The M82 has a barrel length of 20 inches (51 cm, .051 meters) and fires a 45 gram bullet that, at the end of that time, is going 900 m/s. Meaning the bullet goes from having zero momentum to 41 Newton-seconds in 1.13 milliseconds. Meaning the shooter feels over that 1.13 millisecond period of ~36,000 Newtons of force on his shoulder. The person getting shot has to make that bullet go from 900 m/s to 0, but he has to do it over say 2 inches of distance or his organs start getting smushed. Meaning he's experiencing, over that 110 microsecond period, ~360,000 Netwons of force. The exact same momentum, but in the shooter's case it's like getting punched and in the shootee's case it's like getting your torso gummed on by a T-rex.
This is why going from 0 to 100 in a car can either be no big deal (if done over 60 seconds) or kill you six ways from sunday (if done in a few milliseconds when you crash into a wall or something).
We're also not getting into the power of a good muzzle break or the weight of the rifle itself, both of which considerably reduce the felt impulse by the shooter. You can look up people rapid-firing 50 cal rifles from the hip on youtube for an illustration of just how much you can tame the recoil of these guns.
Note that you're at ~80 pounds from wearing just two plates to protect most of your chest and back; you'll collapse under the weight by the time you've armored your entire body.
It's simply not enough to stop the bullet at these kinds of impulses, you need something to distribute the force over time as well as space. Cars use crumple zones for this purpose - the time it takes the front to deform is extra seconds over which the momentum change takes place, thereby decreasing the impulse.
Even if we could develop some sort of powered armor that let you carry absurd amounts of armour I don't see how you could really solve this problem. The suit is still going to push back into the wearer's body with the same impulse, and crack bones when it does.
Ultimately, the truth is human beings are just too squishy. #BringOnTheRobots
What does the word "proportionally" mean in this sentence? Because factually, the slug is about half the weight of the BMG round.
>You need significantly more thickness of armor just to stop the .50 BMG at all, by which point you've added so much more mass that you've gone much of the towards solving the higher impulse as well.
You're looking at elephant-stomping-on-you levels of force, and you're trying to say it'll be mitigated somewhat because you have 5 pounds of steel on your chest rather than 2 pounds. You will be a person salsa even if you strapped a kitchen stove to yourself.
You don't seem to be understanding the magnitude of the forces involved.
the momentum conservation means that the 5 pound of steel would be moving with the speed of 18m/s after full momentum transfer from the 45g bullet hitting it at 900m/s. 5lb at 18m/s - is like somebody would hit you with a frying pan. While painful and dangerous if say into the head, it is still much less so than getting the bullet directly. Even better result would be with a 25 lb steel plate - just 3.6m/s - like somebody would shove an office/kitchen table at you.
Elephant leg say weights 250kg - that would mean that if you have an elephant leg as an armor in front of you, after being hit by a 0.50 bullet with full momentum transfer the leg will be moving at the speed of 0.18m/s - you can just slowly step away from it.
>You don't seem to be understanding the magnitude of the forces involved.
please enlighten us and correct my calculations above.
>the momentum conservation means that the 5 pound of steel would be moving with the speed of 18m/s after full momentum transfer from the 45g bullet hitting it at 900m/s. 5lb at 18m/s - is like somebody would hit you with a frying pan.
The change in momentum over time is what matters, not the momentum itself. As I said above, think of a car. The momentum change on your body from going from 0 to 100 mph is a slight push on your chest....if you spread that momentum change over 60 seconds of steady acceleration. The exact same momentum change, if done over a few milliseconds from say smashing into a brick wall, is probably going to kill you.
I mean this isn't rocket science, it's literally high school physics.
>please enlighten us and correct my calculations above.
I...did the math already? Did you not read it? The momentum change over the distance of 2 inches produces a force of about 360,000 Newton - a 6000 kg elephant just standing on you would produce "only" 60,000 newtons. He needs to be actively trying to stomp your daylights in to get the kind of forces we're talking about.
50 cal is the kind of round that you hit someone in the torso and their arms fly off. It was built to kill vehicles and planes, for people it is absurd overkill.
you're right that the force will be huge, and you're dead wrong about the force effect.
lets say we stop the bullet over the distance of 1cm instead of 2 inches - the stopping force to act upon bullet would be even bigger - 1.8M Newtons (30 elephants!). The same value force will be acting upon our 5lb armor plate. This force will be acting until the bullet stops, ie. for about 0.02 milliseconds. During that time the force would accelerate the armor plate to the speed of 16m/s and the armor plate would travel less than 1mm - only starting to compress the padding under the armor plate. So, 0.02 milliseconds after the bullet impact we have a stopped bullet and the armor plate moving with the speed of 16m/s through the first millimeter of the padding - the situation is no different than being hit by a frying pan.
That's not how impulse propagates. The force carries through the plate, into the person, and does its damage as a compressive wave. Think about seatbelts in a car during a high speed crash - they don't often penetrate the torso of people, but they can and do pop organs through compressive effects if they're worn too high. Yet calculate the momentum of the seat belt at 100 mph and you'll find it's tiny, like a light slap.
But let's assume your analysis is true. Why then does a shotgun slug, with considerably less momentum than the .50 cal and even a frying pan, crack ribs through armor? Why can I put a piece of AR500 steel in front of a watermellow, hit the steel with a .308, and have the watermellon explode despite nothing getting through?
But I'm done. I've explained this same concept 5 different times, and I'm still having to cover basic physics with people too proud to admit their layman's interpretation is wrong. If you think you could survive a .50 with armor, you're welcome to go buy a 1 inch plate from shootsteel.com and an M82 and test if out yourself. Remove one more prideful fool from the gene pool.
That would be true if the plate was pressed hard against the body. A force requires a carrier - a field or a matter. This is why there is padding behind armor. The padding air-gaps the body from the plate. Nothing crosses the air gap during the 0.02ms that the huge force you're talking about is acting between the plate and the bullet. The body isn't aware that something that violent is happening just a few millimeters away. At t=0.02ms the interaction between the bullet and the plate has finished and the plate is flying toward the body with the speed ~16m/s. At that t=0.02ms the plate has so far traveled only for less than 1mm and it will take it ~0.5 milisecond to cross the air gap and to slam into the body at about the same speed of 16m/s. Such slamming is like being hit by a frying pan. Can be pretty damaging if hits a joint or the head. May break a rib. Yet nothing close to being subjected to the force of being stepped on by an elephant or 30 of them.
>Why then does a shotgun slug, with considerably less momentum than the .50 cal and even a frying pan, crack ribs through armor?
The slug momentum (0.03kg at 540m/s) is 2.5 times less than that of .50 cal (0.045kg at 900m/s), so nothing surprising here, especially if it is through a flexible (i.e. different mode of action) kevlar armor. The steel plate armor we're discussing is much heavier.
>Why can I put a piece of AR500 steel in front of a watermellow, hit the steel with a .308, and have the watermellon explode despite nothing getting through?
Even if the watermelon is air-gapped from the steel, the watermelon still can't sustain being hit with a frying pan ( even with less than a full swing of it). If the steel isn't air-gapped from the watermellon - in this case the watermelon do get the force applied if the steel isn't fixed, or a compression wave by the steel plate vibration if the steel is fixed in place.
https://www.youtube.com/watch?v=chZZp-ALV6o
(I looked up the high strength steel armor plates; they do weigh about 5 pounds)
This big chunk of steel stops the bullet:
https://www.youtube.com/watch?v=BrfskAfPB5s
Bit of a kick though and it pretty obviously isn't practical to strap something of similar strength to your body.
This is no better than a political article as far as bringing out the dark side of people.
https://www.americanrifleman.org/articles/2016/4/29/the-barr...
Pretty hard to put a muzzle brake on your body armor.
Also, there are .50 BMG handguns (and no, I'm not mistakenly referring to .50 AE, I mean .50 BMG). They are stupidly impractical, but they exist. You're making this out to be some mythical projectile when it's really just a bigger bullet. It's not like getting hit by a tank shell.
The real flaw with this scenario is that full body armor required to stop .50 BMG would be so bulky and heavy that you wouldn't be able to move. The imparted momentum isn't the problem, it's stopping the penetration of the round.
It's also worth pointing out that this conversation is pointlessly academic, as .50 BMG has not been used in a murder once. Ever. In the entire history of the United States. Out of over one million gun murders total. It's ridiculously impractical for that purpose.