Please, Don't Put Equations Into My Mouth
In
#640:
Good points!
I was going to bring up the freefall problem with Dave Thomas' analysis myself but wanted to be sure he admitted that is what he assumed first. Which he does above where he mentions that he thinks he is being misunderstood.
Dave should know that some of us certainly do understand that his analysis assumes freefall punctuated by brief collisions and that he is trying to show how that could mimic an average continuous acceleration of 2/3rds g. The issue is that his analysis cannot possibly be legitimately describing the collapses of WTC 1 for several reasons:
1. Collapsing/buckling columns still provide a fair amount of resistance. If anyone doubts this they can look at figures 5d and e in Dr. Bazant's paper, where he shows a classic graph of resistance during buckling
http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/405.pdf. The resistance during the buckling never falls below 25% of the original intact column resistance. In the case of WTC 1, where the columns were at least 3 times stronger than needed to support the static load, that means the resistance is almost capable of supporting the static load. In other words, the minimum resistance is 25% of a strength which could support 3 times the static load, or 75% of the minimum support needed for the static load. The fall through this resistance can only occur at about 0.25 g, so the minimum resistance was not negligible and does not support anything close to near freefall acceleration as Dave is claiming.
2. The velocity drops which Dave assumes in his calculations are far too small to provide the energy needed to continue collapse. Dave seems to think I am violating the conservation of momentum here, but in reality his argument is circular.
To determine the velocity loss Dave is taking the kinetic energy difference between freefall acceleration and 2/3rds g. If there wasn't much energy loss required by the upper section for his calculations to determine the velocity drop that doesn't negate the reality of what the columns required to cause their failure. It actually points to other problems and shows he is not considering the full picture.
3. The Verinage demolitions show what a natural collapse should look like in terms of the deceleration of the upper section at impact, since a load amplification is necessary for the insufficient static load mass of the upper section to overcome the reserve strength below. The same measurement techniques used for WTC 1's descent, where they show no deceleration, show significant deceleration of the roofline in every single Verinage demolition. This proves that the measurement technique and frame rate are not the problem and that the effects of any impulse capable of causing continuing collapse are observable. There is obviously no deceleration in the fall of the upper section of WTC 1 and it proves there was no dynamic load.
Props to Grizzly Bear, pgimeno, and ozeco41 for their comments on Szamboti's claims.
Tony Szamboti, what Grizzly Bear was saying about "limiting case studies" is important. You must also consider the scale of physical models being used to study something much larger.
The pressure exerted by beams depends on the size of the structure. As linear size is increased, the footprint increases as the square of the linear expansion, and volume increases as its cube.
So, a quantity like pressure, force per area, at a constant density in the volume, would increase linearly, as pressure = force/area = weight/area = volume*density/area. If density is constant, pressure increases as volume/area = cube(increase)/square(increase) = linearly increasing.
If a man was made twice as big, but with the same density of bones, muscles, and such, the pressure on his leg bones would be twice the normal-sized man's. A ten-times bigger man would have ten times the pressure on bones of similar density and capability; they would be CRUSHED.
Please, do not confuse the behavior of verinage of a building of ten stories or so as indicative of the behavior of a 110-story skyscraper. They are different things.
Look at a spider's legs, then at an elephant's. The elephants legs must be much thicker, relative to body size, to support its weight.
A tiny spider-sized miniature elephant would be much stronger structurally, with less pressure on its bones, than the real elephant.
Now, as for your statement that
The velocity drops which Dave assumes in his calculations are far too small to provide the energy needed to continue collapse. Dave seems to think I am violating the conservation of momentum here, but in reality his argument is circular. To determine the velocity loss Dave is taking the kinetic energy difference between freefall acceleration and 2/3rds g.
This is a
pathetic description of the results I described on Coast-to-Coast, and also posted
here and
here on NMSR.
To determine the velocity loss, I am
USING THE PRINCIPLE OF CONSERVATION OF MOMENTUM.
This is pointed out explicity in my article on momentum. To say that I am "
taking the kinetic energy difference between freefall acceleration and 2/3rds g" is absurd, and shows that you have either(A) not even read my article, (B) read it without a shred of understanding, or (C) intentionally erected a strawman, as you realize the actual model I used isn't as easy a target.
Should you try to perform your own calculations along the lines of my analysis (after reading your comments thus far, I'm not sure you are up to such a task), you would find that the "
2/3rds g" figure is the result of averaging the accelerations for the
FIRST FOUR SECONDS OF TOWER 1'S COLLAPSE.
Over the
last four seconds, however, the short-term acceleration average is only 1/3 g. The short-term averaged acceleration varies for the whole collapse, starting at full g, reducing to 1/3 g at the end. The average over the whole ~12-second collapse is about
0.41g. Again, I point out that these are
averages of periods of true freefall with briefer decelerations from the collisions.
This "2/3g" custard is very ingrained in the truth movement, but is not an
assumption of my calculation, it is a
result of it.
I don't see any need to continue trying to respond to such flagrant strawman arguments. I'm done. I can see why Szamboti's reputation around here is what it is, at least. I hope Chandler can do better.
Dave
) I would have to check Dave's source claims with my tired old brain engaged. But his conclusion is right.
