I have light-bulb rated at 500 watts. You can warm your hands off of it at a few inches away from the light. I also happen to have a two-watt laser.
Stick your hand in front of that, and you'll start to smell that sweet smell of burning protein.
Why is this? It's not just about force. It's about the distribution of that force. I can body-check you and send you a couple feet backwards - or
I can deliver nearly equivalent force in the form of a punch and break some ribs while moving your body very little.
Same concept, here. While the total force exerted on the structure in heavy winds is far greater than that of the airliner - it is distributed across
the entire surface of the structure and successfully countered by each level of supports. A plane is not only much harder than air - it also has much
more concentrated mass and velocity - meaning it is going to cause damage to the structure.
Let it be noted that doing enough damage to a single floor's supports will cause the whole structure to fail (fall down - go boom) - especially
mid-level.
Come on, now. You have to learn to "feel" the world around you. Our brains can do what computers, today, have a lot of trouble doing - allow us to
simulate real-world dynamics - effortlessly. Use that capability. Go up to any steel beam supporting a building - put your hand on it - and 'feel'
the tension its under - feel the weight of the mass it is supporting. go smash rocks with a hammer - just for kicks and grins, then apply what you
have experienced to your mind's ability to emulate the real world.
All of this stuff is simple. Really - it's all particulate physics - everything is made up of tiny particles, can be broken into those tiny
particles - and those tiny particles will behave the same on any scale. If I have a million water molecules rolling down the hill - they will behave
rather similarly to a million boulders (only they will cling together, more).
Physics doesn't change. Just like electronics doesn't change. Just because I've added a capacitor in parallel with an inductor - it doesn't mean
the inductor no longer resists a change in current; and the capacitor doesn't suddenly stop resisting a change in voltage.
The main thing you have to keep in mind is scale. Each floor "was designed to support the weight of five floors above it". However, we'll say
that each floor has a mass of 1 (for math's sake, since I don't want to mess with larger values that complicate things - and this is simply
arbitrary, anyway). Each floor was approximately three meters above the floor below it (about 9-10 feet). 9.81m/s/s is the rate of attraction of
gravity. That means it took 3/[%Force-sub-G%] seconds to impact the floor below it (0.30581039755351681957186544342508 seconds). I do hope that is
within your standards of precision... I know they are quite strict.
Now, having fallen for 0.3058 seconds, this floor, with a mass of 1 (arbitrary), is moving at [%Force-sub-G%]x[%Time%] - where "Time" represents the
duration of acceleration due to gravity (3 meters/second is the result).
So, we have an arbitrary mass of 1 moving at 3 meters/second. Inertia is equal to 1/2[%mass%]x[%velocity%]^2. So, that leaves us with 1/2x1x3^2 - or
"4.5". While not the "official" unit - this would be the equivalent of having 4.5 static floors suddenly appearing atop the floor of subject.
So, one floor couldn't compromise the integrity of the tower, right? Each floor is supposed to support five times the weight of the floor above
it.
Well... so it would seem. Let's start increasing the mass, shall we? We'll say the floor now has a mass of 10. That means each floor can support
a static mass of 50. Rate of acceleration and distance are the same... so no need to go through that again. And we end up with the inertia of the
falling floor to be 1/2x10x3^2 = 5x9 = 45. Standard unit of measure, here, being kilograms - we're not even in the hundreds and thousands of
kilograms involved in one single floor on the WTC.
It is highly unlikely, due to the nature of the structure, that the mass of just a single floor would be at play. Also, in the event that a single
floor collapses, the floor above it will come crashing down on top of it... now pay attention...It fell twice as far - that's
6/9.81=0.61162079510703363914373088685015 seconds of free-fall (at this point the steel structure will provide little resistance as it has already
been compromised).
That's 6 meters per second (hey, that works out nice, don't it?)
That means our original mass of one would come out looking like 1/2x1x6^2=0.5x36 = 18 - with the original floor being capable of supporting five
additional floors. Even if the structure of the collapsing floor managed to slow the descent of the above floor (not counting the mass of the floors
above it), it is apparent that the collapse is completely out of control.
This is also assuming there is zero damage to the structure(s) below, and not taking into account design flaws - such as the bolt&bracket joints -
which do not perform up to the original welding specifications.
If you want to play around with this some more -
www.ajdesigner.com...
had some formulas I used to verify my own. Feel free to explore. The only thing I should note is that I left the final values in representation to a
comparable static force. It's essentially the same, it's just that the notation is different because they are, fundamentally, different things
(inertia (also known as kinetic energy - expressed in joules) implies a body in motion, relative to another body, whereas mass implies no motion).
Have a nice day.
Edit: fixed math problems.
[edit on 15-12-2007 by Aim64C]