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Vehicle protection from artillery shells


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Quick preview of what I've been working on over the weekend:

bMkzNSR.png

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Refining the fragmentation pattern to be soundly based on the shape of the shell compared to the cylinder-based model from before.  Compare the above, 203mm, shell to:

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An 82mm mortar shell.  It seems the larger shells produce somewhat smaller numbers of larger fragments, while the smaller ones with thin walls produce many smaller fragments.  I still have some work to do, including verifying that this behavior is correct.

Edited by HerrTom
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So I looked back through the thread during my coffee break and came across the pictures Armorgunner and Haiduk posted that seem to support the fragmentation data I got from the 203 mm shell. The model predicts about 300 fragments larger than 1 gram, and many of them are quite large - 50 or so are larger than 250 grams! Those are some scary fragments when travelling more than 1 kilometer per second!

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Thanks!  Revisited the shells using the new formulation - analytical fragmentation patterns using the actual shape of the artillery shell.  One big caveat here - the formulation of the fragmentation is designed and programmed to be both 1) easy to deal with as data and 2) accurate particularly in the radial direction - the one we care most about!

So that caveat means that the fragmentation predicted on the up/down directions probably isn't super accurate - and you'll note that (due to how I coded the shape) - some shells see very little up/down spray.  That's simply because I haven't figured out a good robust way to account for the fragmentation of the upper and lower faces of the shell yet.

Also new and improved (TM) is the fragmentation penetration model - instead of assuming spherical fragments (because it's easy), I more correctly assume cylindrical fragments of the thickness of the shell at that location.  This affects the impact area - and greatly affects the penetration capability of certain shells.  This means that a 50 gram fragment from, say, a mortar, will actually be less dangerous than a similar 50 gram fragment from an artillery shell - since the shell fragment is thicker, it has a smaller presented area for penetration than the thin mortar bomb.

So, without further ado:

82mm O-832 mortar shell

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This one has the correct shape now, too!  Drew it in Solidworks and grabbed some points on the perimeter to get it - looks good, I think!

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The O-832 produces around 500 fragments of significant size, with few being larger than 50 grams.

wR5BEsh.png

The mortar bomb produces a blast pattern kinda like this - works very well for something that is meant to land vertically - maximum blast is directed up and away from the ground!  It's really cool to see this in action - since you'll see the artillery shells have a different pattern entirely!

152mm OF-530 artillery shell

VwWbR4C.png

Here's the wonderful 152mm OF-530 shell, which some of you may recognize as the shell I used in my explicit dynamics simulations:

Funnily enough, you can note that the blast and fragments are still primarily directed sideways from the simulation above on a 40mm plate, but to a lesser extent upwards compared to the mortar.

EqKgxh5.png

The fragments have much larger size compared to the mortar shell, with few being larger than 500 grams.

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Comparing to the explicit dynamics simulation above, you can see that the primary direction of the fragments is indeed sideways.  You can imagine this pattern is better for a shell that will be landing at a much sharper angle compared to the mortar bomb.  As it rotates, the blast is still somewhat directed downrange, while there still is a sharp tick on the shallow side.  The odd-looking striations are caused by a combination of overlapping angles on the shell geometry and the size of the grid I used to plot the contours.

203mm OVF34 artillery shell

WjG7UnY.png

I had a hard time coming across good data on 203 mm artillery shells, let alone their shape or weight.  This is the best guess I could pull together, so if anyone has a good source for different types of Soviet artillery ammunition, I'd be grateful!

WxLgtsM.png

This shape of ammunition produces significantly fewer fragments - but note how huge they are!  I extended the fragment distribution up to 2 kilograms, and we still are seeing 5 fragments per shell bigger than that!

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Which leads us to the penetration plot.  Up close, not even 100 mm of steel is going to reliably protect you from fragments from this monster.  Our BTR may not be safe out to 60 meters from these shells (with a 0 degree obliquity impact - angled armor does more than just increase LOS thickness when it comes to fragments, as best as I can tell).

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203mm shells are terrifying! The plots I made are at a relatively low density of fragmentation though. One has to consider the chances of hitting something important even if the fragment penetrates.

An airburst is going to send fragments into the top of vehicles at pretty shallow angles - like 60 degrees AoA or more. That increases the velocity a fragment needs to penetrate by more than 2x (somewhere around 2.2, off the top of my head for the sec(theta)^gamma term).

I'll try to put together some plots to show that angling effect.

So it's a mixed bag. Top armor is thinner, but the impact angle is unfavorable. Ground bursts can penetrate better, given the angle of attack close to zero on the side armor, but the side armor is thicker.

Spaced armor also seems like it would be more effective against fragments - 2 20mm plates May protect better than 1 40mm plate. I need to double check that, though.

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I love what you do with your weekends. ;)

You made a statement about the effectiveness of the penetration based on the cylinder wall thickness. Hmm...quote function: 

15 hours ago, HerrTom said:

Also new and improved (TM) is the fragmentation penetration model - instead of assuming spherical fragments (because it's easy), I more correctly assume cylindrical fragments of the thickness of the shell at that location.  This affects the impact area - and greatly affects the penetration capability of certain shells.  This means that a 50 gram fragment from, say, a mortar, will actually be less dangerous than a similar 50 gram fragment from an artillery shell - since the shell fragment is thicker, it has a smaller presented area for penetration than the thin mortar bomb.

(My bold.) Whereas I agree that the thicker artillery shell casing presents a much more dangerous fragment than a thin mortar shell, the "presented area" would be somewhat random when compared to one another. As well, the artillery shell has much crystallized structures so that the fragments have a very sharp edge. Think a very sharp rhomboid on the acute angles. 

Keep it going. You KNOW some of this will get into the game.

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2 hours ago, HerrTom said:

203mm shells are terrifying! The plots I made are at a relatively low density of fragmentation though. One has to consider the chances of hitting something important even if the fragment penetrates.

I can say that most of artillery fire on Donbas has usual impact, not airburst mode. Several times airburst HE were used for example in 2015 during battle for Shyrokyne and troopers said "Russians use new shells", but indeed that were usual HE. Instead airburst both sides uses MLRS with cassete ammunitions.

But 203 mm really terrify. One hit and 3-storey house ruined (not like in CM, when such tipe of building can survive after several 203 mm hits). Knowingly, several times, separs formations left positions, when seen 203 mm impact even in 200-300 m from own trenches. 

Edited by Haiduk
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1 hour ago, c3k said:

(My bold.) Whereas I agree that the thicker artillery shell casing presents a much more dangerous fragment than a thin mortar shell, the "presented area" would be somewhat random when compared to one another. As well, the artillery shell has much crystallized structures so that the fragments have a very sharp edge. Think a very sharp rhomboid on the acute angles. 

Very astute observations! :lol: These areas are probably one the biggest weak points of the theory.

The THOR equations take the density of the impactor into account, in a sense, by taking both the mass of the fragment and the average impact area into account. (side note - this also accounts for longer APFSDS rounds being more effective - more mass, same area) The Big Fat Assumptions I made here are that

1) the fragment is a flat cylinder with the thickness of the shell casing, and

2) it impacts the armor flat on.

The first is not true in reality because of what you mentioned - the steel will fail along imperfections, grain boundaries, or even its crystalline structure - and this all happens after immense plastic deformation that is going to strain harden the material - so you'll get rhomboids, pyramids and prisms. I'd be hard pressed to find a cylindrical fragment! This likely leads to fragments with better penetration power than you'd really see in the "thinner" real fragments, but I think this is mitigated by the second point.

In reality, these fragments are going to spin and tumble like crazy, impacting anywhere from flat to edge on. Edge on gives better penetration than the cylinder, while flat likely worse. In all, the cylindrical fragment hopefully finds the middle ground between all of these factors.

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HerrTom,

Am dazzled by your work, but from what I can tell you're not modeling the ballooning of the projectile body prior to disintegration. Is this correct? If so, then the impressive assessment you've created perhaps isn't accurately reflecting the effect of distorted projectile body shape on fragment spray pattern. Or is that factor merely in the noise relative to other aspects of the calculations and engineering analysis?

Regards,

John Kettler

Edited by John Kettler
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I did read a paper that addressed the "leaking" that occurs from the pressurization gases, but it's a bit too detailed for me to really be motivated to include it - it introduces a small ( < 5%) decrease in the fragment velocity.  Fragmentation angle output is calculated using the Taylor angle formula in here:

http://www.dtic.mil/dtic/tr/fulltext/u2/b007377.pdf

It seems to match fairly well with the radiograph results they present on pp18-19.

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Thanks for the explanation that you're using flat-faced cylinders to model the fragments. Here's a thought (from someone who doesn't have to do the work. ;) ):

1. Take the same cylinder, but "invert" it, to produce the worst-case penetration model for that fragment.

2. Using the "worst-case" and the "optimal shape", plot the difference penetrations.

I'll expand in a moment. The over-arching thought is to remember that, as effective as artillery CAN be as an anti-armor munition, in general it is very inefficient. 

Assume a shell thickness of 10mm. If, (totally fictitious numbers), given that 10mm length of the cylinder, it seems like the mass is what produces the diameter in your model. So, again, a made up number, a 5 gram fragment, in the shape of a 10mm long cylinder, it would need, say, a 2mm diameter. (This is what I've gathered from your posts.) That 2mm x 10mm cylinder strikes the armor face-on and has a certain penetration value. (Modified by the slope of the armor, hardness, etc.) This is similar to piece of pencil lead.

Now, to simulate the random tumbling of the fragments, but keeping with your model, is it possible to change the cylinders so that their diameters are all equal to the thickness of the projectile and their depth is modified to produce the mass? In the case I gave above, that would yield a 5 gram fragment with a 10mm diameter and a 2mm thickness. This would be similar to a (small) coin. (I've totally ignored geometry and volume for this example. The takeaway is that the length is dependent upon the mass, rather than the diameter.)

This would produce a plot with a very rough first order (half order???) of a tumbled fragment striking armor.

In this case, the value of thicker cases would still be important: mass is mass.

That new plot would be a worst-case of penetration. Your current work would almost be a best-case. Picking an intermediate value from between the two would seem to give better/more realistic results? (Or simply taking your fragment count and reducing it by a percentage to take into account the fragments which hit the "wrong" way?)

Edited by c3k
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1 hour ago, c3k said:

Assume a shell thickness of 10mm. If, (totally fictitious numbers), given that 10mm length of the cylinder, it seems like the mass is what produces the diameter in your model. So, again, a made up number, a 5 gram fragment, in the shape of a 10mm long cylinder, it would need, say, a 2mm diameter. (This is what I've gathered from your posts.) That 2mm x 10mm cylinder strikes the armor face-on and has a certain penetration value. (Modified by the slope of the armor, hardness, etc.) This is similar to piece of pencil lead.

Correct. This fragment would really be a 9 mm diameter cylinder, looking something like the left hand picture, while if I read you correctly - if I check a 10 mm diameter cylinder (height 8 mm), it'll look like the slightly different right hand picture, which will definitely have somewhat different penetration characteristics.  I expect for small masses that this will produce worse results, and better results for higher masses, at whichever point the diameter of the fragment is equal to the thickness of the shell.

mddy3nL.pngxLs5Ut8.png

These two cylinders ostensibly represent the best/worst case of a fragment that may look more like this:

UN5zEfE.png

2 hours ago, c3k said:

That new plot would be a worst-case of penetration. Your current work would almost be a best-case. Picking an intermediate value from between the two would seem to give better/more realistic results? (Or simply taking your fragment count and reducing it by a percentage to take into account the fragments which hit the "wrong" way?)

A good idea!  The smaller fragments are less dangerous on this scale, while the larger ones are more lethal (as discussed above).  The two points (upper and lower) could be points on a Gaussian distribution to get a "normal" penetration table.

 

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Actually, the way I calculated the fragment area, it could be literally any shape you want - it's (mean_impact_area = m_fragment / rho_Casing / t_casing) so whatever shape of constant thickness will give the same area.  I did the sideways cylinder and it quickly got way out of control (talk about 6 meter long fragments coming out of a half meter long shell!).  I'm instead going to calculate the striking area of the above fragment if it strikes solely sideways - so (mean_impact_area_side = sqrt(mean_impact_area) * t_casing) - this gives a good estimate, I think, of the sideways impact case.

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Man, I was implementing an equation that represents a random fragment shape when I discovered that, despite what my above plots say, the frag density is really 0.01 per square meter! That makes a difference in the ranges, if not the power of the fragments.  If you have a 100 square meter target in the above scenarios, you'll hit once per shell (on average) or once per 10 shells on a 10 square meter target, and so on.  After noticing this (embarrassing) gaffe, I went back and double checked all my formulas.  Everything seems in OrdnungThe problem was really with my plot titles saying "0.1" instead of whatever density I actually wanted and input upstream - now they are fairly dynamic, changing depending on what I put upstream :) 

So... a couple of correct graphs:

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Here's our 152 mm shell - the shape is the same, but note that our BTR is protected at this (correct) density at only 30 meters instead of over 50 in the previous graph!  And now the random fragments:

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And these results confused the hell out of me!  I went back and double checked everything again, output tons of variables and drove myself silly sorting through thousands of data points.  Why?  Well, take a look for yourself at the penetration tables for the different fragment types:

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First, the "classic" cylindrical fragment!

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And the random fragment.  Notice the problem?  These charts show that the penetration capability of the random fragment is better than the cylindrical fragment.  So I plotted a few more things, like the fragment weights and velocities to do a lookup manually.  Maybe the interpolation I did was wrong.  Well, nope!

At the data point I looked at, the fragment weight of interest was about 40 grams, and the velocity 1200 m/s - more or less.  So the above charts aren't so helpful at that.  Let's zoom in!

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The random fragment actually is much worse for the smaller fragments.  Huzzah!  Mystery solved!  Also provides what I think the key to making a better fragmentation model.  Small fragments may entirely be random in shape, but the larger fragments will end up closer to the cylindrical shape.

(The staircase at 2 km/s is because I clip the data at that level so it's easier to read)

Though, now that I'm writing this, that probably could have been solved by looking at the color bar scales next to the plots.

So I propose the creation of a model where we look at the estimated cylindrical fragment, and compare the diameter to the height.  If the diameter is significantly larger than the height - say 3x to 5x, then we transition to the cylinder fragment model, while the smaller fragments use the random fragment model.  This could be blended using a logistic function or something to prevent ugly artifacts.

As a bonus, here's the 82mm mortar:

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Note the much higher maximum penetration - this occurs very close in - within a meter or less of the shell.  Some of these oddities I think can be solved by the blending method I mentioned above.

That's it for tonight, I think.  Cheers, everyone!

Edited by HerrTom
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So I made a cool little blending function:

gG71Zva.png

As the diameter reaches 5x the thickness, it is 100% like a cylindrical fragment, but at 3x the thickness, it has 50% of the cylindrical fragment and 50% of the random fragment's performance.

If we call P1(x) and P2(x) the two penetration functions, and B(x) the blending function, the actual penetration I'm doing is P(x) = P1(x)B(x) + P2(x){1-B(x)}.  The end result is a penetration table that looks like this:

8SMhsrn.png

The smaller fragments have somewhat worse performance compared to the pure cylindrical model, and the larger fragments have worse performance compared to the pure random model.  I'd say that's the best of both worlds, since we don't want to overpredict the performance of either fragment!

This generates a protection plot that looks like this:

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Fits the middle ground! :D Close in to the shell, where larger fragments dominate, the penetration is realistically limited.  Further out, where the smaller fragments dominate, the random model's lower performance starts to dominate.  In the middle, it's a mix.  Overall, the protection needed seems to match common sense, I hope!

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I also pulled the maximum value from every radius and plotted this noisy graph.  This shows what you need to be safe at this fragmentation density under the "worst case" in that the densest fragmentation from the shell is pointed at you from any particular range.  It's noisy because of the combination of overlapping angles from the shell geometry and the grid size I used to plot the armor contours.

Edited by HerrTom
Forum ate the rest of my post!
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Quick little addendum:

kcu4jfR.png

Now you can compare all of the shells on the same plot!  Science!  Interesting to see that the 203 shell is less dangerous at the same fragment density than the 152mm shell.  This is probably (definitely) because the model predicts the 203 mm shell only producing some 500 shells compared to the 1500 from the 152 mm shell.  That's not to say the 203 is less lethal - if any of those fragments hits anything, it's going to cause a hell of a lot of damage.

Currently working on calculating what I get compared to the test that I posted in the OP so many moons ago.

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