Physics Response to Flight 77 Trajectory Speculation

[Myriad]

By the way, someone may want to tell Myriad that 23 fps over 3 seconds only equates to 69 feet.

Very good! You got that one correct. Your journey towards becoming a participant in one of the fundamental and universal arts of our civilization has begun. When you combine a correct physical model (in this case, Euclidean space of at least one dimension orthogonal to time), correct units (feet per second * seconds gives you a result in feet), and correct arithmetic (23 * 3 = 69), you can calculate things like this, that are actually true and potentially useful to know. Furthermore, when you calculate something correctly you show that it is true in a way that is completely impervious to anyone's opinion about what is true. You have proven beyond all possibility of rational contradiction that an object moving 23 fps for 3 seconds moves 69 feet. That is a significant accomplishment!

TC, you forgot the rest of that post.

But don't stop there. Keep learning and exploring. With a little more experience and practice, you might be able to figure out and prove (when your physical model, units, and arithmetic are indeed correct) more complex things, also beyond all possibility of rational contradiction. Things like:

If a plane accelerates upward at 1.2g, for 3 seconds, at the end of which it is descending at 23 feet per second, then during those three seconds it will have descended 239 feet.

You are not contradicting anything I wrote. (What you missed is that the v(t) value specifies the velocity at time t, where t = 3 seconds, not a constant velocity, which I would have written as simply "v = [some number]".)

I have specified a flight path that meets the constraints in Rob Balsamo's article "Arlington Topography, Obstacles Make American 77 Final Leg Impossible" without ever exceeding 1.2 g of acceleration (or 2.2 g of stress on the airframe). Thus disproving Balsamo's thesis. I back up that claim with detailed analysis in the latter half of this post: http://www.internationalskeptics.com/forums/showthread.php?postid=3529296#post3529296. The basis of my claim is the physically and mathematically accurate statement in the last sentence quoted above. R.Mackey has worked out many other flight paths that also work.

In three threads on this subject you have managed to make one physically and mathematically correct statement, that an object moving 23 fps for 3 seconds moves 69 feet. Like I said, that's an important accomplishment. But so far you have not addressed the calculation of vertical accelerations at all, and I have come to doubt that you and your friends have the ability to do so. That's why I advised you to "keep learning and exploring" and to seek more practice and experience. That remains good advice.

Respectfully,
Myriad

 

[Myriad]

R.Mackey: Excellent work and very well-presented.

For historical purposes, the previous thread is: http://www.internationalskeptics.com/forums/showthread.php?t=108837

Respectfully,
Myriad

 

[GStan]

Yea, as long as that entails gratuitous nudity then it's a go.

gratuitous nudity ROCKS

 

[Cuddles]

Derail split to AAH. As R. Mackey said, there are already threads to discuss other aspects, this thread is for the calculations.

Replying to this modbox in thread will be off topic  Posted By: Cuddles

 

[Jonnyclueless]

As if TC (or any of them) is going to address Mackey's post...

 

[Terral]

This is the reason so few real 911Truthers post here

Derail split to AAH. As R. Mackey said, there are already threads to discuss other aspects, this thread is for the calculations.

Replying to this modbox in thread will be off topic  Posted By: Cuddles

Edit this . . .

 

[GStan]

Edit this . . .

Why don't you simply address the physics calculations instead of predictably polluting the thread with your spam? BTW, so few 9/11 Truthers post here because it is a place where amateur level logic and science are exposed for what they are.

 

[Par]

Edit this . . .

So, you attempted to derail this thread with your repetitive green-ink nonsense and now you’re sulking because that post has been moved away. Perhaps, instead, you can actually address the subject at issue and save the moderators undue work, us the distraction and yourself the upset.

 

[JimBenArm]

It's fascist of you to expect me to post on topic! My rights are being trampled! My lefts, too!

 

[R.Mackey]

Stupid question. What are the performance limitations on a B757? I tried a quick investigoogle, and got disgusted with the results. It would be helpful to have these explicitly stated here, preferably with citations.

Not a stupid question at all.

I don't have a good reference. In general passenger aircraft are spec'd to a load of 2.5 g in normal operations; anything above but close to that is inherently survivable but eats into the airframe's service life. I've been told (by Boeing) but cannot verify that main spars are destructively tested to 6 g static load. In practice, even seven or eight g might be survivable for a few seconds, though it's not clear if the control surfaces could exert that much authority in the first place.

If anyone has better figures, I'd appreciate them.

Small point - shouldn't the third to last paragraph say 'pwned' somewhere?

No. I'm trying to educate and dispel myths, not "pwn."

BTW - in said third to last paragraph, do you mean inconsistent or consistent?

I mean "inconsistent." The point is that the FDR data and the obstacles can be matched to each other, as well as to a physically realistic trajectory. There's no anomaly to be found anywhere.

Do you really mean ASL or AGL?

I really mean ASL. The original constraints are all referenced to mean sea level. Had I used AGL, the impact would have been at 0 to 6 feet AGL, not 39 feet.

Also, the ground is not flat in the region considered -- the blue trapezoids under the light pole and radio tower in my figures are also to scale, and represent the approximate ground altitude at those two points. I don't have any additional insight into the topology. Not needed for this analysis.

 

[R.Mackey]

I don't have a good reference. In general passenger aircraft are spec'd to a load of 2.5 g in normal operations; anything above but close to that is inherently survivable but eats into the airframe's service life. I've been told (by Boeing) but cannot verify that main spars are destructively tested to 6 g static load. In practice, even seven or eight g might be survivable for a few seconds, though it's not clear if the control surfaces could exert that much authority in the first place.

Just to amplify this, as I mentioned once some time back, China Airlines 006 got crossed up and experienced loads of 4.8 and 5.1 g at various times during an unpleasant 30,000 foot descent; it also was well over its v_ne speed, going supersonic in the process.

The aircraft was a much larger 747, not a 757, and suffered heavy damage, but nonetheless, it landed safely.

ETA: Here is an example of a 757 suffering loads of 3.59 g during a landing attempt, with no evident damage whatsoever. This appears to be the only relevant incident involving a 757.

 

[Hokulele]

Not a stupid question at all.

I don't have a good reference. In general passenger aircraft are spec'd to a load of 2.5 g in normal operations; anything above but close to that is inherently survivable but eats into the airframe's service life. I've been told (by Boeing) but cannot verify that main spars are destructively tested to 6 g static load. In practice, even seven or eight g might be survivable for a few seconds, though it's not clear if the control surfaces could exert that much authority in the first place.

Just to amplify this, as I mentioned once some time back, China Airlines 006 got crossed up and experienced loads of 4.8 and 5.1 g at various times during an unpleasant 30,000 foot descent; it also was well over its v_ne speed, going supersonic in the process.

The aircraft was a much larger 747, not a 757, and suffered heavy damage, but nonetheless, it landed safely.

ETA: Here is an example of a 757 suffering loads of 3.59 g during a landing attempt, with no evident damage whatsoever. This appears to be the only relevant incident involving a 757.

On a somewhat related note, does anyone know how old this plane was? As Aloha Airlines found out the hard way, metal fatigue does become an issue after a certain number of take-offs and landings.

 

[R.Mackey]

From the same site, N644AA first flew in 1991, and had about 33,400 flight hours at the time of the crash. Not a spring chicken, but not unusual either.

 

[Jonnyclueless]

This is a great thread, however there are some problems. 1 is that none of the PFT people are going to be able to meet the challenge. 2 Mackey is not going to go to them, as he should not have to. But would it be acceptable for someone else to use this argument (well I guess it's not technically an argument per say. Whatever you want to call it) on another forum (giving full credit of course?

I have no desire to do so myself, but seeing as I am sure many of the people who disagree are probably banned form this forum for some abuse or another, it might be helpful if it were posed on some of those other forums maybe? Perhaps sort of a proxy?

 

[uk_dave]

I have this mental image of the kids over at pft feverishly trying to make their calculations work while frequently uttering "oh bugger!"

 

[Jonnyclueless]

Well, I think there are people on the CT side who are good with the math and all (relatively speaking), or if nothing more might want to be up to the challenge. But they may not be able to do so here. People here are generally in agreement, or don't know enough about it to be able to try (I fall into both categories).

And it's not beyond the realm of possibility that those CTers could pose factors that we may not think of, which could then be fruitful in the sake of learning. I just think limiting it to this forum will drastically reduce the playing field (which I assume is not much of a concern for Mackey understandably).

 

[beachnut]

Good work, the final path may be somewhat like A or B since the terrorist had just pulled 1.7 gs in the last few seconds. He looks like he was in a PIO of sorts, and twice in the last 10 second of data on the FDR, the terrorist was up to 1.6 to 1.7 gs after going a low as 0.4 to 0.6 gs. (1.0 g is what we are sitting at)
Do not expect jdx to fix his errors; 9/11 truth tends to be open loop posts which are never corrected. P4t waved their hands, and say 11.2 gs. It is easier to skip physics, just make up numbers to mislead others to sell DVDs.

 

[X]

For those who have never taken calculus (I hope R.Mackey doesn't mind) I have worked out the derivations for his formula.

y(x) -> vertical position as a function of horizontal position (above sea level)
y(t) -> vertical position as a function of time (above sea level)
x -> horizontal position (I think Ryan is taking x = 0 at impact point, and x increases away from the Pentagon, correct me if I'm wrong)
x₀ -> horizontal distance from pentagon to a point of known altitude, used to solve quadratic equation
v -> horizontal location of vertex
h -> vertical location of vertex (height of impact)
s -> slope (change of altitude with distance, rise/run)
z = 781 ft/s -> ground speed of aircraft (horizontal and constant)​

To begin, the basic equation for a quadratic curve:
y(x) = s(x-v)² + h

Expanding (x-v)² gives x² - 2vx + v², which make the equation:
y(x) = sx² - 2svx + sv² + h

However, as Ryan states, this is a function of horizontal position, whereas we need a function of time. Fortunately, assuming a constant ground velocity ("g", horizontal) makes this easy. We simply re-define "x" in terms of "t".
x(t) = x₀ - zt
(this term is what make me think Ryan took "x" as distance from impact)

This gives:
y(t) = s(x₀ - zt)² - 2svx₀ - zt + sv² + h

Expanding (x₀ - zt)² gives x₀² - 2x₀zt + z²t², and simplifying the equation yields:
y(t) = sz²t² - 2sz(x₀ + 1)t + 2sx₀(x₀ - v) + sv² + h

The first derivative of this, y'(t), is the vertical speed at a given instant of time:
y'(t) = 2sz²t - 2szt(x₀ + 1)

The second derivative of this, y"(t), is the vertical acceleration at a given instant of time:
y"(t) = 2sz² = 1,219,900(s) ft/s/s


And finally, a question:
Is it reasonable to assume the flight path to be a quadratic?
It occurs to me that the aircraft motion would likely not fit a smooth, simple curve.
As a method of showing the feasibility of the required maneuver (which is all you were trying to do), it works for me.
But I'm wondering what your response would be to someone who challenged your work on the basis that it is not likely to represent the exact flight path?
Would you only say that all you were doing was showing it is possible?

 

[Mr.Herbert]

I just read a response to Mr. Mackey's white paper from Rob Balsamo at the ATS site.......

Mackey is lying. It will be addresed.

http://www.abovetopsecret.com/forum/thread341556/pg2#pid4128158

(the is more but it was banned here and I don't want to be a naughty boy )

 

[Anti-sophist]

Well, since you won't get any corrections from the truther's about their awful math... nor will you get any substantiative criticism, I'll give you some.

You've assumed that the fixed coordinate system of the ground is equivalent to the moving coordinate system on the aircraft. This isn't quite true.

A more accurate model would have parameterized both horizontal and vertical velocities with time, held the magnitude of the velocity constant (instead of the horizontal speed) and calculated the vertical acceleration with respect to the aircrafts coordinate frame instead of the fixed coordinate frame.

The difference between the two accelerations is directly proportional to the tangent of the angle of the aircraft. For large angles, the difference becomes more pronounced.

In your model, the velocity of the plane is slowing (horizontal speed is constant, vertical goes down). This is an additional source of acceleration that serves simply to make the calculations easier (by reducing the need for parameterization). Your model also incorrectly assigns all of the acceleration to the vertical axis of the aircraft, when in fact some of it would manifest itself as longitudinal acceleration (in this case, very specifically, drag). Unfortunately for the truthers, the simplified model you used actually produces a higher g-force than it would in the slightly more complicated model, thereby producing an even more "worst-case" number for them.

That being said my suspicion is the difference between the two models probably won't show up in the first two decimal places. It might for the most extreme angle.