Freefall?

[babazaroni]

Ah...the light bulb just went on and I understand why this makes you see she's a dental engineer.

Teeth have roots.
Trees have roots.

Mohammed Atta was seen at a 7-11 in Venice Florida buying a box of Keebler Tollhouse cookies prior to 9/11/2001.

It's all clear...

Some dental hygienists now use lasers as well. Just scale up, mount in WTC 7 and it all make sense.

 

[Mr.D]

OK, haven't pulled out the back of the envelope in a while so here goes.(Newtonian, frictionless universe ... blah blah ...)

Starting with zero velocity, an amount of energy 'P' used to accelerate a mass 'm.' What is the final velocity of the mass? We can solve that problem using the definition of Kinetic Energy.

P -> KE = (1/2) mv^2

P = (1/2) mv^2
v = sqrt(2P/m)

Now, assume the energy is applied to the mass in such a way as to cause uniform acceleration 'a.' What is the velocity of the mass as a function of time during the acceleration? We are told v(0) = 0, so this is simply

v(t) = at

Now, how long does it take the mass to reach final velocity? All of the energy 'P' is now kinetic, so we can equate the two equations and find

at = sqrt(2P/m)
t = sqrt(2P/ma^2)

Quick check: Suppose the initial energy is gravitational potential energy. The equation tells us that a mass 'm' falling a height 'h' through a uniform gravitational field with acceleration 'g', will take t = sqrt(2h/g).

Whew. Even has the right units.​

Now, suppose this energy is applied for a fixed length 'H' along the track of the mass. Find the acceleration.

H = x(0) + v(0)t + (1/2)at^2
H = (1/2)at^2
a = 2H/t^2

And find the time it takes for such a mass to travel that distance 'H' as a function of the energy 'P' and distance 'H'

P = (1/2)mv^2
P = (1/2)m(at)^2
P = (1/2)m(2Ht/t^2)^2
P = 4m(H/t)^2

t = sqrt(2mH^2/P)

Quick check: Suppose P is entirely gravitational Potential energy. Then t = sqrt(2mH^2/mgH) = sqrt(2H/g).​

Some of the 9/11 deniers would have us believe that controlled demolition explosives would cause the towers to fall 'faster than freefall.'

So let's ask; How much explosives for how much faster?

let To = "Official Time" = the time it took the towers of mass "M" to fall a height "H" due only to the effects of gravitational potential energy 'Po'

let Tc = "Conspiracy Time" = the time it took the towers of the same mass to fall the same height due to gravity plus explosives. (Assumption: the mass of the explosives is negligable). Let the energy of the explosives that contributes to the downward fall = 'Pe'

To = sqrt(2mH^2/P)
Tc = sqrt(2mH^2/(Po+Pe))

So the "Conspiracy Ratio" of "Conspiracy Time" to "Official Time" 'R' is

R = Tc / To = sqrt(Po / (Po + Pe))

Now, calculate as a fraction the amount of explosive energy 'Pe' for a given 'R'

R^2 = Po / (Po + Pe)
(Po + Pe) = Po / R^2
Pe/Po = (1/R^2) - 1

Quick check: both sides dimensionless, The ratio is zero when R = 1.​

Now the fun part. (Thanks for your patience)

The usual numbers cited are something around Po =~ 250 tons of TNT.

So how much explosive energy Pe would be required to cause a WTC tower to fall

5% 'faster than freefall?': Pe / Po = (1/.95^2) - 1 =~ 0.108 --> =~25 tons of TNT equivalent.

10% faster?: Pe / Po = (1/.9^2) - 1 =~ 0.235 --> =~58 tons of TNT equivalent.

'Twice' as fast?: Pe / Po = (1/.5^2) - 1 =~ 3 --> =~750 tons of TNT equivalent.

and the above equivalent tonnage is only valid if the explosives are essentially 100% efficient in directing energy down onto the building structure AND 100% efficent in converting that energy into kinetic energy (AND almost certainly violating conservation of momentum in the process.)

Ain't high school physics fun?

 

[William Rea]

from
Scholars for 9/11 Truth; Why Doubt 9/11?

OK, just doing a quick calculation and adding it up bear with me...(tapping noises from keys on spreadsheet)...Hmm yeah, OK, I make that a total of one source quoted! I can't believe that because it wouldn't be like you guys to take one snippet of information and use that as a basis to debunk the whole set of data would it?

 

[einsteen]

I think this is what has been observed in the beginning, before the cloud covers the 'pancaking'

a_wtc1=(2/3)g
a_wtc2=(3/4)g

 

[Brainache]

OK, just doing a quick calculation and adding it up bear with me...(tapping noises from keys on spreadsheet)...Hmm yeah, OK, I make that a total of one source quoted! I can't believe that because it wouldn't be like you guys to take one snippet of information and use that as a basis to debunk the whole set of data would it?

Well given that it's from Scholars For 9/11 Truth (you know the people that are always trotted out as experts who agree that 9/11 was an inside job) I think it is fair to say they are fairly influential in the Truth Movement (or they were until Scooby blew their cover as Disinfo agents).

Did you miss the other post refering to Loose Change? Another bunch of people who cast a big shadow in Truther land.

Oh and there is always Christophera. I don't understand why that guy isn't more popular with the Truthy set.

 

[westprog]

http://blog.abovetopsecret.com/wecomeinpeace/2006/06/911_disproving_the_wtc_pancake.html

This site does a lot of calculation which ends up showing that the expected collapse time is almost exactly the same as the observed collapse time. Which they then claim is impossible. Note the vast list of numbers.

 

[Dave Rogers]

http://blog.abovetopsecret.com/wecomeinpeace/2006/06/911_disproving_the_wtc_pancake.html

This site does a lot of calculation which ends up showing that the expected collapse time is almost exactly the same as the observed collapse time. Which they then claim is impossible. Note the vast list of numbers.

Brilliant. Observed collapse time = 15 seconds, predicted collapse time >= 14 seconds, therefore the towers fell too fast. The best piece of self-debunking I've seen since the PentaCon.

Dave

 

[eeyore1954]

This is probably the worse comparison I have ever seen:

"The towers are exploding from the top, not collapsing to the ground, where the floors do not move, a phenomenon that Judy Wood has likened to two gigantic trees turning to sawdust from the top down, which, like the pulverization of the concrete, the official account cannot possibly explain."

No wonder she's a Dental engineer.

I wouldn't let her do any engineering on my teeth.

 

[Unfit4Command]

Brilliant. Observed collapse time = 15 seconds, predicted collapse time >= 14 seconds, therefore the towers fell too fast. The best piece of self-debunking I've seen since the PentaCon.

Dave

The North Tower fell too slow.

There's 15 seconds, still more to go. I wish I would have seen this 14 second prediction earlier, they did a great job debunking themselves.

 

[Pipirr]

I wondered about the free-fall 'problem' for a long time. CTers kept on spouting it and I was never convinced there was a problem with how the towers fell at the speed at which they fell.

What I still wonder about is where the whole idea came from. Before Loose Change, was anybody really suspicious about the speed the towers fell? And even in Loose Change (not that I want to go back and check), the narrator didn't really specify a problem. "The towers fell at near free-fall speed", is all that I recall was said. I'm still waiting for the exposition.

So did Loose Change invent this meme, or was it out there all along, just waiting for the movie to give life to it?

 

[Gravy]

OK, just doing a quick calculation and adding it up bear with me...(tapping noises from keys on spreadsheet)...Hmm yeah, OK, I make that a total of one source quoted! I can't believe that because it wouldn't be like you guys to take one snippet of information and use that as a basis to debunk the whole set of data would it?

Is intellectual sloth really a virtue where you live?

 

[sophia8]

Thanks, Gravy - saved me the trouble. I started this thread because every single forum or blog where 9/11 is discussed always has a comment from at least one CTer - often a dozen or more - saying "But it fell faster than free-fall, man!" without presenting any maths or other prooofs.
They seem to think that merely repeating this mantra somehow proves that 9/11 was all a gubmint conspiracy.

 

[Darth Rotor]

OK, just doing a quick calculation and adding it up bear with me...(tapping noises from keys on spreadsheet)...Hmm yeah, OK, I make that a total of one source quoted! I can't believe that because it wouldn't be like you guys to take one snippet of information and use that as a basis to debunk the whole set of data would it?

William, from a previous post on simple equations.

Displacement (d) = 1/2*at^2. ________ Velocity (v) = at

Use 417m for height of building, Time to fall calculation in a vacuum, to street level.

Distance fallen = 417m = 1/2 at^2 (Get rid of the 1/2, multiply both sides by two)

834m = at^2 ( To find t, divide both sides by a, which is 9.8m/sec^2))

(834m)/(9.8m/sec^2) = t^2 ( Meters cancel out by simple division, and sec^2 ends up in the numerator on the left. )

Units match: 834sec^2/9.8 = t^2 (Take the square root)

sqrt(834sec^2)/9.8) = t = 9.225 seconds freefall in a vacuum.

But we are not working in a vacuum. A body accelerating in a fluid (air) will accelerate until it reaches terminal velocity, after which point it will fall at a constant velocity. Terminal velocity of a body falling in air. (See discussion at the end) offers a usable range of values between 54 m/s (a high drag body, not aerodynamicallly shaped) to 90 m/s (a streamlined body.) I'll use a skydiver for modeling purposes, since the numbers are easily available, and a skydiver in high drag mode represents an irregularly shaped, non streamlined body falling in air.

For a stream lined body, similar to a skydiver presnting his body to the relative airstream in the most aerodynamic shape possible, or wrapped into a ball, or approaching the streamlined Gyrefalcon in a dive, you reach terminal velocity (v=at) at roughly 90/9.8 = 9.18 seconds, which is almost the end of the vacuum fall timeline. (9.225 seconds) Are all pieces as streamlined as a falcon or a "tucked" skydiver in a dive: no. If all pieces are streamlined, they hit the ground in roughly 10 seconds. Irregularly shaped chunks of building are not streamlined, so let's use a high drag form, with a terminal velocity of 54 m/s for a "slowest case" fall.

The body reaches terminal velocity om about 5.5 seconds? v = at so v/a = t.

54/9.8 = t

t = 5.5 seconds.

That is just over half of the time of a non decellerated body falling. The v^2 component of air resistance increases from time 0 to time of V(terminal onset). (My problem set up for the differential equation is rusty, with v known and the sum of a and a' (a' being air resistnance in vector opposition to a) being a function of v^2.

d = 1/2 at^2 for how far this drag friendly body falls before reaching terminal velocity. After that, it falls at a constant rate, rather than being accellerated all the way to impact like in the vacuum example.

1/2*9.8*(5.5)^2 = d = 148.225 meters.

After reaching this speed, the non streamlined body falls at 54 m/sec.

417 -148.225 = 268.775 meters to fall.

Divide that by 54 m/sec and you get 4.977 seconds, which we can round up to 5.

So, it takes roughly 5.5 + 5 seconds = 10.5 seconds for a non streamlined body falling against air resistance at sea level to hit the ground from the top of the WTC. The engineers have estimate something near 13 seconds. I expect this is dependent on both their use of integration to account for drag = 0 and v= 0 at time 0, and drag = x at v = Terminal at time = Time of achieving terminal velocity, when a =0. The decision on which coefficient of drag to use can be made mass dependent if you set a = 0 when v = 54 m/s (forces summed) and using a kv^2 convention, yield k (coefficient of drag and other factors) = .00336.

The drag friendly terminal velocity provides a close enough approximation of worst/slowest case, particularly when the dust cloud obscures observation and precludes a lab quality observation and calculation.

In layman's terms, between 9 1/4 to 11 seconds to hit the ground, depending on the shape of the chunk falling.

(Engineer or math majors are invited to demonstrate the simple integral to solve for a more precise t(vterminal) and thus refine my gross estimate of 5.5. seconds as the time to achieve terminal velocity from v = 0 at the top, where a1 = 9.8m.sec^2 and a2 = 0) I am too far from school to give you the precise problem set up, as I am looking to make mass and cross section neutral for the sake of the problem, and combine those and air resistance/drag coefficient in to a generic constant k.)

For example, the terminal velocity of a skydiver in a normal free-fall position with a closed parachute is about 195 km/h (120 mph or 54 m/s). This velocity is the asymptotic limiting value of the acceleration process, since the effective forces on the body more and more closely balance each other as it is approached. In this example, a speed of 50% of terminal velocity is reached after only about 3 seconds, while it takes 8 seconds to reach 90%, 15 seconds to reach 99% and so on.

Higher speeds can be attained if the skydiver pulls in his limbs (see also freeflying). In this case, the terminal velocity increases to about 320 km/h (200 mph or 89 m/s), which is also the maximum speed of the Peregrine Falcon diving down on its prey.

From UVa "How Things Work" "A person has a terminal velocity of about 200 mph when balled up and about 125 mph (56 - 89 m/s) with arms and feet fully extended to catch the wind."

DR

 

[pgwenthold]

Probably the dumbest part of the whole "faster than freefall" bit is that none of the 9/11 deniers have ever demonstrated (or even plausably argued) that controlled demolition explosives would result in a collapse that was "faster than freefall."

This needs to be reiterated (again and again and again).

If they want to claim that the collapse time indicates a CD, then they should show examples of CD that illustrate a collapse time faster than free fall (or near free fall). They won't, of course.

This is just like the thermite claim. Show me what a thermite-driven CD looks like so I can compare the two. Oh wait, that's never happened, either.

Like thermite, I'm guessing this "faster than freefall" collapse has never been observed for real CDs, either.

 

[William Rea]

Is intellectual sloth really a virtue where you live?

267 hits on Google isn't terribly impressive is it.

I get 11 million hits for "gravy".

You're telling me that a Google search like that is intellectual rigour? Laughable.

 

[William Rea]

William, from a previous post on simple equations. ....for the sake of the problem, and combine those and air resistance/drag coefficient in to a generic constant k.)DR

As RWGuinn would put it thanks for the Freefall101.

Your application of terminal velocity is frankly over elaborate and just bored me but, for future reference the value of g for the New York area is 9.802 m/s^2

http://www.internationalskeptics.com/forums/showpost.php?p=2099718&postcount=7551

 

[A W Smith]

Move goalposts much?

267 hits on Google isn't terribly impressive is it.

I get 11 million hits for "gravy".

You're telling me that a Google search like that is intellectual rigour? Laughable.

No. This is laughable! Apparently gravity has speed now.

World Trade Center Seven fell faster than the speed of gravity. This is only possible when a vacuum has been created through the use of explosives

EDIT to add. Holy {rule 8] how couild i miss this in the above description

only possible when a vacuum has been created through the use of explosives

You know what? Your explosives really must suck.

 

[Panoply_Prefect]

This is just like the thermite claim. Show me what a thermite-driven CD looks like so I can compare the two. Oh wait, that's never happened, either.

Like thermite, I'm guessing this "faster than freefall" collapse has never been observed for real CDs, either.

Did ANY of the CT sites ever even at least try to explain how thermite could cut sideways, as per the image used by Steven Jones et. al?

These two assertions, thermite and freefall is used by all of the truthers equivalence of script-kiddes, but I have so far never seen a reasonable explanation how thermite could do that. I was under the impression thermite worked by gravity, downwards.

Cheers,
SLOB

 

[PhantomWolf]

These two assertions, thermite and freefall is used by all of the truthers equivalence of script-kiddes, but I have so far never seen a reasonable explanation how thermite could do that. I was under the impression thermite worked by gravity, downwards.

I think most of the 9/11 movement is just based on making assertions that have no basis in reality isn't it?

- Freefall speeds (no they fell in 15-20 seconds, not 9-10)
- Pools of Molten Metal (never proven rumour and heresay)
- Sideways burning Thermate (yeah right)
- Silence kicker charges (Okaaaaaay)
- No big fires in WTC 1,2,7 (Only 6-7 alarm ones on multiple floors)
- No damage to WTC 7 (except that big hole in the south face)
- No aircraft parts at the pentagon (Other then those bits all over the lawn)
- No aircraft parts at Shanksfield (except the 95% of flight 93 that was recovered)

and when it's shown their assertions are wrong they simply fall back onto their standard "It was planted," "They are lying" claims.

 

[programmer]

Hi, I am new to this forum.
I would like to address some of the topics of this thread, hopefully you will consider them objective.

1. About the claim "faster than the speed of gravity": This certainly is a wrong representation of the whole picture, as it can be seen that the mayority of the mass takes about 15 seconds to complete the collapse. However, it would be very important if somebody measures the speed of the initial collapse (i.e first seconds) and prove that it was not faster than gravity.
2. As some of you pointed out, gravity provokes acceleration, not speed. However, there is a fixed speed increase associated with gravity.
3. The link provided here about the 15 second collapse includes the following vital assumption which is missing in this thread: "Resistance from the structure is zero. As in, there are no vertical columns, and no assembly connections. (point 4 in link) This supports the claim intended by the author.
4. I googled a little on Dr. Judy Woods and cannot find a reference to dentistry, can anybody here please provide this? Thanks.
- What I found is her bio: janedoe0911.tripod.com/Wood_Bio.html
- Found a paper at VirginiaTech about steel: scholar.lib.vt.edu/theses/available/etd-06072006-124140/

Please debate