3 replies to this topic

[lordkrike]

Let me preface this by saying that I think the current armor system is fine and I am not suggesting radical tweaks to it. I'm just a numbers guy and found the following pretty entertaining:

Something a lot of people don't realize is that when you double the edge length of a 3D cube, you actually multiply its internal volume by 8 and its surface area by 4. It's actually, in a sense, eight times larger. There were a couple threads about this topic, but I didn't see any numbers. I wanted to apply this concept to the Atlas and Commando to see what this did to the 'Mech's armor thickness.

Let's start with a human being, which is easily comparable to the Commando and Atlas since they both have the same profile. I used Wolfram Alpha for the median height and weight of a human:

H = 1.74m
W= 79kg

There are formulae out there for calculating volume and surface area of humans. These formulae should also apply to the Atlas and Commando since they have the same approximate shape. I applied them and got the following:

V = 75.2L
SA = 1.94m^2
Density = 1.05kg/L (approximately as dense as water)

So we have a baseline. 'Mechs, ideally, shouldn't be much more dense than humans, since they have a similar form of locomotion. Unlike tank treads, which spread out the weight of a tank, 'Mechs and humans apply all of their weight to a small area beneath their feet. If they were significantly more dense than humans they'd sink into soft ground much too easily to be effective war machines.

The Atlas:

W = 100 short tons ≈ 90700kg.
H ≈ 16m (from the sources I could find)
Therefore:
V ≈ 92000L
SA ≈ 193m^2
Density ≈ .98kg/L

So the density is right on! An Atlas really is what you would get if you scaled a human up to 16m tall!

So the Commando:

W = 25 short tons ≈ 22700kg
H = 9m (official number)
V ≈ 23000L
SA ≈ 71m^2
Density ≈ .99kg/L

Again, dead on. A commando is effectively a 9m tall human being, but made of metal, fusion reactor, and Streak SRMs.

But hold on, let's talk about surface area and armor. After all, if you have more surface area, you need more armor to cover it, right? If you keep the same amount of armor and spread it out over more surface area, it gets thinner and easier to penetrate. Let's see if an Atlas really is that much tougher than a Commando.

From looking at the game, we find that an Atlas can have up to 19 tons of armor. That's 19% of its weight. A Commando can have 5.5 tons of armor, which is 22% of its weight.

So the Commando has 70.85kg of Armor per square meter.
The Atlas has 89.14kg of Armor per square meter.

So even though it has 244% more armor by weight, the Atlas's armor is only 26% thicker!

tl;dr Not much of the physics in this game make sense, so please don't ever use realism in your arguments about balance and the direction of the game.

TL:DR ATLAI TOO STRONK NERF ARMOR PLZ

[Sand Lantern]

A fantastic breakdown. Thanks for that!

[Strum Wealh]

There are several issues with the opening post:

• All of the measurements used in BattleTech are in SI units; 'Mech weights are in tonnes (1000 kg, or 2204.62 lbs), not short tons (2000 lbs, or 907.185 kg).
  
• The average human body as approximately the same density as water... because the average human body is (by weight) ~65% oxygen and ~10% hydrogen, with actual water making up ~57-60% of the body's mass. BattleMechs are not composed of the same elements in the same proportions; a 'Mech using standard materials (no XL, ES, FF, and so on) is composed mostly of steel-based alloys and electroactive polymers.
  
• BattleMechs are generally far more dense than water - hence, why they tend to sink and walk along the bottoms of bodies of water (whereas humans, having nearly the same density as water, tend to be neutrally-buoyant (or very nearly so)).
  
• Strength vs stiffness vs thickness is not always a 1:1 linear relationship (e.g. a panel that is twice as thick is not necessarily twice as strong or twice as stiff).

Also, it would seem that certian elements of BT science and technology (materials science, medicine, space sciences, and computing technologies) have clearly invoked Clarke's Third Law ("Any sufficiently advanced technology is indistinguishable from magic.") and its corollary ("If technology is distinguishable from magic, it is insufficiently advanced.") while others (most weapons technology) have not.

A large part of what makes the BT/MW franchise fun is that it is a "harder" sci-fi setting - its technologies are more reflective of, or can be reasonable explained by, scientific realism than of near (or actual) fantasy.
It's like comparing Planetes (hard sci-fi) to Star Wars (soft sci-fi, bordering on sci-fantasy) and Star Trek (middling hardness).

'Twas a nice try on the OP's part, though...

[RootBeerBaron]

OP, some of the math doesn't seem to make sense. I'm guessing the equation is your problem.

lordkrike, on 13 November 2012 - 10:24 AM, said:

There are formulae out there for calculating volume and surface area of humans. These formulae should also apply to the Atlas and Commando since they have the same approximate shape. I applied them and got the following:

......

So we have a baseline. 'Mechs, ideally, shouldn't be much more dense than humans, since they have a similar form of locomotion. Unlike tank treads, which spread out the weight of a tank, 'Mechs and humans apply all of their weight to a small area beneath their feet. If they were significantly more dense than humans they'd sink into soft ground much too easily to be effective war machines.

I am fairly certain that this equation inherently relies on the density of humans to calculate the volume from height and weight. For example, a 2m tall person of 100 kg will have a predictable volume, given a known average density of humans. To check this, multiply your Atlas volume, not rounded, by 1.05 kg/L. You should end up with 100 tons.

Second, a rock is significantly more dense than humans, but it does not sink into the ground if it is small enough. This is determined by the pressure on the ground, which is Force/Area (weight/area in contact with ground). To put in perspective, an elephant standing on one leg puts less pressure on the ground than a woman in high heels (rough estimate is ~15x less!). The heels would sink into the ground moreso than the elephant's feet, though the elephant is fatter <insert "yo mama joke" here>.

Again, good try with the calc though.

Edited by RootBeerBaron, 15 November 2012 - 11:13 AM.