911 physics for dummies

[Apollo20]

How fast is fast?

chris lz:

The first thing to consider when attempting to discuss the collapse times of WTC 1 & 2 is what is meant by "fast", or "too fast".

It begs the question: How fast do people expect a structure such as one of the twin towers to fall anyway, and why?

In truth, the precise collapse times of WTC 1 and 2 are not known very well. I would say the probable error in most collapse time estimates (I have seen) is +/- 3 seconds. Thus it is no surprise that some give very low estimates ~ 10 seconds, while others have quoted figures as high as 16 seconds.

But we do know that for the first 3 - 4 seconds into each collapse, WTC 2 was moving relatively faster than WTC 1, so WTC 2 fell faster overall. Very roughly we find that the acceleration of the upper section of WTC 2 was 3/4 g, while the acceleration of WTC 1 was about 2/3 g. But remember that this is only true for the first 3 - 4 seconds of collapse which is certainly less than 1/2 of the total collapse time.

As an aside I might add that when anti-sophist says: "He has failed to falsify the official narrative", there is a problem because there really is no official narrative as to the precise collapse times.

Anyway, the fact that the upper sections of WTC 1 & 2 fell at approximately constant accelerations, (that are less than g), tells us that there was an effective resistance being offered by the buildings to the downward motion of the upper block, and this resistive force was approximately constant. This leads to the idea of an energy term E1, defined as the energy needed to collapse one floor, which must be less than the kinetic energy gained per floor by the falling upper section, for the collapse to be self-sustaining.

E1 is also the work performed by the upper block so it is a force times a distance. We can vary the resistive force anyway that appears to model the collapse mechanics. Thus we can have a force that only acts for a fraction of a second on impact, or we can have a force that acts smoothly over an entire floor height of 3.7 meters. Mathematically this may be represented by the integral of F(x)dx, but the bottom line is that you can calculate E1 and it turns out to be less than 1/2 of the available KE for the worse case of the initial upper block of ~ 15 floors for WTC 1. Hence such a model predicts a self-sustaining collapse for WTC 1 & 2.

 

[PhantomWolf]

Let me put it this way. If the question appeared on a physics exam, worded like this:

In the collapse of a high rise building, what would be the path of most resistance?



would the correct answer be

A up
B sideways
C down
D up, then sideways, then down
E all of the above

So far, the answers I've been given have variously been A, C and D. Can you see why that might be a bit confusing to a physics ignoramus?

Thanks

Chris, it has nothing to do with resistance. Forget resistance altogether. It is about energy change. The less energy a object has to expend or gain to follow a path, the greater the chance of the object following that path.

I'm going to repeat that again for you. The less energy an object has to expend or gain to follow a path, the more likely it is to follow that path.

So what does that mean?

Let's look at energy gain. This means that something has to add the energy to the system, in the case of a moving object we're talking about a force acting on the object. For a object in motion to change that motion (i.e. to go from falling down to going sideways) it must have a force applied to it to move it in a new direction, this is Newton's first law of motion.

How does this effect a falling building? It means that the top of the building would have to have a force applied to it to push it sideways, that means it would need energy being applied to it to change it's direction.

What applies that force? Obviously the base of the building. But there is a second part to look at. When the top of the building lands on the bottom, it applies a force to the bottom as well, it gives it some of its energy. That energy is lost to the base in the form of damage to and buckling of the floors below. If the energy lost to that activity is less than the energy required to push the top of the building sideways, then the crushing is going to happen. If to crush the base of the building requires more energy than it would to deflect it over the side, then the base would be strong enough to remain standing and would. This is the heart of the issue. Which required more energy?

A simple bit of thought will answer this for us. The top of the building weighted several hundred tonnes and was for all purposes stationary. To push it over the edge we'd have to apply a force in the order of hundreds of kN to that mass. The floors on the other hand were only designed to carry a several hundred kilograms per square meter, a force of only a few kN. The energy lost to destroying the floor was easily a magnitude smaller than what would have been required to change its direction off the top of the building, and that is why it when directly down, it quite simply took less energy to do it.

 

[Anti-sophist]

Thanks. I take it "inelastic" is key here.

Not really.

If we were trying to come up with the simplest possible model, we'd have to chose either completely inelastic or elastic collisions. Inelastic is what happens when two cars collide and inter-mangle so much they effectively become one object. Elastic is like when two billiard balls collide and there is a near perfect transfer of energy. Given the choice, I think everyone would agree that inelastic is the more accurate description of how collisions between sections of a building would behave.

My most naive model would consist of a bunch of floors spaced equally, and then have the top floors go into motion, and model each collision.

Either model, though, elastic or inelastic, can be run. Both answers, I suspect, will end up somewhere longer than freefall, but not by too much.

You can increase this accuracy (and complexity) by, for example, modeling that some % of the mass is "lost" over time on the way down to the ground. I might be mistaken but I think this is approximately the model in Greening's paper on 911myths. Bazant/Greening/etc put out a paper relatively recently that takes this modeling to a far more accurate level but it requires non-trivial mathematics to understand.

Is there a sample algebraic model (or whatever you'd call it) somewhere on the net I could look at- as opposed to the more complex equations I see in the WTC science papers that throw me for a loop?

Alright, it's relatively straightforward but by no means simple. Basically there are two equations, one that governs the freefall between floors, and one that governs the befores and afters of the collision. This process of fall/collide repeats.. say.. 70 times.. with a starting mass of 30 "floors" and a final mass of 100 "floors". Each time you iterate the equation, you can calculate how long the falling took, and when you finish with all 70 repetitions, you add up each time, and you get an answer.

I could give you the exact equations as they aren't terrible complicated, but actually performing the operation 70 times is probably a bit tedious and is probably better left to a computer to do the actual calculation.

If you really care about the equations,

The falling: http://www.glenbrook.k12.il.us/gbssci/Phys/Class/1DKin/U1L6c.html
The colliding: http://en.wikipedia.org/wiki/Inelastic_collision

I faintly remember someone actually performing this exact calculation on a computer and posting the results. I couldn't find it after a brief search, though, so you might have more luck.

 

[chris lz]

Thank you Apollo.

the fact that the upper sections of WTC 1 & 2 fell at approximately constant accelerations, (that are less than g), tells us that there was an effective resistance being offered by the buildings to the downward motion of the upper block, and this resistive force was approximately constant.

Just want to make sure I understand this correctly: with only air resistance, there would have been a constant fall rate, not an increasingly faster one. And, both towers could be observed in the videos to be moving at an increasing rate as the collapses progressed. Therefore we can be sure there was significant resistance.

As the automated flight info lady says, "Did I get that right?"

 

[Anti-sophist]

Just want to make sure I understand this correctly: with only air resistance, there would have been a constant fall rate, not an increasingly faster one. And, both towers could be observed in the videos to be moving at an increasing rate as the collapses progressed. Therefore we can be sure there was significant resistance.

As the automated flight info lady says, "Did I get that right?"

No. The fundamental equation at play here is F=ma, or force equals mass times acceleration.

The fall rate (ie, the speed) wasn't constant. It's the speed at which the fall-rate increases (ie, the acceleration) that we are measuring.

Apollo describes an acceleration for the falling portion of the two buildings of 2/3g and 3/4g respectively. g is the acceleration due solely to gravity (no other forces, not air resistance, or any other form of resistance). So we can be sure there was significant resistance precisely because the acceleration was measurably less than g. An object encountering no resistance falls with an acceleration equal to g. Since he measured an acceleration of less than g, he could then estimate an average upward force provided by the building below.

The really short version of all that is simply this: since the buildings fell measurably slower than an object in freefall, that proves there was a significant upward force. And that force can be estimated by this difference in fall-times.

 

[chris lz]

If you really care about the equations,

The falling: http://www.glenbrook.k12.il.us/gbssci/Phys/Class/1DKin/U1L6c.html
The colliding: http://en.wikipedia.org/wiki/Inelastic_collision

I faintly remember someone actually performing this exact calculation on a computer and posting the results. I couldn't find it after a brief search, though, so you might have more luck.

Cool (I think). OK, so it's not as easy as I thought. But if I find the exact calculations, I'll post it. That ought to be fun as a reply: Dear truther, please explain which of these 70 calculations is wrong, and what numbers need to be changed.

 

[R.Mackey]

Just want to make sure I understand this correctly: with only air resistance, there would have been a constant fall rate, not an increasingly faster one. And, both towers could be observed in the videos to be moving at an increasing rate as the collapses progressed. Therefore we can be sure there was significant resistance.

As the automated flight info lady says, "Did I get that right?"

No, not quite. Air resistance is not a constant force -- it grows larger as velocity increases. At the start of the collapse, air resistance is effectively zero. (It's also negligible all the way through the collapse, because the "upper block" isn't falling through air, it's falling through building -- but that's not the question you asked.)

What Dr. Greening is saying, correctly, is that the rate of acceleration is less than "g." And it's nearly constant. That means that there are two constant forces at work. One of them is gravity. The other one acts in the opposite direction. This constant force is the resistance of the lower structure.

The collapses did get faster and faster as they progressed. They just did so with an acceleration less than gravity. This is true both at the beginning, where there cannot possibly be any significant air resistance, and at the end, where there might have been some. So the resistance is not air resistance. It's caused by the remaining structure.

For air resistance only, look at some of the perimeter pieces that fall away. Those are acted on only by gravity and air resistance. Those too fall faster and faster over time, and they hit the ground much sooner than the collapse front in the structure. This proves the strucure's resistance was much stronger than any potential air resistance.

 

[jaydeehess]

Thank you Apollo.



Just want to make sure I understand this correctly: with only air resistance, there would have been a constant fall rate, not an increasingly faster one. And, both towers could be observed in the videos to be moving at an increasing rate as the collapses progressed. Therefore we can be sure there was significant resistance.

As the automated flight info lady says, "Did I get that right?"

air resistance really is not significant for a massive, dense object since ma is so large compared to air resistance until the speed of that object gets very large. Besides I do not believe A20 was even refering to air resistance.

Secondly you are really mixing up Force, accelleration and velocity. They are all separate but related parameters

 

[chris lz]

No. The fundamental equation at play here is F=ma, or force equals mass times acceleration.

The fall rate (ie, the speed) wasn't constant. It's the speed at which the fall-rate increases (ie, the acceleration) that we are measuring.

Apollo describes an acceleration for the falling portion of the two buildings of 2/3g and 3/4g respectively. g is the acceleration due solely to gravity (no other forces, not air resistance, or any other form of resistance). So we can be sure there was significant resistance precisely because the acceleration was measurably less than g. An object encountering no resistance falls with an acceleration equal to g. Since he measured an acceleration of less than g, he could then estimate an average upward force provided by the building below.

The really short version of all that is simply this: since the buildings fell measurably slower than an object in freefall, that proves there was a significant upward force. And that force can be estimated by this difference in fall-times.

I guess I better make that trip to MIT before my next post.

 

[jaydeehess]

accelleration g =32 feet per second per second

At an accelleration of g an object will have a velocity of 32 feet per second after one second, 64 feet per second after 2 seconds, 96 feet per second after 3 seconds ,,, etc.


3/4 g = 24 feet per second per second
an object undergoing an accelleration of 3/4 g will then have a velocity of 24 feet per second after 1 second, 48 feet per second after 2 seconds, 72 feet per second after 3 seconds

Force = mass times accelleration

Force due to gravity is mass times g
total force is force due to mass times g minus force acting upwards
in this case total force is 25% less than force due to gravity and thus resistive force was 1/4 that of the force due to gravity alone

MIT is not required. High school physics will suffice.

 

[Hokulele]

I guess I better make that trip to MIT before my next post.

All you really need to understand when looking at the collapse times with a layman's eye is the relationship between distance, velocity (what you called the fall rate), and acceleration.

Distance in this case would be the height from which the collapse started.

Velocity is how much distance can be covered in a certain amount of time. For most of the calculations you will see on this topic, this will be listed in meters per second (m/s). Basically, how fast it falls. ETA: Most people call this the speed.

Acceleration measures how fast the velocity changes. This is listed in meters per second per second, also known as meters per second squared (m/s²). Think of it like measuring the effect of mashing on the gas pedal in your car. Your speed will change over time. In the case of the collapses, gravity is acting like your foot on the gas pedal, and it is basically floored so that the speed cannot change any faster. For a free fall calculation, this would be roughly 9.8 m/s². I do not know off the top of my head what this acceleration would be for the actual collapse, as that is where the math Anti-sophist has been describing kicks in.

So the speed does change over the duration of the collapse, but the rate of that change does not vary. Hopefully this clears this up a bit.

 

[Apollo20]

Thanks guys (and gals?) for all the useful added comments to my last post.

One more point of interest is that as long as the downward force acting on the upper descending block is greater than the upward force of resistance offered by the building's structure, the collapse continues AND accelerates. In the limiting case where the downward and upward force are equal - this could happen if the building was very sturdy on the lower floors - the upper block would cease to accelerate but move with a constant VELOCITY. (This is a great example of Newton's First Law - "A body remains in its state of rest OR UNIFORM LINEAR MOTION unless acted on by an external force.)

However, as far as we can tell the upper sections of WTC 1 and 2 accelerated all the way down - but things get very fuzzy at the end of the collapse as the rubble piles up.... However, if we assume that WTC 1 was 2/3 g, and WTC 2 was 3/4g, throughout the collapse we can use the equation t = Sqrt{2h/accel} to determine a collapse time of 11.3 seconds for WTC 1 and 10.6 seconds for WTC 2. I suspect these are too low, but they give you the concept of collapse times that are short but longer than the free fall time of 9.2 seconds

 

[leftysergeant]

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.

So say that there was resistance. This would, in the meantime, allow some force to travel sideways. This force shoves perimeter columns outward. This stresses the clips that hold the floor slabs to the walls, making them even mopre vulnerable to falling mass, perhaps separating them ahead of the arrival of the mass. But this, it seems to me, would leave segments of the perimeter structure leaning outward, accelerating , more slowly, perhaps, than the floor slabs. Because they are connected in a stepped arrangement, spanning three floors on one end and three on the other, they have to wait for all the floors to which both they and adjoining segments are attached to fall away before they go. Thus, their weight is adding kinetic energy laterally to the outside, even before they fall.

Have I accounted for something here that others have called "missing energy?"

 

[slyjoe]

...

For a free fall calculation, this would be roughly 9.8 m/s². I do not know off the top of my head what this acceleration would be for the actual collapse, as that is where the math Anti-sophist has been describing kicks in.

So the speed does change over the duration of the collapse, but the rate of that change does not vary. Hopefully this clears this up a bit.

Well, Richard Gage thinks the acceleration due to gravity is 9.1 m/s².

 

[Apollo20]

I think it is ........... on Venus!

 

[slyjoe]

I think it is ........... on Venus!

8.8 m/s² on Venus. Actually, he's closer to Saturn (9 m/s²).

 

[rwguinn]

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.

erm... not quite.
Don't go "klunkity-klunk on us, lefty... There is no pause--the floors do start to move as soon as the ceilings hit--but at a lower rate than would be expected with no resistance.
(Find yourself a chunk of installed drywall that you planom tearing out, or you dont care about. Punch it with your fist, being careful to avoid studs, of course (Thinking of the idiocy of twoofer arguments helps here)
Did you fist stop, then go on?
Nope--it just slowed down, and possibly bled. If you didn't take my advice, and hit a stud, it also may have broken (and stopped, too)!

So say that there was resistance. This would, in the meantime, allow some force to travel sideways. This force shoves perimeter columns outward. This stresses the clips that hold the floor slabs to the walls, making them even mopre vulnerable to falling mass, perhaps separating them ahead of the arrival of the mass. But this, it seems to me, would leave segments of the perimeter structure leaning outward, accelerating , more slowly, perhaps, than the floor slabs. Because they are connected in a stepped arrangement, spanning three floors on one end and three on the other, they have to wait for all the floors to which both they and adjoining segments are attached to fall away before they go. Thus, their weight is adding kinetic energy laterally to the outside, even before they fall.

Have I accounted for something here that others have called "missing energy?"

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!"

 

[Dave Rogers]

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.

Not quite. Let's take an example.

Suppose you're driving at 60mph, and you hit a stationary car which has its brakes off. The front of your car and the back of the other car will crumple. Your car will slow down and the other car will speed up, and the two of you will probably be going at about 30mph, locked together in a mess of tangled metal. That's an inelastic collision.

And that's what happened each time the falling bits of the towers hit another floor. They speeded up between floors, then as they hit the next floor they slowed down while the next floor speeded up. Nothing actually stopped, but after each impact the whole lot was going rather slower than it would have been without having to speed up the next floor down.

When you work all that out, you get about 12-14 seconds.

So say that there was resistance. This would, in the meantime, allow some force to travel sideways. This force shoves perimeter columns outward. This stresses the clips that hold the floor slabs to the walls, making them even mopre vulnerable to falling mass, perhaps separating them ahead of the arrival of the mass. But this, it seems to me, would leave segments of the perimeter structure leaning outward, accelerating , more slowly, perhaps, than the floor slabs. Because they are connected in a stepped arrangement, spanning three floors on one end and three on the other, they have to wait for all the floors to which both they and adjoining segments are attached to fall away before they go. Thus, their weight is adding kinetic energy laterally to the outside, even before they fall.

That sounds fairly close to what happened as a layman's account. Now add to that the fact that the perimeter columns on the top part pulled inwards initially, so you've got the top part falling inside the bottom part like a wedge. You'll get collisions between the top part and the columns of the bottom part, which are already leaning outwards, that will throw those falling columns out a lot further. It's a lot like making a fine cut on a pool table; the cue ball travels along the centre of the table, but sends the object ball diagonally into the corner pocket.

And that's why, when David Ray Griffin says that gravity is vertical and so it can't throw things sideways, he's being an idiot.

Have I accounted for something here that others have called "missing energy?"

Not sure. It depends who called it that, and whether it made any sense in the first place.

Dave

 

[rwguinn]

Not quite. Let's take an example.

Suppose you're driving at 60mph, and you hit a stationary car which has its brakes off. The front of your car and the back of the other car will crumple. Your car will slow down and the other car will speed up, and the two of you will probably be going at about 30mph, locked together in a mess of tangled metal. That's an inelastic collision.

And that's what happened each time the falling bits of the towers hit another floor. They speeded up between floors, then as they hit the next floor they slowed down while the next floor speeded up. Nothing actually stopped, but after each impact the whole lot was going rather slower than it would have been without having to speed up the next floor down.

When you work all that out, you get about 12-14 seconds.



That sounds fairly close to what happened as a layman's account. Now add to that the fact that the perimeter columns on the top part pulled inwards initially, so you've got the top part falling inside the bottom part like a wedge. You'll get collisions between the top part and the columns of the bottom part, which are already leaning outwards, that will throw those falling columns out a lot further. It's a lot like making a fine cut on a pool table; the cue ball travels along the centre of the table, but sends the object ball diagonally into the corner pocket.

And that's why, when David Ray Griffin says that gravity is vertical and so it can't throw things sideways, he's being an idiot.



Not sure. It depends who called it that, and whether it made any sense in the first place.

Dave

Better description than mine, although I like my drywall scenario best.
Allows removal of frustrations without violating any laws or decorum...

 

[Dave Rogers]

Better description than mine, although I like my drywall scenario best.
Allows removal of frustrations without violating any laws or decorum...

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