Solving the Range Problem with Armor Piercing Pancakes
There are two types of sci-fi universes: there’s the universe that provides no explanation and uses science as a substitute for magic (like Star Wars), or there’s the universe that tries to justify its awesomeness with plausible explanations. BattleTech has always erred on the latter side but for a few exceptions (the largest, of course, being the Kearny-Fuchida Jump Drives). However, one logical inconsistency in BattleTech has bugged me more than any other.
The guns.
I can understand from a game balancing perspective why the range of your cannons will decrease as the bore size increases, but from a pure physics perspective, this makes absolutely no sense.
image courtesy of Taurus Manufacturing Inc.
Allow me to illustrate. Here, we have a standard 9mm pistol, available anywhere in the United States (depending on the state), and available nowhere in Canada. Effective range: ‘bout 100 meters, if you’re a reasonably good shot.
image courtesy of warfaretech.blogspot.ca
Moving on up, here we have a much larger round, the 30mm M230 cannon (of Apache attack helicopter fame). Effective range: 2000 meters.
image courtesy of turbosquid.com
Next up, the 155mm howitzer. Effective range: well, it’ll depend on which round you use, but the standard M107 HE is 24,000 meters or 24 kilometers.
Anyway, you see the pattern here, right? As a general rule, the bigger the gun, the further your projectile goes.
Now let’s go to BattleTech. The actual bore size of autocannons vary by manufacturer and can range from 25mm to 203mm. Curiously, however, the range on these autocannons decreases as you go higher, with the 25mm AC/2 having an effective range of 720 meters, while the massive AC/20 has an effective range of a mere 270 meters.
Thus, the question for the BattleTech universe becomes what happened to cannons to make them lose range instead of gain it as the bore size gets larger?
The answer, my friends, is in the math.
Curiously, however, the range on these autocannons decreases as you go higher, with the AC/2 having an effective range of 720 meters, while the massive AC/20 has an effective range of a mere 270 meters.
We all know that 1 ton of ammunition gets a standard amount of ammo completely dependant on the size of the autocannon; AC/2 gets 40 shots per ton, AC/5 gets 20, and so on and so forth. On the surface, this seems to make sense, as the bore size also decreases at a similar “divide by 2” rate – 203mm for an AC/20, 101mm for an AC/10, etc. But ammunition doesn’t just take up a linear length – it takes up volume. Simply making the diameter of each round smaller by half doesn’t allow you to keep jamming in half as many rounds in the same amount of space.
I’ll show you what I mean. We’re going to compare the volume of ammunition taken up by an AC/20 versus an AC/2. We’re also going to simplify the shape of each bullet into a rectangle to make the math easier (also to avoid the whole “stacking” problem), and also assume that the length of each round will grow proportionately to the “divide by 2” rate we saw in the bore sizes. Also, since the bore size is in metric, and BattleTech is a metric universe, we’re going to stay metric.
We begin with the AC/2. We know the diameter of the round is the same as the bore size (25 mm), so let’s assume the length of the round is about twice that, so 50mm. A rectangle is length by width by height, and through the power of math we get 31,250 mm3 (or 31.25 cm3)
I’m not going to bore you with the math for the AC/20 – because the numbers are vastly larger, it comes out to 16,730,854 mm3 (or 16,730 cm3, or 0.01673 m3).
Now we do a little more math. An AC/2 is 31.25cm3, times 40 rounds, means we need 1250 cm3 of space to hold those 40 rounds.
For an AC/20 with 5 rounds, we’d need 83,605 cm3. That’s actually 66 times larger than the space needed to house 40 AC/2 rounds.
But if a ton of ammunition holds a proportionate, “divide by two” number of rounds, how can they not also take up the same space?! The only possible answer is one of our assumptions is wrong; the volume of each round does not remain proportional as you go up from AC/2 to AC/20.
In fact, we can work out what the proportion should be based on our above math. In order for the five AC/20 rounds to take up the same volume as forty AC/2 rounds, and keeping the known variable of bore size fixed (203 mm), then the length of each round would have to be a ridiculously short 0.76 mm.
Thus, through the power of math, we have determined that the reason an AC/20 range is so vastly reduced compared to an AC/2 is simply that instead of shooting bullets the AC/20 fires armor-piercing pancakes.
Tasty, tasty Hunchback pancakes. Servin’ ‘em up, hot ’n fresh!
Alright, I know at 0.76 mm the thickness of these pancakes is a shave wider than a human hair, but you cannot deny the amazing image they produced.
‘Till next time, Mechwarriors: Stay Syrupy.
