K.I.S.S. Tried that concept and with my luck the chute would have opened while the bomb was still on the plane, it would have crashed from the drag, and I'd be in a hell of a lot of trouble with the guy who built it. Except for one that really did have a sizable explosive charge in it, all the other bombs used a very small charge (a shotgun shell primer actually) to eject flour from the back end on impact, for safety's sake. It hadn't occurred to me at the time that what I had designed had the potential to be a fuel-air bomb if the flour ignited after it was ejected. The bombs were very light (around two ounces) and I really didn't expect them to fly that far forward after release. The aircraft used to carry the bombs was a old design called a "Powerhouse" that was quite large and actually covered with real silk. It had a very big low rpm engine on it that actually used a sparkplug instead of a glowplug, and it sounded like a small lawnmower in flight.
The only thing I can think of in this regard is Primacord, a super fast burning detonating cord used for high explosives that burns at a rate of 7,000-8,000 m/s:
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seems a lot higher than the speed of sound in the material it's made from, which is a variable that depends on density. That would mean it's burning at around 16,000 mph, which seems high for sound, even going through solid lead.
Being from the midwest, I wouldn't know. But the first time I slept with a first cousin I felt real bad about it. Until my buddy told me the way he got over it was to stop counting!
I gotta learn to stop posting based on recollection.
I WAS WRONG. Well sort of...
I quick review of what's available on the Internet delineates between between the shock wave that initiates the chemical reaction vs the chemical reaction itself.
The 'detonation wave' can proceed through the material at supersonic speed (relative to the material). It physically displaces (compresses) which heats the reactant which then reacts sonically after the 'shock discontinuity' wavefront passes. [1]
The speed of the detonation wave is aided by an increase in the density of the material. According to US Patent 4913053 Primacord uses a process of heating and high pressure to boost the detonation velocity of the fusing by 15-20% [5].
Technically its not 'burning' or reacting at that speed, and again taking a risk IIRC, that is why there's no discernible flame front in a detonation as opposed to a deflagration. The chemical reaction happens after the supersonic shock wave passes through the material which would make it appear to be 'burning' (aka reacting) all at once.
To pick this apart a bit I focused on one type of explosive, RDX and came up with this:
Explosive velocity: 8750 m/s [2] Speed of sound in RDX: ~3300 m/s [3], [4]
Thus the shock wave propagates through the material at roughly
2.65x the speed of sound in the material.
Sources:
[1]'Toward Detonation Theory' by Anatolii Nikolaevich Dremin page 4 para 3 a description of ZND theory.
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[2]
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[3] Molecular Dynamic Simulation of Nanoindentation of Cyclotrimethylenetrintramine (RDX) Crystal
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Google search of 'speed of sound in RDX crystals' yields a reference to this paper with the quote 'the indentation speed is 200 m/s which is 6% of the sound speed in RDX' this calculates to 3,333 and 1/3 m/s.
[4] The elastic constants and related properties of the energetic material cyclotrimethylene trinitramine (RDX) determined by Brillouin scattering by Haycraft, Stevens and Eckhardt.
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See the sound velocity diagrams in Fig 3. I noted the logitudinal mode curves, esp. the ones from the ultrasonic works of Scwartz and Hassul which are in close agreement at around 3300 m/s.
[5] US Patent No. 4,913,053 McPhee for Western Atlas International Houston TX. 'Method of increasing the detonation velocity of detonating fuse'
Not so. Though the definition isn't actually standardised afaik, a high explosive is "brisant", which is French for shattering. I'll explain this term later.
Moreover, it's better to refer to high and low explosions than high and low explosives, as a particular explosive may go off in either high or low mode depending on size, conditions etc.
However some explosives can't be brisant, and can be called low. I don't know offhand of any explosive which is always brisant, but if it existed it would be called high.
(when confined flash most definitely _can_ go high, as can even confined gunpowder in very large quantities, though the latter is rare).
A low explosive is
A low explosion is one which is not brisant. Confinement per se is irrelevant to the definition of an explosive, except maybe for legal reasons [1], though it can turn a non-brisant explosion into a brisant one.
The distinction between "detonate" and "deflagrate" is the key
Not necessarily. All high explosions are detonations, but not all detonations are high explosions.
A low explosive, that deflagrates, generates pressure waves
Indeed. The crucial difference between a deflagration and a detonation is the mechanism of propagation. In a deflagration the mechanisms by which energy is transferred to unreacted material are varied, including thermal transfer by conduction, radiation, hot gases getting between the cracks or gaps in gunpowder, etc.
In a detonation the major mechanism of propagation is by supersonic shockwave. For a high explosive this occurs at typically 2-3 times the speed of sound in the unreacted material.
In a shockwave the pressure can be very high indeed.
Imagine you have some explosive in a container, and you set it off. If the container is really strong and doesn't conduct heat (a force-field?) then the eventual conditions will depend solely on the chemistry of the explosive, and the methods and paths the reaction takes won't change that.
For an imaginary-but-typical explosive XO-nite the final temperature will be maybe 3,000C, the pressure maybe 3,000 bars.
If we now detonate that same explosive, the temporary maximum pressure in the shockwave might be 50,000 bars, or even more.
When a 50,000 bar shockwave hits something it tends to shatter it, rather than break it up - this shattering is known as brisance, as is the ability to cause shattering, and the adjective is brisant.
A high explosion is one where a significant portion of the energy is generated as brisance.
Thus a high explosion must be a detonation, as only shockwaves cause brisance, and shockwaves only happen in detonations, not deflagrations - but if a detonation only produces weak brisance, it's still a low explosion, the line between high and low is not the same as between a detonation and a deflagration.
There isn't a strict line which says how much brisance is needed to make an explosion high however, just a significant amount.
Faster?
Detonation is caused by, and causes, supersonic shockwaves.
Imagine a block of explosive which is detonating. Part of it has detonated, part of it is in the reaction zone, and part unreacted.
At the front of the reaction zone the shockwave hits a new untouched [2] bit of explosive, compressing the bit of explosive to high pressure and accelerating it forward.
The compressed and accelerated bit of explosive then turns to gas, which expands, producing force. This force is exerted on the forward shockwave, and also against an expanding reverse shock at the back end.
The expansion takes place at the speed of sound of the product gases (which is what causes the reverse shock).
So, how fast is our shockwave? The explosive as a whole is staying pretty much where it is, as it hasn't had time to move anywhere yet in bulk - but the reacting bit we are concerned with is already moving forward and expanding at it's speed of sound.
The reverse shock is therefore stationary with respect to the bulk of the explosive, as the bulk of the explosive isn't moving anywhere yet; and the bit is expanding apart between the forward and reverse shocks at the speed of sound in the product gases; so the front end of the bit, ie the forward shockwave, is moving at the speed of sound in the product gases.
For our XO-nite, the speed of sound in the solid explosive is 3,000 m/s. The product gases are at about [3] 3,000 C and 3,000 bar. The speed of sound in these gases is 8,000 m/s, and that's the speed the shockwave travels at.
The pressure of the shock wave is variable, see [3] below.
[1] legal definitions of explosives are typically unrelated to their properties. For instance in the UK if something is on a list, it's explosive even if it can't go bang, and if it isn't on the list it isn't legally an explosive, even if it can go bang.
[2] untouched because everything else that has happened so far in the explosion is bound by the speed of sound in the unreacted explosive - only shock waves and light can travel faster than this. In fact chemical propagation by light can change detonation properties, and opacifiers are often added thigh explosives.
[3] actually slightly less, as some energy goes into the shockwave. The shockwave has to grow in strength or else it dies out, and the expanding gases give some energy to the shockwave. The speed of the shockwave doesn't change when it grows in energy, what happens is that the pressure in the shockwave increases, sometimes to extreme levels.
All true. However, you could have saved yourself a good deal of typing if you had read my follow-on posting where I corrected myself.
It would appear that the shock-wave for RDX detonation proceeds through the material at about 2.65x the speed of sound in the material, based on what I could find quickly on the net.
Brisance is key. It super-explosives the molecular configuration seems (to me at least) key in allowing the shock-wave to propagate.
If I read the paper by Eckhardt et al. correctly, the speed of sound in RDX crystal is also somewhat dependent on the orientation of the molecules wrt to the sound stimulus. To properly detonate I'm speculating that the shock-wave must initiate in the proper 3d direction to which the molecular lattice is most susceptible to brisance. Since most detonators are probably pretty crude in this regard, they probably expend enough energy to force it, but I wonder if you couldn't have extremely efficient ones as well, that like a diamond cutter that taps it with an edge along the correct axis, could set it off with very little energy expended.
Do you know physical principle is behind ZND theory? Brisance is a description of the phenomena, but I don't find it a very satisfying explanation of physically what is happening. Since the shock-wave is propagating at supersonic speed, I have to believe the physical force at work is electrical. Do you know if this is the case?
Well, you addressed this question someone in your footnote #2 where you talk about 'opacifiers' being added to explosives to change chemical propagation by 'light'. I'll leave it at that.
The rest of your descriptions fall pretty much in line with what I understand is called ZND theory.
So is it fair to say that brisance determines the material's ability to change to gaseous state *before* the chemical reaction which is necessary for the supersonic propagation of the shockwave relative to the solid material?
And if enormous pressures are generated in the shockwave, what about the temperature within the shockwave? Since temperature can effect the speed of sound in a gas and according to your footnote #3 the pressure is variable why not the temperature? And if so, wouldn't that make the shockwave speed also variable?
Shockwaves will propagate through any material - the normal behaviour is for them to disperse their energy in the material, and die out.
In a detonation shockwaves are fed by chemical energy and grow rather than die out.
Brisance is one way the energy of a shockwave is dissipated, by shattering material, especially if they are powerful high pressure waves.
Brisance however has little or nothing to do with the detonation process itself.
Mostly RDX is used in polycrystalline form, or plastic bonded single crystals.
Perhaps someone has investigated the detonation of single crystal RDX, but in practice it is of little or no significance.
Yes, it's just like CJ (Chapman-Jouguet) theory, except the reaction takes time and stages, whereas in CJ theory we simply ignore those details of the reaction.
But I wouldn't worry about ZND theory, start with CJ theory.
ZND theory can give predictions for some details which CJ theory can't, for instance the thickness of the reaction zone, detonation limits etc - but the results aren't very accurate, unlike CJ theory, you need computers to do the calculations, and this is far more advanced that just a physical interpretation of what is going on in a detonation.
Okay, there are several physical explanations for CJ theory (all of which are actually the same explanation, but seen from different viewpoints). I'll try again:
Suppose an explosive reacts in a strong completely sealed container which no energy can pass through. It will turn to gas at some high pressure and temperature, say 4000K and 4000 bar, known as the CJ conditions. The speed of sound in the product gas at this pressure and temperature is known as the CJ velocity.
The CJ conditions do not depend on the path of the reaction, how long it took, or whether a detonation occurred or not; only on the constituents of the explosive and the available chemical energy.
Now imagine a plane shockwave is travelling through a block of some non-explosive solid.
Material at the front of the shockwave is subject to high pressure from behind and low pressure in front, and it wants to and does accelerate forward. It presses on the next layer, and this next layer resists quite well, becoming compressed in turn and thereby slowing the previous layer to a stop. This is how a shockwave normally [1] propagates in a solid.
In a detonating explosive, when the shockwave reaches a new layer of explosive, the layer is compressed and accelerated forward at a speed S, where S is approximately the speed of the shockwave.
The layer turns to gas, and expands behind the front edge of the shockwave, starting at the very high pressure of the shockwave and ending at the still-high CJ pressure and temperature.
Now unless a converging-diverging nozzle is used an expanding gas can't reach a velocity faster than the speed of sound, and in this case it expands at (very close to) that value.
In a detonating explosive the shock/detonation wave passes through the explosive quickly, before the bulk of the explosive has time to move anywhere. The velocity of the gas when the post-shockwave expansion is finished is therefore zero, because overall the gases from the explosion haven't had time to go anywhere [2].
The layer of explosive/expanding gas was moving forward at speed S, but it has expanded backwards until stationary at the speed of sound - and thus S, which is the speed of detonation, is equal to the speed of sound (in the product gas, at CJ conditions).
I hope this is clearer.
Typically, the speed of sound at CJ conditions, and thus the speed of detonation, is 2-3 times faster than the speed of sound in the solid explosive. The increased temperature is the main factor (the speed of sound varies with the square root of temperature, so going from say 300K to 4000K will give an increase of 3.65 times), but the stiffness of the solid will decrease that, to about 2-3 times.
[1] it is of course a bit more complicated than that, for instance some of the energy is changed to heat or sound etc, and shockwaves tend to break things too!
[2] the gas will then be at the CJ conditions, and will normally then expand again from there, of course. This expansion is subsonic, but the speed of sound in the gas is high, so it can happen fast.
It's just atoms bouncing off each other, plus a bit of chemical energy, that's all.
No, it's just atoms or molecules bumping into each other. If they get hot enough (= bump fast enough) they can give off light when they bump, but that's mostly incidental.
Compared with a sound wave, the mechanism of transmission of a shockwave through a material is similar except in that in the case of a sound wave the transfer is almost perfectly elastic (and energy conserving), whereas in the case of a shockwave the transfer is more inelastic - this is because the elastic limits in the material have been overcome by the high pressure in the shockwave.
The speed-of-sound limitation no longer applies (the "sound barrier" has been "broken" because of the high energy levels involved), and the actual speed of transmission depends not only on the material condition, but also the maximum pressure, the energy, and the detailed shape of the shockwave.
Because the transfer is inelastic some of the energy in the shockwave is inevitably lost, converted to heat (or sound, or shattering of solids).
An unusual example of this can be seen sometimes when a shockwave from a powerful explosion meets the surrounding air (and no actual material from the explosion has reached that far yet) - the air glows briefly in a wave, because the energy lost from the shockwave heats it up to several thousand degrees. You need high-speed photography to see the wave progress though, usually it's just a glow.
Opacifiers are used mostly to ensure the energetic coupling between nearby parts of an exploding material is good - if opacifiers were not used and if a lot of the energy was given off as light then it might spread out and not reach the next bit of explosive efficiently enough to cause it to detonate/deflagrate.
[...]
Wow, that's a hard question, like "have you stopped beating your wife?"
- it assumes many things which ain't necessarily so.
First off, the chemical reaction is not necessary for the supersonic propagation of a shockwave. Shockwaves can propagate through any kind of material, whether BEC, solid, liquid, gas, sparse or dense plasma. Hope you have got that part now.
In a high explosion the chemical reaction does however drive the detonation shockwave so it doesn't lose energy and fade out, in fact it makes it stronger (constant strength shockwaves in explosions are unstable, and don't happen - this is how the firework guys make whistle noises BTW).
[> for most high explosives an initial shockwave is necessary to cause detonation, otherwise if ignited many (eg TNT) will merely deflagrate, while some others will undergo a deflagration-to-detonation transition - which is a whole entire different subject, and it's verra complicaaated indeed, Capt'n. And if enormous pressures are generated in the shockwave, what
It can get very high indeed, see the example about air glowing above. In an explosion it then decreases rapidly to the CJ temperature (which is still high, usually about 3,000-4,000K).
Since temperature
The temperature is variable during the reaction, and during the expansion to CJ conditions when the speed of sound matches the speed of the shockwave - but the CJ temperature is fixed (actually it's not exactly fixed, but the variation caused by the amount of energy given to the shockwave is small).
Yes, but only to a small extent, a percent or two, as above - and there are usually other factors, like shape and confinement, which can cause it to vary by 20% or more.
Also the small change above is usually offset by another change I'm too lazy to go into just now, and the two changes almost exactly cancel out.
Yes, and seeing things fly. I loved model rockets and managed to get one candles-in-a-dry-cleaner-bag balloon airborne one time, only one out of several tries. I never got those CANnons to work: aluminum cans lined up, taped together, alcohol ignited at one end and a mango at the other end. Think I had too many holes for the pressure to build up. But CATAPULTS REALLY intrigued me and still do. All your power is on the ground so no propellant wasted lifting other propellant. Never built any.
One day, driving down a road in High Point-Greensboro area, NC, a white object, maybe the size and appearnce of a washcloth or small bathtowel, came out of the sky, crossing the road and landing in some woods to my left. (it had the aerodynamics of a somewhat weighty object.) I came close to going back to look for it but decided not to.. I had learned that Southerners have an obsession with catapults and that this probably has something to do with the War Between the States. (Dave Barry). So I pretty well figured what it was I saw and how it got airborne.
I made a rocket based on that principle once. One empty beer can with the top down, taped on top of three others with their bottoms down, with another three under that. You pumped propane or spray paint into it and applied a lighter to a small hole on the side of the top can, the fire propagated down from the top one into the three under it via holes in their bottoms, and from there into the bottom three the same way. Highest flight was around six feet, from the top of a table, allowing it to slam into the ceiling of the apartment and leaving a nice circular indentation there from the force of the impact. If you really want to surprise the model rocket club, fire one from underwater sometime; I fired one from around three feet down once via putting in into a piece of PVC pipe with a cap at the bottom end, and a sheet of aluminum foil the rocket pierced over the top. I used a extremly pointed nose cone to pierce the foil and cut down drag at it traveled to the surface, and it went around 200 feet up after coming out of the water. Stabilization was by four sticks like those on skyrockets that centered it in the launch tube... primitive, but it worked just fine.
But CATAPULTS REALLY intrigued me and still do. All your power is
I made a small torsion one once (a model of a Roman "Onagar) It used nylon rope to serve as the winding material, and had pretty good range for its size - it was around 18 inches long and could hurl a small pebble around 40 feet. If you are looking for the math on how they work and how to design one for optimal performance, latch on to a copy of J. G Landel's "Engineering In The Ancient World" which has a whole chapter devoted to them and the principles they work by.
Yeah, I heard about that fixation they have with hurling watermelons around via catapults and trebuchets. Well sir, when my giant catapult - "Abe's Revenge" is someday built, it shall hurl Yankee cracker barrels full of Greek Fire upon their damnable secessionist heads. ;-)
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