Quick question

[Purple]

I am in need of some information. I tried looking for data and doing the calculations my self but I don't have the knowledge of physics required and honestly don't know where to start.

So to ask here. Can anyone give me any rough estimate of what effect 40KG of TNT (in sticks of dynamite) would have if it detonated at once, standing on the ground on a plain stone paved floor.

I don't need any precise calculations, just an estimate.
As in, just some way of picturing the effects of 40KG of TNT.


Thank you in advance.

PS. Same question for 1 stick of dynamite.

[PeZook]

Well, let's see. We could easily use modern artillery shells for comparison.

They are usually filled with some sort of a stabilized RDX mix, which IIRC produces explosions about twice as powerful as TNT. An M107 (155mm) shell contains about 7 kilograms of explosive, roughly (very roughly) equivalent to 14 kilograms of TNT. It can completely destroy a small residential home, wreck a main battle tank or kill exposed people within a hundred metres with blast and fragments.

So...if the TNT crate is standing inside a room, everyone in that room is dead. Even if they're wearing armor, the blast will kill them anyway. It's quite likely it will also destroy whatever building it's in, unless it's huge/massive and can thus absord the blast.

A stick of dynamite is roughly equivalent to half a kilogram of TNT, which is about equal to a hand grenade (it will also kill everyone in a room).

You can see the effects of a single hand grenade in this enlightening video.

[Feil]

Using military ordinance (which kills mostly with shrapnel) to represent the effects of a bomb with no shrapnel component isn't going to give a very clear picture.

[Korvan]

If we make a couple of assumptions, we can get a quick calculation of the volume of gases produced. First you mention TNT and dynamite, except those are two different explosives. TNT is trinitrotoluene while dynamite is nitroglycerin soaked into sawdust or some other stabilizer. Since TNT energy values are easy to find and I don't want to deal with the combustion products of sawdust, we're going look at the explosion caused by 40 KG of TNT.

We are also going to assume the floor is indestructible and all energy goes into the decomposition products and not the atmosphere until the expansion is complete. Standard conditions apply otherwise (1 atm, 25 degress C). Also, we are going to assume the explosion happens at constant pressure. The molar mass of TNT is 227.13 g/mol, so the 40 kgs of TNT contains 176.11 mols of TNT. The reaction for TNT decomposition is as follows.

2 C7H5N3O6 → 6 N2 + 5 H2O + 7 CO + 7 C

So we have 3 gaseous products and some carbon. Once again to save major headaches we are going to assume none of the energy of the reaction goes into the carbon and the carbon does not react with atmospheric oxygen or anything else. So all it does is just amusingly give any bystanders a sooty face. We end up with a total of 528.33 mols N2, 440.28 mols H2O and 616.39 mols CO. We are going to model all three gases as a single ideal gas of which there is 1,584 mols of. The average heat capacity of this ideal gas is 31.9 J/mol*K

The energy of the reaction is 184 MJ for the 40 kilograms. This results in a temperature change of 184 MJ / (1584 mols * 31.9 J/mol*K) = 3641 K giving a final temperature of 3939 K. Since this is an ideal gas, PV =nRT holds so V= nRT/P

V = ((1584 mols)*(8.314 J/K*mol)*(3939 K)) / (101,325 Pa) = 512 m3 or 512,000 litres (for American readers this is equal to 2146 hogsheads (US), you guys are still using hogheads, right?) This would have made a fireball with a radius of just under 5 metres if the explosives were suspended at least 5 metres above ground. On the ground we get a hemisphere of radius 6.25 metres.

I did have to make a number of assumptions and simplifications to get these results, so just take them as very rough approximations.

[starslayer]

Most people in the US aren't familiar with hogsheads, though I think they're still used in some applications. 512,000 liters is about 135,000 US gallons, ~2500 55 gallon drums, or about one fifth the volume of an Olympic swimming pool.

[PeZook]

Using military ordinance (which kills mostly with shrapnel) to represent the effects of a bomb with no shrapnel component isn't going to give a very clear picture.

Not really true ; Overpressure is just as important for artillery shells as shrapnel. If a brick house collapses it's definitely not because of shrapnel, and you can easily find pictures of craters and explosions caused by shells, which is what Purple wanted.

[Purple]

Thank you for all your replies.

Essentially, the story goes that I am writing something and as one part of the story I have a character having 20 sticks of dynamite tied together dropped on his head from an airship.
But the guy has some heavy duty armor (nothing SF thou) so I have to approximate what kind of damage we are talking about.

In essence, if those 20 sticks exploded in his general vicinity (2-3 meters) I take it that even in full plate armor or in an armored vehicle (non tank) he would stand no chance of staying alive right?

[PeZook]

Plate armor would probably not save him, yeah. Depending on particulars on the situation, an armored vehicle could save his life: people were known to get out of mined APCs just fine.

Of course, bundled dynamite is not quite as effective as proper high explosive, since force of the explosion throws the sticks around, reducing the blast effect.

[Purple]

But am I right to assume that a human in plate armor standing 1 meter from the place where they hit with no cover would die horribly?

[Simon_Jester]

Thank you for all your replies.

Essentially, the story goes that I am writing something and as one part of the story I have a character having 20 sticks of dynamite tied together dropped on his head from an airship.
But the guy has some heavy duty armor (nothing SF thou) so I have to approximate what kind of damage we are talking about.

In essence, if those 20 sticks exploded in his general vicinity (2-3 meters) I take it that even in full plate armor or in an armored vehicle (non tank) he would stand no chance of staying alive right?

In any kind of armor not powered by technology indistinguishable from magic, that man is paste. If he's in a tank (or other armored vehicle that surrounds him with a solid box of metal that can withstand rifle fire, AND if the bomb hits outside the tank and not in direct contact with the armor, he has a good chance of survival. Because there won't be a lot of shrapnel from the explosion and being in a sealed, enclosed space will protect him from the blast.

I think.

But am I right to assume that a human in plate armor standing 1 meter from the place where they hit with no cover would die horribly?

Well, they'd probably die very quickly and before they knew what hit them. I'm not sure that counts as "horrible" for them. But it's certainly "horrible" from the point of view of anyone who isn't the person who just got bombed. It would be very, very ugly.

[Korvan]

You don't need sci-fi armour to survive such an explosion from 2-3 metres (wouldn't want to be any closer tho), but your armour does need to be specialized to handle such blasts. This article gives some idea on how modern explosive ordnance disposal suits work. Basically, you need a rigid exterior to defeat shrapnel and several layers of shock absorbing material underneath to kept your organs from liquefying.

Current suits are pretty heavy and bulky, but with training (and the suits built in cooling system) you can do some pretty impressive feats with them. The current record for running a mile in one of the suits is just under 10 minutes.