posted on Nov, 22 2009 @ 05:27 AM
Note that in some of my earlier posts in the 9/11 threads, I also unwittingly misused the term 'free fall speed', until one day I realised what I
had typed, slapped myself in the face and started to think properly. I am sure that I can be quoted in older posts where I have misused this term.
Good luck to you if you find one, I'll be happy to admit where I incorrectly used the terms in the past (probably nearly a year ago or more).
There are a couple of threads that I have been reading today, where I have seen both truthers and official government story believers, misuse the term
'free fall speed'.
I'll work in standard units, metres, kilometres and seconds. I've got no love for imperial units. Stick your feet and inches where they fit.
Free Fall Acceleration and Air Resistance
Acceleration by gravity is near enough to 9.8 m/s^2. It is not constant, but is close enough to being constant for the heights of the towers.
Air resistance will mean that objects experience resistance to the acceleration by gravity. Most models for air resistance start to become a little
messy, requiring differential equations to be solved. For the sake of simplicity and recognising that air resistance will affect the results a
little, we shall ignore it.
Initial Velocity
Note that the terms velocity and speed are not the same. Velocity is a directed vector, whereas speed is the magniture of the velocity.
Considering that the motion of the towers was basically a one-dimensional, directed collapse, it is somewhat acceptable to interchange the terms speed
and velocity, along with distance and displacement.
Stand at the top of a WTC tower with a brick in each hand. At the same time, let the left hand brick go and throw the right hand brick down. Both
are falling with the same free fall acceleration, but they have different initial speeds. Of course the right hand brick will hit the ground first,
as it has been thrown down.
I have seen some people claim that the right hand brick would be travelling faster than 'free fall' ... which doesn't really make sense, as the
right hand brick is travelling at free fall acceleration with an initial speed.
Parts of the WTC perimter sections appear to be ejected with a downward vertical velocity component, not merely tumbling downwards from rest. Of
course they appear to travel faster than the rest of the collapsing tower, as they have an initial speed. Those ejected sections are still falling
with free fall acceleration.
WTC 1&2
The WTC 1&2 towers were near enough to being 415m high.
Using s = ut + 1/2 at^2, it should take a dropped object 9.2 seconds to reach the ground from the top of the tower.
I kind of remember reading one report (FEMA?) that quoted a 10 second collapse time for the tower. I don't believe that figure, as I've seen videos
that take at least 15 seconds for the tower to collapse. Clearly, the tower took longer to collapse than a dropped object would take to hit the
ground.
We can calculate an average collapse speed for a dropped object.
v = s/t, gives 45.1m/s or 162.4km/h.
However, this is an average speed. Note that the only time the dropped object was travelling at that instantaneous speed was at 4.6 seconds
into its fall. The final speed of the dropped object, given by v^2 = 2as, is 90.2m/s or 324.7km/h.
As you can see, the term 'free fall speed' doesn't make much sense and states nothing about the initial speed of the object.
What I have not seen is a simple plot for the roofline of the WTC towers. A distance-time plot for a point on the roofline can be used to determine
the speed and the acceleration of the roofline's collapse, as that was 415m high and started from rest.
I've read claims that the roofline fell with free fall acceleration. I've also read claims that the roofline fell with linear displacement, meaning
a constant speed, meaning zero acceleration. Both can't be true.
Can anyone provide me with a distance-time plot for a point on a WTC roofline?
WTC 7
WTC 7 is a little different because NIST has provided us with more figures to work with. The height of the tower is near enough to 226m. A dropped
object will take 6.6 seconds to reach the ground. It will have an average speed of 34.2m/s (123.3km/h) and it will hit the ground with a final speed
of 66.6m/s (239.8km/h).
NIST modelled a point on the roofline from when it started to descend and broke the motion into three sections.
Section 1 was for t = 0 to t = 1.75 seconds, where the acceleration was less than free fall.
Section 2 was for t = 1.75 to t = 4.00 seconds, where the acceleration was the same as free fall.
Section 3 was for t = 4.00 to t= 5.4 seconds, where the acceleration was less than free fall.
It is plainly clear that the acceleration of WTC 7 was not constant for the entire collapse. However, for 2.25 seconds, there was a constant free
fall acceleration.
The term 'free fall speed' when used for WTC 7 is not appropriate.
Is the 'free fall speed' referring to an initial speed, a final speed or the average speed?
Anyway, it's been a long day and I haven't checked the calculations for accuracy beyond a decimal place.
Please pay careful attention to when and why you wish to use the term 'free fall speed' and if you're really thinking it through properly. There
is a distinct difference between the terms 'free fall speed' and 'free fall acceleration'.