Anti-air bobcat design to take away driver's hearing in maximum efficiency
SH11 155mm SPG
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:
You will also need to model your projectile, in this case a tungsten-carbide cored APCR round:
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:
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:
Filling in my Powley inputs gives me this:
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!):
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:
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:
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:
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:
And for my 85mm, we get:
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:
And then scroll down to the bottom to click "calculate", which gives us a big ol' chart that goes out to 2,000 yards:
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:
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:
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:
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:
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!
Backstory (skip if you don't like alternate history junk)
The year is 2239. It has been roughly 210 years since the world was engulfed in nuclear war. Following the war, the United States splintered into hundreds of small statelets. While much knowledge was retained in some form (mostly through books and other printed media), the loss of population and destruction of industrial capability set back society immensely.
Though the Pacific Northwest was less badly hit than other areas, the destruction of Seattle and Portland, coupled with the rupturing of the Cascadia Subduction Zone in 2043, caused society to regress to a mid-19th century technology level. However, in the early 2100s, the Cascade Republic formed, centered near Tacoma. The new nation grew rapidly, expanding to encompass most of Washington and Oregon by 2239. The Cascade Republic now extends from the Klamath River in the south to the Fraser River in the north, and from the Pacific roughly to central Idaho. Over time, the standard of living and industrial development improved (initially through salvaging of surviving equipment, by the late 2100s through new development); the population has grown to about 4.5 million (comparable to 1950 levels), and technology is at about a 1940 level. Automobiles are common, aircraft are less common, but not rare by any means. Computers are nonexistent aside from a few experimental devices; while scientists and engineers are aware of the principles behind microchips and other advanced electronics, the facilities to produce such components simply do not exist. Low rate production of early transistors recently restarted.
The current armored force of the Cascade Republic consists of three armored brigades. They are presently equipped with domestically produced light tanks, dating to the 2190s. Weighing roughly 12 tons and armed with a 40mm gun, they represented the apex of the Cascade Republic's industrial capabilities at the time. And when they were built, they were sufficient for duties such as pacifying survivalist enclaves in remote areas. However, since that time, the geopolitical situation has complicated significantly. There are two main opponents the Cascade Republic's military could expect to face in the near future.
The first is California. The state of California was hit particularly hard by the nuclear exchange. However, in 2160, several small polities in the southern part of the state near the ruins of Los Angeles unified. Adopting an ideology not unfamiliar to North Korea, the new state declared itself the successor to the legacy of California, and set about forcibly annexing the rest of the state. It took them less than 50 years to unite the rest of California, and spread into parts of Arizona and northern Mexico. While California's expansion stopped at the Klamath River for now, this is only due to poor supply lines and the desire to engage easier targets. (California's northward advanced did provide the final impetus for the last statelets in south Oregon to unify with the Cascade Republic voluntarily).
California is heavily industrialized, possessing significant air, naval, and armored capabilities. Their technology level is comparable to the Cascade Republic's, but their superior industrial capabilities and population mean that they can produce larger vehicles in greater quantity than other countries. Intelligence shows they have vehicles weighing up to 50 tons with 3 inches of armor, though most of their tanks are much lighter.
The expected frontlines for an engagement with the Californian military would be the coastal regions in southern Oregon. Advancing up the coastal roads would allow California to capture the most populated and industrialized regions of the Cascade Republic if they advanced far enough north. Fortunately, the terrain near the border is very difficult and favors the defender;
(near the Californian border)
The other opponent is Deseret, a Mormon theocratic state centered in Utah, and encompassing much of Nevada, western Colorado, and southern Idaho. Recently, tension has arisen with the Cascade Republic over two main issues. The first is the poorly defined border in Eastern Oregon / Northern Nevada; the old state boundary is virtually meaningless, and though the area is sparsely populated, it does represent a significant land area, with grazing and water resources. The more recent flashpoint is the Cascade Republic's recent annexation of Arco and the area to the east. Deseret historically regarded Idaho as being within its sphere of influence, and maintained several puppet states in the area (the largest being centered in Idaho Falls). They regard the annexation of a signficant (in terms of land area, not population) portion of Idaho as a major intrusion into their rightful territory. That the Cascade Republic has repaired the rail line leading to the old Naval Reactors Facility, and set up a significant military base there only makes the situation worse.
Deseret's military is light and heavily focused on mobile operations. Though they are less heavily mechanized than the Cascade Republic's forces, operating mostly armored cars and cavalry, they still represent a significant threat to supply and communication lines in the open terrain of eastern Oregon / southern Idaho.
(a butte in the disputed region of Idaho, near Arco)
As the head of a design team in the Cascade Republic military, you have been requested to design a new tank according to one of two specifications (or both if you so desire):
Medium / Heavy Tank Weight: No more than 45 tons Width: No more than 10.8 feet (3.25 meters) Upper glacis / frontal turret armor of at least 3 in (76mm) LoS thickness Side armor at least 1in (25mm) thick (i.e. resistant to HMG fire) Power/weight ratio of at least 10 hp / ton No more than 6 crew members Primary armament capable of utilizing both anti-armor and high explosive rounds Light tank Weight: No more than 25 tons Width: No more than 10.8 feet Upper glacis / frontal turret armor of at least 1 in thickness Side armor of at least 3/8 in (10mm) thickness Power/weight ratio of at least 12 hp / ton No more than 6 crew members Primary armament capable of utilizing both anti-armor and high explosive rounds
Other relevant information:
Any tank should be designed to operate against either of the Cascade Republic's likely opponents (California or Deseret) The primary heavy machine gun is the M2, the primary medium machine gun is the M240. Use of one or both of these as coaxial and/or secondary armament is encouraged. The secret archives of the Cascade Republic are available for your use. Sadly, there are no running prewar armored vehicles, the best are some rusted hulks that have long been stripped of usable equipment. (Lima Tank Plant ate a 500 kt ground burst) Both HEAT and APFSDS rounds are in testing. APCR is the primary anti-armor round of the Cascade Republic. Either diesel or gasoline engines are acceptable, the Cascade Republic is friendly with oil producing regions in Canada (OOC: Engines are at about a late 1940s/early 50s tech level) The adaptability of the tank to other variants (such as SPAA, SPG, recovery vehicle, etc.) is preferred but not the primary metric that will be used to decide on a design. Ease of maintenance in the field is highly important. Any designs produced will be compared against the M4 Sherman and M3 Stuart (for medium/heavy and light tank), as these blueprints are readily available, and these tanks are well within the Cascade Republic's manufacturing capabilities.