The 9/11 Forum

SanderO wrote:I can't understand what Chandler could be tagging on the object... and at best it's the whole thing and this would ignore rotation... sort of a gross measurement at best.

I think that is the main issue of concern about the measurement.

The current discussion "in another place" seems to be down a funny side track distracted by "rotation".
Without doing any sums I cannot see that rotation would have anywhere near enough effect to put below G acceleration over G. The vertical falling distances are orders of magnitude greater than the length of the object.

Would this depend on the rate and axis of rotation? How many revolutions did the sectio make during the fall? Couldn't the motion be more complex than 1 axis rotation?

OneWhiteEye wrote:Amelius Brown's argument parroted, coincidentally by a parrot:

GlennB wrote:Welcome Amelius Brown and ... bingo.

Sorry, no. Not bingo. Ridiculous, in fact.

Good save by parrot:

GlennB wrote:True in itself, but from the outset I've been mostly looking at:

Marrokaan wrote:
David chandler:

"The object (apparently a perimeter wall unit) raced ahead of its neighboring debris, but its acceleration was about 1/3 of gravity. This is an indication that it was kicked downward initially by an explosion, after which the air resistance partially canceled the effect of gravity as it approached terminal velocity.

and been commenting on the origin of this original "sproing" of energy that got the unit "racing ahead".

That's true.

SnowCrash wrote:Didn't Chandler just manually pinpoint/encircle the entire object and then use the center of that circle as the reference point? And you Femr2? Just thinking out loud here.

It's difficult to say for DC's, as the trace marker reticule completely covers the trace location.

I've tried to ensure that the trace point is in "the CoG", not a rotating "extremity".

It's really rather moot, as "it" is a collection of fuzzy pixels, maybe about 6 of 'em, pixels that is.

I'll upload the visual trace shortly...

still a quick DRAAFT ...image processing to do before a fully automated trace is possible, so there are some wobbles...

ozeco41 wrote:Without doing any sums I cannot see that rotation would have anywhere near enough effect to put below G acceleration over G. The vertical falling distances are orders of magnitude greater than the length of the object.

That was my first thought, too, but this argument really depends only on the spatial resolution of the measurements. For the mechanics itself, it doesn't matter. It's when the length of the member corresponds to only a few pixels in the video the resolution is insufficient to detect acceleration variations. I believe this is what you're getting at.

Even a pencil dropped from 100km in a vacuum can exhibit 1.5g at an end, no matter how far it has dropped, no matter how fast it's going. If the shape can be resolved, then that's all that's needed. Can this be detected in a video? Not if the pencil length subtends an angle which is a pixel or less. There may be a pixel shift here and there, but the motion captured is not that of the tip, more the object as a whole and that's falling at g. Same holds true for a column.

More to come in a bit.


Appendix - The mechanics

Vertical position as a function of time for end of freely falling uniform rod of length L rotating about its center of mass (excluding air resistance):

y = y₀ + v₀t + 0.5gt² + 0.5Lsin(θ)

with θ = θ(t) being the angle between rod axis and horizontal axis.

Differentiating once with respect to time

v = v₀ + gt + 0.5Lωcos(θ)

where ω is the time derivative of θ, or the angular velocity. Assume angular velocity ω is a constant. Then rewrite the above as

v = v₀ + gt + 0.5Lωcos(ωt + φ)

with φ being initial phase angle, then ω is related to frequency f by ω = 2πf.

Differentiating again with respect to time

a = g - 0.5Lω²sin(ωt + φ)

The magnitude of acceleration due to rotation is 0.5Lω²sin(ωt + φ), obviously. Dependent on radial distance from center of rotation, the angular velocity and its current position.

Let's try to fit this (very roughly). Not only eyeball, but picking worst case deviations from the trend, making some assumptions, etc. At t₁ = 0.75 sec, v(t₁) = v₁ = 37 m/s. At t₂ = 1.65 sec, v(t₂) = v₂ = 50 m/s.

Δv = v₂ - v₁ = 13 m/s
Δt = 0.9 s

Average acceleration over this period is therefore Δv/Δt = 14.4 m/s² or about 1.5g, as Chandler states. So,

0.5Lω²sin(ωt + φ) = 0.5g
Lω²sin(ωt + φ) = g

If L = 11m, then it becomes (after plugging in g):

5.5ω²sin(ωt + φ) = 9.8
=>
ω²sin(ωt + φ) = 1.78


The value of the initial angle φ is unknown, but we can choose it so as to maximize acceleration. Note that the maximum possible value of sin(ωt + φ) is 1, and the RMS value is 0.707. Substituting 0.7 for the quantity, just for a rough look at the likely mean value over an arbitrary interval, it then becomes

0.7ω² = 1.78 => ω ≈ 1.6

This corresponds to a frequency of 0.25Hz, or angular velocity of 90 degrees per second. In the interval of interest, the total amount of rotation is then 0.9 * 90 = 81 degrees.

Whether it did actually rotate that much, or had the proper orientation (φ) needed, or whether the measurements are of sufficient resolution is another matter. That's about what it would take to produce an average over-g of 150%.

femr2 wrote:I've tried to ensure that the trace point is in "the CoG", not a rotating "extremity".

It's really rather moot, as "it" is a collection of fuzzy pixels, maybe about 6 of 'em, pixels that is.

Hard to put much onto rotation then.

femr2 wrote:still a quick DRAAFT ...image processing to do before a fully automated trace is possible, so there are some wobbles...

Great work so far Femr2...

OWE, very interesting explanation there, thanks for going in-depth. Almost feels like a shame it may have no bearing on the measurement.

OneWhiteEye wrote:

ozeco41 wrote:Without doing any sums I cannot see that rotation would have anywhere near enough effect to put below G acceleration over G. The vertical falling distances are orders of magnitude greater than the length of the object.

That was my first thought, too, but this argument really depends only on the spatial resolution of the measurements. For the mechanics itself, it doesn't matter. It's when the length of the member corresponds to only a few pixels in the video the resolution is insufficient to detect acceleration variations. I believe this is what you're getting at....

Not quite. Thanks for your explanation. My first reaction was a sort of mental gut feeling BEFORE I put brain in gear. Too confused still to explain at this time. I may try later.

It's teeny, but...



Increase your browser scale (ctrl and mouse wheel for firefox btw) to zoom in a bit.


As you can see, the rotation (with this processed view) does complicate trace location.

Where to put it ? Manually in the middle ? Follow one end, follow the other end, average them ?

Using the base video this was extracted from I've got a much cleaner velocity profile (and it's different to my earlier one ) but before I finalise, I thought I'd get opinion on the above.

Any objection to two traces, one following one end, the other the other, and avg'ing the two ?

femr2 wrote:Any objection to two traces, one following one end, the other the other, and avg'ing the two ?

No objections at all, sounds good.

femr2 wrote:...Any objection to two traces, one following one end, the other the other, and avg'ing the two ?

Seems a good way to progress it.

That latest gif shows a relatively constant rate of rotation.

If I took the little rocket stuff seriously, I'd look for odd alterations in the angular rotation.

I'd look for evidence of torque.
.....................

How can anyone strap a little rocket engine on a single column that is rotating and not wildly alter the rate of rotation as a result?

Major_tom wrote:How can anyone strap a little rocket engine on a single column that is rotating and not wildly alter the rate of rotation as a result?

One of the many reasons it's a hard pill to swallow. What was it? I try to believe 2π impossible things before breakfast, but only about eⁱ of them actually stick.

This is like WTC7 to me; a bit weirder, naturally. Why is this event associated with so much crackpot shit? I'm not talking about theories, I'm talking about observations.

---

Thinking out loud..

1) measurement error (or issues, if you prefer)
2) rotation
3) push from down-rushing air
4) propulsion
5) magnetism(!)

These are the choices. Did I miss any? Some are faring better than others. #5 hasn't been kicked around; surely that's got to come behind a stray magic oxygen tank as a rational explanation...

#3 I would like, but I think for air to push a column down means the smoke would be going down, too (and faster).

I put measurement problems at the top, along with the related rotation, because this seems most likely to me. We are talking position versus time from video. In this category, included are everything from video distortion to scaling and perspective. femr2 has done an extraordinary job of making a horrendous process seem shrinkwrap smooth on the outside - though it may still be quite a pain we don't hear much about - but there are inherent limitations, and it sounds like this case is not clear cut.

I'm sure I needn't remind you of the all discussions about measurement, interpolation, fitting and so on. My most recent take on it is a simple comparison between the above analysis and the same data with some sinusoidal error thrown in. This doesn't even account for the measurement process itself, since it's all analytical, neither does it treat issues like perspective however amenable they are to analysis.

The first graph shows what happens when you follow the prescription in my 'appendix' above with φ = 0 and angular rotation of 90° per second in a plane perpendicular to the optical axis, the tracking point fixed on the end of a 36 foot section. No air resistance. Blah, blah.



The solid line is position, the dashed is velocity, the (blue) dotted acceleration. The position appears very nearly parabolic. The deviation from a straight line with slope g is evident in the velocity curve. Finally, the acceleration is a large sinusoidal variation about g due to the rotation. The dotted red lines depict g and 1.5g acceleration.

The shaded area is the velocity range of interest in this topic. Notice the rotation causes an over-under g of the expected magnitude. It's obviously a sine wave when you look at the bigger picture, but not at all obvious when considering only the smaller shaded area.

Next, the same function has two sinusoidal components of 'error' added at a peak magnitude of less than 20% of the rotation component, one component at the same frequency in phase, the other twice the frequency out of phase - multiplied - but still very regular and synchronous with the original signal.



And both:



Putting them together, you can see that the position curve is very close, velocity a bit different, acceleration wildly different. There is no distortion, scaling, perspective, interpolation - it's all analytical with zero loss or error. This is like putting a recognizable face on error bands; you'll never see anything as regular or identifiable in the real world where there is true uncertainty.

And that uncertainty is amplified by taking differences.

The position curves are very, very similar. At the frame sizes, pixel rates, etc, we are talking about, these curves would be within a couple of pixels of each other at all times. Above the shaded area, where the curve is steeper, they appear to lay atop one another. Not to say the measurements aren't better than within a couple of pixels, it's just that a marginal video itself can easily have a couple of pixels worth of funk built into it.

As far as #4, propulsion, I have been allowing for the possibility despite any mistaken associations or conclusions drawn by Chandler. This is quite generous, though there may be some far-fetched avenues in cold exhaust - but that wouldn't serve the cause, would it? (it would also fail Major_Tom's objections)

Chandler associates the increase in smoke trail visibility with the acceleration bump and there is apparently a temporal association but there is also an unspoken implication that one would expect visible evidence of propulsive exhaust and that the smoke might be it. I do indeed expect to see such evidence, but I do not and the smoke is definitely not fitting the bill for more than one reason.

For propulsion, physics demands ejecting at least 30kg of material upward at near sonic velocity over a half second in time for the 4 ton quoted mass - adjust to taste. I can certainly see why Chandler might want the smoke to be the necessary evidence. I'm ready to kiss a propulsive mechanism goodbye, all open minded generousity aside.

#3? Like I say, pressure differential means moving air, in the direction of the gradient. There is a lot of fast moving stuff above which is pushing air out of the way, but the gradient must be shallow and the trailing smoke seems to confirm it. If it can't push smoke down, it can't push an already accelerating mass of steel down much faster.

If femr2 traces both ends, it should resolve the question of #2. If I can see the shape, and I can, good tracking should show any significant rotation effects. Personally, I hope it is rotation or some other apparent motion which can be discerned with the measurement techniques which femr2 has employed, a most encouraging result.

Suppose #2 falls. The only real contender is #1. Now, femr2 typically sticks the tracking right there in front of your eyes so you can see for yourself how good it is. Suppose it's good to the eye (though that's not saying much if you try to imagine following the position curves above as just dots moving frame to frame). It is a poor target and source video, silk purse from a sow's ear and all that... but, if it's good enough to eliminate #2, how can it be bad enough to be #1?

The answer to that question should be most enlightening, if it comes to it. The alternative is for someone to articulate a 6th mechanism.