Dust Explosion - Grain, flour, wheat

[Varyon]

Originally Posted by Anaraxes

A half sphere of 50 m radius is 4 / 6 * pi * 50^3 = 261,000 m^3. At 750 g / m^3, that's nearly 200 tons of flour. Whatever the genie can do, 50 mages still need to carry 4 tons of flour each.

At the 2 ton total given previously, you can manage 2418.67 m^3. You'll only need a cylinder around 2 meters high (if that), you can manage a radius of 19.62 m, or around 21.5 yards. If 1 meter high is sufficient, you could manage around a 43 yard radius.

Let's say the djinn is able to take those 2 tons of flour and make a 15 yard radius of more-or-less optimally dispersed flour in a 2 yard cylinder. That's 1080.86 m^3, or 810.645 kg. That's the equivalent of a little over 7000 lb of TNT. Let's go instead with a suboptimal dispersion that only manages the equivalent of 2,500 lb of TNT (note this means only a little better than 15% of the flour properly detonated). That's 6dx100 damage at the epicenter, and (as a thermobaric explosion) you divide by distance in yards to determine damage elsewhere. Against most foes, 15d injury is pretty much guaranteed death, 10d is likely death, 5d is possible death, 3d is likely incapacitation, 2d is possible incapacitation, and 1d will cause lower-quality troops to feign death or flee. As this is an explosion, Large Area Damage Reduction (LADR) will typically be around 50% (for partially armored targets) and 75% (for fully armored targets) of Torso DR. See the following chart.

LADR	15d	10d	5d	3d	2d	1d
0	40	60	120	200	300	600
1	39	58	113	182	262	466
2	38	56	107	168	233	381
3	37	55	102	155	210	323
4	37	53	97	144	190	280
5	36	52	93	135	175	247
6	35	51	89	127	161	221
7	35	50	85	120	150	200
8	34	48	82	113	140	182
9	34	47	79	107	131	168
10	33	46	76	102	123	155
11	33	45	73	97	116	144
12	32	44	71	93	110	135
13	32	43	68	89	105	127
14	31	42	66	85	100	120
15	31	42	64	82	95	113

Even if the 1000-man enemy reserve has LADR 15, if it's arranged with 1 man every 2 yards in a roughly square formation (for roughly 60 yards by 60 yards), a dead-center "hit" will instantly kill (15d+ injury) roughly 80% of them, and the rest will be critically wounded (10d+ injury). If the epicenter of the blast is 30 yards from the center of the formation, you'll instantly kill (15d+ injury) roughly 40% of them, critically wound (10d+ injury) another 30%, and seriously wound (5d+ injury) the remaining 30%.

If the mage successfully pulls this off, expect him to invest in acquiring some large quantities of flammable dust (sawdust, flour, coal dust, etc) and making heavy use of it in future engagements. Unless the enemy figures out what he just did, however, and opts to dedicate a large deal of their magical oomph to countering it (which is still a strategic victory for the PC, as the enemy will be diverting a lot of resources).

EDIT: I should also note that using this may be extremely demoralizing to the enemy, at the very least requiring some penalized Fright Checks by the less-disciplined troops. If the enemy is likely to realize what you did, it may be worthwhile to load some ballistae with flour bags afterall. Not so you can repeat the action (I'm assuming the djinn is only going to be available for 1 summoning during the battle), but because the enemy doesn't know you can't repeat it - after seeing half a brigade vaporized after being showered with flour, getting hit with flour oneself will likely call for a Fright Check to avoid an unplanned retreat.

[Anaraxes]

Originally Posted by Varyon

At the 2 ton total given previously, you can manage 2418.67 m^3.

A lot of volume depends on the assumption about the shape, certainly. I went with 4m just because that's the Magic standard for Area spell height. 2m should be good enough for people, I agree.

Luckily, we have a literally magical dispersion method that could presumably handle any shape we like.

That's the equivalent of a little over 7000 lb of TNT.

I looked only a little for some energy numbers to try to get a REF for dust, but didn't get very far. I wasn't sure energy density as fuel was right (TNT is not very impressive in that respect.) And it wasn't obvious to me how REF could come from that anyway. There's apparently more to "TNT equivalence" than energy content.

How did you get this value?

[Icelander]

Originally Posted by Varyon

At the 2 ton total given previously, you can manage 2418.67 m^3. You'll only need a cylinder around 2 meters high (if that), you can manage a radius of 19.62 m, or around 21.5 yards. If 1 meter high is sufficient, you could manage around a 43 yard radius.

Very cool calculations. Note, however, that no matter how much more theoretically effective it would be for the cloud to be no higher than a man*, the practical reality is that the fastest way to get the flour or grain dust to make a cloud involves dropping it from a great height and then moving a whirlwind around in the area where it dropped. The djinni-cum-whirlwind will need to take a form with a decent height, as there is a correlation between the height of the whirlwind and the power and coverage.

A lot of the flour is going to be going up to at least 60'. It will start drifting downwards from there, hopefully mixing well with the air, but as the highest dust drifts down, some of the dust that was spread around at lower altitudes will be clumping and settling on the ground. So waiting too long is just as bad as not allowing enough time for the dust to mix with air. As a rough guess, at the moment of explosion we should probably expect the cloud to be a lot higher than 6'.

We might as well assume 60'. That will just be one part of the incredible inefficiency that will result from trying to do something that requires carefully controlling conditions in combat. If it even works.

*So as much of the volume as possible is instead devoted to covering a larger ground area, packed with more people.

Originally Posted by Varyon

As this is an explosion, Large Area Damage Reduction (LADR) will typically be around 50% (for partially armored targets) and 75% (for fully armored targets) of Torso DR. [...]

Even if the 1000-man enemy reserve has LADR 15,

The ordinary enemy heavy infantry will have DR 11-12 against large area attacks, assuming that their shield is between them and the source. Heroes might go up to DR 24 or so.

On the other hand, for an explosion at ground level, ranks of men between you and the epicenter count as cover DR. Not perfect cover, granted, but enough so that an explosion in the middle of a group of men will cause a lot fewer casualties than analysing each of them subject to the blast in an Infinite Featureless Space would suggest.

If the epicenter of the blast is above ground level, however, their cover DR from each other will be much less.

Note that it's probable that the enemy reserve, situated to exploit any breach in the walls or gate, will number more than a thousand men. I just mentioned that number because it's the equivalent of a regiment among the opposition. In fact, there will probably be some five regiments in reserve, but not, of course, packed into a neat circle for him to destroy all at once. Getting just one of them in a column of companies would be great.

Originally Posted by Varyon

If the mage successfully pulls this off, expect him to invest in acquiring some large quantities of flammable dust (sawdust, flour, coal dust, etc) and making heavy use of it in future engagements. Unless the enemy figures out what he just did, however, and opts to dedicate a large deal of their magical oomph to countering it (which is still a strategic victory for the PC, as the enemy will be diverting a lot of resources).

The mage PC has always invested in as much Alchemist's Fire as he can get, so I wouldn't expect anything other from him than further attempts at alchemical-magico-technological mass murder.

However, even with extremely good rolls, I'm doubtful that the PC will get even 15% of the grain dust to explode. And he'll never get it to explode in a neat flat 6' tall cylinder cloud that is shaped exactly like his target, even to the point of not 'wasting' explosive dust with volume above the targets.

Frankly, I think he'd be pleased with anything that makes a big boom, even if he doesn't get more than 300 casualties or so. After all, the alternatives that he has been weighing look like they'd yield maybe 200 casualties and nowhere near as concentrated or as shocking. As long as this causes a lot of disruption to the heavy infantry moving to exploit a breach, it's all good.

Originally Posted by Varyon

EDIT: I should also note that using this may be extremely demoralizing to the enemy, at the very least requiring some penalized Fright Checks by the less-disciplined troops. If the enemy is likely to realize what you did, it may be worthwhile to load some ballistae with flour bags afterall. Not so you can repeat the action (I'm assuming the djinn is only going to be available for 1 summoning during the battle), but because the enemy doesn't know you can't repeat it - after seeing half a brigade vaporized after being showered with flour, getting hit with flour oneself will likely call for a Fright Check to avoid an unplanned retreat.

All good points.

There will just be the one djinn. It's a summoning scroll, captured from the stores of an enemy high priest.

[Icelander]

Originally Posted by Anaraxes

A lot of volume depends on the assumption about the shape, certainly. I went with 4m just because that's the Magic standard for Area spell height. 2m should be good enough for people, I agree.

Luckily, we have a literally magical dispersion method that could presumably handle any shape we like.

Theoretically, yes.

However, constraints of deployment speed* pretty much dictate that the djinni will take a whirlwind form that is as large as he can, so the height of the cloud will probably be closer to 60', at least in parts.

*Aside from everything else, it's no good to have a perfect explosive dust cloud in a location where all the enemy have long since marched through and taken your city. We'd want to give the djinni less than a minute to work and the less time he needs to create conditions that appear conductive to a dust explosion, the better. I'm assuming that the PC will use Measurement spells every second to determine the progress, ordering the flaming once he's satisfied that several random hexes within the cloud appear to show the right air-to-dust mix.

Originally Posted by Anaraxes

I looked only a little for some energy numbers to try to get a REF for dust, but didn't get very far. I wasn't sure energy density as fuel was right (TNT is not very impressive in that respect.) And it wasn't obvious to me how REF could come from that anyway. There's apparently more to "TNT equivalence" than energy content.

How did you get this value?

I'd really like to know that too.

[Nereidalbel]

I got my value for TNT equivalence with this calculator, and this file gives some heat of combustion values.

[Varyon]

For REF, I simply used Nereidalbel's information of 1 lb flour = 4 lb TNT at optimal mixing.

Now, with the way thermobaric explosives work in GURPS, we don't really need to figure out the dimensions of the detonated flour cloud - rather, we just need to know how much flour it contains at the optimal mix, and where the epicenter is. I don't think we have any way to properly estimate the first, but the second would probably be based on a roll by the PC - essentially an attack roll probably using Combat Engineering, with scattering as usual. Let's assume 15 yards between the epicenter of the blast and the army beneath. At that height, cover from others caught in the blast should be negligible.

An explosion of 100% (2 tons) of the flour is going to deal around 6dx125 cr ex3. Every -2 SSR to the amount of flour that actually blows up is -1 SSR to damage. So, an explosion of 1% of the flour - which is -12 SSR - corresponds to 6dx12.5 cr ex3 - which is -6 SSR.

Have another chart. This time I'm assuming the foes have LADR 12. In this case, the listed yards aren't yards from the actual epicenter (which is somewhere up in the air), but yards from the point at ground level that is directly below the epicenter.

%	15d	10d	5d	3d	2d	1d
1	N/A	N/A	N/A	N/A	N/A	8
2	N/A	N/A	N/A	7	12	19
3	N/A	N/A	4	13	19	25
4	N/A	N/A	9	18	23	30
5	N/A	N/A	13	21	27	35
10	N/A	9	24	34	41	52
15	5	15	31	43	52	64
20	10	20	37	50	60	75
25	14	23	42	57	68	84
30	16	27	46	62	75	92
35	19	29	51	68	81	100
40	21	32	54	73	87	107
45	23	34	58	77	92	113
50	24	37	61	82	97	120

Note you need to get a decent amount of the flour involved to get a lot of casualties. I've no clue how the enemy is likely to arrange itself, but with 2 yards between each warrior your fireball wands wouldn't be likely to injure more than 1 foe with each shot (average damage is 21, divided by 4 for 2 yards distance and ex/2 means 5.25 damage, insufficient to pass DR; shooting between two warriors would yield an average of 10.5, which also wouldn't get past DR on average but could on a decent roll), so we'll assume the enemy has arranged itself like that. With these being elite troops you probably need 5d injury for them to become casualties, so that means no casualties with 1% or 2%, around 16 casualties with 3%, around 81 with 4%, and around 169 with 5% (square the yards to determine number of troops at that concentration that would suffer that level of damage). This assumes the troop arrangement includes a square with length/width equal to the listed ranges.

[Anthony]

Using energy values for TNT equivalence assumes perfect shockwave formation and all fuel being consumed in the initial blast, both of which are unlikely to be the case (most dust explosions are actually deflagration, not detonation, and continue burning for some time after the initial blast). For example, a tanker truck explosion involves around twenty tons of flammable material with a heat of combustion about ten times the detonation energy of TNT, but it isn't equivalent to a tactical nuclear weapon.

[Icelander]

Originally Posted by Varyon

Now, with the way thermobaric explosives work in GURPS, we don't really need to figure out the dimensions of the detonated flour cloud - rather, we just need to know how much flour it contains at the optimal mix, and where the epicenter is.

Originally Posted by Anthony

Using energy values for TNT equivalence assumes perfect shockwave formation and all fuel being consumed in the initial blast, both of which are unlikely to be the case (most dust explosions are actually deflagration, not detonation, and continue burning for some time after the initial blast). For example, a tanker truck explosion involves around twenty tons of flammable material with a heat of combustion about ten times the detonation energy of TNT, but it isn't equivalent to a tactical nuclear weapon.

The reason I think the dimensions of the dust cloud will be important is because of the physics that Anthony points out. We don't have an ideal air-to-dust mix that leads to a confined explosion, we're trying to set a still-swirling cloud of clumpy flour or grain dust afire. The TNT equivalency and using the GURPS rules to figure out the effects of a FAE explosion of that size just gives us a benchmark for what theoretically perfect efficiency of that much grain dust as a dust explosion would look like. It's not going to be anywhere close to what, in fact, happens.

Assuming that we get any detonation at all, more likely than a cataclysmic explosion is a series of irregularly shaped smaller explosions in those pockets where the mix happened to be good enough and, in between, a lot of rapidly burning dust that doesn't quite merit the term 'explosive'.

Lack of a big BOOM does not mean harmless, however. I'm not holding out hope for any 6dx100+ damage here, but I'm hoping that for anyone actually inside the cloud of grain dust or flour, there will be decent burning damage over the next couple of seconds.

[Anthony]

Originally Posted by Icelander

Lack of a big BOOM does not mean harmless, however. I'm not holding out hope for any 6dx100+ damage here, but I'm hoping that for anyone actually inside the cloud of grain dust or flour, there will be decent burning damage over the next couple of seconds.

Oh, that's certainly the case; you'll get a quite dramatic fireball, which will consume all available oxygen in the area and produce flame temperatures of more than a thousand degrees. It looks like you actually can't fully burn more than about 0.1-0.2 kg/m^3 of flour, oxygen shortage will starve your flame, but that's still a fireball you don't want to be in the middle of.

[Anders]

Won't the djinni be SOL?