WTC Question

Lord Poe · Post by **Lord Poe** » 2006-09-13 04:17pm

Would tower two have fallen if only tower one was hit by a plane? I was thinking of WTC 7 that fell after all the debris and fire leveled that building. But what of tower 2? Would its proximity to tower 1 being hit and collapsing doom it because of collateral damage?

Ted C · Post by **Ted C** » 2006-09-13 04:56pm

I'm no expert on architecture, but the fact that less-massive buildings in the immediate vicinity that were not directly hit also collapsed does not bode well for Tower 2.

Lord Poe · Post by **Lord Poe** » 2006-09-13 05:19pm

Ted C wrote:I'm no expert on architecture, but the fact that less-massive buildings in the immediate vicinity that were not directly hit also collapsed does not bode well for Tower 2.

Did you see that documentary, "9/11" by the two French filmmakers who filmed the only footage of the first plane hitting tower 1? One of the brothers ws in the tower 1 lobby filming even after tower 2 fell. Anyway, the firefighters saw the state of tower 1's lobby (They got there minutes after the first plane hit) and said it looked like the plane hit the lobby! All the glass was blown out, and burning jet fuel had shot down the elevator shafts. If the concussion from the top of the tower blew out the windows in the lobby, I'd imagine tower 2 would have to be in serious danger from the force of tower 1's fall.

Post by **Broomstick** » 2006-09-13 08:50pm

The force of just one of those towers coming down was pretty spectacular. Not to mention the flying debris involved. Even if the other tower hadn't been knocked over I'm pretty sure there would have been serious questions about its structural integrity

I remember seeing a documentary that talked about the force generated by the collapses, but my physics/math isn't up to talking about it in a meaningful way. Would be interesting if someone with that capability ran the numbers.

Lord Poe · Post by **Lord Poe** » 2006-09-13 09:38pm

Broomstick wrote:I remember seeing a documentary that talked about the force generated by the collapses, but my physics/math isn't up to talking about it in a meaningful way. Would be interesting if someone with that capability ran the numbers.

Check this out:

Collapsing towers caused seismic shock

The devastating impacts on the twin towers of the World Trade Center and their subsequent collapse shook the ground with the force of a small earthquake.

Scientists have released seismic recordings made at several monitoring stations situated in northeast America.

The seismic signals generated by the collapsing north and south towers were much stronger than those from the two airliner impacts.

Many smaller signals were registered at the Palisades monitoring station - a short distance from Manhattan - that may have originated from the further collapse of the Twin Towers and the fall of walls and other debris in the surrounding area.

The seismographic monitoring stations are situated in southern New York, northern New Jersey, western Connecticut, and Pennsylvania. The closest station, at Palisades, New York, is located just 34 kilometres (21 miles) north of lower Manhattan in Rockland County.
The Palisades recordings of the twin tower collapses were comparable in size to the signals from a small earthquake of magnitude 2.4 that was felt on the east side of Manhattan and in the western parts of Queens earlier this year, on 17 January.

However, the seismic signals from the five events on 11 September differed from a small earthquake in significant ways.

They were richer in low-frequency energy and poorer in high-frequency energy. The differences can be attributed to the short-time duration of the fault rupture responsible for the earthquake as compared with the long and complex collapse of the buildings.

Post by **Darth Wong** » 2006-09-13 09:45pm

If you know the mass of the towers and their height, you can make a very rough estimate of the gravitational potential energy by treating the structure as a point-mass located halfway up (in order to average out the heights of all the parts of the building). In other words, if the building's mass is X kilograms and it is Y metres tall, then its GPE in joules would be roughly X*g*(Y/2), or 5XY. That allows you to produce a very rough estimate of how much energy must have been released in one form or another when the building collapsed.

Wyrm · Post by **Wyrm** » 2006-09-14 01:34am

I did a calc using DW's formula and compared it to the amount of energy thought to be released in earthquakes.

I got the pertinent facts located here. The WTC was approximately 500,000 tons (453,592,370 kg) and 1,362 ft (415.1376 m) high. Plugging in DW formula, you get a GPE of 9.2268e11 J of energy, or 220 tons (0.22 kiloton). I'm not sure if this is for one tower or the both of them.

According to this source, the seismic energy released in an earthquake of magnitude M is log E_S = 11.8 + 1.5 M, where E_S is in ergs (1e-7 J). When we convert the energy to ergs and solve for M, we get energy equivalent to a magnitude 4.7767007379 earthquake. Obviously, most of that energy went elsewhere.

Lord Poe · Post by **Lord Poe** » 2006-09-14 08:54pm

I'm still floored by the statements firefighters made who were digging through the rubble. One of them in the "9/11" documentary said "We didn't find a desk, a chair, a computer, a phone..."

Straha · Post by **Straha** » 2006-09-14 09:14pm

If I recall correctly after the first WTC Attack (the Truck Bomb) there was a report made which said that if one tower fell the other one would be so damaged as to make collapse inevitable, or something to that effect. Don't quote me on the details of this, but I'm sure with enough google action you could find it online.

Oh, and as for the energy released in the collapse of the buildings, Charles Pellegrino in Ghosts of Vesuvius gives the total energy released as 1.6 Kilotons, but I remember hearing larger figures bandied about shortly after the attacks...

Post by **Broomstick** » 2006-09-14 09:23pm

Lord Poe wrote:I'm still floored by the statements firefighters made who were digging through the rubble. One of them in the "9/11" documentary said "We didn't find a desk, a chair, a computer, a phone..."

Yes, well, all that energy has to go somewhere - pulverizing objects into hot dust would qualify as an outlet.

FSTargetDrone · Post by **FSTargetDrone** » 2006-09-14 10:13pm

Nothing but dust and paper...

Post by **Surlethe** » 2006-09-16 02:52pm

I'm doing some back-of-the-envelope calculations on the global collapse of the World Trade Center, and I'd appreciate criticism. The force of gravity on the section of the North Tower above the impact zone was about 4.54e8 N (since the impact zone was 0.9 up the building, and assuming an even density, and mass as given above by Wyrm).

If the six floors which were impacted lose their weight-bearing capabilities, then the top of the building will fall a good 18 m, gaining some (4.54e8 N)(18 m) = 8.2e9 J of kinetic energy. If the 92nd floor is going to stop the collapse, it will need to exert a force F over, say, 3 meters, or else the floor will collapse, such that 3F = 8.2e9 J. Solving, we have F = 2.7e9 N, which is an order of magnitude above the force the floor needed to exert to keep the tower standing.

Is this analysis decently in step with reality?

Admiral Valdemar · Post by **Admiral Valdemar** » 2006-09-16 08:16pm

The survivors of the second tower falling were at least able to show that not all of the mass fell straight on to one spot, so dispersion of the kinetic energy was what helped them stay alive. But as they mentioned, the storeys above them essentially fell with the force of a freight train ever growing in speed (to the extent that the initial collapse made people bounce off the floor before it was anywhere near them). That energy not only pulverised any office stationery, it made it very hot pulverised stationery. The dust cloud was dense and quite capable of burning airways if inhaled.

Post by **Darth Wong** » 2006-09-17 11:46pm

One other note about the energy involved in the WTC collapse: I don't know how much fuel those planes carried, but if the energy density is similar to gasoline, you're looking at something around 45 MJ/kg. With a density of roughly 730 kg/m^3 (0.73 kg/L), this means you get roughly 33 MJ per litre, or 132 MJ per gallon. If the plane's fuel capacity is, say, 50,000 gallons, that's more than a kiloton right there.

Mind you, I have no idea what the fuel load of those planes was, because I didn't bother looking it up. And it's always possible that jet fuel has substantially different energy density than gasoline. But this energy will also be distributed differently; the structural collapse involved the rapid conversion of gravitational potential energy in a few seconds, while this fuel burned for quite a while.

Lord Poe · Post by **Lord Poe** » 2006-09-18 12:45am

Someone posted the entire "9/11" doc on Youtube. Here are the two videos which show the firefighters in the lobby of tower 1 as tower 2 collapsed:

http://www.youtube.com/watch?v=J7StlvKjkuI

http://www.youtube.com/watch?v=5OKrTZOvbcU

As tower 2 collapses, from the outside shots you can see a LOT of debris hit tower 1. Even without a plane, it would have fell.

Here's the quote from the fireman who said he didn't even find a desk:

http://www.youtube.com/watch?v=ZRCZ6bizoXE

Post by **Surlethe** » 2006-09-18 03:11am

Darth Wong wrote:One other note about the energy involved in the WTC collapse: I don't know how much fuel those planes carried, but if the energy density is similar to gasoline, you're looking at something around 45 MJ/kg. With a density of roughly 730 kg/m^3 (0.73 kg/L), this means you get roughly 33 MJ per litre, or 132 MJ per gallon. If the plane's fuel capacity is, say, 50,000 gallons, that's more than a kiloton right there.

This gives between 41 and 49 MJ/kg as the energy density of jet fuel; Wikipedia says the jets splashed about 10,000 gallons of jet fuel into each tower (the claim is cited, so I'm giving it a little more weight than usual). Who can look at something like this and not think there was a huge amount of energy being released?

The other thing to keep in mind about the energy released by the fires is that the jet fuel wasn't the only thing burning; pretty much everything in the six-floor impact zone caught fire because the planes' explosions injected the burning jet fuel throughout the buildings, igniting all flammables in the area.

Post by **Broomstick** » 2006-09-18 06:19am

Darth Wong wrote:Mind you, I have no idea what the fuel load of those planes was, because I didn't bother looking it up. And it's always possible that jet fuel has substantially different energy density than gasoline.

Jet fuel is essentially kerosene with a pedigree. If you've got figures for kerosene they'd be more accurate to use in that sort of calculation.

If the plane's fuel capacity is, say, 50,000 gallons, that's more than a kiloton right there.

A 757-300's fuel capacity is 43,400 liters (I even looked it up in metric for you. For the Americans, that's 11,466 gallons). I believe that was the WTC model, but I'm not 100% sure.

The 757-200 holds 43,490 liters. I don't view that as a significant difference under the circumstances.

But this energy will also be distributed differently; the structural collapse involved the rapid conversion of gravitational potential energy in a few seconds, while this fuel burned for quite a while.

I think that's a point that gets lost on folks sometimes - they underestimate the potential energy of a structure like that. Just like they forget there was more fuel than just what came with the jet - everything on the impact floors that could burn was burning.