How to calculate shaped-charge damage for theoretical explosives?

[Sam Baughn]

I've been trying to make sense of ultra-tech warheads, and figure out what the assumptions are behind them.

High-Tech gives standard TL7 40mm grenade launcher shells (I think that's the right terminology) 4d of damage. This seems to be consistent with 32g of Composition-B filler, which seems to have been standard for 1970s shells.
At TL8 that goes up to 6d+2, which is about 163% of the TL7 damage, which implies the TNT-equivalent of explosive in the shell is 264% of what is in the TL7 one. I can't find a source for what filler is used in modern shells, but some internet research suggests that the explosive used isn't much more powerful, probably just having more RDX in the mix, giving it about 10% better REF. That means the main difference must be packing more explosive into the shell. RDX is a bit denser than TNT, so replacing most of the TNT with RDX would help somewhat, but not nearly enough. I guess the difference is a thinner casing and smaller fuse, allowing a bit more material to be jammed in.
The TL9 HE 40mm warhead in Ultra-Tech does 8d. That's only about 23% more damage than the TL8 one, or about 51% more TNT-equivalent. Assuming the TL8 warhead uses an explosive with REF of about 1.6, and no improvements from density, that implies an REF of around 2.4, which seems pretty conservative.
High-Tech lists CL20 as a TL8 explosive with REF 2.3. It seems that might be outdated, because Wikipedia lists it as REF 1.9. It also seems to need mixing with about 5% binder for practical use, which would bring it down to around 1.8.
Octanitrocubane apparently has an REF of 2.38 according to some sources (although others suggest it might be closer to 2 and it could require mixing with less powerful explosives or inert binding agents to be practical, but it's also a bit denser than most explosives). It's possible to make it now, but very difficult. If a manufacturing process were invented to make it cheap, or a similar but easier to make substance discovered, that would be a good fit for the TL9 warhead filler.

Looking at shaped-charge warheads, things seem more complicated.
The TL7 HEDP shell does 4d(10) with its jet, and 4d+2 explosive. That implies a bit more explosive filler than the HE shell, around 27% more TNT-equivalent, so likely something like 40g of Composition-B.
The TL8 HEDP does 6d explosive, so probably around 78% more TNT-equivalent. Like the HE shell, this seems to be mostly a case of packing more explosive into it than significant improvements in REF.
The jet damage goes up to 7d(10), or 75% more than the TL7 one. That looks a lot like the jet's penetration goes up in a linear fashion with the force of the explosion.
That seems counter-intuitive to me. Most sources (including High-Tech) suggest that explosive force needed to penetrate something goes up with the square of its thickness; that is, penetration depth (directly linked to damage in GURPS in a linear fashion) should scale with the square root of explosive energy (or TNT-equivalent weight, which is basically the same thing as far as I can tell).
Finding formulas for expected results of different explosives in shaped charges is difficult. The only thing I was able to find was that 'jet length' seems to be the crucial figure, assuming size, shape, liner material, and target material all stay the same. It looks like penetration is simply related to jet length (i.e. twice as long a jet means twice the penetration), but I can't find anything that says how to calculate expected jet length. I did find one document which said an LX-19 (CL-20 with binder) hemispherical shaped charge generated a 50% longer jet than an LX-14 (HMX with the same binder in similar proportions), but also said this may be 'an experimental anomaly', so it's hard to draw conclusions from that.
It seems possible that much of the difference between the TL7 HEDP shell and the TL8 one is not due to the increased force of the added explosives, but other factors like higher detonation velocity (which seems to be related to REF, but not in a simple way), better liner materials (I think the transition from copper to tantalum, copper-tungsten or molybdenum would have been in the late 70s or 80s), and better understanding of the physics leading to more efficient geometry.
However, the TL9 shaped charge warheads in Ultra-Tech make a massive jump in effectiveness, with the 40mm one doing 6d×4(10) with 4d explosive. The relatively low explosive damage implies that this isn't a super-high REF explosive, but I find it hard to believe that other factors could account for more than triple the penetration, even if you use uranium or something as the liner material. Even if we ignore the explosion damage and make the generous assumption that explosive force translates directly into damage, that's ~3.43 more damage than a TL8 40mm shell, implying an REF of about 5.49, which is on the high-end of estimates for Octaazacubane, a completely theoretical metastable form of nitrogen, which seems to be about the limit for practical near-future explosives without getting into weird forms of matter or atomics.

So, it seems that the shaped charge damage in Ultra-Tech is way off and the HE / HEC damage might be a bit low. Adjusting normal explosive effects (e.g. HE damage) to account for different effectiveness in future explosives seems fairly straightforward; just figure out the REF and weight of explosive, then multiply them together and use the usual explosion rules.
But for shaped charges, I have no idea what appropriate values are. My instinct is to make them scale at the same rate as normal explosives, i.e. at the square root of mass × REF, but since I'm not a mathematician, scientist, or engineer, I don't think my instincts are to be trusted on this.

Can anyone who actually knows what they are talking about comment?

[Varyon]

I don't really know the physics behind it all, so can't help with that level of things, but for the TL scaling, first off keep in mind HEAT was a rather new technology at TL 7 (it was first developed during WWII, and that more-or-less sets the transition point between TL 6 and TL 7), so the huge increase in performance between TL 7 and TL 8 may simply be the result of it becoming a mature technology. The TL 9+ performance is probably just some sort of extrapolation, much as the performance of TL 9+ armor was (note you fairly consistently see +1 SSR to DR per +1 TL).

[Sam Baughn]

Looking at TL7 anti-tank weapons in the 55-70mm range, we've got:
Bazooka, 60mm, HEAT, TL7 (1943): 8d(10) + 10d ex.
Firestone M18, 57mm, HEAT, TL7 (1945): 8d(10) + 8d ex. This seems to be more 'efficient' than the bazooka in terms of getting more penetration from less explosion and slightly smaller diameter.
M72A2, 66mm, HEAT, TL7 (1963): 18d(10) + 12d ex. Significantly better than the 1940s weapons, with a better proportion of penetration to explosion again.
M72A4, 66mm, HEAT, TL8 (1993): 30d(10) + 12d ex. A huge leap in penetration compared to the M72A2, apparently without increasing the amount of explosive (same explosive damage). Possibly a sign of significant improvements in factors other than explosive power.
If we assume that explosive damage indicates the power of the explosive material, and penetration from the jet goes up at the square root of that, then the 40mm HEDP shells went up about 31% in damage from other factors between 1971 (late TL7) and sometime in the 80s (early TL8), while LAW damage went up ~67% from (presumably) similar factors between 1963 (mid TL7) and 1993 (mid TL8), after going up about 50% from early to mid TL7. That looks like a fairly steady increase of about two-thirds more penetrating damage over one TL, but I expect that to fall off in the future, since shaped charges are a rather mature technology now.
On the other hand, the gap between the TL9 64mm warhead (42d) and the M72A4's one (30d) is significantly smaller than the difference between the 40mm shells. That implies that 40mm shaped charges are not as efficient as ~64mm ones at the moment, but could improve significantly in the future with miniaturisation of some components, better materials, and 'tighter tolerances' in manufacturing. With that assumption, simply improving REF to around 3.2 would result in 40mm HEAT with performance as listed in Ultra-Tech (except for the explosion damage, which should be about twice what is listed).
On the gripping hand, the M72A6 has a HEDP warhead and does the same blast damage as the M72A4, but less than half the penetration with its jet! Since Ultra-Tech shaped charge warheads all do fragmentation damage, that seems like a better model, but there aren't as many data points to compare existing ones.

[Rupert]

Originally Posted by Sam Baughn

High-Tech gives standard TL7 40mm grenade launcher shells (I think that's the right terminology) 4d of damage. This seems to be consistent with 32g of Composition-B filler, which seems to have been standard for 1970s shells.
At TL8 that goes up to 6d+2, which is about 163% of the TL7 damage, which implies the TNT-equivalent of explosive in the shell is 264% of what is in the TL7 one. I can't find a source for what filler is used in modern shells, but some internet research suggests that the explosive used isn't much more powerful, probably just having more RDX in the mix, giving it about 10% better REF. That means the main difference must be packing more explosive into the shell. RDX is a bit denser than TNT, so replacing most of the TNT with RDX would help somewhat, but not nearly enough. I guess the difference is a thinner casing and smaller fuse, allowing a bit more material to be jammed in.

A much smaller fuse is the big advance here.

Looking at shaped-charge warheads, things seem more complicated.
The TL7 HEDP shell does 4d(10) with its jet, and 4d+2 explosive. That implies a bit more explosive filler than the HE shell, around 27% more TNT-equivalent, so likely something like 40g of Composition-B.
The TL8 HEDP does 6d explosive, so probably around 78% more TNT-equivalent. Like the HE shell, this seems to be mostly a case of packing more explosive into it than significant improvements in REF.
The jet damage goes up to 7d(10), or 75% more than the TL7 one. That looks a lot like the jet's penetration goes up in a linear fashion with the force of the explosion.

HEAT shells improve not just in the power of the explosive, but in the shape of the hollow cone, and also in the composition of the liner.

However, the TL9 shaped charge warheads in Ultra-Tech make a massive jump in effectiveness, with the 40mm one doing 6d×4(10) with 4d explosive. The relatively low explosive damage implies that this isn't a super-high REF explosive, but I find it hard to believe that other factors could account for more than triple the penetration, even if you use uranium or something as the liner material.

The low explosive damage can also mean that more energy is being pushed into the penetrator jet, leaving less to cause the omnidirectional explosion.

So, it seems that the shaped charge damage in Ultra-Tech is way off and the HE / HEC damage might be a bit low. Adjusting normal explosive effects (e.g. HE damage) to account for different effectiveness in future explosives seems fairly straightforward; just figure out the REF and weight of explosive, then multiply them together and use the usual explosion rules.
But for shaped charges, I have no idea what appropriate values are. My instinct is to make them scale at the same rate as normal explosives, i.e. at the square root of mass × REF, but since I'm not a mathematician, scientist, or engineer, I don't think my instincts are to be trusted on this.

Can anyone who actually knows what they are talking about comment?

Assuming the same tech, form factor, materials, etc., my recollection is that HEAT penetration is proportional to the diameter of the warhead (and thus the cube root of mass). However given the complex interaction of explosive, liner, geometry, etc. that does not mean it scales with the cube root of explosive energy in any other situation.

One thing to be aware of is that UT's 40mm shaped-charge grenade stats were taken from real life, and HEAT warheads that small tend to be terrible. There just isn't room for good geometry, and a fuse, and a good stand-off distance, and a decent amount of explosive. They also try to be HEDP, and that costs weight and volume for fragmentation layers and/or enhanced blast.

[Fred Brackin]

Originally Posted by Rupert

Assuming the same tech, form factor, materials, etc., my recollection is that HEAT penetration is proportional to the diameter of the warhead (and thus the cube root of mass). However given the complex interaction of explosive, liner, geometry, etc. that does not mean it scales with the cube root of explosive energy in any other situation.

Hans likes to rate HEAT penetration in multipliers of the caliber of the warhead but ISTR numbers that go from 5 to 15x over the TL7-8 period. Much of this really does seem to be the "art" in "state of the art" and hence not very subject to mathematical; extrapolation.

[Sam Baughn]

I'm unclear if the poor performance of modern-day 40mm is an inherent issue, or simply a case of us not having small enough components, reliable enough manufacturing, good enough computer modelling, and so on, which all seems likely to improve a lot with generally more advanced technology. The existence of 25mm and smaller (for HEMP) shaped charges in Ultra-Tech seem to imply that the authors felt that improvement was either realistic or at least in keeping with common genre assumptions (and I'm inclined to say the former, since I don't think I remember shaped charges being mentioned in any SF I've watched or read).
I know that diameter (and shape, and composition) of the liner is basically the most important factor, but I assume that having a more energetic explosive which explodes faster has to provide some benefit.
One obvious issue I just thought of with shaped charge penetration scaling with more explosive force is that it must be no better than the cube root of the relative force, or have some upper bound, because otherwise there would be no point in making large-diameter charges; you could do the same by simply adding more explosives. On the other hand, it can't be much worse than scaling with the cube root, or nobody would bother trying to jam more explosive force into HEAT shells, and it looks like they do (with later designs generally having more TNT-equivalent in the same package).

[sir_pudding]

The M433 was developed in the 60s. There are a couple of DoD procurement efforts to find a replacement.

Its also possible that the M433 waa deliberately less explosive than is possible in 40 mm x 46 mm grenades. The original procurement specs called for a 5m kill radius.

You don't really want a huge kill radius on a low velocity grenade that you fire from an infantry weapon.

[Rupert]

Originally Posted by sir_pudding

The M433 was developed in the 60s. There are a couple of DoD procurement efforts to find a replacement.

Its also possible that the M433 waa deliberately less explosive than is possible in 40 mm x 46 mm grenades. The original procurement specs called for a 5m kill radius.

You don't really want a huge kill radius on a low velocity grenade that you fire from an infantry weapon.

It was about all they could do to get that much effect into the 40mm shell at the time - the fuse filled the whole front half of the shell.

[Willy]

Originally Posted by sir_pudding

SNIP
You don't really want a huge kill radius on a low velocity grenade that you fire from an infantry weapon.

The problem is not the kill radius, such a underbarrel launcher is mostly used at distances farther than 100m, and at that range even a 80mm mortar grande is not killing the guy who pulls the trigger.

Originally Posted by Rupert

It was about all they could do to get that much effect into the 40mm shell at the time - the fuse filled the whole front half of the shell.

That is the real problem, the tech was to low to make a grenade that could be pprogrammed to explode only after a secure distance from the shooter, and ALL new machine greande launchers work with programmable grenades and can be of smaller diameter. At the point where the 40mm was introduced it was cutting bleeding edge of the technology, now even 3rd World nations could do better. So yes refurbishing the underbarrel launcher with induction to program the grenade, add a laser distance meter and a target computer to the rifle, and fit out the grenade itself with the necessary parts would work - but raise the price per shoot drastically.

Sometimes cheap, dump and reliable is a advantage on the battlefield.

[RyanW]

Originally Posted by Rupert

HEAT shells improve not just in the power of the explosive, but in the shape of the hollow cone, and also in the composition of the liner.

And some designs may actually be less efficient armor penetrators on purpose, because they prioritize other capabilities. Greater behind armor effect, greater blast effect, or reducing the effectiveness of reactive armor, for example.