Solving the Range Problem with Armor Piercing Pancakes

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There’s 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 a 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 because instead of shooting bullets, the AC/20 fires armor piercing pankcakes.

Tasty, tasty Hunchback pancakes. Servin’ ‘em up, hot’n’fresh!

Alright, I know at 0.76 mm the thickness of these pancakes are a shave wider than a human hair, but you cannot deny the amazing image they produced.

Till next time, MechWarriors. Stay syrupy.

This entry was posted in Editorial, Software on by .

About Sean

Hooked on BattleTech at an early age, Sean honestly can't remember whether it was the cartoon, the serial novels or the short-lived TCG that did him in. Whatever it was, his passion for giant shooty robots never died, so now he writes about the latest and greatest in 'Mech related news.

18 thoughts on “Solving the Range Problem with Armor Piercing Pancakes

  1. Crackerb0x

    There’s a couple other answers to this question, too. The AC2 rounds could be larger from more propellant, for example. There’s also the problem of inconsistent sources to deal with. In some canon, the autocannons fire a stream of shells rather than a single round. We could justify this with saying that an AC20 would require a lot more equipment in order to spit out ten times as many rounds per shot as an AC20 and because of the extreme rate of fire, accurate targeting is affected. But I’m no engineer, so my thoughts are speculation at best.

    The weaponry of Battletech has always been an interesting conundrum with decent, primitive targeting found on modern military equipment being forever lost, but neural interfacing being required for these machines.

    Reply
    1. Ruebezahl54

      It was mentioned that BT is a “metric game”… An AC/2 ammo ton has 45 shots, an AC/20 has 5 shots. That gives us (1000/45)=22,222kg per AC/2-shot and (1000/5)=200,00kg per AC/20-shot. The loading mechanism must be much more durable and stronger with an AC/20 than the light-weight AC/2; also the other forces in recoil and exhaust fume not to forget, but 45 shots need to be stored and delivered…
      In regards to damage-capacity per ton compared with missile ammo tons, AC ammo has a disadvantage in smaller calibers. A LRM-5 ammo tons can inflict as much damage as a LRM-20 ammo ton (120 damage points). An AC/2 ammo ton can deliver only 90 damage points, AC/5 can 100 [20shots*5], as AC/10 [10*10] and AC/20 [5*20].
      Volume of an ammo ton, hmm, did you heard about criticals in Mech construction? Every ammo ton consumes 1 critical, so loading mechanism AND ammunition weight take allways nearly the same room/volume. Of course, ammo volume in an arm will look different than in a torso location or in a leg or even the head (nice place for Gauss ammo) but it TAKES only 1 critical.
      Back to the “bakery-thesis”: Each one of those “AC/20 armor piercing pankcakes” weights 200kg, its components surely have densities over 1kg/liter (metals, chemical propellants) so I asume for an “AC/20 pancake” about 80-150 liters…And not the above mentioned 0.76 mm in thickness, that is 3/4 of millimeter, an orderly french crèpe has between 1,5 and 3mm, my grandma did apple slices into the pancake pie and carbonate for volume, so some were between 1,5 and 3,5cm…

      Reply
  2. sadlerbw

    Now I have this delicious idea for a silver dollar gauss rifle that fires a bunch of smaller pancakes instead of one big one! Also, I’m hungry now.

    Seriously though, this is just one of those instances where BT gives up and just says, “Ok guys, this makes no sense but it would break the game if we did it the ‘real’ way.” Kinda like pulse lasers and TC’s not working together, or the difference between aerospace and ground weapon ranges. It’s nice that they TRY to be semi-reasonable with tech and science, but as long as the game is reasonably balanced and fun to play, I can forgive the occasional bout of ‘because techno-magic’.

    Of course, maybe the projectiles are largely hollow and pack neatly into one another like a giant stack of disposable plastic cups! Or maybe one ‘shot’ of AC/2 ammo is actually multiple rounds in a cassette, while an AC/20 is a single shell. Don’t forget, the AC/2 is just a class of weapons with a similar damage output, and one ‘shot’ in BT land doesn’t have to mean only one shell was fired. See! Ambiguity to the rescue!

    Reply
  3. Andy in Indy

    Your analysis glossed over a few relevant points:
    Range is not dependant on bore size. A 9 mm Parabellum round will travel further than a .45 ACP, and will penetrate further (often passing through someone who has been shot) while the .45 is less likely to pass through, but the .45 is likely to do more damage when it hits because of the transfer of kinetic energy.

    The Bore Size is not the same as the diameter of the round in flight. Most direct fire tank rounds are enclosed in a sabot which pulls away and lets the long rod penetrator carry the kinetic energy. For example, a 120mm cannon may fire a round that is only 30mm across.

    We can take up a few more relevant points:
    Kinetic and chemical penetrators do not work the way the armor system in Battletech does. Generally speaking, they tend to put a small hole on the inside and then break up and do damage inside. They do not, as a general rule, wear down the armor like sand blasting (on the other hand, a laser may actually do that).

    Armor does not work the way that the Armor system in Battletech works. Rigid armor with a small hole in it does not lose much in its protection. On the other hand, a flexible composite armor (like body armor) will. But that is not how damage in BattleTech is represented.

    Penetration can be simplified to a logarithmic equation, where the penetration is a function of range, but that gets modified by the angle that the round happens to hit, relative to the piece of armor. On a giant robot’s leg or arm, that angle will be constantly changing. Add also that the thickness of one section is certainly not uniform, and the tabletop level modeling would be outrageous.

    TL:DR Don’t bother to try to make BattleTech seem real. It would be too complicated to try to model the real world physics to a game of miniature giant robots. Just accept that reality was set aside for a fun game, and go blow something up.

    Reply
    1. Sean Post author

      These are all valid points, and I absolutely agree with you. My counterargument is: a Hunchback shooting pancakes. It’s real, and it’s coming.

      Reply
  4. John Michael

    I’m curious how the rounds are fired in the BT universe. If they are all Gauss or rail gun types, then it may take considerably more energy to fire the larger rounds. And again, if they are propellant based, then the amount needed to fire an AC/20 round a decent distance may be too much to fit in the mech’s limited space. Either way it may be an actual decision to balance the round size/damage vs space or energy capacity on the mechs.
    Does the same ‘larger caliber=shorter range’ rule also apply to their large ships and planetary guns?

    Reply
  5. Aemielius

    The analysis also forgoes everything about internal ballistics.
    In BT/MW, assuming that most ballistic weapons are propellant based, smaller calibre weapons have longer barrels compared to the larger weapons which better utilize the thrust of available propellant.
    This is a huge reason why larger weapons in real life have far greater ranges.

    Couple of other points: * The typical 9mm parabellum fired from the typical handgun does not have an effective range of 100m, that is pretty much its maximum range, period. That is holding the weapon at something akin to a 45 degree up angle with a 50 mph tailwind. This can be offset by various propellant loads, lighter bullets, firing configuration/weapon modifications…etc
    * Effective range for artillery, that is all based on a huge number of factors that include everything already mentioned for smaller weapons plus things like high altitude atmospheric conditions, projectile drift(due to projectile rotation) and rotation of the Earth.
    (I spent 10 year of a 20 year Army career doing just this sort of thing, computing firing data for artillery-155 and 203 mm)

    Reply
  6. Maximum_Overkill

    Gun design is a lot more complicated.
    Main physical properties: Barrel lenght and twist rate, gun powder (energy stored / ignition time / expansion), Shell (weight / length to diameter / material)

    As long as you have very similar shells and guns the muzzel energy is a benchmark.
    In terms of Mechwarrior where the barrel length seems limited and almost the same for all (IS) AC’s and only the shell diameter is altering the behavior is legit. (Maybe the amout of gun powder is also increasing.) The actual numbers may be debatable (shell energy vs range).

    Here are some informative wikipedia links:

    https://en.wikipedia.org/wiki/Shell_(projectile)
    https://en.wikipedia.org/wiki/Rifling
    https://en.wikipedia.org/wiki/Muzzle_energy
    https://en.wikipedia.org/wiki/Depleted_uranium
    https://en.wikipedia.org/wiki/Gunpowder

    Reply
  7. Michael

    Fun read, thanks :) I always figured barrel length would have something to do with it. The Rifleman got’s barrels, the Hunchback, not really ;)

    Reply
  8. Chris

    As a BattleTech nerd and a firearm enthusiast, please allow me to shoot a few holes in your article.

    Caliber is the measurement of bore diameter, but has no bearing in overall length of the projectile. To compare, let’s use two standard rounds in NATO, the 5.56 x 45mm and the 7.62 x 51mm. In common lexicon only the first number is used often in identification (5.56 and 7.62mm) which is only the bore diameter. The second number is the overall length of the projectile, 45mm and 51mm. Next let’s compare the actual weight of the projectile. The M855 is the NATO designation for the projectile used in the 5.56 x 45mm cartridge and has a weight of 62 grains, or about 4 grams. The M80 is the designation for the projectile used in the 7.62 x 51mm cartridge and has a weight of 144 grains, or about 9.3 grams. So even with a small increase in the size of the projectile, the weight will increase pretty dramatically.

    When a cartridge is fired the propellant is ignited and the expanding gas pressure causes plastic deformation in the bullet which creates a seal and prevents gas from escaping the barrel before the bullet. As the bullet travels down the barrel it engages the rifling, which is a number of helical grooves in the barrel, that then causes the bullet to spin. It is the spinning motion of the bullet that allows the marksman to accurately hit what they are aiming at. But the twist ratio of revolutions per inch is not one size fits all. The relationship between bullet weight and barrel twist is very close, if the marksman wants to accurately hit their target.

    For example, the M855 bullet can be fired from an AR-15 which can have a barrel twist of 1:12, 1:9, 1:7 (read as 1 revolution in x inches of barrel length). When the M855 bullet is fired from an AR-15 with a twist of 1:7, you can achieve a high level of accuracy. When fired from the 1:9 twist AR-15, you will still have good accuracy, but not as good as the if you were using the 1:7 twist AR-15. If you use an AR-15 with a 1:12 twist, you will be lucky to hit your target at all.

    This interdependence between barrel twist and bullet weight has to do with the amount of time the bullet spends traveling down the barrel as well as the velocity of the bullet itself. I’m not a physicist or a mathematician, so the rule of thumb is basically light and fast projectiles prefer a slow barrel twist like the 1:12 and heavier bullets prefer a tighter twist like the 1:7.

    Lastly there are a few more things to consider for accuracy which have more to do with the firearm than the projectile. The length of the barrel plays a pretty big role in accuracy. Up to a certain point, more barrel length means the bullet has more time to engage the rifling, which means it will have a more stable spin, which means it will be more accurate. Where as a shorter barrel will not be able to adequately spin the bullet so it will not be as stable in flight.

    Next there is the action type. Generally speaking, overall accuracy decreases when the action type has more moving pieces than another. While there are many different types of actions, I will focus on two, the bolt action and the automatic action. A bolt action is relatively simple in that the user must manually open and close the action by moving the bolt to extract a spent cartridge and insert a fresh one. The automatic action is much more complex since all the work of removing the spend cartridge and loading a fresh one is done by the firearm and not the user. To do this, an automatic action will generally harness
    some mechanical energy from the cartridge being fired, such as using the rearward moving recoil, or siphoning off some of the expanding gas to move a piston. This extra movement in the firearm will generally cause a reduction in accuracy versus a simpler action type.

    Lastly we have what is known as the crown, which is the very end off the barrel. It is significant because it is the very last thing the bullet touches before it leaves the barrel. Any defect, or damage to the crown will cause the bullet to have uneven pressure applied to it as it leaves the gun, causing the bullet to destabilize and lose accuracy.

    Reply
    1. Sean Post author

      I love everything about this most meticulous of replies.

      Now do all that again, except using pancakes.

      Reply
  9. Mario Lara

    Quote – I’m not going to bore you with the math for the AC/20

    Ha ha, I see what you did there…. :D

    Seriously though, this is a fascinating post. I love stuff like this! Thanks for writing it! :)

    Reply
  10. John Leary

    The answer to all of the comments is found in the range of the Battletech assault rifle.
    What ‘rifle’ in ‘real world’ history equates to the range and accuracy of the
    rifles in Battletech. Answer: the smoothbore musket.
    The Battletech universe never got beyond black powder weapons.
    If this rationalization is extended to the AC series of weapons it is
    logical that the weapon range will decrease with size of the projectile increase,
    assuming the powder charge does not change size. The ammo for the AC series is simply
    a chain driven series of cannon breaches that move another round into position behind
    a barrel of the correct size. This concept is confirmed by the enormous weight per round
    of the AC ammo.

    Reply
  11. Carns

    I think you are being too literal in the game concepts of hit, miss, and maximum range.

    Weapon range in Battletech is not the maximum range that a projectile, or light beam, will fly. Hits and misses do not refer to the the ability of computer aided weaponry to line up on a building sized target. It is fairly safe to assume that most weapons “hit” the target at nearly any visible range… or at least center it up.

    Instead, “in universe”, a weapon has strike the target with enough force or heat to knock loose, or melt, the ablative armor scales covering it. Small lasers have a low energy output, and thus can only do this at extremely short ranges. At greater ranges, it still “hits” the target… in the same way you can hit your buddy on the other side of a football field with a laser pointer.

    Despite a few fluff mentions of the 185mm Chemjet, caliber is rarely specified in the Battletech Universe. Once again, some people reference 203mm AC/20s and 100mm AC/10s because this lets them visualize large sized modern tank cannon firing thousands of shells per minute, instead of 6. Unfortunately, this doesn’t work. An AC/20 is simply not damaging enough in comparison to the 2 point machine gun to be firing more than 1 203mm shell per round, and the weapon simply does not weigh enough. Even gyro assisted, it would be nearly impossible for a top heavy, upright machine to remain that way while dealing with the recoil of that. You can fairly safely assume that the caliber of most of the autocannon weapons is roughly 40mm. What changes is the rate of fire.

    An AC/5 fires at a set rate of fire, the recoil being such that the hail of metal being vomited from the barrel is reasonably accurate enough to knock off 5 points of armor at 360 meters. At 550 meters, the weapon’s cone of fire is too large, and too many shells miss or hit with insufficient force… thus the maximum range is listed at 540 meters, even if the “safe” range is a few kilometers more than that.

    An AC/10 fires at double the rate of fire, with greater recoil, thus a larger cone of fire, and thus a shorter effective range. The UAC/5 also fires at twice the rate of fire, weighs less than the AC/10, and has a longer range than the AC/5. How does one explain that? The UAC/5 is a full tech class ahead of the obsolete AC/10. However, one should also note, the UAC/5 does not actually fire as fast as the AC/10. Though a combat round is 10 seconds, the autocannon fires its entire burst a little less than 2 seconds… thus the 10 point hit. If it fired continuously for the full 10 seconds, AC damage would look something more like Missile or LB shotgun damage spreads. The UAC/5 does not hit in a 10 point cluster… it is simply a faster reloading AC/5.

    TL;DR: Hit, Miss, Maximum Range are game terms, not In Universe. A game term HIT is only scored when the weapon strikes the target with enough power to knock loose armor… regardless of how many Game Term MISSes bounce off the in universe hull.

    Reply
  12. Chris Lyons

    The Autocannon range issue probubly comes down to the leangth of barrel it is practical to put on the front of a mech. WWII tanks for example frequently had assault gun models that fired a larger lower velocity round out of a shorter barrel then those of the standard models. These frequently had shorter range then the standard tank armorment. AC20s are probably these sort of short ranged assault guns. Anouther issue is accuracy a 200mm gun fireing 10 rounds in 3 seconds out of vertualy no barrel (Hunchback) might have a maximum range of several km but an effective range range far shorter. Finally modern technology may explane the volume issue with autocannon ammunition. For example the Brittish are beginning to deploy a 40mm Autocannon that fits in the space of a 20mm by using Teliscoping Ammunition were the round is completely stored inside of it’s propelent rather then sitting in front of it.
    https://en.wikipedia.org/wiki/Telescoped_ammunition
    https://en.wikipedia.org/wiki/Ajax_(Scout_SV)

    Reply

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