Pilots For 9/11 Truth Present Their Math

[The Big Dog]

Say, has old unstable Aldo checked in yet?

I see that our double banned member and his cohorts still want the coordinates for the pull up (heck, if I had a scientifically corroborated flight path, I'd make sure that I would have nailed down the little detail of, you know, where the flight path was).

Anyway boys, here is where ALDO described it: "and then pulled up into an ascent right before the wall" at the Pentagon.

Fire up those computers boys!

 

[jaydeehess]

Near the end of my post #293 I wrote

So the plane would go from 1.141 g to 1.11 g then to 1.8 g and if the desent and ascent lasted equal time then the plane would end up at the same altitude where it began.

Quite obviously there is a typo and it should be 1.41 g to 1.11 g then to 1.8 g for an aircraft that , starts in a level turn generating a 1 g horizontal load, descends at half the acceleration due to gravity, then climbs at half a g acceleration.

"below the horizontal" refers to an angle to the horizontal in which the vector points towards the earth whereas "above the horozintal" refers to an angle for the vector pointing towards the sky.

911files, your g calculations in this chart

, are they for the vector perpendicular to the wings , the vertical component of the horizontal component?

 

[jaydeehess]

Say, has old unstable Aldo checked in yet?

I see that our double banned member and his cohorts still want the coordinates for the pull up (heck, if I had a scientifically corroborated flight path, I'd make sure that I would have nailed down the little detail of, you know, where the flight path was).

Anyway boys, here is where ALDO described it: "and then pulled up into an ascent right before the wall" at the Pentagon.

Fire up those computers boys!

Well since the sole report of any pull up comes from Turcois it might be at the roadway, except that same witness says the plane disappeared from sight beyond the embankment/roadway. That means that the plane had to be below Turcois' line of sight. Lagasse, who is taller than Turcois says he saw it hit the Pentagon so he would then have had to be able to see at least the upper portion of the tail all the way in. Let's assume Lagasse's eyes are 6 feet from the level of the ground at the Citgo and that the plane did not pull up until it was just over the lawn.

I leave it then up to the brain trust at PfT to come up with the values at that point.


,,,,,, and of course this ignores the fact that in order for Brooks, Lagasse and Turcois to not see the pull up the fireball would have to occur behind the aircraft, not in front of it. If the plane flew up through the fireball then the pull up cannot commence until it enters the fireball emanating from the front of the Pentagon. If the fireball extends 100 feet in front then that is where the pull up starts.

A 757 is capable, under full power of a climb rate of 6000 ft/min IIRC but we also must note that in this case it will have to lower such a climb rate very quickly so as not to be observed exiting the top of the fireball.


Then there is that little problem of how one gets a fast transport sized aircraft to roar through a fireball and not cause a hugely obvious vortex through it, not ingest so much dense material that the engines tear apart and not get hit by anything large enough to damage the airframe .

 

[twinstead]

I still don't get this pull up thing at all. I guess I never will. Why pull up? If you want people to believe it crashed into the Pentagon, just crash the flippin' thing into the Pentagon, from Christ's sake.

 

[Reheat]

I still don't get this pull up thing at all. I guess I never will. Why pull up? If you want people to believe it crashed into the Pentagon, just crash the flippin' thing into the Pentagon, from Christ's sake.

Hey now. Stop that. You not a member of the cult, so stop trying to think logically.

 

[BCR]

Near the end of my post #293 I wrote


Quite obviously there is a typo and it should be 1.41 g to 1.11 g then to 1.8 g for an aircraft that , starts in a level turn generating a 1 g horizontal load, descends at half the acceleration due to gravity, then climbs at half a g acceleration.

"below the horizontal" refers to an angle to the horizontal in which the vector points towards the earth whereas "above the horozintal" refers to an angle for the vector pointing towards the sky.

911files, your g calculations in this chart
[qimg]http://aal77.com/jref/p4tarith.jpg[/qimg]
, are they for the vector perpendicular to the wings , the vertical component of the horizontal component?

They are the centripetal acceleration component of the banking equation. Please note the general equation for banking angle.

[latex]$$ \theta = tan^{-1} \left({\frac {\left(\frac{v^2}{r}\right)}{-g}}}\right) $$[/latex]

I defined the vector earlier as:

[latex] {a_L}sin{\theta} = \frac{v^2}{r} $$[/latex]

It is the acceleration component resulting from the curved path and its direction is defined in the illustration below (red arrow).

[qimg]http://aal77.com/jref/banking1.jpg[/qimg]

I am defining the acceleration component resulting from the path, NOT the g-load. G-load is an aeronautical term and I will defer to the aeronautical guys to define that. I know the boys at CIT are upset because there is a 0.2 g difference (in their favor) in the g-load they are picking up from some chart they googled. That could be due to a number of factors, such as g-load being a composite vector aligned with the plane's axis, not the path axis.

If P4T would provide the equation and conversion factors they are using (not some chart), then I could tell them exactly what the difference is. In the meantime, I'll defer to the aeronautical guys on that one.

 

[jaydeehess]

Well I note they are using load factor
(g load)=1/cos(theta)
however such a formula is completly bereft of any units. Cos(theta) and of course 1/cos(theta) are simply unitless numbers, a ratio.

For an object moving in a circle the centrepetal acceleration would be determined by the velocity as you have in the equation
a_Lsin(theta)=v²/r

In level flight the vertical acceleration for the force vector is simply that of gravity where a_v=g and to calculate the magnitude of the result of the vector sum of these two forces is simply (a_L)² + (a_v)²= (a_total)²The angle to the horizontal is given by
tan(theta)=a_v/a_L


a_total=a_v/cos(theta)
Using units of g for the acceleration then and leaving a_v =1g ie. level flight.
a_total=1/cos(theta)
(a_L² +1)^1/2=1/cos(theta)

 

[BCR]

Well I note they are using load factor
(g load)=1/cos(theta)
however such a formula is completly bereft of any units. Cos(theta) and of course 1/cos(theta) are simply unitless numbers, a ratio.

For an object moving in a circle the centrepetal acceleration would be determined by the velocity as you have in the equation
a_Lsin(theta)=v²/r

In level flight the vertical acceleration for the force vector is simply that of gravity where a_v=g and to calculate the magnitude of the result of the vector sum of these two forces is simply (a_L)² + (a_v)²= (a_total)²The angle to the horizontal is given by
tan(theta)=a_v/a_L


a_total=a_v/cos(theta)
Using units of g for the acceleration then and leaving a_v =1g ie. level flight.
a_total=1/cos(theta)
(a_L² +1)^1/2=1/cos(theta)

Let me express this in Newtonian physics terms and I think we'll come to the same conclusions. I made it clear when I started this that I wished to stay away from aeronautical stuff because I did not want the P4T boys screaming "he ain't a pilot so he don't know what he is talking about!"

In this updated graphic, the g-load is defined as the vector [latex]$$ F_N $$[/latex] resulting for the vector components [latex]$$ F_{cf} $$[/latex], which is centrifugal force (a pseudo-force opposite of centripetal force) and gravity [latex]$$ F_g $$[/latex].

To find the acceleration associated with this vector,

[latex]$$ F_N = \sqrt{{F_{cf}}^2 + {F_g}^2} $$[/latex],

and the magnitude, [latex]$$ N $$[/latex] expressed in terms of acceleration in g units (recall that [latex]$$ m $$[/latex] cancels),

[latex]$$ N = \sqrt{{-a_c}^2 + {a_g}^2} $$[/latex].

Here is the first table with N calculated:

Here is a table with it calculated for various sagitta values:

I think P4T will find that the N value compares quite well with their little table.

Note: I did not define the other vectors since they are defined in earlier posts. Geeezzzz, do I have to do all the work for these children?

 

[BCR]

Forgot to add parenthesis in the equation (due to negative vector) in my last post. It should be:

[latex]$$ N = \sqrt{{\left({-a_c}\right)}^2 + {a_g}^2} $$[/latex].

I should have noted also that [latex]$$ F_N $$[/latex] is not a true force either, but a pseudo-force like centrifugal force. It is essentially the inverse of [latex]$$ F_L $$[/latex]. The force notation is for illustration ONLY for both of these.

Also assumed is constant velocity in z (altitude) and y (speed). For the purist (me), the following equation would be prefered.

[latex]$$ N = |a_L| = \sqrt{{a_x}^2 + {a_z}^2} $$[/latex].

 

[Reheat]

Arguing about the math is a waste of time. Well, it's all a waste of time, but nonetheless.... The key (as has been stated multiple times in this thread) is the FLIGHT PATH as supported by their witnesses.

Unless the quote is taken out of context, no one ever said that flying North of the Citgo was impossible, without the qualifying statement "in accordance with the "witnesses statements". I realize they think we are stupid, but I for one am not that stupid. There is no difference in the air North of the Citgo as opposed to the air where we all know AA77 flew. [Well, that's true once the a wind has cleared the stench from the Ranquisamo obsession with the Citgo Station.]

All that's been done with this problem is that a key witnesses has been ignored in ALL of the addressed flight paths. Well, they ignore more than one, but in Morin's case, they totally ignore him in EVERY SINGLE PATH they "examine".

Here's Morin's original statement again:

“The Attack

I had just reached the elevator in the 5th Wing of BMDO/Federal Office Building (FOB) #2 – call it approximately 9:36 AM. I was already trying to make some sense out of the World Trade Tower attacks having heard about them on the radio. The news was sketchy, but the fact that it was a terrorist attack was already known. I then realized that I was wearing sunglasses and needed to go back to Lot 3 to retrieve my clear lenses. Since it was by no means a short walk to my car, I was upset with myself for being so distracted. Approximately 10 steps out from between Wings 4 and 5, I was making a gentle right turn towards the security check-in building just above Wing 4 when I became aware of something unusual. I can’t remember exactly what I was thinking about at that moment, but I started to hear an increasingly loud rumbling behind me and to my left. As I turned to my left, I immediately realized the noise was bouncing off the 4-story structure that was Wing 5. One to two seconds later the airliner came into my field of view. By that time the noise was absolutely deafening. I instantly had a very bad feeling about this but things were happening very quickly. The aircraft was essentially right over the top of me and the outer portion of the FOB (flight path parallel the outer edge of the FOB). Everything was shaking and vibrating, including the ground. I estimate that the aircraft was no more than 100 feet above me (30 to 50 feet above the FOB) in a slight nose down attitude. The plane had a silver body with red and blue stripes down the fuselage. I believed at the time that it belonged to American Airlines, but I couldn’t be sure. It looked like a 737 and I so reported to authorities.

Within seconds the plane cleared the 8th Wing of BMDO and was heading directly towards the Pentagon. Engines were at a steady high-pitched whine, indicating to me that the throttles were steady and full. I estimated the aircraft speed at between 350 and 400 knots. The flight path appeared to be deliberate, smooth, and controlled. As the aircraft approached the Pentagon, I saw a minor flash (later found out that the aircraft had sheared off a portion of a highway light pole down on Hwy 110). As the aircraft flew ever lower I started to lose sight of the actual airframe as a row of trees to the Northeast of the FOB blocked my view. I could now only see the tail of the aircraft. I believe I saw the tail dip slightly to the right indicating a minor turn in that direction. The tail was barely visible when I saw the flash and subsequent fireball rise approximately 200 feet above the Pentagon. There was a large explosion noise and the low frequency sound echo that comes with this type of sound. Associated with that was the increase in air pressure, momentarily, like a small gust of wind. For those formerly in the military, it sounded like a 2000lb bomb going off roughly ½ mile in front of you. At once there was a huge cloud of black smoke that rose several hundred feet up. Elapsed time from hearing the initial noise to when I saw the impact flash was between 12 and 15 seconds.

The Reaction
Many of the FOB people had been looking at the news reports flowing out of the attack on the World Trade Center Towers, going about their normal work routine as they watched. Maybe half or a bit more already knew of the New York attacks. However, within seconds of the impact -- less than a minute after the FOB flyover-- several thousand people started exiting the FOB.”

One reason Morin is crucial is that he is the BEST QUALIFIED witness they have as he has an aviation background.

Supposedly, there was a subsequent "interview" with Morin in which he "clarified" his position. There is no evidence of this "interview" except the word of the instigator of this charade. No transcript, no video, no recording were made.

This "interview" supposed clarified his position as being between the wings of the buildings and not outside of the wings as he originally stated. I believe he also stated that the aircraft was not South of Columbia Pike. How convenient to their fantasy. They originally attempted to erroneously plot his position as being inside the wings and now they have poof! However, he still stated that the aircraft was essentially right over the top of me and the outer portion of the FOB. Even if we ignore the parallel part there is no way any of his statement could have been true according to the cartoon which passed a considerable distance away.

Now, how do we resolve both the original statements and the "new clarified one" with an aircraft position over the center of the Navy Annex as was depicted for all flight paths in the cartoon? Basically, ALL of Morin's statements were ignored to make the cartoon "Aerodynamically Possible" "Witness Compatible". The one word to describe that is HORSE MANURE.

Cap'n Bob likes to quote what people have said in the past, so how bout that video of the aircraft flying over Morin's head? Oh, we'll need to just forget about that one, won't we.

Before you start to argue that Morin's statements destroy the known flight path, go stuff it. Morin is YOUR witness, he is not needed to support or deny the path we all know that AA77 flew. The further South the path he described was would tend to support his statement more than if it was actually further North as depicted in the cartoon. Where the aircraft flew as depicted in the cartoon is no where near what he described.

Here's a graphic to help you. Draw a small circle around him and go over that position, not over the middle of the building.

 

[BCR]

I agree Reheat, but someone started this thread asking for their math and they responded with some math. I'm just trying to help them understand the math they are using and where all of these equations and charts they googled came from.

Besides, someone needs to let them know they blew it on their radius estimates

 

[jaydeehess]

I wrote:
tan(theta)=a_v/a_L
I skipped a few steps after this. Just to ensure that readers can follow......
tan(theta)= sin(theta)/cos(theta) so from the above then we get;

sin(theta)/cos(theta)=a_v/a_L
rearranging

a_Lsin(theta)=a_v/cos(theta)
but basic trig states that both a_Lsin(theta) and a_v/cos(theta) will give the value of the hypotenuse which is simply the magnitude of a_total

a_total=a_v/cos(theta)
Using units of g for the acceleration then and leaving a_v =1g ie. level flight.
a_total=1g/cos(theta)
(a_L² +1g)^1/2=1g/cos(theta)

This would apply as well to non-level flight that has already entered a descent or climb and is now in a steady rate of climb(descent) (ie. a_v=zero

In the transition between level and steady descent or climb the a_total will NOT equal 1g/cos(theta)

It will be;

(a_L² +a_v²)^1/2=a_v/cos(theta)=a_v

as I already stated in my post above.


Note also that although all the above are for acceleration they will also apply for forces(as per 911files' diagrams) on the aircraft since force is mass times acceleration and the mass of the aircraft remains constant (except for burned fuel mass) throughout the flight.

Yes, PfT I know the difference between acceleration and force and that g is a psuedo-unit equal to the acceleration due to gravity at the nominal surface of the Earth.
Some people state that one 'feels' the acceleration due to gravity while we are affixed to the ground, but this is not technically correct. We 'feel' the resultant force, our mass times the acceleration due to gravity. We feel the pressure on our feet of the ground impeding movement downward.

 

[jaydeehess]

Reheat posts;
Supposedly, there was a subsequent "interview" with Morin in which he "clarified" his position. There is no evidence of this "interview" except the word of the instigator of this charade. No transcript, no video, no recording were made.

This "interview" supposed clarified his position as being between the wings of the buildings and not outside of the wings as he originally stated.

In his original statement he says he was at the elevator when he turned around. If he left it at that when speaking with PfT later then it would sound like he was still there when he saw the plane.

However he says in his original statement not only that he was "Approximately 10 steps out from between Wings 4 and 5" but also that he was "making a gentle right turn towards the security check-in building" which definitivly puts him at the outer limit of the complex, and not still between the wings.

Furthermore he describes how he watched the plane after it passed by him. If he were still between the wings of the building this would be absolutely impossible. Nor would he have been able to follow the plane if it were further north, over the Annex complex(in fact he would only see any part of the craft for a split second before the Annex would obscure his view of the plane).

So, Morin's statement about the aircraft being directly over him then has both he and the fuselage south of the Annex complex and PfT will have to re-calculate since the ranges they used for a possible flight path all have the plane further north as it goes by Morin.

 

[BCR]

This would apply as well to non-level flight that has already entered a descent or climb and is now in a steady rate of climb(descent) (ie. a_v=zero

In the transition between level and steady descent or climb the a_total will NOT equal 1g/cos(theta)

It will be;

(a_L² +a_v²)^1/2=a_v/cos(theta)=a_v

as I already stated in my post above.

I suspect you are correct that as long as [latex]$$ a_z = 0 $$[/latex] then [latex]$$ v_z $$[/latex] would have no impact on the g-load, since it is a function of [latex]$$ a $$[/latex].

 

[Reheat]

So, Morin's statement about the aircraft being directly over him then has both he and the fuselage south of the Annex complex and PfT will have to re-calculate since the ranges they used for a possible flight path all have the plane further north as it goes by Morin.

Do you really expect a re-calculation? Of course, you don't. They are all cowards and fully realize that if they included Morin in the equation they are dead in the water.

Morin would never have seen the belly of the aircraft if it was as far North as they placed it, he would have been looking at the TOP of the aircraft as it passed in a steep bank (if he could even see it at all). In fact, ALL of their "independently confirmed, quadruple corroborated" witnesses would have either been looking at the top or the bottom of the aircraft (depending on their position) as it passed by in an airshow type maneuver. How 'bout Roberts is it any wonder they avoided the 25 + G's that turn would require. Speaking of Robert's, how is it that they are claiming that the aircraft remained level when Roberts described it at 50'-100'. I can't even type this with a straight face. It's hilarious.

What's really funny too is that they want to keep most of the witnesses who saw the aircraft impact the building and disregard Paik and Morin in order to show those shallow bank angles. That is hilarious and further illustrates the insanity of their delusions. Well, at least the samo portion of the Ranquis gaggle knows. I don't think Ranquis has a clue either way. All they do is swallow the load......

 

[jaydeehess]

911files, do you have to do all the work for the chill'ins. Yes apparently you do.

They complain that we are using 460 knots and one well known denizen there is complaining that we are using extreme bank angles, mentioning 60 degrees used by one member here.

Well I used 45 degrees several times. I got that from PfT, and they stated that their interpretation of eyewitness accounts has any angle less than 22 degrees as too shallow a bank.
If 60 degrees is too extreme and 22 degrees is too shallow then I would suppose my using 45 degrees is pretty much splitting the difference.

Shall we settle on 45 degrees bank angle then, the aircraft passing over the south edge of the Annex(as per any statements by Morin other than how PfT wishes to interpret a separate interview they had with Morin) in such amanner as to allow Morin to be able to see the aircraft after it passed by him?

 

[BCR]

You are throwing Lagasse and Brooks under the bus

 

[jaydeehess]

You are throwing Lagasse and Brooks under the bus

Well 60 degrees is under there according to PfT so where does a 45 degree bank after it passes Morin put the a/c?
Yeah, moot point since if it goes north of the Citgo, or if Morin is between the wings of the Annex , or if the plane flies over the cetral portion of the annex at all, the Morin will not be able to see the a/c for long let alone watch its passage all the way to the Pentagon.
Unless Morin recanted his story of seeing the a/c most of the way to the Pentagon( to where the trees obstructed his view) let alone seeing the vert.stab. all the way in then he is mistaken about how close the plane was to the south edge of the Annex. PfT states they interpret the later interview as his saying he was still between the wings of the building. They do not state that he recants his story of seeing the a/c all the way to the trees and the vert.stab. all the way to impact.

I have been in a car 75 feet to the side of the button of an active runway as a 747 came in for a landing. (and 737's C-130's an Argus sub hunter etc)The plane landed further down the runway and as it passed by me it very much looked like it was directly overhead when in fact the fuselage was a good 100 feet forward of my position.... and I got to watch the plane come in, it was not a sudden thing as ATC ground control told me to wait for it.

As for Lagasse, he was looking south when he heard the plane and then dove into the car to use the radio when he knew the plane was on a collision course with the Pentagon. He is mistaken about where he saw the a/c come from, that's all.

Same with Brooks, as you point out in your analysis of his statement.

 

[BCR]

A 45 degree bank reduces the sagitta to around 100 feet. That brings the curve well back and perhaps Morin could see it overhead then. I agree about Lagasse and Brooks, but we are working on the P4T/CIT path and they might not like throwing them under the bus.

Now if I had my way it would extend pretty much straight from the last three or four DCA points towards the poles, making a slight bank after passing the Navy Annex (over Columbia Pike) and corresponding to the shadow I found on the Citgo video (south side). But, that is just me.

BTW - thanks for correcting my math. Do you think the boys at P4T will figure out the 'correction'?

 

[BCR]

Over the weekend jaydeehess and I have been playing a little with the g-load and load factors for the benefit of the gang at P4T. For the benefit of JREF members, I figured I needed to clarify some things about the math thus far. Keep in mind that I have been approaching the problem from a purely Newtonian physics aspect. My interest is in the component vectors, not fulfilling aeronautical terminology. I solved the problem for sagitta, bank angle, and centripetal force (in g's). Although I attempted to stay away from aeronautical issues, I thought it a simple matter that only one of the two vectors discussed thus far was variable and had to be determined (centripetal force) and the other vector component was fairly constant, gravitational force (g = 1). So I simply smiled as the folks at P4T and SPreston jumped up and down about how my g calculation for centripetal acceleration did not match some g-load chart they were using. Well of course it didn't! My calculation was for the variable component ONLY, centripetal force.

I don't visit the P4T or CIT forums very often and it is only by those of you who do that I am aware of the "issues". Everything I have done so far is NOT in aviation terms, and I have been very clear about that, but once again P4T took the bait and has gone on ramblings about something they have no clue about. So, since pilots are interested primarily in how much lift is required to keep the plane from falling out of the sky, I decided to do my best to in Newtonian physics terms provide a general equation for resolving that, but once again staying away from the aeronautical terms the best I could.

Well, jaydeehess decided to throw a monkey wrench at the P4T boys and define the same thing in aeronautical terms. Of course, not understanding that jaydeehess and I were talking about EXACTLY the same thing, but using different terminology, P4T invented this little game of how jaydeehess had to come along and "correct" my math. Personally, the whole thing had me on the floor laughing because all P4T was doing was once again revealing their ignorance of math.

So, pay close attention P4T.

My solution for acceleration (g-load) expressed in g's for [latex]$$ \theta >0 $$[/latex]:

[latex]$$ N = |a_L| = \sqrt{{a_x}^2 + {a_z}^2} $$[/latex]

Jaydeehess's solution for the load factor (no units, aviation definition):

[latex]$$ N = \frac{1}{cos \theta} $$[/latex]

Since,

[latex]$$ a_x = {a_L}sin{\theta} $$[/latex] and,

[latex]$$ a_z = {a_L}cos{\theta} $$[/latex] and,

[latex]$$ a_z = |{a_g}| $$[/latex] for the range of normal aviation altitude,

my equation becomes,

[latex]$$ |a_g| = \left({\sqrt{{a_x}^2 + {a_z}^2}}\right){cos{\theta}} $$[/latex] or,

[latex]$$ \frac{|{a_g}|}{cos{\theta}} = {\sqrt{{a_x}^2 + {a_z}^2}} $$[/latex]

When [latex]$$ \sum{a_z} = 0 [/latex] the equation becomes,

[latex]$$ \frac{1}{cos{\theta}} = {\sqrt{{a_x}^2 + {a_z}^2}} $$[/latex].

Oh my, jaydeehess and I are saying exactly the same thing. Thanks again for the 'correction' jaydeehess