911 physics for dummies

[leftysergeant]

Yeah. I still have a mis-shapen bone in my left hand from an instance of that style of frustration removal over 20 years ago. It's a long story, involving far infra-red interferometry and sound absorbing foam rubber.

Dave

This is one of the reasons I spend so much time at the rifle range. I don't hear very well, but I can still type and hold a knife properly for Chinese cooking.

 

[jaydeehess]

Okay, let me see if I am visualizing this correctly. Free-fall speed could only be achieved if the floors began moving as soon as the cielings hit them. They didn't, obviously, based on the correct time of 16-24 seconds that more rational investigators accept.

Actually a true 'free fall' cannot be obtained unless the entire[u/] structure all starts moving downward at the same insant. If a section starts falling and then impacts a stationary section which instantly becomes detached from the structure then the total velocity of the now combined mass will be less than that of the initially moving section at the instant contact was made.

It arises from conservation of momentum.

Even if the first section hits a lower section that began moving sometime after the initial movement of the upper section but before the upper section reaches the starting point of the lower section the two sections will collide BECAUSE the upper section is moving faster than the lower one. When they collide their total mass velocity will be less than that of the original upper mass's velocity at the instant of contact.

 

[jaydeehess]

drywall punching stories......... I guess I am smarter than the average frustrated idiot. I kicked a wall rather than punch it. Missed the center of the stud but still managed to sprain my ankle as it bounced off the edge and twisted my foot to the outside past where one normally can get it to go.

I also threw a screwdriver in a fiberglass hemispheric radome enclosure.
It bounced around hitting the walls 3 times as I ducked and covered.

Live and learn lol

 

[leftysergeant]

Traveling sidways is not an option without some means of transfer-of-direction (An object in motion stays in motion unless acted on by an outside force). That means is generally a result to bouncing off of an inclined surface, or, in many cases, release of energy from a bent (but not yielded) steel beam (column) breaking loose from its moorings, or by buckling of members, or some of the other chaos involved in the collapse.
Again, there is "no waiting during collapse!"

Things do not always fall into a neat stack, especially if we are dealing with bendable and breakable elements like the floor slabs, pans and trusses. Add in irregularly-shaped office furnishings. We now do not have an even pile. This would deflect some materioal, still having momentum, thus the ability to transfer energy to whatever they strike, moving in random directions, but, because randomly-moving objects tend to straighten out once they have collided with enoguh objects to give them direction, they would, as I see it, tend to move outward toward the lowest concetration of other moving objects. This would pile stuff up against the insides of the walls.

 

[rwguinn]

Things do not always fall into a neat stack, especially if we are dealing with bendable and breakable elements like the floor slabs, pans and trusses. Add in irregularly-shaped office furnishings. We now do not have an even pile. This would deflect some materioal, still having momentum, thus the ability to transfer energy to whatever they strike, moving in random directions, but, because randomly-moving objects tend to straighten out once they have collided with enoguh objects to give them direction, they would, as I see it, tend to move outward toward the lowest concetration of other moving objects. This would pile stuff up against the insides of the walls.

Bull's eye! 10 ring for sure.
Why can't troofers not see that?

 

[EternalSceptic]

I have seen several statements in this thread where air resistance was said to be negligible. This is of course correct for free falling debris, but not necessarily for the towers themselves.

What I read about the progress of the collapse seems to work with two assumptions:
(I may misunderstand something)
1) The resistance of the storey which is hit by the falling part of the building is more or less constant for the whole falling height of that storey
2) It is only the resistance of the construction which decreases the falling acceleration.

well, ad 1)
IMO as soon as the fallig building part hits the next lower storey (assume this storey is still more or less intact) it will for some tens of inches have an acceleration of zero or less because an undamaged structure is still able to hold the static weight of the falling block plus built in safety factor. But after 10 inches or so I guess most of the bolts, welding and other material holding the structure together will be broken, the columns will be bent and from this moment the storey is no more than a number of steel pieces without any inner strength.
Not sure of this is clear enough in my english so I give an example: Take an empty and totally unbent beer-can and place it upright on the floor. step carefully on it - it will carry your weight (at least if you are not heavier than about 70 kp). But if you bend the sides of the can just slightly it will collapse immediately at a load of only few kp.
But at 2): inside the storey ther is quite a big amount of air, and this air must get out at a speed which is a multiple of the falling speed. At some point during the collapse the air alread partly must have reached sonic speed and due to the compression it must have become pretty hot. This airstream is methinks, at least partly responsible for debris being thrown out to the sides and also for reducing the acceleration of the falling block. It is sort of an aircushion.
The size of the footprint of the towers was if I am not mistaken some 5000 square meters, and the air, if compressed to 2 bar had a resistance of 50 000 000 kp, which is a considerable part of the weight of the falling block. To me an assumption that the air resistance prolonged the collapse tim by some 2 seconds sounds credible.

 

[R.Mackey]

There is no possible way in the universe you will compress the air inside the building to 2 bar (200 kPa or about 30 PSI). Exterior windows in an undamaged structure, without debris flying all over the place, can only contain about 10 kPa or so at best.

The BLBG paper adds the interesting insight that, very late in the collapse, evacuation of collapsing floors may have approached the sound barrier. There will be some "resistance" from this, naturally. However, treating the falling upper structure by the standard drag equation -- which is what is implied by "air resistance" -- is totally wrong. But since it only happens late in the collapse, it has little effect on the overall time of collapse. This force is also negligible compared to the intertial forces resulting from momentum transfer to lower floors, and to the stress caused by lower parts of the structure. A simple comparison of the masses involved will confirm this: The air contained in a WTC Tower totals about 2,000 tons, whereas the structure itself is on the order of 300,000 tons.

Had the Towers acted as a piston in a well-sealed pressure vessel, then your intuition would be correct.

 

[EternalSceptic]

I beg to differ:

1) You have doubled my pressure value - bar counts from 0 kp/cm², so the actual pressure is 1 kp/cm² (but maybe that was my fault, I should have mentioned that, and I do hope the exponent 2 will show up in your browser)
2) The mass of the air alone is not the only factor - it is the force necessary to accelerate this mass to about 20fold the speed of the falling block plus the additional air around the building which must also be accelerated in order to give room for the air from inside the building, the mass of the debris which is accelerated by the air rushing out, the resistance of breaking and blown away inner walls etc.

I agree that my figures are/maybe wrong - they are just guesses, but I am quite sure that, at least during the second half of the falling distance they are much less wrong than what you suggest. If we estimate the collapse time with 12 seconds then we get
an acceleration of b = 2s / t² = 820 / 144 = 5,69 m/sec²
a time until half of the height is reached of t = sqrt(2s / b) = sqrt(410 / 5,69) = 8,48 seconds
and a speed at this point of b * t = 5,69 * 8,48 = 48,25 m/sec.
The air as an average must move at least 20 times as fast to get out of the building in time, this is 960 m/sec, pretty much over sonic speed.
That means we have to accelerate a mass of 5 tons (your value for the mass of the air) from zero to 960 m/sec in about 0,08 seconds (I assume 1 storey is 4 meters high) that requires a force of 6000 tons. for the air outside to be "pushed away" we can assume another 6000 tons. I have no idea how much the debris, friction and turbulences will add to this value, my wild but for sure very low guess is something around another 10000 tons.
22000 tons alltogether - that will decrease the acceleration noticeable.
And it becomes worse the farther we come down.

 

[Mince]

911 dummies for physics:

http://s1.zetaboards.com/LooseChangeForums/index/

 

[Apollo20]

EternalSceptic:

Why do you say that "the air as an average must move at least 20 times as fast to get out of the building in time"?

And what about air being pushed down stairwells and elevator shafts and exiting from lower floors?

 

[EternalSceptic]

The average distance from the centre of the floor to the outside is about 20 times as big as the height of 1 storey, the air must be out of the storey in the same time it takes the storey to be smashed, so while the upper, falling block comes down about 4 meters the air must move th whole distance from the centre of the building to the outside.

(The numbers are rough estimates, just sufficient to get an idea about the order of magnitude)

And the area of elevator- shafts and stairwells is so much smaller than the area of the complete front around 1 storey (perimeter length of the building times appr 4 squaremeters) that IMO it can safely neglected for that rough estimate.

An experiment to that:

Take a perfectly straight board of about 1 square meter to a perfectly straight floor. Both should have a smooth surface and the board may be pretty heavy, say 20 kg. Put the board to an upright position and let it fall over. You'd expect a lod bang, but instead all you hear is a slighr "hsh" and the board settles down smoothly. the aircushion slows it down just before it hits the ground.

 

[R.Mackey]

I beg to differ:

1) You have doubled my pressure value - bar counts from 0 kp/cm², so the actual pressure is 1 kp/cm² (but maybe that was my fault, I should have mentioned that, and I do hope the exponent 2 will show up in your browser)

Ah. No, it's not the exponent, it's gauge pressure vs. absolute pressure. I see what you're saying now.

Nonetheless, no ordinary structure will allow net pressurization anywhere near 1 bar. That kind of overpressure would blast the entire structure into pieces.

2) The mass of the air alone is not the only factor - it is the force necessary to accelerate this mass to about 20fold the speed of the falling block plus the additional air around the building which must also be accelerated in order to give room for the air from inside the building, the mass of the debris which is accelerated by the air rushing out, the resistance of breaking and blown away inner walls etc.

Yes, it's not the only factor, but it's a good hand-wave. Think of momentum transfer from the structure to the air. m v is conserved. Since m_air is about 0.8% of m_building, the momentum loss to air is just not that significant. Multiply by maybe 2 to 4 due to wake formation and turbulent dissipation, but still, it's minor.

Anyway, I agree that fluid flow could approach the sound speed at some places late in the collapse, but this still isn't going to give you a huge correction in terms of momentum or energy. Transsonic flow implies some pressurization, but this would not be contained in the structure and would not efficiently oppose collapse. Think of those lower windows as Laval nozzles, and you'll see what I mean...

 

[EternalSceptic]

Right:
m(building) times v(building). But m(air) times v(air). and v(air) is roughly 20 times m(building) and m(air) is not only the air inside one storey, it is also the m(air) of the air around the building which must give way. Let alone the additional energy needed for turbulences, to smash obstructions etc.

In my calculations v(air) exceeds sonic speed before the upper block is halfways down, and at supersonic speeds the air does not move like at subsonic speeds, it does not move around obstructions, instead it is compressed in front of them and streams in straight lines away from the sides. I don't say my calculations are correct - you may be more right than I. To get the real numbers we would need all the data about what was in a certain storey, how big, how heavy, where, was it fixed and how and and and.

Most likely the truth will be somewhere in the middle.

Just an afterthought:

You wrote that a pressure of 1 bar would blow the structure into pieces - Isn't that exactly what we see on the videos, debris flying to all sides with speed and distance increasing the deeper the collapse goes down. I don't say airflow is the only reason for that, snapping of columns also plays an important role and many other factors. But there are really clouds of debris coming out at high speeds, and methinks that airflow plays quite a role here.

 

[leftysergeant]

There appears tp have been a lot of air moving UP the corses, so the width of the floors is not as important in calculating the speed at which it must move. If the floors were breaking as they fell, some air would escape upward through the falling debris.

 

[EternalSceptic]

To a certain extend yes. But I guess that the air above will be pretty much filled with falling debris and to a certain degree already compressed. The problem is, that we cannot reliably look at just one storey. In the videos it can be seen that large parts of the fassade are falling off before the collaps actually reaches that place (NO, CTers, THAT IS NOT A PROOF FOR EXPLOSIONS, DON'T BE STUPID !!). Some storeys will be damaged before the collaps reaches them because of the shockwaves coming down from the smashing of the higher stories etc.

As I wrote, all that can be only rough estimates.

 

[R.Mackey]

Right:
m(building) times v(building). But m(air) times v(air). and v(air) is roughly 20 times m(building) and m(air) is not only the air inside one storey, it is also the m(air) of the air around the building which must give way. Let alone the additional energy needed for turbulences, to smash obstructions etc.

I mentioned this factor above. I still expect momentum losses to the air to be less than 5% of the total momentum available. The loss of kinetic energy will therefore be < 1%.

In my calculations v(air) exceeds sonic speed before the upper block is halfways down, and at supersonic speeds the air does not move like at subsonic speeds, it does not move around obstructions, instead it is compressed in front of them and streams in straight lines away from the sides. I don't say my calculations are correct - you may be more right than I. To get the real numbers we would need all the data about what was in a certain storey, how big, how heavy, where, was it fixed and how and and and.

Like lefty said, you also have to make some optimistic assumptions about alternate gas escape paths. Air will also evacuate down elevators and through windows in advance of the collapse wave. This is what conspiracy types call "squibs," for instance. I think you've overestimated the volume of air that reaches the compressible flow regime.

Just an afterthought:

You wrote that a pressure of 1 bar would blow the structure into pieces - Isn't that exactly what we see on the videos, debris flying to all sides with speed and distance increasing the deeper the collapse goes down. I don't say airflow is the only reason for that, snapping of columns also plays an important role and many other factors. But there are really clouds of debris coming out at high speeds, and methinks that airflow plays quite a role here.

Nope. The debris flow starts early in collapse, before there can be any appreciable airflow apart from the thermal plume. It's kinetic in nature. Also, at early stages of collapse, the airflow is slower -- well below sonic -- and therefore is essentially incompressible. It will have some effect pushing dust, of course, but not much pushing denser structures.

On the other hand, pressurizing the entire Tower to 15 PSI would be equivalent to a bomb of roughly 200 tons TNT equivalent. Boom!

 

[EternalSceptic]

You win.

Just one sentence about the exponent thingy - this was badly written by myself - the exponent was not meant for the absolute vs relative pressure, i just was not sure whether the power of two in the formulas later in that post will show up

like here "an acceleration of b = 2s / t² = 820 / 144 = 5,69 m/sec²"

HAND

 

[Newtons Bit]

I mentioned this factor above. I still expect momentum losses to the air to be less than 5% of the total momentum available. The loss of kinetic energy will therefore be < 1%.


Like lefty said, you also have to make some optimistic assumptions about alternate gas escape paths. Air will also evacuate down elevators and through windows in advance of the collapse wave. This is what conspiracy types call "squibs," for instance. I think you've overestimated the volume of air that reaches the compressible flow regime.



Nope. The debris flow starts early in collapse, before there can be any appreciable airflow apart from the thermal plume. It's kinetic in nature. Also, at early stages of collapse, the airflow is slower -- well below sonic -- and therefore is essentially incompressible. It will have some effect pushing dust, of course, but not much pushing denser structures.

On the other hand, pressurizing the entire Tower to 15 PSI would be equivalent to a bomb of roughly 200 tons TNT equivalent. Boom!

15 psi would be catastrophic. A 90mph wind comes in at only about 20psf, or 0.1psi.

 

[leftysergeant]

It still appears to me that we are leaving out a factor generated by the nature of the perimeter columns and their multi-story configuration.

We are thinking of energy as increasing according to a constant formula and moving mostly vertically. The lateral movement, though it may seem of far less significant, may be more important than has been considered in that it gains some mechanical advantage through leverage, and that it may take surprisingly little force to push the walls outward, as compared to a more conventional structure because the perimeter columns basicly formed three-to-six floor-high levers. Gotta be hard on the floor-to-column connections, right? It seems to be that it would reduce the amount of energy needed to set the next floor slab in motion. This would speed up the process somewhat, I would think.

 

[Apollo20]

A bit off topic, but according to an article by Chang in Civil Engineering (ASCE), published in June 1971, a 140 mph wind against the face of a twin tower was predicted to generate a pressure of about 50 psf or ~ 0.35 psi (2.2 kN/m^2) and deflect the top of the building about 1 meter.

By comparison, typical hydrocarbon fuel/air explosions generate pressures up to 120 psi, but only for a fraction of a second!

Britain's largest peace time explosion was on June 1st, 1974, at Flixborough, when 40 tons of cyclohexane ignited. The pressure at the center of the explosion was estimated to be about 360 psi or 2.5 x 10^6 Pa.