I posted a link to Ryan's paper over at ATS. There was a detailed response:
Here's the parts I liked in that link you supplied:
Mackey:
The proposed boundary conditions of our problem are not well summarized, but can be extracted from articles and follow-up discussion on the Internet, initiated by a group known as "Pilots for 9/11 Truth."
That's a great start so far... they can't be sure of the boundary conditions.
Mackey:
There was also a substantial radio tower, operated by the Virginia Highway Patrol, reaching a total height of 304 feet ASL further back along the line of travel. This tower was located roughly 3,400 feet downrange. The aircraft did not destroy this tower, though accounts vary as to whether it missed the tower entirely or brushed it slightly.
They are guessing as to whether the plane hit the radio tower or not. Wow, how much error will that introduce into their parabolic model? Any impact will affect the velocity of the plane and change the displacement in all three vector directions.
Mackey:
The aircraft's last known velocity was approximately 781 feet per second. We will assume this is the groundspeed in all cases. For shallow angles of pitch, this is approximately constant; we further have no insight into thrust or drag in the final few seconds before impact.
Velocity is a vector quantity. It is meaningless to mention velocity without also mentioning a heading. Considering the alleged plane was in 3D space, the velocity was lacking pitch, roll and yaw characteristics to determine the plane's true heading. If the article meant 'speed', then the author has already shown that he knows very little about mathematics.
They have assumed a constant speed for the final approach of the plane, without knowing anything about the thrust or drag. Again, that's going to cause error to their parabolic model.
Mackey:
FDR data, which stopped at approximately the distance of the radio tower, suggests the actual altitude at that moment was 408 feet (using RADALT data) or 480 feet (possibly using a moving average or air data). These altitudes at the radio tower, 408 feet ASL and 480 feet ASL, are Case D and Case E respectively.
Finally, the NTSB animation -- which does not appear to be calibrated for this purpose -- suggests a height of 699 feet ASL as it passed over the tower. This is Case F.
Did you read that? The NTSB data does not appear to be calibrated - so was it or was it not calibrated? They don't know so that's going to create more error for their parabolic model. Can any of the 'official' data actually be verified with regards to high the plane allegedly was?
Mackey:
At this time we do not have any insight into the aircraft altitude, rate of descent, or attitude apart from the conditions listed above. To provide a simple trajectory model, we use the following assumptions:
We assume the aircraft exerts a constant pull-up maneuver, beginning at the radio tower, and ending when the rate of descent reaches zero.
This point is the vertex of a parabolic curve. If the aircraft reaches the vertex prior to striking the Pentagon, it continues flat and level from the vertex until impact.
Please, you have to be serious? They admit to having no insight to the altitude, decent rate, etc... but they are prepared to assume a SIMPLE PARABOLIC flight model? Was this article written by a comedian? Perhaps a 10th Grade student in high school, who just found out how quadratics and turning points work? Those assumptions are LAUGHABLE and totally devoid of any SERIOUS mathematical modelling.
The plane was flying in 3D space and they are assuming a 2D model? What about the effects of cross-wind shear? ANY deviation from their 2D approach will affect the planes velocity (and resulting speed). They're assuming a 2D model, given an initial 'speed' without knowing the 3D velocity direction? Come on, don't make me laugh - that's a load of BUNK!
Sure, we'll solve it all with a 10th Grade quadratic, after admitting we know very little about the conditions that will distort the plane from flying a smooth gradient until it hits zero at the vertex.
Don't try and bluff me with false mathematics, CaptainObvious - I know the danger in assuming an INCORRECT mathematical model.
The over-simplified parabolic model is utterly false and does not take into account any of the twin jet engine thrusts or dynamic airflow over the fuselage and wings. It completely ignores the effects of atmosphere drag on the airframe and the flight path. It condenses a 3D flight path into a 2D model that can't support the dynamics involved that would simulate a real plane flying through a real atmosphere into a real target.
Laughable.
