The 9/11 Forum

OneWhiteEye wrote:A hypothetical debris zone in the middle portion of a tower collapse (at a terminal velocity of 25 m/s) would pass through the first 10cm of a lower story in 4ms. A 1m tall model with 10 stories which collapses at g will pass through the lowest story, also 10cm, in about 23ms.

A few top-of-head observations...

a) g doesn't scale, right ?
b) I'd use relative units, so 1m of the actual tower would be better expressed as 1/417m (or whatever relative scale). Perhaps a 1:400 scale would be simpler, so a 1.0425m tall model...rounded off okay to 1m ? Probably.
c) 10cm of the tower is not equivalent to 10cm of the model. Model equivalent would be 0.025cm. 0.0575ms.
d) Terminal velocity (25m/s) isn't the same as freefall (g)

(temporary snip until viewpoint on above confirmed)

Scaling problem?

I'd say so, yes.

OneWhiteEye wrote:In a tower-sized model, assuming a void interior, the volume of air expelled over that interval is about 200m³

~289 (assuming that 10cm is not the actual floor slab)

if a core comprises half the footprint and does not get expelled.

I used the correct outside core area.

Assuming a cubic story aspect in the tiny model

Why ?

and no core

Why ?

the volume of air expelled in the 'crushing' of the lowest story

You mean the first 10cm equivalent ?

is 0.001m³.

4.5E-06 m^3

Scaling is not possible as femr2 and OWE have noted. You can scale the size, but not the properties of materials. You can't scale down how a gas will behave, or even the force of gravity. You can't scale down even how heat will be part of the equation or scale an explosion (similar to the gas behavior noted).

We can see in nature how various sized animals "perform" structurally to deal with the issue of scaling and fixed physical properties. A tiny elephant the size of a mouse would probably be able to run as fast as squirrel. Or a squirrel the size of an elephant could be caught by my dog, though he wouldn't know what to do with it!

Scaling is a major issue for model testing and to suggest that we build a garage size model to demonstrate whether a gravitationally driven collapse is possible is ridiculous and shows a profound lack of understanding of science, physics and the world we inhabit.

SanderO wrote:to suggest that we build a garage size model to demonstrate whether a gravitationally driven collapse is possible is ridiculous

It's not entirely ridiculous, but the issues of scaling drastically reduce the usefulness and scope of any results.

Material properties are a significant problem of course. Stuff like spaghetti is great in certain scopes, but to replicate the gradual thinning of things like core columns would be nigh-on impossible.

A material to mimic the concrete floor slab equally so. What would I suggest ? Er...dust *cakes* ? Get some talc, put it in a mould, add some water, let it dry out. Very fragile. Would have to be a powder that doesn't get *sticky* when wet. That would end up far too strong.

Someone looked!

femr2 wrote:a) g doesn't scale, right ?

Right.

femr2 wrote:b) I'd use relative units, so 1m of the actual tower would be better expressed as 1/417m (or whatever relative scale). Perhaps a 1:400 scale would be simpler, so a 1.0425m tall model...rounded off okay to 1m ? Probably.

Sounds like a good idea. Hadn't put much thought into it.

femr2 wrote:10cm of the tower is not equivalent to 10cm of the model. Model equivalent would be 0.025cm. 0.0575ms.

Intentional. Should work out similarly either way, except at 0.025cm the small model could also use the fixed orifice size approximation. The choice of 10cm for both was arbitrary, having it be the same absolute distance versus relative was arbitrary. The calculation might be misconstrued as unfair if the little model barely moved over the sample interval, but will be more accurate as an approximation.

femr2 wrote:d) Terminal velocity (25m/s) isn't the same as freefall (g)

Again, by design. Wanted to favor ejection velocity in a small model so I let it collapse as quickly as possible, while choosing lower than actual for a tower size model.

femr2 wrote:~289 (assuming that 10cm is not the actual floor slab)

Just a tower sized model, not an exact replica. Well, it was supposed to be, but I didn't remember the actual core area and didn't want to look it up so approximated it as half the footprint (which I took to be 64x64m).

femr2 wrote:Why ?

cubic aspect
Because I get to make up the conditions in my thought experiment and it made for a simple arrangement, 10 stories 10cm each; true it does not favor a high velocity but it also seems like something someone might actually build. If the aspect were like the tower, it would be very hard to get it to collapse since story heights are so small for a fairly big footprint model.

femr2 wrote:Why?

no core
Would you build a 1m model with core? I just know I wouldn't. But a 400+m tall model would need one!

femr2 wrote:You mean the first 10cm equivalent ?

Like I say, the choice of the same distance for each was pretty arbitrary, just need a delta displacement to produce a delta volume.

I just got to thinking about how Darkwing claimed that, because his paper and block tabletop model pulled mass inward as it collapsed, all collapsing structures would do so. In the video of his model, it's obvious how the pull-in forces resulted: paper 'floors' were pushed down, pulling their ends in and dragging the walls inward with them until they fell. Originally, I was considering the differences in material, construction and contents which could account for exactly the opposite happening in the real tower. But then, I thought, people have done air evacuation calculations, using simplified geometry and escape provisions, and have shown the potential speeds to be incredible. Stuff will get picked up and blown out the windows, so much for infalling only.

Was just a small exercise to illustrate another scaling issue. Nothing you build in your backyard is going to have significant expulsion velocity.

Not saying air evacuation would prevent infalling of perimeters if they were so inclined, though they would be going against the flow, so to speak. They span multiple floors, would only get a pull in while a region of floor connections fail, all other force is directed outward, whatever there is.

A lot of light material, dust and smoke are going to be expelled in any region with floor collapse. A real sectional collapse has multiple escape paths, including into the rest of the open floor region, and wouldn't likely resemble a neat, flat pancaking process. Of course. But maybe a 400m simplified model would.

OneWhiteEye wrote:The volumetric flow rate for the large model is 200m³/0.004s = 50000m³/s. This passes through an effective orifice size of about 1620m² for a linear flow rate across the boundary of 31m/s.

The volumetric flow rate for the small model is 0.001m³/0.023s = 0.0435m³/s. This passes through an effective orifice size of 0.02m² for an average linear flow rate across the boundary of 2.2m/s, though considerably higher towards the end.

A crude approximation of a crude calculation using very crude models. The little model gives a puff with a little whack at the end, the large model produces Category 1 hurricane winds. Scaling problem?

Did a quick test with Full scale and 1:400 scale, and flow rate accross the boundary comes out with the same value for each...

Mistake ?

femr2 wrote:Did a quick test with Full scale and 1:400 scale, and flow rate accross the boundary comes out with the same value for each...

Mistake ?

Probably not, but I think we're approaching things differently. I chose not to scale all lengths identically for a few reasons. While the tower size model is supposed to be as much like a real tower as practical, it is also a model in my scenario. Some aspects differ because of practical necessity, others to illustrate the desired point.

The surface to volume ratio is independent of scale, and it's also independent of vertical displacement of a 'plunger' through the interior space. If the two models have all the same proportions, all geometric ratios and things having dependence on relative lengths will be the same by definition. Something had to be different (but it probably clouded the issue to have too many differences).

The important differences are velocity and side width to story height ratio.

For a moment, forget about the core and consider large and small models identical except for (square) footprint width, story height and story count. Let y be the vertical displacement of a monolithic debris zone, upper block, slab, plunger, what have you. Let x be the generalized position coordinate of the leading edge of a volume of incompressible fluid extruded through only the exterior via a surface of one story height. The width of a side and the height of a story are w and h. The boundary condition is the value of y is h at t0.

By considering only a small vertical displacement, the change in exit surface area during the displacement can be ignored without substantial error, so I'll focus the situation when the slab first enters a given story volume, something I didn't do earlier with the small model. We can see what the instantaneous changes are at that point in time using the constant exit surface of the four wall planes (where there are no walls). Moreover, changes of velocity over a small distance can be neglected.

This is not precisely the mechanics of air flow and nothing like a real tower, but applicable to the small model I have in mind. That's also why I used the word 'crude' three times in one sentence.


The change in volume for a vertical displacement Δy is

ΔV = w²Δy

The (constant) cross-sectional area through which the fluid initially escapes is

A = 4wh

The way I've framed the problem dictates solving for the velocity in the x direction as a function of the givens which include velocity in the y direction. So, here goes, with dot notation used as shorthand for the velocities.


(edit: ignore the double equals signs; typo)

The sensible thing to do, before plugging in real values for either model, is examine the dependencies above and the relation between the horizontal velocities in two systems. The horizontal velocity varies in proportion to the width and vertical velocity, and inversely with the story height, as one might expect. In taking the ratio of two systems:



you see identically proportioned models will only have a different exit velocity if the vertical velocity differs, entirely length-scale independent. If this is why you get the same result for both of your models, it makes sense and perhaps you can see why I chose different proportions to illustrate the point. Besides, I'm not considering a perfect replica of the tower in the small because that's not what's been done or proposed.

If you used different absolute velocities but got the same exit velocity, I think you made a mistake.

The ratio of story height to width, as well as the relative velocities, determine the disparity between exit velocities. With the real tower or a model of comparable dimensions, the velocity can exceed the theoretical limit of a freefall descent for a small model by having even a modest terminal velocity (hence a lowballed figure from the actual collapse). While it would be simple to build a small slab model with the same overall height:width ratio as a real tower, it's not the total height that matters here but story height, and incorporating 110 stories would be no minor effort. Plus it would provide little delta PE between collisions!

A manageable small model must have at least 10 stories to qualify for a non-issue like the Heiwa Axiom, which is frequently an issue despite the absurdity. Excluding slab height, that's a 10cm story in a 1m high model - barely tabletop size already despite having only 10 floors with a modest drop between each. Hence the 10cm height I chose for the small model. The same figure for the base makes it a model like what might be constructed using the bathroom tiles I showed towards the beginning of the thread. Simply a practical choice, nothing special.

So let's plug in some realistic values (meters and seconds) now to the last formula above.

Large model:
h = 3.7
w = 64
y_dot = 25

Small model:
h = 0.1
w = 0.1
y_dot = 4

The ratio of exit velocities, large to small, is then (0.1)(64)(25)/(3.7)(0.1)(4) ≈ 108. The reason I didn't have such a huge difference before is because I provided a core for the large model exit surface and halved the exit surface size of the small model.

Why? I wanted to be antagonistic to the premise, as a general manner of choosing or estimating. Present a conservative case, show the result is still very lopsided - as it was. If two wall-less slab models were built, 417m and 1m, the factor of 108 would be much closer.

The purpose was not to be precise or calculate what might really be expected for an actual tower, rather to illustrate the manner in which scaling affects even such a peripheral issue as air expulsion. If a tabletop model lacks violent ejections, who can be surprised? I suggest pillow feathers as mock office contents which could be expelled by such a model and, like you say, powder for the dust and chips.

Now one other interesting thing about air expulsion in a slab model. As two slabs approach contact, the free path to escape remains the same but the time interval in which the escape occurs becomes smaller and smaller. This leads to the last bit of air escaping at ever increasing velocities, theoretically unbounded. The back pressure from accelerating even a small amount of air out from between surfaces can present a very high resistive force if the slabs are parallel or very nearly so. Bazant and co-authors make mention of this and do some similar crude calculations to show supersonic ejection is possible on lower floors, under this sort of scheme.

Of course, this would have little global relevance in the real collapses, but might have an effect regionally which will act to retard descent by providing a cushion of air which would diminish the peak impulse force produced by collision.

In a small model, the same thing can certainly occur. If the modeler is aiming for complete collapse, one factor to control is how much energy goes into slab rotation and another is to ensure maximum peak impulse experienced by supports below, otherwise arrest or falloff of the top could occur due to factors which are NOT analogous to the towers. The towers had a width to story height ratio of greater than 17. This constrains slabs to a rather small maximum rotation before next impact and in effect acts to keep a slab collapse oriented stack-wise even without perimeter restraints.

In a small solid slab model, UNLIKE the towers, the only air escape is via the means I describe above; there will be no punch-through or fracture to open new venting routes. Thus, one constraint the modeler must observe to ensure collapse also acts in opposition to collapse, but only in a small model made of everyday material which is strong relative to its size and mass and is unlikely to shatter from small drop heights. As a small slab approaches the next, the backpressure and therefore momentum change afforded by squeezing the last little bit of air out is not insignificant compared to the momentum of the impacting slab. A slab can be rapidly decelerated by this over a short distance before contact. The momentum acquired by the air is lost to the environment; it is not a closed system.

Therefore the modeler cannot necessarily succumb to the temptation to go with a large footprint compared to story height (which is determined by energy criteria in failing the vertical supports) even though it restricts rotation and mass loss like a real tower, because it can end up dissipating too much energy to the environment. I have observed this phenomena directly in a number of circumstances where dropping a large sheet of material flat and level onto the ground or another sheet. Plywood, plexiglass, even regular glass. Instead of a sharp whack at collision, there is an air-cushioned impact. It's how air hockey works.

Even slabs frangible at these energies (fragile! think thin glass) will not help because they will shatter only after this effect has been encountered, unless they are significantly out of plane.

Despite the factors which could allow air to escape more easily from confinement in a tower than a simple slab model, Dr. Greening did some work a while back at physorg that suggested air expulsion may have been a significant factor in slowing the descent of the towers. What steel could not hold, air may have slowed.

All of the above is rather simple; of course, if I've made any errors, my bad (up to and including the whole thing being wrong! but I don't think so). In any case, it show the pitfalls of building short and small models with an intent to collapse. It could be every bit as difficult as engineering tall buildings to stand! I've brought this up before, but naysayers like Darkwing and Pavlovian Dogcatcher (and 'experimenters' like psikeyhackr) have not acknowledged it, that I've seen.

The question keeps coming up: if progressive collapse is such a straightforward phenomena, why is it so hard to reproduce physically and why are there no backyard models to demonstrate it, like there are (a few) which demonstrate arrest? It's mostly because the objectives are opposed and real-world materials favor arrest when short and collapse when tall.

It is easy to build a model which arrests. I can throw 4x8' plywood sheets into a pile hapahazardly and it won't even start to lean until it hits 3 feet high, if then. I can't make a 3 ft pile of 4x8s or worse yet cinder blocks collapse any further without heavy power equipment. Dropping more of the same from above will not do it. They're effectively incompressible. Not skyscrapers which are >90% void space!

Is it possible, through the same process, to erect a quarter mile high skyscraper? Nope. Even though it would be solid and provide zero office space and support no load but itself (plywood, not even that). Even if there were a footprint the size of the towers and a relatively neat stacking job done, I doubt the quarter mile height could be achieved. It would just fall down at some point during construction.

So it's easy to build small things and tough to build large ones, if your aim is to keep them standing. Conversely, if the intent is to have them collapse, it's tough to build small things. This is really so very simple once the basic notions of scaling influence are understood. The tabletop collapse modeler is faced with engineering challenge not dissimilar to that faced by architects and engineers designing very tall buildings, only in reverse.

This is nothing new and has been mentioned in this forum many times. There is no excuse to ignore it and continue to clamor for physical models; it is certainly OK to try to address it (the scaling and materials issue) in some way but good luck, these are very solid and elementary principles. Anyone clamoring for physical models, yet with no awareness or appreciation for these principles is unequivocally demonstrating an inability to grasp and apply the principles towards successful scale modeling. They will not understand where correspondence can and cannot be established, where real world constraints force adoption of sub-optimal aspects and what it takes to counter those aspects and still avoid invalidation in matters of correspondence.

If you don't understand why building a physical progressive collapse experiment is far more difficult than making an arrest and, conversely, why making a really tall but stable building is far more difficult than making one which collapses during construction, then you really have no business clamoring for said models. You are only foolish for rejecting analytical and computational models in absence of a corroborating physical model. You are very likely to err in applying lessons learned from isolated and abstracted simple experiments.

There is no reason, though, to commit grievous errors of logic in over-generalizing specialized results because that doesn't require engineering knowledge, only common sense.

So what do you think, femr2? Makessense or nonsense?

I'm getting a rap for saying Bernoulli doesn't apply in another thread. That's not exactly what I said, but that's the rap. Fancy that after the above posts, but there's no Bernoulli there, either.

Might be worth mentioning that the Bernoulli effect is the opposite of the Janssen effect. The Bernoulli effect applies to non-viscous, Newtonian fluids, essentially ideal. The kinds of debris that might be found in the tower, especially at any crushing interface, will certainly be a mixed bag of sizes, shapes, density, rigidity, malleability, ductility, restitution, static and dynamic friction coefficients, resonant modes, fracture characteristics, moment of inertia, elasticity, plastic compressibility (did I miss anything? then =>) and so on. Hardly a Newtonian fluid, let alone ideal. So no, debris flow will not be subject to Bernoulli's principle.

Air? That's a different matter. But, since the interior loses volume at a rapid rate, it's pretty reasonable to expect air expulsion paths to the outside to vastly exceed air intake on the whole, though there may be some turbulence or vortices which induce some sucking here and there. As the building descends, air will rush in to fill the volume left void above the building and some will be entrained with the building as it descends, leading to reduced local pressure in the manner of the Bernoulli effect. This will all be exterior, however. Air flow across boundaries will be outward and into the core (then out the top or underground) because an interior OOS overpressure is mandatory.

Relation to crushing models?

If the model is small, there will be no high solid mass velocities. There can, depending on the construction, be significantly high air velocities but only of one sort: where air is constrained to follow a long path to the ambient environment in a very short time, when two large perfectly mating surfaces come together in a perfect fit. Small masses, low velocity -> low momentum -> low impulse on collision. Having a layer of air between two flat slabs could be too much air hockey effect, with energy being dissipated into accelerating air into the 'reservoir'.

Knowing this will prevent attributing arrest in such cases to magical, unexplained forces...

Pays to provide air flow around the contacting members, slab or otherwise. But not too much. Drag can start to become a factor. In the type of pole model femr2 has suggested, I'd consider washers for ballast and primary collision surface, at least on one side of the discs.

PS I know all this is moot. None of these imaginary physical (oxymoronic?) models will represent.