I read an article this morning which, in passing, stated that the second jet to hit the WTC was just a few MPH from breaking up in mid-air. From the video tapes I have seen, it seemed to be fairly level and not performing any rapid turns or anything that would cause the plane.
Do I answer the OP, or the sig?
Um…
Both planes were traveling much too fast for their altitude. This was immediately noticed by the ATCs.
Its been assumed (obviously) that since the terrorists wanted to inflict as much damage as they could, they firewalled the throttles as they approached the towers. And when you watch the tape the 2nd plane makes a bank before impact.
But I believe the 2nd jet was only estimated to be going about 520 mph and the VNE (velocity not to exceed) of a 757 is listed as 590 mph. So I don’t think it was that close to ripping the wings off.
The published Vne (never-exceed speed) on an airplane usually has a safety margin built into it - not sure what that margin is in a jet like that, but even in a small airplane hitting the Vne does not result in instant disassembly.
More commonly, what you get is popped rivets, permanent deformation of things like wing and tail control surfaces, wrinkling of the skin, stress fractures in the airframe… airplanes HAVE been flown at speeds beyond their Vne and landed - but that’s often their last flght, they’re too damaged to safely launch again. And that damage may not by visibly apparent, particularly to the untrained eye.
With jets, the altitude has an effect on how fast you can fly before damage starts occuring. Remember that air does have a certain density. Plowing through sea-level air at 500 mph exerts more pressures and forces on an airplane that flying 500 mph at 30,000 feet above sea level where the air is much thinner. Partly, this “near breakup” line in the news media is from the fact that those jets were flown much faster much closer to sea level than a Boeing 7x7 normally ever is. At those speeds, in air of that density, even a very gentle turn can exert sufficient extra force on the airframe to cause damage. That final bank into the WTC was actually fairly steep. If they were already close to Vne that might have been enough to start breaking things in and on the airplane. Not that that would make any difference to the final outcome since the end intention was death and destruction.
Wouldn’t a 747 flying relatively slowly into a building be just as bad as one flying relatively quickly? After all, it’s still a huge object being inserted into a building not designed to have a jumbo jet loaded with fuel in the middle of it?
It’s not like the jets were going to hit gently and bounce off.
Basic physics. F=MA.
The amount of force (F) that an object exerts is a function of it’s mass (M) times (A) acceleration. To take it to the extreme, a bullet going at 1 foot per second does a lot less damage than a bullet fired at normal speeds.
Zev Steinhardt
But zev, a bullet going at 1 foot per second could still have a very high accelration and therefore force, surely you mean 1 foot per second per second.
P=Mv. Conservation of momentum.
But my point is that there was still a lot of M in those planes.
The momentum of a plane is directly proportional to the velocity. Twice the velocity, twice the momentum. P can be communicated in kg m/s. Lets say it was 100,000 kg at the time, and going 835 kph, or 232 m/s. P=23,200,00 kg m/s.
At 600 kph, P=16,670,000 kg m/s, or proportionally less.
Would you rather be hit with a car doing 5 mph or 50 mph? The transfer of energy to the static body (you, or the WTC) is a little different. You can make a bigger bang with the same M by using more v.
I think the crux of the velocity issue is the total kinetic energy of the planes as they struck.
KE=½mv²
Where m=mass of the object and v=velocity
This means even a modest increase in velocity would cause a significant increase in the kinetic energy of the plane. This is all energy that the structure of the tower would have to absorb on impact. The more there is, the more chance there is of causing damage.
In the real world it’s not quite that simple since we know a lot of wreckage went right through the towers and out of the other side.
Some back-of-the-envelope calculations I’ve done:
I’ve converted imperial measurements to metric ones, giving:
Mass of a fuel-laden 707 = 117000kg
520mph = 250ms
WTC tower = 63m on a side
I’ve rounded slightly in most cases for simplicity.
At the point of impact a laden 707 going at 520mph has about 7,312 megajoules of kinetic energy.
If we assume, say, 30% of the mass of the plane stopped inside the tower then the structure would have had to absorb over 2000 megajoules of energy. This doesn’t count the effects on debris that passed through the structure but was slowed down, giving up some of its energy.
At 520mph an object takes just over 0.25 seconds to cross the width of one tower. Assuming 30% as the figure for mass of the plane stopped by the structure, then the force on the structure during the collision would be in the order of 35 million Newtons (for non-scientists this is a bit like letting the weight of about 3500 metric tonnes hang horizontally off the tower at the point of impact for a quarter of a second).
Assuming I’m not way off with these hasty calculations then I’m amazed the towers weren’t toppled or torn in half by the impacts.
I like that explanation better.
A more useful measurement would be Kinetic Energy:
KE = [sup]1[/sup]/[sub]2[/sub]MV[sup]2[/sup].
Increase either mass or velocity and you’ve got a bigger crunch. Since the terrorists evidently intended to inflict the maximum amount of damage possible, it makes sense to go as fast as possible.
God, I love you people.
God bless us, everyone.
To address the OP:
Dated February 27, 2002.
This website has the entire NY Times article posted.
So is Liz an idiot, or is she exaggerating, or is she just trying to give the reporter a juicy sound bite, or was the plane in danger of breaking up in midair?
I would have thought it would be more useful to talk in terms of momentum than in kinetic energy, due to the fact that momentum must be conserved, whereas kinetic energy need not neccessarily be conserved.
-Oli
starman, kinetic energy isn’t conserved except in some idealised circumstances. But that’s the whole point. The plane’s kinetic energy is used to bend, break and heat the building.
Ah. My apologies, I posted without thinking.
-Oli
I should have made it more clear in my post that when I calculated the force on the tower I was using a conservation of momentum calculation. Both momentum and kinetic energy need to be considered when thinking about the collision. Energy would be conserved during the collision. Some of the KE of the plane would pass into KE in the structural members of the tower, some into heat, some into sound.
As a side note I found this site that shows some different figures for the forces involved during the collision.
That site also shows the wind loading the towers were designed to resist (about 58 million Newtons on a face), though it doesn’t really speculate as to the effects of applying such forces at a single point high up the tower. The wind loading figure is supposed to be appllied across the entire face of the tower, top to bottom. Application of this force at a point high up will obviously cause a far greater moment around the base, making it much more dangerous.