einsteen wrote:http://911blogger.com/news/2011-09-26/analysis-rocket-projectiles-wtc2
we've seen the ridiculous artifical nist collapse function of wtc#7 that had a >g double derivative. But now David Chandler used his physics toolkit for a falling part he found on a video. Has this already been analysed here? He claims a >g due to ejective force. He should provide an error margin but it is an interesting piece.
Hello, einsteen. At first this seemed ridiculous, but I gave it a wee bit of thought from one angle to see how ridiculous it actually was.
The accelerations Chandler gives are g/3 prior, 15 m/s
2 for 0.5 second during and "a little less" than g after. The difference between prior and during is 11.7 m/s
2, but take the more conservative figure of 50% greater than g, or an additional 5 m/s
2 due to downward force in addition to gravity.
a = 5 m/s
2Δt = 0.5 sec
increase of velocity due to this force in g-accelerated frame:
Δv = aΔt = 5(0.5) = 2.5 m/s
From the
rocket equation,
Δv = veln(m0/m1)where
m0 and
m1 are the initial and final masses, respectively, which differ by the mass of the so-called propellant. Again, being conservative, assume all propellant was expended in the half second interval of increased acceleration; this will produce the greatest thrust and velocity increment, all other factors being equal. Expressing the mass of the falling panel as
m and the mass of the expended rocket propellant as
mr, the equation above can then be restated as:
Δv = veln((m + mr)/m)so
Δv = veln(1 + mr/m)Δv/ve = ln(1 + mr/m)exp(Δv/ve) = 1 + mr/mmr = m(exp(Δv/ve) - 1)This last form expresses the mass of rocket propellant in terms of
- panel mass
- change of panel velocity over high acceleration interval due to 'thrust'
- effective exhaust velocity
For the first two, I'll use Chandler's values, four tons (=>
m ~ 3600 kg) and 2.5 m/s. Effective exhaust velocity can only be estimated. From the table
here, solid fuel motors are around 2,500 m/s, both turbofan jet engines and generic ion thrusters are 29,000 m/s, and the extreme high is 115 km/s.
The idealized rocket equation above assumes exhaust gas velocity is directed uniformly opposite to the direction of net thrust, so-called
effective exhaust velocity. The disparity between effective and actual is quite substantial for open combustion on a surface, versus a
rocket optimized to convert chemical energy into kinetic energy where the effective exhaust velocity is much closer to actual. While the hypothetical energetic substance may have higher energy density than rocket propellant, yet be unsuitable as such, the orders of magnitude reduced efficiency in propulsion suggests a somewhat unrealistic upper bound of effective exhaust velocity to consider is 2500 m/s, with no real lower bound that I can establish at this time.
I've graphed the propellant mass as a function of exhaust velocity and shaded the region from 250 m/s to 2500 m/s, in other words the upper order of magnitude of what seems even possible:

Much to my surprise, the result is not entirely outrageous. At 250 m/s, the mass expended would be 36 kg, or 1/100th the mass of the panel itself. I consider 250 m/s a more realistic upper bound, considering the inefficiencies associated with the momentum transfer, with the real value probably being considerably less. The red line on the graph represents the range 100 - 110 m/s, which verges on more like propellant being 10% of the panel mass. Even in that range, the disparity between effective velocity and sonic velocity is only a factor of 3.4; considerations of propulsive efficiency suggest the actual velocity must be higher, thus the gas at the reaction surface must be exiting at supersonic speeds.
It would have to either be really loud or else a significant mass of propellant. In the former, any trailing smoke would be observed to be going upward at a significant separation velocity then slowing rapidly (but still going up) whereas trailing smoke or dust would be seen to emanate at a net downward velocity, however small. This is one possible way to discriminate, but Chandler's video is not good enough for me to tell by looking. The former possibility - a significant mass of propellant (upwards of 10-20% of panel mass) would necessarily produce a huge volume of gas and/or particulate in the short 0.5 second interval.
So, take your pick: loud, violent smoke expulsion or a huge billow. That's what it takes to stay in a band of what's reasonable. Just common sense from conservation of momentum. The velocity change is small, but the mass of the panel is large and there's only a half second for thrust.
My conclusion at this point is it doesn't seem possible given the visual constraints, though it's not as outrageously far-fetched as I originally thought.