Plane vs. Dome Part Deux: The Somewhat Bogus Attempt to Determine the Altitude of the Plane at Impact.
So, since my original analysis (apparently) went so well, It occurred to me that one could apply mathematics to estimate the altitude of the plane when it struck the dome. ... And this is where the sad and weepy part starts for your humble narrator.
Assumption #1: Filmed/Videoed Time = Real Time
Assumption #2: Object #1 (a small scrap that hit the ground first) might have acquired additional downward velocity/acceleration as a result of the plane exploding.
Assumption #3: Object #2 (the large tail section) probably encountered terminal velocity conditions which would explain why it took longer to reach the ground.
Object #1 took ~7.04 seconds to hit the ground.
Object #2 took ~9.39 seconds to hit the ground.
The Somewhat Bogus Part of the analysis:
Since I don't want to give myself a stroke trying to estimate masses, drag coefficients and the resulting terminal velocity conditions or the possible additional acceleration due to the explosion, I'm just going to average the times for Object #1 and Object #2 and use the standard formula for displacement as a function of acceleration due to gravity (yes, I know this is completely wrong ... but don't panic yet ... wait until I get to the end of the story.)
So for Object #1: The Altitude of the plane would have been ~798 feet.
For Object #2: The Altitude would have been ~1421 Feet (assuming no terminal velocity effect.)
Even though both of those numbers are probably wrong, they do, at the very least, establish a reasonable range of "possibilities," and, as we will eventually see, they actually confirm that what we saw on screen is more or less mathematically consistent.
If one takes the average of the two times (~8.22s,) the altitude of the plane would have been ~1088 feet.
So back to the original analysis:
Set Radius to 5 miles; Set Altitude to 1088 feet; Then the debris should have fallen ~22.4 feet from the edge of the dome (not counting the rebound distance.) As much as I hate to admit it, that looks right in the center of the target zone.
OTOH, at an impact altitude of 798 feet, the distance of the debris from the edge of the 5mi radius dome would have been ~12 feet (not including rebound.) Furthermore, if the plane were actually flying that low, then there would be a wide range of dome radii that would at least be "in the right ballpark," but 2.5 miles might be the best guesstimate.
That is all ... carry on.Edited by HDTVChallenged - 6/30/13 at 11:59pm