Originally posted by exponent
R Mackey's analysis shows that this is complete rubbish, and is in fact artificially inflated values, essentially lies propagated by CIT / P4T.
R mackey's analysis is complete rubbish. Well, maybe not completely rubbish, but rubbbish none-the-less. I read some of his work around a year ago
and I don't care to go over it again, so I'm working from memory here.
Facts:
The EXACT flight path was NOT parabolic. Fitting a parabolic flight path only approximates what might have happened. How many data points did Mackey
use to obtain his parabola? Where is his regression analysis that shows how well all of his data points fit the parabola? Any approximation is only
valid, if there's mention of the error margin, or goodness of fit. It takes far more than three data points to fit a 'good' parabola.
Mackey concludes from his parabolic flight path that there was an average load of 4g. This leaves two possible scenarios:
1. The flight path was exactly circular, meaning that the radius was constant, so the plane was always experiencing a constant 4g force. We can
discard this scenario, as Mackey used a parabolic flight path - not a circular one.
2. Given the parabolic flight path and an average 4g across the interval, there must have been points where the force was greater than 4g and other
points where the force was less than 4g. This is easily verifiable by using the Mean Value Theorem (applicable here due to a closed, bounded
interval). When the rate of change of the parabola's gradient is larger (further from the pentagon) the forces must have been greater than 4g. As
the plane levelled out, close to the Pentagon, the forces would have been lower than 4g.
There is a distinct difference between averaged forces across an interval, as opposed to instantaneous forces experienced at individual points. We do
not have a constant stream of data from the flight, so we have to approximate using intervals. The smaller the intervals (in other words, the more
data points), the better the approximations will be. That's why calculus works, when we shrink interval widths to an arbitrarily small absolute
value.
So, while Mackey's work looks like 'cute' mathematics to the untrained eye, it is NOTHING more than guess work, based on a poorly approximated
flight path. Between the 'known' points of the flight path, there is no way to tell how many minor variations in flight path the plane experienced.
There could have been many instants where the force loads could have peaked, due to the pilots over or under correcting their path.
If Mackey concludes an average 4g across an interval, then there were points during that interval which experienced higher than a 4g force.
NONE of us will know the exact g force loading on the plane, unless we know the exact continuous data stream of the flight parameters. NONE of us
have that information.
Also, the plane actually flew in 3-D space. Reducing the problem to a 2-D frame of reference, based on an alleged 'straight' approach, further adds
to the errors. There is a third velocity and acceleration vector that is being conveniently overlooked by all of these overly simplified flight path
models.
By the way, I neglected to type the word 'alleged' when I refer to the flight path and the plane.
At least Mackey is prepared to put his name to his work, which shows more balls than some other people.
