What I'm wondering is would the final velocity of a 2 g steel sphere placed 2 cm away from 200g of TNT be equal to the final velocity of a 20g steel sphere placed 20cm away from 2kg of TNT? Sorry if that is weirdly worded question, but basically what I was wondering how the proportions of an explosion are related to scale.

The force something is hit with when near an explosion decreases by the cubic root every meter farther away the thing is... or something like that...

So like... really close perhaps the pressure spikes to 1000psi... 1 meter from there it will only be 10psi...

Note, thats not exact, i can't remember what the exact relationship was. It would probably be in urbanski.

basically what I was wondering how the proportions of an explosion are related to scale.

Oooh! Oooh! I know! I know!!

For the rant in this post, we'll be considering an overidealized detonation - a shockwave traveling in perfect vacum (itself a self-contradiction, but meh), always arising from the detonation of a mathematical point of zero volume. Also impossible, but hey - the simplified crap makes the basics easier.

Now... there are two factors at play here.

The first, of course, is starting energy. The arrangement of a molecule from a less-stable form to more-stable byproducts tends to release a fixed amount of energy, and if you're really damned lucky, it may even do this over a fairly-reproducible period of time.

It's that last which is a doozy, and why dustbombs explode for substances which barely smoulder - moar surface area = less time of combustion.

But... just for the fuck of it, let's say that degradation occurs simultaneously across all parts of a sample in a known and reproducible time frame. In this case, you're getting a given unit of energy in a given time period for each molecule of said substance, 'n it's going to basically scale exactly like that... in the ideal sense, anyways.

The other factor you mentioned was, well... distance. 'n for that, you've got to recognize that the energy calculated from the first factor - let's assume it was released instantaneously - is spread out across a given area, and that area is the surface area of a three-dimensional sphere of the radius between one's point of measurement and the theoretical point of detonation.

So... let's take a theoretical "explosive"... the conversion of 2(HNO3) into H2 + N2 + 3(O2), shall we?

Looking (http://www.cem.msu.edu/~reusch/VirtualText/react2.htm) at the bond energies, we find that the N=O bond, for which we have two of the buggers per molecule, is 143kcal/mol, or 143 * 2 * 2 = 572kcal for both of 'em, while the N-O bond is 55kcal, or 110kcal for both, and the H-O bond is 110kcal, or 220 for both.

This leaves a starting bond energy of 572 + 110 + 220, or 902kcal for 2 mol of H-O-N(=O)2.

So, what are the ending products? Well, like a bastard, we're not even calculating the 2(H2) + O2 -> H2O exothermogenesis, because... we suck. Yeah. So, O2 is 119kcal, or 357kcal for all three, H2 is 104.2kcal, and we'll just call it 104, and N2 is probably the 226kcal n=n configuration, but who knows?

902-687 = 215kcal per 2 mols degradation of nitric acid, or 107.5kcal/mol... not counting the formation of H2O. Continuing senselessly to ignore that, the theoretical energy per square unit in a truly-instantaneous degredation from a theoretical zero-volume point of detonation would end up being somewhere along the lines of (107.5 * mol)/(4pi*r^2) kcal/unit_of_volume_squared.

Plus the ensuing hydrogen explosion... but hey, we're not counting that.

Cool. Thanks. BTW, the site you cited looks like a good organic chem resource. I'll be sure to do read up on it if I can find the time.

I am rather interested in the safe observation of FAE explosions, I like getting as close as possible but still keeping the probability of death to a minimum. No metal is ever used so shrapnel is not a problem...reflection of the shock wave is not a problem either as all tests are carried out in a flat barren area.
Temperature is also a factor but as I live in a mild climate it is usually ~15 C

I tried using the equations found on the following page http://www.boomershoot.org/general/Effects.htm but I was unable to get the air pressure equation to work out.

My first question is how does one relate a gasoline explosion to relative pounds of TNT?
Secondly as I love feeling the shock wave (blast wave) hit me when explosives(fuel) detonate I would like a measure of how many PSI of overpressure this phenomenon occurs at?

In regard to ''the probability of a fatal injury'' equation, since it never really goes to zero, what is an optimum probability for safe viewing but to also ''feel'' the explosion? I know that duration of overpressure plays an enormous role in FAE's so I would like something like a graph of injury which has overpressure on one axis and duration on the other.
I certainly do not to succcumb any of the following:

Blast lung (pulmonary barotrauma)

TM rupture and middle ear damage

Abdominal hemorrhage and perforation - Globe (eye) rupture- Concussion (TBI without physical signs of head injury).