Chris,
One of us, and ONLY one of us, knows what he is talking about here. The other one is struggling to interpret what NIST is saying, is pulling phrases out of disparate sections and trying to string them together in a way that makes sense.
I see that my simply saying that I've got a mechanical engineering degree, 35 years experience & taught this stuff in college was not enough to get you exercise a modicum of caution. Even if technical respect was too much to ask.
You've caught me in a good mood, Chris, so I won't cut you off at the ankles. I'll give you a FINAL chance to open your ears & learn a little bit.
Let's discuss for a moment this reply of yours. And I'll explain where you are misunderstanding. I'll also explain where NIST kinda/sorta screwed the pooch. (With a generous explanation as to why.)
Look at NCSTAR1-9, vol 2, Figure 12-77, page 603, (pdf pg. 265)
This is the graph that you are insisting shows that "the north face descended at free fall acceleration".
He did not explain away the fact that ... WTC 7 fell at free fall acceleration for 105 feet!
On NIST 1A pg 45 it says:
"In Stage 2, the north face descended at gravitational acceleration"
This is another way of saying "free fall acceleration"
They continue:
"This free fall drop continued for approximately 8 stories or 32.0 m (105 ft)"
The entire building* fell at free fall [gravitational] acceleration for 105 feet.
* 9-1 Vol.2 pg 588 [pdf 250]
"the entire building above the buckled-column region moved downward as a single unit, resulting in the global collapse of WTC 7."
It does NOT say that the building "fell at free fall [gravitational] acceleration for
THE FIRST 8 stories (105 ft)".
In fact, the building does NOT fall at free fall acceleration for THE FIRST 105 feet. Or for the first 2 seconds. It falls near "G" for the time between 2 seconds & 4 seconds. Between 0 & 2 seconds, it falls at dramatically "lower than G" acceleration.
Try to understand this. It is rudimentary.
Figure 12-77 is a velocity versus time graph. The SLOPE (i.e. the steepness) of any velocity vs. time graph at any given point gives the instantaneous value of the acceleration at that point.
Now look at Fig 12-77 again.
The black line is the velocity. The slope of the black line at any time is the acceleration at that time.
Between 0 and 2 seconds, the slope of the black line starts out close to zero (virtually horizontal) and gradually increases to a value that causes the curve to run approximately parallel to the straight (i.e., linear) red line.
Now look at the red line. It's equation is given in the box in the lower right as v(t) = -44.773 + 32.196t.
Do you see that "32.196" number. That is the SLOPE of the linear (red) curve. Since the velocity is given in (ft/sec) and the time is given in (seconds), that means that the slope of that line is calculated to be 32.196 feet/sec^2.
Guess what the acceleration of gravity is, Chris. At sea level, it is just about 32.2 ft/sec^2. (It varies slightly, due to altitude, latitude & local masses.)
Next, do you see that "-44.773" number, Chris. That number tells you INSTANTLY that what you have been assuming (that it fell at G for the
FIRST 105 feet) is wrong. If what you said were true, that -44.773 number would be zero. And the red line would go thru the origin (0,0) of this graph.
__
Now look at the "power equation" (velocity as a function of time) given in the upper left corner of the Figure.
v(t) = 247.52 (0.18562 t)
2.5126 e
[-(18562 t) 3.5126]
This is an empirical "best fit" equation. It fits the data points pretty well between 0 and 4 seconds. Above 4 seconds, it goes to hell. This curve is singularly meaningless, EXCEPT that we can use it to numerically calculate the real value of the acceleration for the first couple of seconds.
Taking the time derivative of this equation gives you:
(c'mon, Chris. It's calculus. It's fun.)
a(t) = c1*c2*c3*e
(-c2*t)c4) * ((c2*t)
(c3-1)) - c1*c2*c4*e
(-c2*t)c4 * (c2*t)
(c3+c4-1)
where {c1, c2, c3, c4} are the constants used in the empirical equation {247.52, 0.18562, 2.5126, 3.5126} respectively.
Plugging in the values for time between 0 and 3 seconds (at 0.5 second intervals) gives you:
Time | Accel
(sec) | (ft/sec^2)
0.0 | 0.00
0.5 | 3.17
1.0 | 8.98
1.5 | 16.2
2.0 | 23.9
2.5 | 30.6
3.0 | 34.4
3.5 | 33.4
4.0 | 26.3
.
Note that the math agrees with the visual of the curve. The acceleration starts very low and increases to a value CLOSE TO (slightly greater than) the value of G (32.2 ft/sec^2).
This is real, Chris. These are the real values of the downward acceleration of the North Wall, after it starts to fall.
Now I repeat what I knew before, and you didn't understand. It does NOT fall at "G" as soon as it starts to collapse. There is a substantial resistance to falling for the first 2 seconds. It falls much slower than "G". The acceleration increases, until for a 2 second interval from 2.0 seconds to 4.0 seconds in this time frame, it falls slightly less than (i.e., near, not "at") "G". (Note: this interval is from 8.9 seconds to 10.9 seconds in the "standard, east penthouse" time frame.)
Are you starting to understand?
Do you want to continue to toss a temper tantrum? Or would you like to calm down a bit & learn?
Tom
NIST's mistakes on this curve are the following:
1. They never should have published their numbers to 5 decimal places. 3 TOPS. A generous interpretation is that the person who prepared this chart knew this, but couldn't figure out how to get MS Excel to only print 3 digits. (I've been there myself.) A less generous interpretation is that the person is a product of the "calculator generation" (instead of the "slide rule generation"). Calculators deny a person a visceral understanding of the "imprecision of experimental data".
2. The empirical exponential equation is meaningless. They shouldn't have included it. This is an example of a kid who put the equation in there because he COULD put it in. Not because it meant something. The curve itself is OK, but they should have truncated it above 4 seconds.
3. The data point at 1.75 seconds is an outlier. It should not have been included in the linear data regression. This is an "artistic" call. My art is better than this graph-author's art.
