View Single Post
Old 5th December 2009, 12:18 AM   #4017
tfk
Illuminator
 
Join Date: Oct 2006
Posts: 3,454
A Flight Path Model Calculated from the data

Here's my take on the flight path: I'm believing the raw data.

You can calculate the vertical velocity (second by second) by taking the difference in PA. Since it's sampled once per second, then the simple difference between each successive data point (in feet) is the vertical velocity in ft/sec. I've assigned that value to an arbitrary time 1/2 way between each time increment.

You know the plane's calibrated air speed.

Then = sin-1(Vv / Vc)
where Vv = vertical velocity (ft/sec)
Vc = calibrated airspeed (ft/sec)
= the Glide slope over each interval.

From here, you can either start stringing together displacement vectors, or calculate the horizontal distance between points using:

∂x = Vc * ∂t * cos()
where Vc = computed air speed (ft/sec)
∂t = 1 second intervals
= glide slope over interval (Deg)
∂x = horizontal distance traveled over each interval (ft)


Now it is easy to plot horizontal distance traveled [= ∑ ∂x] (ft) vs Pressure Altitude (ft). Simply set the aspect ratio of the plot to 1:1, and you've got the true flight path of the plane.

Here's what the curve looks like for the last 68 seconds.



You can see that it is a succession of 5 virtually straight line segments. Meaning that the g forces aren't going to stray much from a nominal around 1g, with small excursions above & below. Especially at the transition points between segments. This is borne out by the vertical acceleration data in the FDR output.


The following graph shows a blown up portion of the same flight path, focusing on the last 14 seconds before the End of Data. This encompasses two straight line segments, with very high linear regression coefficients.




Note that the vertical offset is still arbitrary, and the distance to actual collision is unknown from this data. We do know that Hanjour was pulling positive Gs over the last 2 seconds or so. Which would shallow out the 4 terminal glide slope segment shown in these graphs.

My conclusions are that the data shows that neither a circle nor a parabola are the best curves to model his flight path. But instead, it is best modeled by a succession of 5 virtually linear flight path segments over the course of the last minute of flight.

Tom

Last edited by tfk; 5th December 2009 at 12:23 AM.
tfk is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top