# Theoretical Armor Question - Joules Conversion

Okay so I was poking around the wiki for the video game Fallout 3 the other day when I came across this page:

http://fallout.wikia.com/wiki/T-51b_Power_Armor [Broken]

It has specs on the armor (keep in mind this is mostly the type of stuff the game designers make up for interesting backstory, so it is all theoretical and highly unrealistic) which include various things about its power supply, protection, manufacture, etc.

One part in particular interested me: the fact that it can absorb 2500 joules of kinetic energy. Now, to the average person, such as myself, a joule doesn't mean much. I looked it up but didn't find out much more than I already knew, though the specifics were somewhat new.

So, my question, in short is... what's the easiest way to describe this in common terms? I was thinking of trying to convert it into something along the lines of pounds of pressure per square inch during a split second collision (say with a bullet, for example). However, I wasn't able to find anything near that - so I'm feeling that my conversion and lack of physics knowledge might be getting in the way. Any ideas? All I'm really interested in getting is a more simple (yet still based on hard numbers and science) explanation of the type of protection this theoretical suit of armor would provide.

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Pengwuino
Gold Member
Easy. Kinetic energy, E = $$\frac{{mv^2 }}{2}$$ where m = mass in kilograms and v = velocity in m/s. Example: ~20g .45 acp traveling at 300m/s = 900 Joules.

Quite lame armor. In terms of pressure, it's simply the force per area. To make a calculation, you have to decide the force and this requires determining an impact time. The force will be the change in momentum divided by the change in time and the momentum is simply the mass * velocity. So let's say with our example, the impact is 0.1 seconds. Our force is simply $$\frac{{0.02kg*300m/s}}{{0.1s}} = 60N$$. Divide by the area of impact (the bullet's impact cross section) which is probably 0.01m^2 or 1cm^2. So your force is 600,000N/m^2. You can do the conversions but the psi is almost 90psi.

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Thanks for the reply! I did realize though, that just because it doesn't absorb the impact doesn't mean the wearer isn't going to be protected. Absorption would help weaken the punch of the bullet, but with an excess of 6500 joules in this example, my guess is that it would punch through, depending on what sort of composite it actually is made out of.

At any rate, thanks again for the reply - it was very helpful.

Pengwuino
Gold Member
oops I made a stupid calculation error, 200g did sound way too big for a bullet :rofl:. New calculations are up and it makes more sense now.

Oh, haha! I didn't even notice that. In retrospect, a .308 is about 160g and carries a force of 2600 joules so yes, a 200g .45 ACP does sound a bit odd.

However, this does change things significantly - the armor could fully absorb a .45 ACP. This isn't anything huge, as modern body armors are designed to stop pistol rounds (and I believe military flak jackets stop a 7.62mm bullet).

Still, realistically speaking (and it IS a game, after all!), this would probably be a massive waste of taxpayer dollars. Still, with only a 100 joule difference between the force of the bullet and the absorption amount, that's pretty decent. Don't think I'd risk my life on it though...

Thanks again, especially for the correction.

Yes, specifying some sort of kinetic energy rating (on the surface at least) is useless/gibberish. A bullets kinetic energy is (1/2)mv^2 but how that bullet is received, in terms of you not dying, depends on the area of impact and such. However, if one assumes that caliber (the size of bullets) can be standardized then one could simply say this ranking means "given a bullet of size X with this much kinetic energy, the armor will not crack and the bullet will not penetrate". However, keep in mind that conservation of energy requires that the energy in a bullet go SOMEWHERE (or else the bullet keeps on moving). Which is generally a misconception about armor/bullet proof vests in general. The laws of physics guarantee that if you stop a bullet, it is going to cost you. The best armor can ever do is spread that kinetic energy over a larger area or dissipate the force over a longer time. For example, even a perfect hit to a bullet proof kevlar vest (such that the buller doesn't go through) almost certainly leaves the shootee with a couple cracked ribs and the vest gets super hot (in real life the vest does this and people have the desire to tear it off since it is burning them). This is, of course, not consistent with Hollywood, where they set up someone to get shot but, don't worry, they give them a bullet proof vest, and the person takes 2 bullets in the chest and is like "wow, good thing I was wearing this" (which it was a good thing, otherwise they might be dead, but 2 bullets in the chest at point blank will probably break every rib they have, so they're not walking away from it).

P.S. Huge fallout fan.

In other words, the goal of armor is to stop that bullet from ripping through your flesh, it can never circumvent Newton's Laws.

Pengwuino
Gold Member
Remember, something doesn't carry a force, it carries energy. Joules is energy. The force depends entirely on how the bullet impacts. A bullet that slams into a mile long block of marshmellows will hit with a much much smaller force since the impact time will be much longer. Plus penetrating armor is greatly influenced by the pressure that's created. The energy an armor piercing round has behind it is comparable to a weakly thrown baseball and a weakly thrown baseball won't penetrate any armor let alone kill someone :)

Remember, something doesn't carry a force, it carries energy. Joules is energy. The force depends entirely on how the bullet impacts. A bullet that slams into a mile long block of marshmellows will hit with a much much smaller force since the impact time will be much longer. Plus penetrating armor is greatly influenced by the pressure that's created. The energy an armor piercing round has behind it is comparable to a weakly thrown baseball and a weakly thrown baseball won't penetrate any armor let alone kill someone :)

Which is why I said "The best armor can ever do is spread that kinetic energy over a larger area or dissipate the force over a longer time."

Ah yes, many interesting points. It makes sense to say that a lot of things besides energy impact how a bullet damages the target - but correct me if I'm wrong, certain philosophies revolving around larger bullets (due to increased size and thus increased impact) exist in the militaries of modern countries.

For example, the US military is considering using the 6.8mm bullet rather than the 5.56mm. Reason being that it's a nice bridge between the 5.56 and the 7.62 in terms of power, accuracy, and recoil (on average). So typically speaking, the more energy the bullet can generate, the more pressure is applied upon impact (assuming the marshmallow scenario doesn't take place), and thus the better it is for the shooter - all things aside and only focusing on the power of the bullet itself.

And yeah, Fallout is pretty awesome. Unfortunately, Power Armor must only be focused on stopping very primitive types of damage - a simple slug with no penetration, etc. However, the divergent world concept could explain why their firearms technology developed differently, perhaps lacking armor penetration and such.

I do still stand by my statement that a project revolving around this would probably be a waste of our money... but then again, they're talking about putting refined spider silk in car bumpers so... what the heck, right?

Oh and can't the angle of impact change things substantially, as well? My reason being that they angle tank armor for a reason - to deflect the impact upwards and deter (two r's?) penetration. There is a physics reason behind this I'm assuming?

Ah yes, many interesting points. It makes sense to say that a lot of things besides energy impact how a bullet damages the target - but correct me if I'm wrong, certain philosophies revolving around larger bullets (due to increased size and thus increased impact) exist in the militaries of modern countries.

For example, the US military is considering using the 6.8mm bullet rather than the 5.56mm. Reason being that it's a nice bridge between the 5.56 and the 7.62 in terms of power, accuracy, and recoil (on average). So typically speaking, the more energy the bullet can generate, the more pressure is applied upon impact (assuming the marshmallow scenario doesn't take place), and thus the better it is for the shooter - all things aside and only focusing on the power of the bullet itself.

And yeah, Fallout is pretty awesome. Unfortunately, Power Armor must only be focused on stopping very primitive types of damage - a simple slug with no penetration, etc. However, the divergent world concept could explain why their firearms technology developed differently, perhaps lacking armor penetration and such.

I do still stand by my statement that a project revolving around this would probably be a waste of our money... but then again, they're talking about putting refined spider silk in car bumpers so... what the heck, right?

Oh and can't the angle of impact change things substantially, as well? My reason being that they angle tank armor for a reason - to deflect the impact upwards and deter (two r's?) penetration. There is a physics reason behind this I'm assuming?
Well the "power" aspect of the science fiction power armour is not related to its ability to prevent damage but your ability to move in it. "Power" armour (like in starship trooper and stuff) is armor where there is mechanical assistance to the wearers movements (this is the same in fallout). So in other words "power" armor is armor that has such thick plating and such that one would not be able to move while wearing it if not for this mechanical assistance (think robo cop). Ultimately, in any sci-fi outlet i've read/seen, the source of the protectiveness of power armor is still just having really thick/heavy layers of a hard material covering the body.

I have to say I don't understand what you're trying to say about caliber. Perhaps you could elaborate. If you increase the size of the bullet you potentially increase the damage it can do (assuming it can be projected at the same muzzle velocity). However, there are a number of disadvantages to a larger caliber bullet.

Yes, the worst situation is when a bullet hits head on against a flat surface, If it hit at an angle it'll reflect with a smaller angle of reflection and transfer less kinetic energy. This is why a lot of medieval armor was so angular and jagged (aside from the intimidation factor).

My whole thing about caliber and bullet size is this:

Assuming everything is the same, including velocity

And also that factors such as accuracy, recoil, and the like are removed

That a larger bullet (for example, the 6.8mm over the 5.56mm) would have more energy and thus correlate to more damage. Now I'll admit, my physics knowledge is quite limited but this seems rather basic; bigger bullet means larger mass and assuming everything else is the same as the smaller bullet, it'll carry more energy.

I do realize that energy, pressure, damage, etc are not the same. But at the same time, higher energy must in some way factor into higher damage or penetration.

My whole thing about caliber and bullet size is this:

Assuming everything is the same, including velocity

And also that factors such as accuracy, recoil, and the like are removed

That a larger bullet (for example, the 6.8mm over the 5.56mm) would have more energy and thus correlate to more damage. Now I'll admit, my physics knowledge is quite limited but this seems rather basic; bigger bullet means larger mass and assuming everything else is the same as the smaller bullet, it'll carry more energy.

I do realize that energy, pressure, damage, etc are not the same. But at the same time, higher energy must in some way factor into higher damage or penetration.

Yes. the kinetic energy of a something is equal to its mass times the square of its velocity times a half. So you increase the mass at the same speed and it have more kinetic energy (you double the mass and it doubles the kinetic energy, assuming the same velocity). However, there is a lot more to consider when making a bullet/gun. For example, armor piercing bullets aren't FASTER. They're SHARPER (so the initial impact is spread over a much smaller area) and harder (so they don't lose kinetic energy to deformation). But, for example, in terms of "harder" one has to consider a pay off. Harder things are generally more dense (heavier per given size), however, a lot of materials that are more dense are also more brittle which means a properly designed armor or barrier would shatter the bullet and thus they would be, in that case, less useful then your standard bullet. In general armament (like military tactics in general) is about design/strategic compromise and knowing what you are up against.

In other words, the goal of armor is to stop that bullet from ripping through your flesh, it can never circumvent Newton's Laws.
Bringing this back into the real world a little bit, body armour is broadly speaking designed to do two things. One, stop the bullet from physically penetrating the armour layer and hence not enter your flesh. Two, reduce the peak depth of deformation behind the armour. For the first, the armour will be tested to find its ultimate ballistic limit - the speed at which a given bullet will penetrate the armour at least 50% of the time. The second is a case of measuring back face signature, which is the peak depth of deformation into some calibrated clay behind the pack.

Most vests do pretty good jobs of protecting from penetration against a certain threat. What often causes more injury and death is behind armour blunt trauma (BABT).

Lok
http://world.guns.ru/ammo/am03-e.htm

A good site for these things. Most normal rifle bullets ( even Fallout's) have energies of under 2500 J.

Still energy is one thing but usually bullet hardness and speed decide if the armor resists. The latest trend in firearms is a high-speed lightweight bullet like in P-90, MP-7. They do not have a lot of energy but the high speed enables them to pierce most light to medium armor. g means gram and rifle bullets do not outweigh 20 g. ( gr. is too imperial :P )

Impact strength is the most important factor to any armor, as it decides the ultimate speed that a penetrator must have.

In terms of heat energy, 1 gram of gasoline contains about 44,000 joules. 1 gram of TNT contains about 4000 joules and 1 gram of a Snickers bar contains about 19,500 joules. See
http://www.peertrainer.com/DFcaloriecounterB.aspx?id=5624
266 calories in 57 grams = 4186 x 266/57 = 19,535 joules