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Author: Subject: Calculating VoD
rot
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Calculating VoD

How can I calculate the VoD of an explosive? (If this is possible)
And how about other properties like brisance and pressure?
sylla
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That is a good question. I'm currently working with Philou Zrealone on an article about that hot topic, "towards a computer-based model of explosives". Calculating the VOD is a hard process requiring computer power for calculus.

Actually the VOD is easy to modelizate but the products of the explosive reaction are hard to determinate. So far my program gives the VOD of any CHON explosive with fairly good approximations. On RDX at its highest density I have an error of less than 3% for the VOD.

Currently, we are working hard on the evolution of the model towards iodine, chlorine, bromine and sulfur.

To talk a little bit more about the VOD it seems to be a linear equation made of two kind of VOD :

* The density VOD. VOD grows of 3500m/s for each variation of 1 in density. Q(D) = 3500*(D-1). Philou may give you more informations about the constant in the different famillies of explosives.

* The gaz VOD. VOD squared is proportional to the number of mol of gaz generated per g of explosive and the temperature (in kelvin). So, P(T,N) = 430*sqrt(T*N).

Finaly, VOD(T,N,D) = Q(D) + P(T,N)

We are aiming to several objectives which are :

* Integration of chlorine, bromine, iodine and sulfur. This will allow us to compare strange chemicals that might never exists at standard T&P, like hexaiodoxybenzene.

* Addition of equilibria. This will give better approximations on the products, close to empirical measurements.

* Discussion of the later constant (3500) depending on structural properties of the explosive.

Coming soon... ^_^
Boomer
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I guess you try to get a simpler form of e.g. Stine's formula:

V = 3.69 + d(-13.85C + 3.95H + 37.74N + 68.11O +.6917f)/M

V = Velocity of detonation in Km / s
d = density
C = number of Carbon atoms in formula
H = number of Hydrogen atoms in formula
N = number of Nitrogen atoms in formula
O = number of Oxygen atoms in formula
f = Heat of Formation in Kcal /mole
M = Molecular weight

Or the formula of Rothstein:

V = ( 100 x ( n(O) + n(N) - n(H)/2n(O) + A/3 - n(B)/1.75 - n(C)/2.5 - n(D)/4 - n(E)/5 ) / MWt) - G

G = 0.4 for liquid explosives else 0
A = 1.0 if the compound is aromatic else 0
n(O) = Nº of oxygen atoms
n(N) = Nº of nitrogen atoms
n(H) = Nº of hydrogen atoms
n(B) = Nº of oxygen atoms in excess of OB=0
n(C) = Nº of oxygen atoms double bonded to carbon
n(D) = Nº of oxygen atoms singly bonded to carbon
n(E) = Nº of NO3 either as nitrate ester or nitric acid salt

The first does not consider *how* atoms are bonded, the second does not include density.

I like the first better, it seems less random (GF=1 if your girlfriend has her period, else zero ), and was closer to published values for the HEs I tried it on.

Did you hear of the formula for mixtures, i.e. the average of the VoDs weighted by *volume* percentage, with voids being assigned a 'characteristic velocity' of 1500 m/s? It predicts velocity of PETN down to density 0.01, i.e. dust suspended in air.
There is a list of inerts with their 'characteristic velocity' showing why semtex is *not* slowed down 30% by the binders, and answering the all-time question why PETN with glycerine or even water is faster than without (if you don't fill the space left with more PETN of course).
rot
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Thanks a lot! this really helped me. But what exactly is heat of formation? how do u calculate that? I managed to look up the heat of form. for HMTD, and the VoD worked out at 5500m/s, that's pretty close to the actual VoD of 5100m/s. not bad!
deiki
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Thx boomer for this formula. I included it in my personnal prog (just a lil thing) and it seems to give rather good results.

You can try it here :

[Edited on 14-3-2006 by deiki]
Swany
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Good timing, I was going to write one, in visual basic. Your program is nice though. Good job.

Using the program, it quoted MHN at 1.6g/cm3 to have a det velocity of about 8650m/s. Does this sound right?

EDIT: For curiousity, I calculated NH4NO3 with this, and yeilded at det velocity of 7500m/s at 1.0g/cm3.

[Edited on 14-3-2006 by Swany]

sylla
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I have (from scratch, using only the structural formula) arround 2700m/s @d1 for ammonium nitrate and 7510m/s @d1.6 for MHN (C6H8O18N6). The later seems to suits the results found on google

[Edited on 15-3-2006 by sylla]
Boomer
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Both formulas give 6-7 km/s for AN at TMD. Re-calculating the 5.27 km/s @1.3 g/cc from Cooper to TMD, you get 6.5 km/s. These velocities are never reached in reality, but cast mixes with AN come close (i.e. if you calculate backwards from the real values, AN is always above 5 km/s, often above 6 km/s). This is especially true if the AN is mixed in on a molecular level, not like in amatol but in cast eutectics like AN/MAN/EDDN or AN/HDN/UN.

UN gives even higher values, IIRC above 8 km/s, and NU above 9 km/s. MHN also gives high values, around 9 km/s at TMD. Then again, I feel the formulas overestimate straight molecules, and underestimate branched ones. They put MHN, ETN and even nitro sugars above PETN
rot
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Thanks deiki for the program!
Some years ago I also wrote progs in C++ (think that's what you've used),
But i forgot everything about it
Good thing is i don't need to calculatate molar mass and heat of formation anymore.
btw how do u calculate the vod of mixtures?

[Edited on 17-3-2006 by rot]
Boomer
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Look above:

"Did you hear of the formula for mixtures, i.e. the average of the VoDs weighted by *volume* percentage, with voids being assigned a 'characteristic velocity' of 1500 m/s? "

Say you got 40% TNT, 50% RDX and 10% voids (i.e. pressed to 90% of max density). Gives (guesstimated) 42% TNT and 48% RDX by volume since RDX is denser (do the math yourself).

VoD = 0.42x7km/s + 0.48x8.8km/s + 0.1x1.5km/s

PETN at half its TMD gives 0.5x8.5km/s + 0.5x1.5km/s...

and so on. Note that you need the VoD at TMD (theoretical max. density), not the one stated in most tables (xyz @ 1.5)!

[Edited on 20-3-2006 by Boomer]

 Sciencemadness Discussion Board » Special topics » Energetic Materials » Calculating VoD Select A Forum Fundamentals   » Chemistry in General   » Organic Chemistry   » Reagents and Apparatus Acquisition   » Beginnings   » Responsible Practices   » Miscellaneous   » The Wiki Special topics   » Technochemistry   » Energetic Materials   » Biochemistry   » Radiochemistry   » Computational Models and Techniques   » Prepublication Non-chemistry   » Forum Matters   » Legal and Societal Issues