Welbyt said:
What we're trying to do is determine the qty of explosives used. We have reason to believe that it was a non-shaped charge, likely a simple blast charge. However, no witnesses saw the explosion, and the debris is highly irregular due to the location of the blast.
so, it is looking like we're SOL on this one. Thanks for the advice.
you
could at the very least calculate rough upper and lower limits to the amounts of explosive used by assuming a particular kind of explosive. for instance, if you acquire all the pertinent properties of C4 you'd need to know (such as burn rate, shockwave expansion rate, and whatever else), and you assume C4 was used in the explosion, you can at least estimate the upper and lower bounds of the amount used depending on the fraction of the total energy of the explosion imparted to the 100kg object. you have the rough cross-sectional area of the object, you know how far it moved, you know the angle of incidence, and I'm assuming you know the object's distance from the charge before it was detonated.
if the charge was shaped, then its a matter of knowing whether it was aimed directly at the object or elsewhere, in which case either an appreciable fraction of the explosion's total energy will be imparted to the 100kg object or hardly any energy (perhaps even zero energy) will be imparted to it at all. if the shaped charge is aimed directly at the object or near it, then your calculation also depends on the expansion characteristics of the explosion as it expands toward the object - at the given initial distance, would a shaped C4 charge still be collimated well enough to fall entirely on or within the cross-sectional area of the object? or will the explosion have expanded enough by then such that some of its energy misses the object altogether and escapes around its outer edges? once you calculate how much energy must be imparted to the object at the given blast distance for a shaped charge explosion aimed in a particular direction in order to move the object horizontally 16m, you should be able to calculate/estimate the amount of explosives used. if you calculate the imparted energy for a range of different shaped charge directions, you'll eventually create a data set with upper and lower limits.
of course you mentioned that you have reason to believe the charge was non-shaped, so the explosion was more or less symmetrical in energy distribution and expansion (or more specifically, roughly spherical if the charge was suspended i.e. not resting on or near the ground). in this case, its simply a matter of knowing the distance to the 100kg object. you can calulate the ratio of energy contained in a cross-sectional area of a non-shaped C4 charge detonation at that distance (that area would be equal to the cross-sectional area of your object) to the explosion's total energy. you know that a particular amount of energy is needed to move the 100kg object 16m horizontally. therefore, the specific amount of energy per unit of cross-sectional area at the distance of the object must be equal to the amount of energy needed to move it 16m horizontally. working backwards, you can use the energy per unit of cross-sectional area and the distance the blast travels before it reaches the object to calculate to explosion's total energy, and from there you can calculate how much C4 was used.
of course the process is repeatable for other kinds of explosives, provided you can acquire all the pertinent properties about those explosives. i know these would be crude estimates, and that's far from calculating the exact amount of explosives used. but i figured a range of possible amounts of explosives might still be useful to you...
