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kbluck
29 Aug 03, 19:53
I've long had a nagging feeling that mortars were being shortchanged in ATF. The relative impotence of mortars in the game just doesn't jibe with my historical reading. So, I did a little research, did a little math, and came up with some interesting results and what I think is a justification to improve the kill effectiveness of mortars. Comments welcome.

It seems to me that the best way to evaluate the comparative effect of different artillery rounds is to compare their weights rather than their caliber. I believe this would most accurately account for their relative explosive power and fragmentation potential without getting into a lot of complicated physics.

If you accept that, then lets look at the rounds in question. A M107 155mm HE round weighs in at around 95lbs, while a M933 120mm HE bomb tips the scales at around 30lbs, about 1/3 the total weight. So, you would expect the mortar to be about 1/3 as effective.

But wait! We're not talking about equal areas of effect here! If we're assuming that the concussion and fragmentation is being distributed evenly through the area of effect (a game abstraction) then we find that the 120mm, with its 20m radius, is "attacking" a total area of only 1/6 that of the 50m radius covered by the 155mm. (Pi*r^2, if you've forgotten elementary geometry.) So, it seems to me that if you keep the radius at 20m, the 120mm round should be roughly twice as effective as the 155mm over that reduced radius!

If we expand the mortar's radius to 30m, which would have an area roughly 1/3 that of 50m, we get a pleasing concordance: the 120's "effect per square foot" runs about 85% of the 155. Given the "declining return" per pound for large charges vs. small ones, and the denser fragmentation pattern typically generated by cast iron mortar bombs vs. machined steel artillery shells, I think it is reasonable to "upgrade" the mortar a few percent to 95% or so over the 30m radius.

So, I think there is a compelling case here that mortars have been seriously shortchanged in database1. Am I deluded?

--- Kevin

Deltapooh
02 Sep 03, 19:49
In short, you think database1 should have 120mm mortar with a setting of .85 lethality fraction and 30 meter blast radius.

I recall that in BCT: Commander the 105mm howitzer had a lethality fraction (I believe it was called EO) of .75

I'm not a expert in indirect fire though. I think about tickering with the indirect fire information, but I'm scared will CPT. Proctor give me an "indirect fire beating." However, you position makes since for HE munitions. Don't the US employ the same type of explosive in both the 120mm and the 155mm?

kbluck
03 Sep 03, 11:51
I'm the first to admit that this analysis is very simplistic. Based on what I know of the behavior of explosives, though, I do think that mortar rounds have been shortchanged.

In general, as bombs get bigger, the "effectiveness per pound" declines. Speaking as an engineer, I know that you often get more useful work out of multiple small charges than the equivalent weight of explosive all in one mass. Actually, ICM is the logical extension of this observation; many small bomblets are much more effective than one big shell, even though the total weight of the bomblets is less than the big shell. As such, I think that a direct correlation based on overall weight actually understates the true effectiveness of smaller rounds on a per-pound basis.

Quite honestly, based on the studies I've been reading, I think that 50m is a bit wide of a radius even for 155mm HE. While that is certainly well inside the "danger" radius for the round from a safety officer standpoint, the concussion is not likely to seriously injure past 20-30 meters and the chances of a shrapnel hit are also quite low past that range. (ICM is another story, of course.) Not that I'd want to be that close, but we're talking military effectiveness here.

Add on to that the oblateness of the destruction footprint. Consider the nature of the shell; it is basically a cylinder. When it explodes, most of the shrapnel flies out approximately perpendicular to the long axis. However, the shell is not impacting in a vertical posture; most cannon artillery rounds will come down at a fairly low angle. So, the shell is tilted. That means the shrapnel flies out at "grazing" altitude pretty well to the right and left of the shell's path, but in front and behind it tends to fly up in the air or down into the ground. So, what you get is two "kill lobes" out to the side and greatly reduced effectiveness fore and aft.

Mortars, by comparison, are less cylindrical in shape, thus producing a more uniform pattern, and also generally impact at a much higher angle than cannon shells, again producing a more dangerous distribution of shrapnel --- their "lobes" are wider. Thus, they are arguably more "effective per pound" than larger artillery shells.

I freely admit there is a lot of hand-waving going on here. My experience with all this is largely academic. In the end, this is all going to go into my own database, and we'll see how it plays out.

--- Kevin

"Artillery is the God of War, and the mortar is its prophet."

Pat Proctor
03 Sep 03, 23:24
You have once again, foolishly stumbled into my favorite topic. ;)

You are correct about the weights of 155mm and 120mm mortar ammo, but you are comparing apples and oranges. The 95 lb figure for 155 is ONLY the round, with its shrapnel producing casing. The 30 lb figure for the 120mm ammo INCLUDES the packaging, AND the propellant. The projectile itself probably weighs around 20 lbs.

Now, before I go on, I will say that I based the pK's on the SAWE (Surface Area Weapon Effects) tables from MILES II (the system used at NTC). I did not originally figure these numbers out. And I am speculating about the way they arrived at the numbers and the relative numbers. But it is, I think, a pretty educated guess.

Explosive energy is proportional to the cubed root of the mass of the projectile. The cube root of 95 is around 5, and the cube root of 20 (the mass of the 120mm PROJECTILE) is about 2.5, so it follows that the 120mm round is about 50% as lethal as the 155mm round.

By contrast, the average 105 round is around 35 lbs (also PROJECTILE ONLY). The cube root of this is around 3.5, so it would follow that it would be about 70% as lethal as the 155mm round.

The burst radii used in ATF are from Army Doctrine. It is not concussion that kills with artillery, it is the 12 inch long strips of 2-3 lb, razor sharp shards of shrapnel that get you. And a 155mm round throws more of them farther and faster than a 120mm round, hence the bigger radius. In fact, concussion causes very few injuries with rounds this small, other than hearing loss.

kbluck
04 Sep 03, 11:47
Explosive energy is proportional to the cubed root of the mass of the projectile. The cube root of 95 is around 5, and the cube root of 20 (the mass of the 120mm PROJECTILE) is about 2.5, so it follows that the 120mm round is about 50% as lethal as the 155mm round.

Heh! Got you into the math after all.

Yes, I agree with this entirely. And, of course, it is what I meant when I was talking about smaller charges being proportionally more effective. But, here's where I think you're "double-counting":


The burst radii used in ATF are from Army Doctrine. It is not concussion that kills with artillery, it is the 12 inch long strips of 2-3 lb, razor sharp shards of shrapnel that get you. And a 155mm round throws more of them farther and faster than a 120mm round, hence the bigger radius.

The different burst radii are a direct consequence of the difference in explosive power. As you say, a 155 throws more shrapnel farther. Why? Because it has more explosive power! But, you've already accounted for the reduction in explosive power completely when you reduced the lethality. So, by dropping lethality to 50% and reducing the effective radius, you're penalizing the mortar round twice.

I propose that lethality and burst radius should not be treated as two unrelated issues. Instead, figure out the explosive power ratio, reduce the radius to the doctrinal value, determine how much of the power reduction has already been accounted for by the reduced radius, and then apply the remainder, if any, to the lethality.

So, using your cube root figures above, we still find that a 20m radius would produce about 200% lethality "per square foot", while 30m would produce about 100% lethality over that reduced radius.

As for "Army Doctrine", the question is: which doctrine? I just looked up FM 7-90, "Tactical Employment of Mortars." In Appendix B it lists the lethal burst areas of various mortar shells. I swear I didn't read this until just now, but you'll never guess what they list for M57 120mm: a radius of 30m! So, I'm feeling better and better about this idea of mine.

I wish I could legally get access to the JMEMs, which would probably settle this with some authority, but unfortunately they are confidential materials.

--- Kevin

kbluck
04 Sep 03, 13:29
Thinking about it a bit more, I realized that cube root probably isn't the best equivalence formula. Cube root is actually the function of blast damage from a given charge at a given distance. Put another way, blast damage decreases as the cube of distance from the blast. But, as you mentioned, we're more interested in shrapnel effect than blast.

Looking at some "equivalence tables" from WWII, I noted there is a strong correlation between the square root of shell weight and effectiveness ratio. In other words, given a target of fixed size, if you need 6 rounds of 155mm to affect it, you would need sqrt(43kg)/sqrt(15kg) = 1.7 times as much 105mm (about 10 rounds) to affect the same area to the same degree. Or, you could rephrase this as saying that 6 rounds of 105mm HE will affect an area 1/1.7 = 58% as large with equivalent lethality. If the area in question is a circle 50m in diameter for 155mm, then the equivalent lethality radius for 105mm should be about 38m. Based on this, we should be able to say that 105 would be around 95% lethality in a 40m radius (since the game makes us pick a multiple of 10.)

Doing the equivalent calculations for 120mm mortar, we find that even after reducing the weight for propellant and packing, a 120 is about 130% as lethal over a 30m radius. If, however, we wished to affect a 50m radius target equivalent to 1 round of 155mm, we would need a bit more than two 120mm rounds.

Would you agree that it is more dangerous to be standing 10m from a bursting 120mm than to be 50m from a 155? If so, then you have to agree that radius has some relationship to effectiveness. Since the game requires us to pick an arbitrary radius, doesn't it make sense to pick a radius that makes the rounds more or less equivalent in effect over that radius? Isn't that exactly what the "doctrine" tables of burst radius are doing?

--- Kevin