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Estimating the Performance of Tank Guns

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Let's say you're developing a tank with a unique (AKA non-historical) gun for one of our competitions here on SH. It would be nice to have an idea of the size of the gun, its shells, and what their performance both in terms of shell weight and velocity but also penetration, wouldn't it? Well, fortunately there is a way to do this with reasonably accurate results using your solid modeling software and some free to use browser tools.

First, you want to have a general idea of the size and performance of your gun. For this example, I decided I wanted an optimized, high velocity 85mm caliber gun with a case about as big as the 7.5cm KwK 42 (as it happened, I ended up with a case that had significantly greater volume, but that fact is unimportant for this example). The cartridge I decided on has a 130mm wide rim and a 640mm long case, of course in 85mm caliber. My first step was to model this case in SolidWorks:

mR8Jng0.png

 

You will also need to model your projectile, in this case a tungsten-carbide cored APCR round:

zF8oEUa.png

 

Next, we need a bit of freeware: A Powley computer. Originally developed by DuPont engineers for small arms ammunition, the Powley computer is an accurate enough tool to use for much larger tank rounds as well! When you click the link, you'll be greeted with this screen:

 

VKsohPV.png

 

You'll note the dimensions are in inches and this thing called "grains" (abbreviated "gn"). The grain is an archaic Imperial mass unit equal to 1/7000th of a pound which is still used in the small arms field, today. Another quirk of small arms has the case capacity - a volume measurement - listed in grains as well. This is in fact grains of water (gn H2O), or the weight of water that will fill the case to the top. To find this, simply multiply the volume in cubic centimeters by 15.43 - which is also the exchange rate between the metric gram and grains mass.

 

Finding the volume of the case is easy with a solid modeling program; simply model the interior as a solid and find the volume of that solid:

Yta50nM.png

 

Filling in my Powley inputs gives me this:

 

44GmmwV.png

 

Note that I typically use the diameter of the projectile across the driving bands for "Bullet Diameter", but it really makes very little difference.

 

So far, though, we haven't actually produced any results. That's because our gun is well outside the bounds of DuPont production IMR powders, hence the output "Much slower than (IMR) 4831" in the lower left. So, we need to override the computer by checking the box next to the blue "Pressure" function, and typing in a pressure value in CUP that is reflective of tank guns of whatever era we are trying to represent. My tank gun is trying to represent something from about the late 1940s/early 1950s, so I'm going to use 45500 CUP EDIT: USE 41000 CUP for APCBC and 42800 CUP FOR APCR (or better yet, do your own calibration!):

 

WXTLRxF.png

 

This gives me an estimated muzzle velocity of 3,964 ft/s for my L/50 barrel. Not bad! Note the outputs on the left, which tell you a bunch of fun facts about your round but aren't terribly relevant to what we're doing here today. Next, we need to put this gun's performance in terms of penetration. The way I like to do this is through comparative analysis.

 

The first thing we need is to know to find penetration the ballistic performance of our round. We can estimate this using JBM's ballistic calculator and a few rules of thumb. When opening the calculator, the first thing you'll see is this:

 

xZ1vSUK.png

 

We care about basically none of these settings except BC, velocity, and maximum range. Caliber, projectile weight, chronograph distance, etc are all pretty irrelevant to us. Keep the environmental settings (temperature, pressure, etc.) set to their defaults. First, change the ballistic coefficient type from G1 to G7 using the dropdown menu. Then, change the muzzle velocity from 3000 to whatever the muzzle velocity was that was calculated by the Powley computer. Finally, set the maximum range to your desired distance - in my case 2,000 yards.

For my round, I now have inputs that look like this:

 

7CnkLrA.png


We also need to get some idea of how fast our projectile loses velocity, something we can't know for certain without actually building a real gun and test firing it - or at least without some really sophisticated simulations. However, projectiles with the same shape tend to fly the same way, and that's something we can exploit here. To figure this out, we need a graph showing us the performance of a real-life gun. Fortunately, there is a handy one for an IRL gun similar to what I'm designing, the 90mm M3 from World War II, and its M304 HVAP-T, which is broadly similar in construction and shape to my 85mm APCR projectile:

 

post-245156-0-77676400-1465281935.jpeg

 

Based on this chart, we see that the M304 should drop from its 3,350 ft/s muzzle velocity to about 2,500 ft/s at 2,000 yards. Doing a little trial and error with JBM tells me that this means the M304 has a G7 ballistic coefficient of about 1.13.

 

Now, our projectile will not have the same ballistic coefficient, due to it being a different size and mass. But, we can figure out what its ballistic coefficient would be by finding its sectional density and comparing that to the sectional density of M304. To find sectional density, take the projectile's weight in grains and divide it by the square of the projectile's diameter in inches, times 7000. So for M304, we get:

 

oylGn49.png

 

2JDNvGn.png

And for my 85mm, we get:

LU6AqPE.png

 

8cDOIry.png

 

This means that the ballistic coefficient for an identical-shape projectile with our size and weight will be about 1.019/1.330 - or 76.6% as much - as that of the 90mm M304. That means a BC of 0.866 G7 should be approximately correct for my 85mm APCR round. Let's plug that in:

QZW8VJq.png

 

And then scroll down to the bottom to click "calculate", which gives us a big ol' chart that goes out to 2,000 yards:

 

etA2qbs.png

 

O-Kay! Now we have some data. It looks like at 2,000 yards, my projectile holds about 2,800 ft/s striking velocity. It's important to note here that what we really care about isn't the striking velocity of the projectile per se, but the velocity and energy of the projectile's core. The core is what's actually doing a lot of work to the armor, so for now let's stop thinking in terms of the whole projectile, and take a look at these two cores, that of the M304 90mm HVAP, and that of my 85mm APCR round. The core of the 90mm M304 is an approximately 8 pound lump of tungsten-carbide that is about 45mm in width. My penetrator is also 8 pounds, but it's longer and thinner in proportion - just 40mm wide, rather than 45mm. This means my penetrator will penetrate more armor at a given striking velocity, and we can estimate how much more by taking the specific energy of the rounds and comparing them. That is, the energy in Joules of the penetrator alone, divided by the penetrator's diameter squared:

 

sUPi1xI.png

 

cSOmBme.png

So the specific energy at 2,000 yards is about 826J/mm^2. Now, we need to find out at what impact velocity the M304 penetrator produces this same specific energy. Do do that, we go backwards, using the figures for M304:

 

8d3FHfr.png

 

9NqcXqH.png

 

Therefore, the equivalent impact velocity for my 85mm APCR round at 2,000 yards is 3,150 ft/s for the M304. That means, in theory, that the M304 would have to impact a target at 3,150 ft/s to produce equivalent penetration of RHA to my 85mm APCR striking at just 2,800 ft/s.

Now, we head back to that chart:

post-245156-0-77676400-1465281935.jpeg

 

On the left side of the graph, we put our cursor on the line that corresponds to approximately 3,150 ft/s velocity, and follow it over until it hits the curved line that corresponds with the angle of plate we care about - arbitrarily, let's pick 20 degrees. Then, we follow that point straight down until it hits the x-axis:

d2jeWBB.jpg

 

Therefore, we estimate that at 2,000 yards, my 85mm has just over 10 inches of RHA penetration - not bad at all for a lowly APCR round!

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@N-L-M expressed some skepticism that the pressure value I was using was correct, so I recalibrated for the 90mm M3 gun:

T33 APCBC:

 

g9Sj7JV.png

 

T30E16 HVAP:

 

4fv6ANb.png

 

Therefore I would recommend using 41000 CUP for APCBC and 42800 CUP for APCR, instead of 45500.

 

Corrected figures for my 85mm are 3,845 ft/s muzzle velocity, 2,000 yd impact velocity of 2,692 ft/s, and approximately 9.5 inches of RHA penetration at 20 degrees at 2,000 yd.

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The gun designer Excel thingy I mentioned: https://drive.google.com/open?id=1CvD4XOW-iKXxuuXQq5xSpNXHayUIVs2a

 

Functions:

  • Odermatt calculator (sheathed long rods version)
  • De Marre calculator
  • Statistical mass/performance estimators for HE, HEAT, HEAT-FS
  • Cartridge designer (note: accuracy may vary - WW2-era cartridges differed wildly in terms of the performance extracted from a given case volume)
  • Black powder cartridge designer (note: for steampunk guns)

 

Note: for longrods I recommend using Solver with the following values:

  • Velocity greater than 1250m/s
  • L/D ratio less than 30
  • Core diameter greater than or equal to 15mm

 

Also keep an eye on the core/jacket ratio to make sure that stupid things aren't happening.

 

Edit: also note that the longrods output is currently set to tungsten rather than DU and the steel monoblock equivalent isn't shown. Additionally, the target is steel at 0'.

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Probably niche and not useful for most people here, but: 

 

https://forum.warthunder.com/index.php?/topic/373522-id0054325-additional-aphe-fragmentation-and-power-addendum/

 

Estimating fragmentation (velocity and direction) of APHE shells. Seems solid from my ignorant point of view. 

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