Once having determined the radius of the path, it is possible to calculate the centripetal acceleration for any speed using:
a = v2/r
where a is acceleration, v is velocity and r is the curve radius.
Centripetal acceleration produces the sensation of an outward “centrifugal” force which feels like gravity. This can be expressed as a horizontal g-force, gh, by evaluating the ratio:
gh = a/g
where the denominator, g, (for Washington D.C.) is 9.801 m/s/s in SI units or 32.16 ft/s/s in imperial units. The bank angle is found from arctan(gh).
For a plane in a level turn, the sideways “pseudo gravity” is combined with the downward actual force of gravity, to give the total or resultant force, gt, using the Pythagorean Theorem:
gt = √(gh2 + 12)
CIT videos illustrate their concept of the flyover with a plane slipping unnoticed over the roof of the Pentagon in a horizontal orientation hidden by the smoke cloud. Referring again to the work of Jim Hoffman, who shows how easy it would be to see the plane flying over the Pentagon, even in a horizontal orientation, consider how remarkable his images would appear if he showed the fuselage a wing-length above the roofline at a bank angle of 77°, and the other wing protruding an equal distance higher, as it started to fly over the Pentagon.
We have shown that at the very high speed the plane was traveling, and with the very short distance available for the turn, even a slight deviation from a straight path would require a steep bank angle. We can safely conclude that the plane must have been flying virtually straight, since many witnesses affirm and none (including those who reported a NOC path) deny that the plane was close to level. To claim that the plane could follow the NOC path without banking very steeply is to defy the laws of physics.
It should also be noted that the plane is being asked to do two difficult things simultaneously. On the one hand it must bank steeply to force the plane round the required curve. On the other hand it must pull out of the rapid descent which witnesses describe. The FDR data show that the pull-up was largely confined to the last 2 seconds of flight and that an upward force was generated of about 2g. This would be easy for a plane which is close to level but at a bank angle of 77° the problem posed is far more difficult. The pilot, already pulling back hard on the control column to achieve the turn, would have to turn the wheel left to reduce the bank and create lift. This will use up some of the distance available for the turn. The pilot would have had to anticipate this need and start his turn even more steeply, and with more g-force than calculated above, in order to still arrive above the point where the smoke was to be generated.
Even if the pilot managed to work all this out, and apply it at the precise moment required, he could not avoid passing over the Citgo service station, and some distance before and beyond, steeply banked, but this was not observed. It is evident that it did not occur.
Given that there is no evidence the plane was steeply banked, and ample evidence that any bank was slight, simple physics and geometry show that the curved NOC path must be false. Furthermore there is no rational justification for the perpetrators to make the extremely difficult maneuver, which would not only endanger the plane but would also put the entire project at risk of failure.
No one has made a case for a flyover on a direct approach, and there is no evidence for such an event. Voluminous eyewitness testimony, independent radar tracks from four separate agencies, the FDR data and the damage trail, place a large aircraft, consistent with a 757, at the scene approaching the Pentagon at a low level, at high speed and still accelerating. Impact with the Pentagon therefore cannot be avoided. It follows that the CIT claim that it would be impossible for the plane to do the observed damage, and that explosives would be required, is also false.
The claim by CIT that the plane flew NOC, strengthened by incorrect calculations published by PFT, has caused many researchers to pay attention to arguments that suggest the plane did not hit the Pentagon. Those who have been convinced by a few photographs that appear to show a hole too small, or insufficient debris outside the Pentagon, are advised to reconsider the work of Hoffman, Legge,and others who have done a careful analysis of the plausibility of a 757 collision. It will be found that all of these arguments are flawed or unsubstantiated, leaving impact with the Pentagon as the only reasonable conclusion.
Summary and Conclusion
The calculations we have displayed here show extreme values for the g-force required to deviate from the initial path to pass north of the Citgo service station, 4.3g being the lowest conceivable value, requiring that Morin’s testimony be totally set aside for no apparent reason, and the impossible 12.1g if some of Morin’s testimony is accepted. The bank angles are even more telling, since they would be clearly observable, 77° being the lowest possible. These values are confirmable by the reader using free software tools.
The force calculated is well beyond the design limit for this aircraft, 2.5 g, and also above the likely strength safety margin. Control of the aircraft, even at the lowest computed g-force, would be impossible for other than a highly trained aerobatic pilot and the physical survival of the aircraft would be at least in doubt.
The bank angle would be so steep as to astonish observers and be well remembered and frequently reported, but steep bank angles were not reported at all. Nothing more than a slight bank was described, even by those observers who claimed to see the path of the plane clearly enough to feel sure it was north of the Citgo service station.
It is physically impossible for a passenger plane to pull sharply out of a descent at a steep bank angle. The plane was descending steeply but managed to quickly level off, hence could not have been steeply banked.
It is physically impossible for any plane to pass NOC at the reported speed without banking steeply, hence the few witnesses who claimed to have observed the north path were necessarily mistaken about the path of the plane. Several such witnesses reported that the plane was flying level in the vicinity of the Navy Annex, in complete contradiction of the curved NOC path.The NOC witnesses are outnumbered by witnesses to impact by about 10 to 1, or about twice that if we disqualify the NOC witnesses who contradicted themselves by reporting that they saw the impact. There is a complete absence of witnesses to the plane flying over the Pentagon, though hundreds of people were in a position to see it and the sight would have been striking, commencing, or approaching, with a remarkably steep bank.
If, as we have shown, the plane did not fly north of the Citgo service station there is no reason to suspect that it did not hit the Pentagon. If it was flying close to the ground in the vicinity of the light poles, as described by many witnesses, it could not miss. The FDR file, the damage to the light poles, the fence and the generator and the shape of the damage on the face of the Pentagon all indicate impact. All arguments used to suggest that the plane could not have hit the Pentagon have been shown to be unfounded.CIT is shown to be presenting a hypothesis which is physically impossible. According to the scientific method this hypothesis must be abandoned.
It is to be hoped that those who have been puzzled by the apparently contradictory assertions surrounding the Pentagon attack, will now see that it is appropriate to withdraw support for the divisive notion that no plane hit the Pentagon. There are many disturbing issues which deserve our close attention related to the Pentagon attack, as have been clearly set out by Kevin Ryan and others, but the question of whether a plane hit the Pentagon should not be on that list.