Sudden impulse due to explosion

[Welbyt]

I'm doing a project for my job, and am currently stuck with a situation that I'm unsure of how to proceed. Note: not homework.

The situation is that I have an object of approximately 100kg, which was thrown a horizontal distance of 16m from it's original position by an explosion. We've determined that the explosive was located approximately at a 35degree angle underneath the object. So, what I'm looking at, is a sudden impulse acting on this object at 35 degrees, projecting it at that angle, and resulting in a horizontal displacement of 16m. I'm looking for the sudden acceleration that would cause this so that I can figure out the overpressure that would cause the required acceleration, for which I have computer models set up.
Is this indeterminant or is there a solution for this?

Just to outline known variables:

 

[zhermes]

If you know the initial angle (35 deg) and the distance traveled, its trivial to find the initial velocities---which you can use to find the acceleration. The problem lies in how much you want to simplify the problem. In reality the impulse delivered is the integral over the (highly) varying force-applied. This depends a lot on the nature of the object and explosion, etc. Do you have any additional information? High speed footage? etc?

 

[sophiecentaur]

The impulse (change in momentum) is given by force times time. Many combinations could give the same result. You would need to be more specific about times to find the average force but the impulse would be given by the launch velocity and that is something you could easily calculate. If it was an explosion, the impulse time would be very short c/w the flight time.

 

[Danger]

Welcome to PF, Welbyt.
If you happen to be trying to reconstruct the bomb itself, you have to look in all directions rather than concentrate solely upon the ballistics of one object. As a very broad and crude example, a lofting charge is far different from a bursting charge. The former is meant to launch/propel something, while the latter aims to blow something to bits. In the latter case, you have to determine whether or not it was a shaped (directed) charge or a general "kaboom" charge.
As Zhermes said, much more information is required, and even then we might not be able to reconstruct the incident.

edit: And I see that Sophie also weighed in while my back was turned.

 

[Welbyt]

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.

 

[sophiecentaur]

I guess that knowing the cross sectional area of the thrown object and then knowing / guestimating the time of the explosion (probably a known quantity if the type of explosive were known) would give you the average pressure over a hemisphere (assuming the blast was not directed). That would yield some idea about the total energy in the explosion.
I imagine there are a lot of experts with loads of data and forensic experience about typical effects of different amounts and types of explosive.
It rather depends on how theoretical or practical your problem is.

Didja turn your back again, Danger?

 

[Welbyt]

We do have the cross sectional area (approximate, as it is highly irregular), but I have been unable to find any other data online, I've been looking for about a month and have found nothing of particular use. This was my last hope for a solution that I would be able to work out, given my background of mechanical engineering.

 

[Danger]

Didja turn your back again, Danger?

Not this time; you flat-out posted when I had nothing further to say (in fact, I was responding to a different thread). The first time, both you and Zhermes posted while I was composing my own. I paused part way through to double-check the OP's name, and spotted Zhermes' post. After I submitted mine, I saw that yours had been added and then edited mine to acknowledge that.
You've already covered the first thing that came to mind after Welbyt's last post; ie: what sort of explosive was involved? Given the ballistics of the projectile, it could be anything from a large black-powder charge to a smidge of C4. Hell, I'm pretty sure that given a funnel and a few feet of tubing, one of my 5-megatonne beer farts could accomplish the same thing.

edit: And now Welbyt has sneaked in on me. I must ask whether or not you have access to chemical trace analysis equipment. If you do, then you can at least narrow down what sort of explosive was involved. From there, it will be a lot easier to reconstruct the original event. If it happened to be construction-grade dynamite, for instance, there would be marker tags lying about which denote the batch that the stick(s) came from. They are moulded into the sticks at the factory.

 

[sophiecentaur]

If you knew what the explosive was, you could get a good idea of a typical 'burn time', I reckon. It all depends on how accurately you need to know the amount of explosive. Are there no other marks around the explosion?
You can be pretty sure of the takeoff speed and, given a value for impulse time then the force would be CSA times overpressure - with pressure as the only complete unknown.
Time for you to break out the pad and pencil kit, I think.

Can't 'the authorities' help you? Was the explosion a criminal offence?
I'm not too surprised that there's not a lot of public info about this as it could be useful for nasty people when making plans for bombs.

edit Touche you got me this time.

 

[Danger]

Touche you got me this time.

So now that we're both one-for-two, I call for a truce. Leave we become comrades and thump upon uncouth interlopers.

 

[94JZA80]

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...

 

[Danger]

I should stress here that I used C4 merely as an example. If this was an eco-terrorist attack, or a pissed off farmer, or anyone else with no military connections, I would assume the explosive to be x number of sticks of 60% Forcite (dynamite) with a Pentomex detonator. That detonator, in turn, is ignited by a blasting cap of either fused or electrical triggering.

 

[sophiecentaur]

So now that we're both one-for-two, I call for a truce. Leave we become comrades and thump upon uncouth interlopers.

Put it there pal!

 

[Danger]

Put it there pal!

Consider it put.

 

[Welbyt]

Thanks for the information- I also have a relatively extensive knowledge on military explosives (was a combat engineer), so it was just a matter of trying to apply my limited knowledge of projectile motion to what I already knew.
Appreciate the assistance, went ahead and started on another approach, and got an answer that I believe to be reasonable.

Regards