brain can grasp how much force there was pushing the perimeter columns outward so that they fell away from the building in an arc, rather than just dropping into the footprint of the building.

They were basicly kites at the moment they broke away. I just want to get some idea of how strong was the wind on which they rode.

[JoeyDonuts]

Would atmospheric displacement have translated into outward force with enough strength to dislodge them? I'm sure there were a myriad of forces at work, I've always kind of understood air displacement to be one of them.

[leftysergeant]

The pseudo-squibs demonstrate clearly that the interior was over-pressurized by both the falling debris and the air trapped within it. And with all the slabs of concrete and steel and such whamming into each other, there would be some heat generated, thus expanding the air within the plumes.

So,, I get the impression that we need to consider the weight of the debris trapped inside the box and the volumn of air that it captures in order to determine how much force was directed outward against the perimeter columns.

[jhunter1163]

I think our man R. Mackey has expertise in fluid dynamics that would be useful here.

[newton3376]

I think our man R. Mackey has expertise in fluid dynamics that would be useful here.

I would think that is the exact topic we would need someone to know well to address this question, since the forces involved would likely be restricted to the compression of the fluid (air).

[R.Mackey]

Yep, my ears have been burning all day. Now I know why.

You guys are making this calculation much too complicated. The turbidity flow in question is turbulent, yes, but it's also decidedly subsonic (possibly excepting ejection very low in the structure during collapse), and so it is incompressible. Under those conditions, the force on any given object hit by the flow is simply the drag:

Fd = 1/2 Cd ρ A v2

where ρ is the density, Cd is the drag coefficient, A is the facing area, and v is the mean fluid velocity. For something like a column being washed over, we approximate as a flat plate or a square prism, so Cd would be approximately 1. Nothing to it.

The only real challenge in this case is estimating the fluid density. Since it's a heterogenous flow, the density could vary by several orders of magnitude... The best way to estimate this is through conservation of mass. Look at the distribution of mass before and after collapse, and then try to come up with a simple analytical function that describes how it spreads out as a function of height and distance.

This is an approximate equation, of course, but it will get you well within the ballpark.

Also keep in mind that there will be individual events that don't fit this model. A turbidity flow of uniform density is just a model. Some parts of it will be basically smoke and air and dust, others will have a huge freakin' chunk of steel bouncing around in it. Think of this as an average.

Most of the large ejected pieces are clearly not driven by the flow anyway. Their distances, and the fact that the largest pieces flew the farthest, proves they were propelled by direct contact with other massive pieces, not merely blown by dust and chunks.

[leftysergeant]

I kind pictured the upper segments of perimeter columns being shoved out a little bit by the dust before they snap loose. We can see the dust rising up over the tops of them before they give way, which is where the twoofers get the impression of explosive ejection of dust.

500 feet up, I don't think it would take too much force to make a hundred tons of steel land 300 feet away.

[Jackanory]

I cant see the purpose of this thread and why a debate on a formula should be required. Why does everything have to be so scientificy? Why the need for formula?

The buildings where 1300ft tall. It would therefore be expected that simple gravity and a tilt would be enough for columns/beams/girders etc to be found 1300ft+ away. Fascade falling from the top being carried further due to it being directed by wind and resistance therefore effectivly floating further away. Do we really need a formula to explain that?

A 300mm length of spaghetti stood upright and left to fall on its own will displace spaghetti how far? Do we really need a turbititytyytityytytwooowoo formula or equation to account for the spread of material at GZ or is it just a case of something else to chase for the sake of chasing? The mind boggles as to why intelligent people are being lead down the garden path with more and more stupid and that you continue to feed it by even getting into science - science that the majority of your truther audience do not understand or care to.

[newton3376]

Yep, my ears have been burning all day. Now I know why.

You guys are making this calculation much too complicated. The turbidity flow in question is turbulent, yes, but it's also decidedly subsonic (possibly excepting ejection very low in the structure during collapse), and so it is incompressible. Under those conditions, the force on any given object hit by the flow is simply the drag:

Fd = 1/2 Cd ρ A v2

where ρ is the density, Cd is the drag coefficient, A is the facing area, and v is the mean fluid velocity. For something like a column being washed over, we approximate as a flat plate or a square prism, so Cd would be approximately 1. Nothing to it.

Interesting....I had to look up why it would be incompressible since I was unaware of the way compressibility is defined mathematically....very interesting stuff. The math isn't as bad as I thought it would be either...

The only real challenge in this case is estimating the fluid density. Since it's a heterogenous flow, the density could vary by several orders of magnitude... The best way to estimate this is through conservation of mass. Look at the distribution of mass before and after collapse, and then try to come up with a simple analytical function that describes how it spreads out as a function of height and distance.

This is an approximate equation, of course, but it will get you well within the ballpark.

Makes sense....

Also keep in mind that there will be individual events that don't fit this model. A turbidity flow of uniform density is just a model. Some parts of it will be basically smoke and air and dust, others will have a huge freakin' chunk of steel bouncing around in it. Think of this as an average.

Most of the large ejected pieces are clearly not driven by the flow anyway. Their distances, and the fact that the largest pieces flew the farthest, proves they were propelled by direct contact with other massive pieces, not merely blown by dust and chunks.

Sure...that sounds reasonable.

Good post Mackey.

[R.Mackey]

Just for completeness, the drag equation applies in compressible flow as well, but it's kind of a kludge. The drag coefficient Cd is typically more or less constant in incompressible flow, but once things go sonic, it tends to change a great deal. So in compressible flow, you're folding all the complex dependence into that coefficient, hiding it just to keep the formalism correct.

[JimBenArm]

Would another factor in this be the amount of force that would be needed to apply to the member to get it to break free to begin with? Wouldn't this apply some angular momentum to it at the start?

Please be tolerant, I'm only a layman, so if it's a stupid question, I'm sorry.

[JoeyDonuts]

Please be tolerant, I'm only a layman, so if it's a stupid question, I'm sorry.

Science is for contractors and those mooks out in Dahlgren, Jim. Guys like us need only enough to be dangerous...and also to B.S. the wet-behind-the-ears DivO straight out of the Academy.

[ktesibios]

500 feet up, I don't think it would take too much force to make a hundred tons of steel land 300 feet away.

Let's see- to fall 500 feet would take about 5.575 seconds, so to travel 300 feet in that time would require a horizontal velocity of about 53.79 feet per second.

I'm more comfortable dealing with SI units, so we'll convert:

500 feet =152.4m
300 feet = 91.44m
100 tons = 90661.8 kg

91.44m/5.575s = 16.4 m/s

So your 100 ton piece would have a momentum of 1,486,853.5 kg*m/s. To impart that much momentum would require a total impulse of 1,486,853.5 N*s, or a force of, say, 1.49 * 107 N acting for 1/10 second.

Using approximate dimensions from NCSTAR1 for an exterior column assembly (columns 14" wide x 30' high, spandrel plates 106" x 52", 3 columns and 2 spandrels per assembly), I get a projected surface area of roughly 16.87 m2 for a column assembly.

Using RMackey's drag equation and the density of dry air at STP (1.2754 kg/m3, I get a fluid velocity of 1042.08 m/s, which is around 3 times the speed of sound. Even if the density of the air/smoke/dust flow is ten times greater than that of air, the velocity required to exert enough force to accelerate a hypothetical mass weighing 100 tons and the size of a column assembly to 16.4 m/s would be just barely subsonic.

Of course, I don't know what the column assemblies weighed at any given level of the buildings- I'm just using your hypothetical values of 100 tons and a fall of 500 feet, landing 300 feet away. Even so, attributing the ejection of massive pieces outward to collisions with falling debris or possibly to the release of strain energy when their connections broke seems rather more plausible.

[newton3376]

Science is for contractors and those mooks out in Dahlgren, Jim. Guys like us need only enough to be dangerous...and also to B.S. the wet-behind-the-ears DivO straight out of the Academy.

What's a "mook"?

And what do you have against the guys over at Dahlgren? Some of them are okay....;)

[newton3376]

Let's see- to fall 500 feet would take about 5.575 seconds, so to travel 300 feet in that time would require a horizontal velocity of about 53.79 feet per second.

I'm more comfortable dealing with SI units, so we'll convert:

500 feet =152.4m
300 feet = 91.44m
100 tons = 90661.8 kg

91.44m/5.575s = 16.4 m/s

So your 100 ton piece would have a momentum of 1,486,853.5 kg*m/s. To impart that much momentum would require a total impulse of 1,486,853.5 N*s, or a force of, say, 1.49 * 107 N acting for 1/10 second.

Using approximate dimensions from NCSTAR1 for an exterior column assembly (columns 14" wide x 30' high, spandrel plates 106" x 52", 3 columns and 2 spandrels per assembly), I get a projected surface area of roughly 16.87 m2 for a column assembly.

Using RMackey's drag equation and the density of dry air at STP (1.2754 kg/m3, I get a fluid velocity of 1042.08 m/s, which is around 3 times the speed of sound. Even if the density of the air/smoke/dust flow is ten times greater than that of air, the velocity required to exert enough force to accelerate a hypothetical mass weighing 100 tons and the size of a column assembly to 16.4 m/s would be just barely subsonic.

Of course, I don't know what the column assemblies weighed at any given level of the buildings- I'm just using your hypothetical values of 100 tons and a fall of 500 feet, landing 300 feet away. Even so, attributing the ejection of massive pieces outward to collisions with falling debris or possibly to the release of strain energy when their connections broke seems rather more plausible.

As a rough approximation I can't see any thing that sticks out to me as an error in your analysis (unless I missed something....I looked very quickly) but I did want to ask one question..

Why did you choose to use 1/10 of a second for the impulse?

Not trying to nitpick I'm really just wondering...

[HeyLeroy]

In the case of the truth movement, the sheer volume of excrement can overwhelm the toilet and cause a complete absence of turdbidity. Then it will just overflow onto the floor.

Liarrhea?

[R.Mackey]

91.44m/5.575s = 16.4 m/s

Using RMackey's drag equation and the density of dry air at STP (1.2754 kg/m3, I get a fluid velocity of 1042.08 m/s, which is around 3 times the speed of sound. Even if the density of the air/smoke/dust flow is ten times greater than that of air, the velocity required to exert enough force to accelerate a hypothetical mass weighing 100 tons and the size of a column assembly to 16.4 m/s would be just barely subsonic.

More importantly, the descending debris pile itself was moving faster than 16.4 m/s at that level, so there's no reason to look for a mysterious source of velocity. If hit directly by the collapse itself, which weighs far more than 100 tons, the momentum imparted to the pieces is in no way remarkable.