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HerrTom

Vehicle protection from artillery shells

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I fired a 36m area fire mission from a single gun on basic training so I can get shells on target faster. That also affect the precision and the number of spotting rounds. A CEP of 20 meters seems pretty tight though, I agree. Some shells landed further than 40m away that I didn't grab for this plot.

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Recht & Ipson

So, the BTR-70 has 10mm armor at its thickest.  Seems artillery shell fragments can easily penetrate this!

38y8svh.png

Here's the maximum velocity of a 1 gram fragment as it travels from the blasts.  It can be seen that the fragments barely lose their velocity This can be used to calculate the velocity if a fragment impacts something.  Say... a 10mm thick plate of armor on a BTR.

8BKNkPK.png

So you can see the velocity of the fragment after penetrating a 10mm plate at any point in our artillery distribution.

f0QcTBM.png

We can combine this with the density of the fragments greater than a certain mass.  And, for the sake of thoroughness (if you can call it that haha), the same plots for a 5 gram fragment:

Gh9NZVn.png

 

kI5s0dV.png

At the BTR's position, we have the following data points:

Density of fragments > 1 gram: 2.42 frags/m^2
Density of fragments > 5 grams: 1.49 frags/m^2
Penetration velocity of fragments > 1 gram: 98 m/s
Penetration velocity of fragments > 5 grams: 270 m/s

I showed earlier (the common knowledge) that heavier fragments are more deadly - and this is confirmed here (probably because I used the same model).  If we take the dimensions of a BTR-70 (7.5 m X 2.8 m X 2.3 m) and call the average cross section presented to the artillery shells here as the average between the front and side cross sections, we get about 12 square meters.

So this barrage hit our BTR with 29 fragments greater than 1 gram, which probably don't have enough energy to cause significant damage inside the vehicle.  It also hit with 17 fragments greater than 5 grams, which certainly have enough energy to cause some significant damage to whatever they hit.

According to Recht and Ipson's model.  Next post, I'll run it using THOR.

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THOR

So as not to clot this up with duplicate plots, I only grabbed the interesting ones from the THOR runs:

HUuAcPI.png

Here's the penetration velocity from a 5 g fragment according to THOR.  Not much at all, eh?  THOR, as previously mentioned, was the standard, as best as I can tell, for modeling armor protection.  Unfortunately, as I previous mentioned, it seems to have problems with fragment-like objects.  This is further reinforced by the surprising results that the Soviet Artillery Effects study showed, which as far as I can tell, old armor/artillery models used THOR.  I suspect the truth lies between R&I and THOR here.  THOR predicts the armor is pretty resistant to 5 gram fragments at ranges beyond 5 meters, while R&I predicts danger out to 20 to 30 meters.

7WXpal4.png

If we step up to 10 gram fragments, shown above, we can see the density start to fall off.  It does so sharply.  If you refer to the probability curve I posted earlier, you can see that the probability of has a strong negative curvature to it, so the larger we go, we'll see much fewer fragments.

UAGnXZx.png

These 10 gram fragments are impressively dangerous, however.  THOR predicts these 10 gram fragments maintaining a velocity of 146 m/s after punching through 10mm of armor, at a density of 1.03 fragments per square meter.

Even under the conservative THOR model, our BTR gets perforated with 11 fragments of greater than 10 grams.  That's going to cause some damage - whether it's injuring crew members or passengers, or damaging equipment.

Unfortunately, this same barrage in CMBS presents absolutely zero identifiable damage to the BTR.  It's worth noting that all this data is probabilistic, but CM clearly doesn't reflect this data.  I'd say, from what I've shown here, at least light armored vehicles are more resistant in-game to artillery fire than they should.  Combine this with the reports that we've seen from the SAE as well as front-line combat in Ukraine, and I'd say there's a fairly strong case here.  I know these plots only show a single case of 12 shells, but it takes a while to write and generate them!  I've recorded observations from a number of tests, both in real games and purposeful tests, in addition to the one presented here, but I don't have good enough data to present more plots on those cases.

I leave tonight with this question: What else do we need to know here?  What more can I do to help us understand this?

Thanks everyone for helping in this thread, and I hope to see more discussion.

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It looks like you have provided good evidence that very soft skinned vehicles, such as unarmored humvees, UAZs and BTRs should be a bit more vulnerable to shrapnel than what is currently modeled in game. 

This data also seems to support that if a vehicle is rated to defend against .50 caliber rounds (which are around five times heavier and move around 10 times faster than these artillery fragments) then artillery fragments will do little more than scratch and divet the metal. 

At this point, now that you have well modeled and presented data, I am interested to see what BFC thinks about all this. It may be worth sending them this data so they can look over it in private before releasing official statements or anything like that here on the forums. 

Good job @HerrTom on your models and presentation of the data! At the very least, this should be helpful to those who have questions about the general effectiveness of artillery. 

Edited by IICptMillerII

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Thanks CptMiller. I thought of a couple more plots that might be more directly useful at showing the danger from artillery shells. I'll try to put them together tonight. I want to show the thickness of a 1 square meter plate that has a 50% chance of being perforated as you move around an artillery shell.

 

Not sure where you got 10x faster from. A .50 calibre bullet has around 2700 FPS muzzle velocity, or 833 m/s. These fragments are travelling up to 50% faster, though I didn't show any that have similar mass to a 42 gram bullet. These are also steel compared to lead, and offer slightly better penetration power.

I might put together some charts for bullets as a better grounding source, however limited that can be. Thanks for the idea!

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4 minutes ago, HerrTom said:

Not sure where you got 10x faster from. A .50 calibre bullet has around 2700 FPS muzzle velocity, or 833 m/s. These fragments are travelling up to 50% faster, though I didn't show any that have similar mass to a 42 gram bullet. These are also steel compared to lead, and offer slightly better penetration power.

You're right, my mistake. I accidentally converted an artillery fragments 250 m/s to a .50 cals 2900 fps (feet per second) in my head.

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With the granularity of the damage model versus something like health bars I'd be very interested to see how artillery fragments shred sub-systems, something that is absent now. A BTR-70's armour might be pierced, but even more than that the antennae being damaged would have a big impact.

Likewise using airburst to break the radars of AAA and SAMs would be a nice detail.

Thank you for all the work and the attention to detail!

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So we can solve the THOR equations to figure out what kind of velocity a fragment needs to penetrate a certain thickness of armor:

wWfAb64.png

As you can see, the heavier fragments (as expected) perform better at penetrating armor - requiring less velocity to do so.  As the armor gets thicker, the fragments begin to require prohibitively fast speeds to penetrate.  Typically on an artillery shell it seems the initial velocity is in the realm of 1.5 km/s.

K7mCv6L.png

Using the data generated for the angular dispersion plus some more to accommodate the shape of the shell, we can arrive at the fragmentation pattern for a shell travelling in the negative x direction.

The dip in the negative x direction comes from the nose of the shell obstructing some fragmentation, and the larger dip in the positive x direction is the same for the base - a more significant effect for the more significant blockage provided by the base of the shell.

This can all be combined together by some clever interpolation (good god it took a while to figure out how to massage the data to make that possible!).  If we select a fragmentation density - say 1 fragment per square meter, we can generate a contour plot showing us the thickness of armor required to generally have no perforations.

Uz3D1r3.png

Note the axes are not the same scale - this is to provide a better visualization of the regions.  At this density, a single artillery shell is likely to perforate a BTR 12 times at ranges up to 7 meters.

Vz6Hq8s.png

If we set the criteria to only 1.2 perforations per artillery shell (on average), we can see that our BTR isn't safe even up to 20 meters away!

sibcIgA.png

This can all be consolidated into a few lines showing the maximum distance that you're likely to penetrate a 1x1 meter target with 0.2, 0.4 ... 1.8 fragments per artillery shell.  The flat region at the top might be because I capped the maximum fragment size I analyzed.

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@HerrTom, excellent posts!!!

20 hours ago, HerrTom said:

A .50 calibre bullet has around 2700 FPS muzzle velocity, or 833 m/s.

I'm too obvious but nonetheless. To compare effects you may consider including distance to the target for .50cal model. At practical distances for vehicle engagement by .50cals the projectile speed/energy will fall sufficiently.

PS Really marvellous info you gave here.

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On 5/24/2017 at 11:41 AM, IICptMillerII said:

It looks like you have provided good evidence that very soft skinned vehicles, such as unarmored humvees, UAZs and BTRs should be a bit more vulnerable to shrapnel than what is currently modeled in game. 

This data also seems to support that if a vehicle is rated to defend against .50 caliber rounds (which are around five times heavier and move around 10 times faster than these artillery fragments) then artillery fragments will do little more than scratch and divet the metal. 

At this point, now that you have well modeled and presented data, I am interested to see what BFC thinks about all this. It may be worth sending them this data so they can look over it in private before releasing official statements or anything like that here on the forums. 

Good job @HerrTom on your models and presentation of the data! At the very least, this should be helpful to those who have questions about the general effectiveness of artillery. 

Have you noticed yet that you tend to read stuff that doesn't say things are protected against fragments as saying they are protected?

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I think the important thing to now its that the ratings tend to be along the lines of, STANAG 4569 Level IV, protection from 14.5mm at 500m or 155 artillery shell at 30 meters. 500 meters is a fair distance, but also puts some thought into the power of these fragments. Unfortunately, I still haven't been able to find out what STANAG defines as "protection," particularly against what is as variable as an artillery shell.

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@HerrTom great stuff...but a quibble. ;)

Your artillery fragment plots are very nice. The classic dispersion looks like a butterfly's wings, and your plots come very close. However, your plots are not directly translatable into fragments striking a target...unless the artillery round is travelling parallel to the ground and detonates over the target. In reality, they would come in with a vertical component to their trajectory. A significant vertical component. That will "squash" your plots.

In a perfect world, you'd be able to plot these at various trajectory angles (measured from the ground up) from as flat as 40 degrees all the way to 90 degrees (vertical).

Thanks.

Ken

 

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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.

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2 hours ago, cool breeze said:

Have you noticed yet that you tend to read stuff that doesn't say things are protected against fragments as saying they are protected?

Not sure what you're getting at so I'll try and explain it.

Physics is a constant. Just because one piece of metal is a bullet and another is a shell fragment, does not mean one has superior ballistics over the other just because its a shell fragment. A .50 caliber bullet weighs much more than a typical artillery fragment (here the fragments were 5 and 10 grams, a typical .50 caliber bullet is around 50 grams) and maintains is ballistic speed over much greater distance than an artillery fragment. The only way to get a 10 gram piece of metal to penetrate a significant amount of armor, more than a .50 caliber bullet, is to accelerate it to extreme speeds. Much faster than what is being presented. Even then, other things become factors, like the mechanical strength of the fragment, etc. 

One of the original arguments made in all of these artillery vs vehicles thread was that artillery shells should be able to kill tanks reliably just from the fragmentation of the artillery shell going off near the tank. My position has been that if a .50 caliber, or a 25mm shell cannot penetrate the side of a tank, then a fragment from an artillery shell will not be able to penetrate the side of a tank either. Obviously, if the side of a tank can be penetrated by smaller munitions, then it will be more vulnerable to shell fragmentation. 

HerrTom has shown that a 10 gram fragment can penetrate a BTRs armor. A .50 caliber bullet can also penetrate a BTRs armor. There is a correlation, which provides a good example and rule of thumb. As I said I also bring it up because others in the past have argued that shell fragments should be turning tanks into shredded messes, oblivious to the reality of ballistic physics. 

I bring this up because HerrTom specifically made this thread to continue a constructive discussion on the study and effects of artillery verses vehicular targets. The discussion is being continued. 

Hope that clears things up.  

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@IICptMillerII, you disregard cross section. Though having a superior energy .50cal will have a much large cross section than 5/10g shell fragment. So .50cal will spend WAY MORE energy penetrating the armour.

@HerrTom, angle is accounted for by mere adjusting for the probability of a target to be ahead, sideways or behind center of the impact. Probability is easily derivable from the form of HEFRAG impacts seen on sat pictures.

Edited by IMHO

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If shell fragments were only a 10th the speed of bullets they wouldn't be a real weapon.  The fact that you got it so wrong shows you have not much idea about HE, and reflexively read things you read wrongly to back up the idea that tanks are immune to fragments.

Momentum goes up linearly with speed so the factor of x15 you missed the speed by mean you get 1/15 accurate momentum.  But energy goes up with velocity squared.  So your energy would be 1/(15^2) of true energy or 1/225th

Edited by cool breeze

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15 minutes ago, cool breeze said:

If shell fragments were only a 10th the speed of bullets they wouldn't be a real weapon.  The fact that you got it so wrong shows you have not much idea about HE, and reflexively read things you read wrongly to back up the idea that tanks are immune to fragments.

Momentum goes up linearly with speed so the factor of x15 you missed the speed by mean you get 1/15 accurate momentum.  But energy goes up with velocity squared.  So your energy would be 1/(15^2) of true energy or 1/225th

Read the posts for cryin out loud. HerrTom pointed out my mental gaff, and I acknowledged it and explained what happened.

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5 hours ago, HerrTom said:

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.

Yes..."drag them to a left a bit" is what I meant by "squash" the plots. The plots are great. I truly love the colorized graphs and plots (and gifs) you've posted. Maths in action, as it were. The angle of impact would change the distribution of the plots...not the penetration. (I don't think that gravity would matter nearly as much as aerodynamic drag on random-shaped bodies of ~gram masses.) My point was purely that your plots were for horizontal shell orientation rather than the normal, non-horizontal, approach that shells are on prior to their detonation. (Gotta love a pun...)

Ken 

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So for sanity, I looked at the classic .50" M8 API bullet.

WUYsM0l.png

Here's its speed as it travels downrange - important in figuring out how much it can penetrate!

z7un6hW.png

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!

YRvsSnX.png

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.

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