I�ve been wanting to write this one up for some time now, and fortunately for me the time I happen to chose to put in the effort happens to coincide with the time I am able to post once again(well sometimes post). So here goes.

We all �know� that brisance is the time until peak pressure is obtained during detonation right? Well what if we take an ordinary, fairly low brisance explosive, and we, without messing around chemically, just decrease the time it takes to reach this pressure.
What am I talking about? Good question actually, I don�t know. Only joking.
The setup I had envisioned involved taking some run-of-the-mill ANFO, which for calculation purposes, we�ll chose to detonate at 3500m.s-1. Now we take a train of explosive with an inherently higher vod, for this purpose we shall assume a tube packed with picric Acid at max detonable density, in a tube of greater than the critical diameter, all detonating at 7000m.s-1.
We then take a cylindrical drum full of ANFO at its 3500m.s-1 specifications, and we insert the PA filled tube smack bang down the centre of the ANFO charge. The initiation of the charge is brought about by detonating the PA tube through the ANFO, which detonates the ANFO as well.
The theory is now this: Instead of the ANFO detonating slowly (well not really SLOW, it IS going 3,5 kilometres per second, but you know what I mean) and taking its own sweet time reaching the bottom of the charge, as well as reaching peak pressure somewhere along its length, we have the PA detonating at twice the vod of the ANFO, propagating down the length of the heterogeneous tube (sorry, couldn�t resist the big word) initiating the ANFO along its full length in approximately half the time. This should reduce the time needed for the ANFO to reach whatever stage during its detonation that peak pressure is attained. Thus we increase the ANFO�s brisance.

I did some rudimentary calculations based on several (shit off big) assumptions.

Take a 1m tall, by 0,5m wide cylindrical container and pack with the ANFO. Insert the PA tube. Then make the following assumptions:

Assume:
-The picric acid filled tube is of negligible width.
-Peak pressure is attained only once all the explosive has been completely consumed by detonation.
-The time taken for the explosive to be completely consumed is given by: Time taken for length of charge to detonate (assuming end-burning) + Time taken for an explosive disk of width = radius of the charge container to be consumed radially by detonation. I.e. time to detonate downwards + time to detonate outwards.
-Brisance will be assumed to be purely a function of time taken to develop peak pressure.
-Brisance for the purposes of this discussion will be given as the relative brisance of an unmodified charge compared to that of the PA tube modified charge.
-Ignore the effects that the actual peak pressure attained by detonation has on the brisance.

And yes, yes, yes, I do realise the glaringly obvious things that these assumptions disregard, but I had to simplify the calculations to enable me to quantify some sort of theoretical result. Plus I really don�t enjoy integration.
Unfortunately these assumptions tend to fall apart when comparing different explosives to each other, for example it gives the second modified ANFO charge (4 PA tubes, see later) as more brisant than the same charge using pure PA instead of ANFO)

Unmodified charge:
With no PA tube, the charge will take this long to reach peak pressure:
Time for height to detonate (end-burning):
1m / 3500m.s-1 = 2,857x10-4s (pretty quick ain�t it?)
Width:
0,5m / 3500m.s-1 = 1,429x10-4s

Total time unmodified = 4,286x10-4s

Modified charge:
Time for height to detonation (end-burning):
1m / 7000m.s-1 = 1,429x10-4s
Width:
0,5 / 3500m.s-1 = 1,429x10-4s


Total time modified: = 2,858x10-4s

Relative time gain:
2,858x10-4s / 4,286x10-4s = 0,6668
0,6668 x 100 = 66,68%
Time required to reach peak pressure has dropped by 33,32%
1 / 0,6668 = 1,500
Relative brisance has increased by a magnitude of 1,5

Personally I think that increasing the brisance of an ANFO charge 1,5 times simply by adding a tube of picric acid to the works is quite a nice idea. However, getting the world of explosives to obey all those ridiculous assumptions I had to make is another story.

By comparison, a 1m by 0,5m cylinder of TNT (@6900m.s-1 Meyer et. al.) would take 2,174x10-4s to reach peak pressure. Therefore our modified ANFO is not that far behind TNT, but the TNT charge is FAR simpler to make.

By a similar calculation, using 4 tubes of PA placed vertically though the same charge of ANFO at exactly one quarter of the diameter of the charge cylinder in from the outside of the charge, all initiated at the same time, i.e. 4 tubes evenly spaced in the cylinder of ANFO, the time taken to reach peak pressure is:
Time = 1,786x10-4s
This represents an increase in brisance of a magnitude of 2,400 (41,67% of the unmodified charge�s time is needed to reach peak pressure). It�s even faster (read more brisant) than the TNT charge.

So now, instead of increasing the brisance by 1,5 times, we�ve more than doubled it, and exceeded TNT, all for the price of 4 x 1m tubes of PA. Kinda cool ain�t it?

Another advantage of initiating a slower explosive with lengths of faster explosives is that instead of the detonation gases being given time to dissipate while the rest of the charge is still undergoing detonation (the pushing effect of ANFO), more of the explosive is converted to gas in any given amount of time. Meaning that there is less time for gases to dissipate during detonation, increasing the actual peak pressure of the detonation, increasing the brisance even further.

Of course, using an even faster explosive will increase the brisance even further; while the closer the vod�s of the 2 explosives used are, the less the gain in relative brisance. Of course using different shapes of charges will also affect the extent to which the brisance is increased; for example, using a longer cylinder will increase the brisance even further, while a wider cylinder will decrease it. Basically, the degree to which brisance is increased depends on how much, or rather what proportion, of the charge (in the direction of propagation) is made up of the faster explosive.

Now, the question stands, can anyone think of a use for doubled brisance ANFO charges? I mean the whole reason they�re used is for their pushing effect. Although maybe if one wanted to blow out a huge rock, and needed to break it apart even more than regular ANFO would.
But I guess when ANFO is simply used out of convenience, e.g. Oklahoma City and various other type car bombs, then increasing its brisance might just come in handy.

NBK, you got any of those bright ideas where this could be used to someone�s advantage?

Anybody who feels like it, by all means, go ahead and let me know if you can see any assumptions I may have made but forgot to include them. And also let me (and others) know what effects ignoring these assumptions would have in the real world, e.g. ignoring the actual peak pressure reached when determining relative brisance is a big one, it means that one can�t use those calculations to compare different explosives.
Please let me know what you think, especially about applications.

What do you guys think would happen if we varied the shape, e.g. used a sphere with a centre charge of faster explosive?

It sounds like you have independently rediscovered what a booster charge is. Arial bombs filled with ammatol had boosters in them to ensure complete detonation and boost det velocity.

I seem to recall reading something long ago about experiments where large amounts of detcord were "threaded" through multi-ton ANFO charges (basically lots of of lengths of detcord at Xcm intervals running parallel through the charge) to try to make them behave more brisantly.

IIRC the results showed it was rather impractical and didn't work very well at all.

Note that this only refers to using detcord, more powerful boosters (i.e. a 30mm tube filled with something very brisant) may work much better.

As Shooter3 has already stated, your �idea� embodies the entire concept of a booster charge, this is nothing new to most of us.

Besides the velocity of detonation, there are many more factors which you are overlooking such as the loading density of the explosive, as well as the gases produced and the heat of explosion to name a few.

There is now way in hell your calculations are correct, it is not possible when you have not even figured in all of the other variables. I even highly doubt that you have the tools, equipment and �know-how� to accurately calculate, measure and to document the correct figures so I suggest you do a good deal more reading.

I've seen patents where a strip of bridgewire detonators is running the entire length of the borehole with the ANFO in it, so that the ANFO is simultanously initiated at multiple points along its entire length, rather than running from one end to the other.

Perhaps this principle is what you're thinking of?

Brizance is a complex characteristic.

Lets speak about detonation pressure and power (P[J/s]=E/t)
Detonation pressure of the anfo will not change no matter what kind of booster you use. It is in any case less than 10 gigapascals. This is the peak pressure - the detonation wave has - when running through the explosive.
For hexogen at 1,8g/cc it is 35 GPa. Any object in contact with the explosive will experience this exact pressure (constant for each type of explosive and its density).

Anyway, the power of the bomb will double if the explosive is consumed twice the usual speed. The bomb will be more destructive!
This change in power could be observed in changes of "pressure-time" graphics shot at every 5 meters from the detonating device.
The initial supersonic wave will most possibly remain the same, but the speed of the expanding gasses should be higher.

No need to quote an entire post. :)


Could this be (what you are dealing with in your original post as well): the "over-drive" concept...not that of a booster.....(?)
A wonderful book you may want to glance at is : Detonation, Theory & Experiment by W. Fickett & Davis. I believe what you are speaking of is in Ch. 2 and is called the ZND model (as opposed to the Steady Plane detonation model).
It's quite something. You may be able to perform this concept in a small scale as well.
The book is not one of those $300 monsters either. You may really like it.
It's ISBN 0-486-41456-6 - plus it has a fantastic bibliography for related subject matter that I thought was non-existant (journals and such).

The total energy available isn't going to change, but the rate at which it is released can be. 'The candle that burns at both ends, burns twice as bright, but half as long' concept.

@NBK: That's similar to what I was thinking. My idea is basically trying to get an explosive charge to detonate and reach its peak pressure in a time shorter than a normally initiated charge. So the strip of bridgewire detonators running a charge's length would essentially be the same as what I proposed.
What I was thinking of is not really a booster, although that would be a side effect. A booster is just to provide that extra oomph to ensure that the reaction gets going well. I was wanting to effectively increase the charge's vod without having to switch explosives, or use an unpleasantly high density (which could prove problematic with something like ANFO).

@ The_Duke: I am aware that I have huge gaps in all my assumptions, and that I no where nearly covered all the simplifications I had to make, but the calculations were meant to be examples to illustrate the effect I was looking for, they were not meant to be taken as anything even remotely as in the area of factual. I believe I even called my assumptions ridiculous at one point in my earlier post.
That being said, that you for informing me of gaps (canyons) in my idea as per my request in my abovementioned post

@quicksilver: That's basically exactly what I was thinking about, 'over driving' the detonation. Thanks man, I wasn't aware of any books dealing with the idea (although I hadn't UTFSE's my Fedoroff). Thank you for the reference.
BTW, what's 'ISBN' I know precisely shit about computers and electrical technology, so forgive my ignorance. I guess I'll UTFSE now.

@simply RED: You've got it man. Thanks for bringing up some more specifics, I didn't want to have anything left out in this discussion.

P.S. Welcome back home!

Me234,
ISBN isn't computers, it is books. An ISBN number uniquely identifies a book (at least in theory) so that you can be sure you have the right one. It lets libraries and bookshops order the right version of a magazine, or a second edition instead of the first, etc.

Grab pretty much any book you own, and look on the back, above the barcode.

Brisance has nothing to do with 'how fast the hole mass is consumed', but with 'how fast it hits the confinement'. It is a measure of detonation pressure, which in turn is a constant for a given material (neglecting the first cm where it can be overdriven) and proportional to density, but to the square of velocity. Detonation pressure is in the range of 100-400 tons per square cm, while the pressure of the hot gasses is more like 5-15 tons once the shock wave has passed. Det pressure is what breaks/cuts, gas pressure is what throws/heaves.

So the brisance will stay the same, but it might still be an advantage in a borehole, i.e. better breaking of the rock because more surface gets pressurized in the same time.

Boomer: For my idea, I probably should have stated this earlier, I'm taking the definition of brisance to be the time to reach maximum detonation pressure in conjunction with the maximum detonation pressure obtained/reached. From this definition, you're obviously right with the fact that the maximum pressure reached won't change (ignoring overdrive effects), but what can change is how quickly we reach that pressure:
It's no good having something that reaches huge gigapascal pressures, but takes 3 hours to get there. An ANFO type charge won't generate all that much pressure, but what we can do is try to get it there quicker. That was the purpose of my idea.
I'm also going with the idea that max pressure would be reached sometime when enough explosive has been consumed in the shortest possible time (gives you a lot of gases quickly), as opposed to when all the charge has been consumed, but the earlier gases are diffusing away.

Anyway, thanks for the constructive criticism guys, it's good to know when one falls short.

I've seen patents where a strip of bridgewire detonators is running the entire length of the borehole with the ANFO in it, so that the ANFO is simultanously initiated at multiple points along its entire length, rather than running from one end to the other.

Perhaps this principle is what you're thinking of?

Is this also why the bigger ANFO bombs produced by the IRA contained shockwave-propagating metal tubing, or was this technique merely a simple, relatively cheap way to give additional shrapnel?

I doubt that a conducting a shock wave along a metal tube would be able to set off ANFO. But with something much more sensitive, who knows...
Just to check, you are trying to say that the shock wave travels down the tube (by cause massive amounts of high frequency vibrations along its length, kinda like hitting a wall with it and having it hurt your hands from the shock right?) and these high energy vibrations then set off explosive along its length by transferring enough energy form the tube to the charge?
Is that what you're trying to say? My head's a little slow today, so I'm sorry if I interpreted it completely wrong, but I just want to double check.
And anyway, even if it didn't work, I suppose you still get the extra shrapnel like you said.