HerrTom

Thank you cool breeze. I guess while I'm attempting to summon people, I'm wondering if this matches the intuitions of @TheForwardObserver and @panzersaurkrautwerfer Another note/clarification from the plots on page 7 - they may look scarier than reality. While a BTR would see 10 hits at 0.1 fragments per square meter - those hits still have to hit something important. Those important bits are somewhat smaller than the vehicle. Additionally, very few fragments from any single artillery shell will hit the armor straight-on, which is what the plots show. Add in an impact angle and armor gets even better.

0825 A surprisingly quiet minute. A pair of 152 mm shells land on the bridge. Most of the Russian force appears to have already crossed, unfortunately. Would have been a great hit on a BMP. Another BMP-2 gets nailed by the Russian BMP-3s in the treeline. No new map - nothing seems to have moved as best as I can tell. There appears to be some small arms fire inside Pryvitnoe shooting at the company HQ, but I can't really tell where it's coming from.

I did some more reading and it seems Mott is the best for my particular application - as I break down the shell into short sections where the Mott distribution pans out pretty well, while for looking at shells overall, the Wiebull or Held distributions work out better some of the time. At this point, I'm curious what Steve @Battlefront.com thinks, if anything! --- John, I think it may lie in the Mott distribution underpredicting the smaller fragments. If you were modeling personnel danger, it may be important, but for the armor penetration models larger fragments are more important. Thankfully, Mott is pretty good in those ranges, as best as I can tell. This might account for the discrepancy in the impact numbers - the ones that can actually penetrate the target are accounted for, more or less, but the smaller ones are not.

Are you sure about that? The 2A70 low pressure gun seems to have a muzzle velocity of 250-350 m/s depending on the round. Ignoring drag on the projectile, that's between 2.8 and 3 seconds to travel 1 klick.

Just compared the 1/2" plate from the study. 162 square feet target at 90 feet (27 meters). Experiment: 476 hits, 41 perforations Model: 114 hits, 32 perforations Again, I seem to lowball it, but I'm not sure if that's a bad thing in this case. I found a paper that said the Mott distribution might not always work out and suggested a few others, but they seem too empirical for my tastes - it makes them less useful in creating general models like I am. At any rate, Mott seems to underestimate the number of smaller fragments compared to reality (sometimes, it's all very confusing).

I admit my nomenclature here was confusing. What the plots say is that if you take the largest fragment present in that space at 0.1 per square meter, you'll need 30mm RHAe to protect against it. Increasing that desired density will bring the contours closer to the shell impact, and lowering it will bring the contours further out. It's really a cross section of a 4 dimensional surface Perhaps a better way of explaining it is that with the 0.1 fragments per square meter density, a 10 square meter, 30 mm thick, RHA target at that location will see (on average) 1 perforation per shell. This is one of the weak points of my presentation. I'm scratching my brain trying to figure out how best to present the data I have, and haven't been able to come up with a better way. Edit: Perhaps this will be a bit more enlightening, John: This plot shows the actual density of fragments greater than 1 gram as they fly away from the impact site. If it lands directly on you, every square meter will see 1,000 fragments hit it. Then, by around 10 meters, there's only 1 fragment greater than 1 gram per square meter, and so on. So to reiterate the above, I specifically looked at what fragment mass can I look at such that the density is always .1 fragments per square meter greater than a certain mass. I hope that makes sense Pretty much. I calculated the plot by taking the maximum penetration calculated at any point at that radius from the shell. If you look at the contour plots and look for the highest value at any vertical section, you'll get that plot. Damn! You're correct. Bah, proofreading is for technical writers! You'd definitely have passed if I had been clearer! Thanks for asking for clarifications, I know my mind can get a little crazy. --- In other news, I did a quick calculation to compare the results of the 155mm shell from the Protection Provided by Steel and Aluminum Armor Against Fragments from High Explosive Ammunition on the first page of this thread. From 36x 155mm rounds, their 144 square foot, 3/8" (9.5mm) targets saw 585 hits and 55 perforations at 90 feet (27 meters). My model predicts 101 hits and 48 perforations. I'm not sure how they count hits here, and may be counting impacts from fragments smaller than what my model predicts. Regardless, I think the interesting part is the perforation comparison: Experiment: 55 Model: 48 Definitely good looking in support! That's all for tonight!

Quick little addendum: 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.

So I made a cool little blending function: 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: 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: Fits the middle ground! 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! 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.

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 Ordnung. The 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: 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: 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: First, the "classic" cylindrical fragment! 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! 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: 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!

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.

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

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.

So my off the top of my head prediction was a little off - the exponent is a fair portion larger: So a fragment striking armor angled at 60 degrees will have to be going 3.4x faster to penetrate the same thickness of armor.

Very astute observations! 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.

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.

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 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! The O-832 produces around 500 fragments of significant size, with few being larger than 50 grams. 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 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. The fragments have much larger size compared to the mortar shell, with few being larger than 500 grams. 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 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! 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! 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).

I anticipate that they'll be very dangerous. Somewhere beyond 100mm of steel dangerous.

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!

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

@Sgt.Squarehead - the version I'm playing right now, posted earlier in the thread: https://drive.google.com/file/d/0B2rdazkKVNJXUEh3bjRHSXY4QUk/view 0824 A Russian BMP finishes off an abandoned BMP-2. The shots arc over another that is creeping into position to better identify something to shoot at. One of 1st Platoon's BMP-2s identifies a Russian IFV crossing into the forested area by the canal and unloads autocannon fire into it. Unfortunately, the target and its friends don't take kindly to that and unload a number of 30mm cannon fire in return, killing the driver. Not much movement that I'm aware of. I think I saw an infantry squad moving through Pryvitnoe, but I hope my machine gun team can give them some trouble while I sneak my RPG squad away.

Ach! Full circle! Wasn't there another thread a while ago showing exposed gunners were fired at more accurately than infantry otherwise are? It was in CMBN or CMFB, if I recall correctly. Perhaps that also effects Stryker gunner survival rates?

I've only seen two notable graphical errors using reshade. Transparent objects (really anything that isn't in the depth buffer) isn't affected by any depth based shaders (like SSAO). This means largely tree leaves (but not the 2d distant trees), smoke and windows. Any unrendered areas, behind loading bars or the edges of the main menu go crazy with screen based shaders. Terrain clipping wise, nope. Haven't seen anything like that. I don't generally give orders and such with it on though, it's mostly for screenshots.

I'm partial to 3-and-change inch slugs myself. One reason to take the fifties is that they hold a bunch more ammo, so they have better longevity in protracted battles.

So for sanity, I looked at the classic .50" M8 API bullet. Here's its speed as it travels downrange - important in figuring out how much it can penetrate! The THOR equations can tell us how fast the bullet needs to go to penetrate a plate thickness. Data for the M8 varied from source to source by about +/- 3mm, so I have that marked as error bars. I know, I know, it's incorrect to do it that way. I think it's a helpful visualization here. Probably should have plotted two points instead, but I'm lazy and don't want to do it again! We can do a reverse lookup using the kinematics chart above, showing the range and penetration in a format that's both more useful and more familiar. So it seems THOR overestimates the penetration for the thinner plates. Why is that? Well, I did some more reading - and Recht & Ipson developed their model particularly to get better results for armor of similar thickness to the penetrator. So what I had before has the big asterisk in that Recht and Ipson's model is particularly good for heavier fragments against thicker armor, and smaller fragments on thinner armor. THOR, meanwhile, picks up the slack between - largely for fragments smaller than the armor's thickness. Anyway, the data looks promising compared to the M8, so that makes me happy! That's it for tonight.

if I'm following you correctly, Ken, I think you'd get the same plus but rotated that angle. Unless you're talking about the effect of gravity, in which case you're entirely correct. The fragment velocity equation doesn't take that into account. But since I know v(x), I can derive v(t) and back out the kinematics to do that. Not sure if it's entirely worth the effort there, though. Over the 20 meters these fragments travel, gravity effects the velocity by ~.2 m/s, or position by 2mm. If you're talking about the velocity inherited from the shell, then that won't change with the angle the shell lands, but it would pull the fragmentation plots to the left a bit.