Speed of WTC7 Collapse
How fast did WTC 7 Fall?
The NIST plot of the downward movement of WTC7 measures acceleration at greater than freefall for a short period of time just after the beginning of movement.
NIST's WTC 7 collapse velocity function is given on page 603 of NCSTAR 19:
v(t) = 247.52(0.18562t)^2.5126 exp[(0.18562t)^3.5126]
The function can be differentiated to determine the acceleration. When done, a 2 second period of greater than freefall acceleration is discovered.
The NIST position graph is examined
here
Since the NIST measurements, more accurate measurements and analysis have shown various mistakes in the NIST measuring technique and a complex interplay between early core downward movement and inward perimeter flexure.
3 key mistakes by the NIST were:
1) The poor choice of a t=0 starting point. Penthouse and perimeter begin to move down at slightly different times. Each has a separate t=0 starting moment. The t=0 problem is discussed at the link above. A small variation of the beginning of motion results is sizable changes in acceleration measurements.
2) Mixing traced points on the penthouse with those on the perimeter roof. Since the penthouse falls before the perimeter, blurring points would produce misleading data. Early acceleration measurements would be artifically stretched producing lower measured accelerations. This indeed happens in the NIST measurements. A point is traced along the roofline as the penthouse starts to move.
3) Inclusion of both horizontal and vertical components to the earliest observed motion.
Inward flexure of the perimeter as the penthouse starts to fall means that the earliest movement along the perimeter roofline is horizontal, not vertical. If it is considered as vertical motion, a false t=0 downward descent start time will be used and downward motion will be measured artifically early.
Each mistake is explained
here
The best measurements and analysis of WTC7 early downward movement available.
Measurement of greater than g acceleration of the NW corner
here
Effort to determine early downward acceleration while correcting for horizontal component of early motion
here
The collapse, especially the onset, is too rapid to be the result of natural failure
Why? Because if we compare the fall with any of the following:
1) fall times of known demolitions.
2) computer simulations of collapsing buildings.
3) estimates of fall times applying physics.
especially during the first 3 seconds of collapse, all methods show WTC 7 to fall much faster than what demolitions or other models predict.
Accelerations approaching freefall for a brief period during the first 3 seconds of collapse were measured by many researchers including the NIST.
This means, expecially during the first 3 seconds of falling, the building provided almost no resistance to being destroyed.
Even in known cases of buildings being destroyed intentionally during demolitions, initial accelerations are measured to be noticably less than that of WTC 7 as the next section explains.
Comparing the fall speed of WTC 7 to that of known demolitions.
In the thread topic
"Did WTC7 fall too fast?", Dr G compares the roofline fall of known demolitions with WTC7 using data in the paper of E Yarimer. From the thread:
E. Yarimer at London University appears to be one of the few engineer/scientists who has studied real building demolitions by explosives. He has at least two papers on this subject, both written back in the 1990s, (and unfortunately hard to find on the web).
Here is a quote from the first (1994) paper:
“The current practice in controlled demolition (CD) by explosives is to preweaken the building on most floors, and to blast only a portion of the floors, for example one floor in two, or one floor in three. Even so, the number of charges to be placed in individual boreholes can be large: up to 6000 charges have been used depending on the size of the job. The blast floors will readily disintegrate, but the nonblast floors need the force of the impact in order to breakup. Even on the blast floors, the perimeter walls above the ground floor are usually not charged for safety reasons, and they are expected to break up by impact. The entire process is driven by gravity but the downward velocities are attenuated by the energy absorption at the point of impact, and the motion will accelerate less than a case of free fall; it may even decelerate. A spectacular case of decelerating motion was that of Northaird Point in London in 1985, which came to rest with 10 floors still intact.”
In his second, (1996) paper, Yarimer used electronic and photographic timing devices to study a number of real CDs. One of great interest to the present discussion was the 1995 demolition of a 20story highrise known as Sandwell East Tower. This demolition showed  as was observed for some other CDs studied by Yarimer  a latency period of ~ 1.5 seconds before significant bulk motions were detected.
I have taken Yarimer’s data to look at the accelerations for the Sandwell East Tower CD. Some timedrop data for the first 5 seconds are: 0 s, 0 m; 1 s, 0 m; 2 s, 1.8 m; 3.0 s, 10 m; 4.0 s, 22.3 m; 5.0 s, 35.9 m. These data show the collapse was well below free fall. Indeed, Yarimer states in his discussion of this data: “Near time t = 0, the calculated accelerations are influenced by the observed latency, thus lifting the estimate of the upwards reaction force.” It appears that even Yarimer had t(0) problems!
Nevertheless, I have analysed Yarimer’s data (with allowance for the t(0) problem) using the same approach many of us have applied to WTC 7 collapse data. What is most significant is that, even with a time shift of ~ 1.5 seconds, the Sandwell East building fell only about 40 meters in the first 4 seconds of bulk motion with an acceleration of no more than 5 m/s^2. And let’s remember that this was observed for a realworld CD on a 20story building. Scaling this result to a 47story, (WTC7sized building), I would predict a 50 % collapse to take at least 6 seconds and allowing for a latency period of about 1.5 seconds, a full collapse to take ~ 10 seconds or more.
Thus we see experimental and theoretical confirmation that the global collapse of a 20story building would take at least 10 seconds to partially collapse from deliberate manmade explosive or natural seismic trauma to lower portions of its structure.
We thus see that even known demolitions fall slower and have a much smaller initial acceleration than we witness in WTC 7.
(end of quote).
The papers mentioned are
"Factors Affecting the Numerical Modelling of Demolition by Explosives" In Transactions on the Built Environment, Vol 8 (1994)
"The Effect of Rubble Accumulation on the Mechanics of Demolition by Rapid Collapse" In Structures Under Shock and Impact IV. (1996)
Other papers are
YARIMER, E and LAPA, J.A.M.  "A Numerical Model for Demolition of Buildings by Explosivess", in Structures under Shock and Impact, SUSI1996, Italy (submitted).
YARIMER, E and LAPA, J.A.M.  "Factors affecting the Numerical Modelling of Demolition by Explosives", in Structures under Shock and Impact, SUSI1994, Madrid.
LAPA, J.A.M. and BROWN, C. "Demolition of Structures by the Use of Explosives", Curso da Ordem dos Engenheiros, Coimbra, 1995
.
Comparing the fall speed of WTC7 to computer simulations of falling buildings.
From the same forum thread Dr G writes:
D. Isobe et al. have carried out finite element calculations on a 20story steel framed building subjected to a Kobewave type of seismic collapse. Isobe found that incremental collapse begins
after an initial 26second period of vibration during which time plastic hinges are formed and column fractures occur near the ground level of the building. The modelled structure was 50 % collapsed about 10 seconds after the first bulk downward motion, and still only about 35 % collapsed after 14 seconds!
The link to his simulation is
here
If we compare the estimated fall time of a 20 story building in a large earthquake, it falls much less rapidly than WTC7, a 47 story building.
.
Comparing the fall speed of WTC7 to estimates applying physics (analytical models and solutions)
Another very good way of seeing the contradiction in WTC7 fall time is in the OP of the
A Building 7 Collapse Conundrum thread where Dr G asks,
A Building 7 Collapse Conundrum:
Continuing with the question of how fast Building 7 could possibly have collapsed I wish to present here a few more thoughts on this topic. While this obviously overlaps some existing threads I hope it offers something new and specific about the theory and observational data for WTC 7 collapse times.
Let’s assume that the columns supporting a lower floor of Building 7, say floor 8, suddenly failed (by some unspecified mechanism) allowing the 39 floors above to start moving down as a solid block without any significant resistance. Eventually the 9th floor would impact the 8th floor. Let’s assume that the columns supporting the 8th floor were very strong so that the 9th floor was completely stopped by the lower part of the building.
Consider now the motion of the 9th floor. Although the floortofloor height in Building 7 was close to 4 meters, a freely descending floor would nonetheless have to meet significant resistance well before it had fallen the full floor height. If you think of a typical office in a modern highrise building there is a lot of furniture, partitions, computer hardware, printers, bookshelves, filing cabinets, water coolers, etc, on more or less every floor. This office “live load” is typically about 1 meter tall and we can reasonably assume it is crushable only down to an average height of about 25 cm. Thus we see that a collapsing floor will always be decelerated over a distance of about 0.75 meters. And while a free fall drop of 4 meters takes 0.903 seconds and reaches a velocity of 8.86 m/s, our collapsing 9th floor will of necessity take longer and be moving a little more slowly than in the case of an ideal floor dropping under free fall.
In order to make a rough estimate of the motion of a collapsing floor under these circumstances let’s assume that office live loads present a constant retarding force, starting after 3 meters of free fall, that brings the floor to rest after 3.75 meters. Thus for our collapsing 9th floor we have initial free fall motion for a time of Sqrt[6/g] = 0.782 seconds, by which time the descent velocity had reached 7.67 m/s. We now need to calculate how long it would take the 9th floor to come to rest after crushing everything on the 8th floor down to a compresses mass 0.25 meters tall. Because we have assumed a constant retarding force we must have a constant deceleration, a. It follows that the stopping time is (7.67/a) seconds. We can then use the relation v^2 = 2a.s, where s is the stopping distance of 0.75 meters, to find a. Substituting appropriate values into these equations we have a = v^s/2s = (7.67)^2/1.5 = 39.2 m/s^2, or a deceleration of the 9th floor of close to 4g’s, and the stopping time of 0.196 seconds.
We need to compare this time to the time to go from 3 to 3.75 meters under free fall, which is 0.092 seconds. Hence we see that the crushing of the office live loads adds 0.104 seconds to the 9th floor collapse time. Working backwards, we find that the average acceleration over the 9th floor collapse would have been (2 x 3.75) / (0.782 + 0.196)^2 or approximately 7.84 m/s^2, which is significantly less than g.
Something I have glossed over in this analysis is the question of what happens to the floors above the 9th floor during its collapse onto the 8th floor. There are two limiting cases to consider:
(i) The upper floors sequentially loose their support columns at the instant the retarding force kicks in, (as in a controlled demolition!). For this case we can simply repeat the calculation presented above but with an initial velocity calculated from the final velocity of the upper block before retardation sets in. Based on the need to crush live loads on every floor this can only further delay the collapse, leading to a collapse acceleration well below g.
(ii) The upper floors resist further collapse as in WTC 1 & 2. Here we need to consider the energy to collapse one floor and this would certainly be at least 0.5 GJ. In this case the overall collapse acceleration is going to be in the 5 " 7 m/s^2 range or significantly less than g.
Thus the conundrum I set readers of this thread is to explain the physics behind measured WTC 7 collapse accelerations “close to g”, namely in the range 8.8 to 9.8 m/s^2.
Good question which nobody has/could answer.
How fast did WTC 7 Fall?
The NIST plot of the downward movement of WTC7 measures acceleration at greater than freefall for a short period of time just after the beginning of movement.
NIST's WTC 7 collapse velocity function is given on page 603 of NCSTAR 19:
v(t) = 247.52(0.18562t)^2.5126 exp[(0.18562t)^3.5126]
The function can be differentiated to determine the acceleration. When done, a 2 second period of greater than freefall acceleration is discovered.
The NIST position graph is examined
here
Since the NIST measurements, more accurate measurements and analysis have shown various mistakes in the NIST measuring technique and a complex interplay between early core downward movement and inward perimeter flexure.
3 key mistakes by the NIST were:
1) The poor choice of a t=0 starting point. Penthouse and perimeter begin to move down at slightly different times. Each has a separate t=0 starting moment. The t=0 problem is discussed at the link above. A small variation of the beginning of motion results is sizable changes in acceleration measurements.
2) Mixing traced points on the penthouse with those on the perimeter roof. Since the penthouse falls before the perimeter, blurring points would produce misleading data. Early acceleration measurements would be artifically stretched producing lower measured accelerations. This indeed happens in the NIST measurements. A point is traced along the roofline as the penthouse starts to move.
3) Inclusion of both horizontal and vertical components to the earliest observed motion.
Inward flexure of the perimeter as the penthouse starts to fall means that the earliest movement along the perimeter roofline is horizontal, not vertical. If it is considered as vertical motion, a false t=0 downward descent start time will be used and downward motion will be measured artifically early.
Each mistake is explained
here
The best measurements and analysis of WTC7 early downward movement available.
Effort to determine early downward acceleration while correcting for horizontal component of early motion
here
Measurement of greater than g acceleration of the NW corner
here
Created on 10/01/2009 10:41 AM by admin
Updated on 05/09/2011 03:13 AM by admin

