Myriad has the aircraft at 1 G from the VDOT antenna to pole 1 and then pulling 3.2 G's from pole 1 to the pentagon.
Since I was fixing the mistakes in Rob Balsamo's calculation, I used the same trajectory he did: straight line from the VDOT tower to pole 1, and then uniform upward acceleration to the impact point, adjusted to also avoid dropping too low.
The only difference is, I calculated the G forces correctly, and he did not.
So I guess the question remains why doesn't Mackey & Myriad use the altitudes reported in the FDR data?
I used the altitudes Rob Balsamo used in his article. When you posted the article, you didn't mention any criticism of those altitudes. Do you now think they're not valid? If so, then when did you change your mind, and why?
R Mackey numbers make more sense.
Right, because R Mackey didn't follow all of Rob Balsamo's silly assumptions about the trajectory.
However, very different requirements from what the FDR shows. Same with Myriad numbers.
I'm not discussing the FDR in this thread. The trajectory I used is the same one that Rob Balsamo used. You didn't mention any objections to the trajectory he used in his article when you posted it here. In fact, you seemed to approve of the article and uncritically trust the results it reported. In any case, your opinion of Rob's article and the altitude figures he used therein isn't my concern. You can take those up directly with him. I only care that his math is wrong and should be corrected, if he wishes to present an honest case.
R Mackey's or Myriads numbers do not show up in the FDR data at all.
They do show up in Rob Balsamo's article, which claims that a pull-up of over 11 G's is
required for the plane to get from pole 1 to the impact point if the plane was descending at 75 fps at pole 1. This claim is false, because the calculations he presents supporting his case have three elementary and significant errors.
With that said, we do thank R Mackey and Myriad for your time critically analyzing the math.
You're welcome.
...and we will be re-checking our calculations and revise the article if required.
We'll see whether any evidence to support this claim appears.
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As I've said before, I don't believe that Rob's scenario of a continuous 75 pfs descent from the tower to the pole, followed by a sharp pull-up in the last 1.3 seconds, is a very likely scenario. Let's try a different scenario:
For this analysis, I'll use Rob's time marks which are reasonable: 3.0 seconds from the tower to the pole, and 1.3 seconds from the pole to impact.
For altitudes I'll use 45 msl for the impact hole (Rob's figure), 75 msl for pole 1 (5 feet lower than Rob's number, to make sure it hits), and 314 msl for the tower (10 feet higher than Rob's number, to make sure it misses).
The trajectory I'll use is this: From the tower to the light pole, the plane is descending but is arresting its descent at a constant acceleration. From the light pole to the impact point, the plane descends at a constant vertical velocity.
So, first, the easy part: the descent rate from the pole to the pentagon. A change of -30 feet in 1.3 seconds is -30/1.3 = -23 fps.
Now, from the tower to the pole:
I'll use the formulas for position and velocity of a uniformly accelerating object
position(time t) = pos(initial) + (v(initial) * t) + (1/2 * a * t^2)
velocity(time t) = v(initial) + (a * t)
The knowns are:
velocity(t) = -23 fps (positive is upward)
pos(t) = 75 ft
pos(initial) = 314 ft
t = 3 seconds
...and we need to solve for a.
substituting:
position(time t) = pos(initial) + ((v(time t) - a*t) * t) + (1/2 * a * t^2)
solving for a:
a = 2 * ( p(initial) - p(time t) + v(time t)*t ) / t^2
plugging in the knowns and doing the arithmetic:
a = 2 * ( 314 - 75 + (-23 * 3) ) / 9
a = 37.8 feet/second-second
37.8 / 32 = 1.18
So, the upward acceleration needed to accomplish this maneuver is just under
1.2 g, making the force on the airframe
2.2 G's.
And, this leaves only a steady 1 G descent (no vertical acceleration) for the final 1.3 seconds from the pole to the impact.
Respectfully,
Myriad