Armor vs. Fast Projectiles or Slower Weapons

Summary
Armor vs fast collisions and slower heavier collisions
Yeah this is for an RPG. So my understanding is that a bullet would penetrate plate armor (only a few mm thick) while a sword swing even with more KE would not even though both the bullet and the sword have their energy focused into a small area.

I assume this has to do with the armor having more time to decelerate the sword swing or something but I haven't figured it out yet. I'd like to be able to quantify this as well (super accuracy is not necessary) if you guys can point me to a formula as well. Thanks! This forum has been awesome but I may be done with my physics coursework now. Maybe I'll be on now and again to talk about comp. Sci. or to ask about random math things.
 

Steelwolf

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Armor vs fast objects, the difference between a bullet and a sword is that the bullet is likely moving at 1800 feet per second while the sword is travelling at 18 feet per second. Even if the bullet is 1/10th the weight and 100 times the speed of the sword then the formula ( Energy(kinetic)= Mass x Velocity^2 ) applies. As mass goes up it is a linear relationship, damage due to mass is limited ratio of 1 to 1, increase mass by so much, it only does that much extra damage.

Increasing the Velocity gives the square of the speed (times the mass) as the energy so even with 1/10 the mass, the bullet is doing 1/10m x 1800^2..so you can see that even though the weight is 1/10th that the sword, that 1800 x 1800 feet/second being 3,240,000 x 1/10, or almost 324000 times the energy of the sword swing on impact.

THAT is what pushes a soft lead bullet through a thin sheet of steel while the heavier, slower sword only makes scratches and dents.

The same basic reason is why we no longer use castles as the projectiles will eventually win and those in the castle have no mobility and a lack of resupply. Is also why tanks can be taken out with high velocity explosions, emphasis on that High Velocity. Maces in the Medieval European areas, and even swords were more to crush the armor rather than actually cut it. Most armor of the time was leather boiled in oil, making it like a hard plastic and reasonably light. This was often covered with strips or scales of iron and the whole idea of armor is not 'complete protection' but enough to give some protection and allow offensive mobility, since mobility is better than full coverage of armor. Being in heavy armor is fine, unless you cannot move away from the enemy. Breaking or crushing your opponent's armor is at least as effective as cutting them

So the slow heavy collision has somewhat less energy than lighter objects moving much faster and warfare, weapons and armor all have to obey the math concerning mass, velocity^2 and kinetic energy, so the slow, heavy sword has a LOT less kinetic energy than that tiny fast bullet.
 
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I'd like to be able to quantify this...
That's difficult. The energy consumed by the deformation of armor is a good starting point but to quantify it... Plenty of things can ruin an RPG and too much difficult calculations sure one of them.

By the way as I recall the KE maximum available through direct utilization of human muscles is ~ in the lower ranges of small arms bullet KE. Some energy storage and mechanics (bows, for example) can multiply that.
 

FactChecker

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The OP does say that the sword has more kinetic energy. It also says that they both have "their energy focused in a small area", but does not quantify that. I can only guess that either the contact area of the bullet is much smaller than that of the sword, or that the comparison of kinetic energy is wrong.
 
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Thrust or slash: trench knife or broadsword... Too many variables for any quantification of reasonable length IMO.
For a thrust (for any weapon which is for thrusts) the affected area will be a few cm2, while for a slash it's a few cm wide stripe. Even if the slash has the energy the result won't be comparable to a bullet (on an armor).
 
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FactChecker

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Suppose they have equal kinetic energy and equal shape of the penetrating point. As the OP suspected, the higher velocity, lower weight object should have the advantage in penetrating. It would cause a much higher initial acceleration of the target and a greater initial force.
 
I was imagining a strong warrior swinging a sword. A pitcher can throw a ball at 50 m/s. I used that number a few times for punches (30 - 40 m/s is probably better assuming a professional fighter).

Unlike a ball which will have the same velocity as the hand when it releases the ball, a sword or other melee weapon will have some extra velocity due to its length. The impact zone of the sword would benefit from how the velocity of an object being swung in a circle is equal to the angular velocity times the radius (I think).

Also consider how similar a sword swing is similar to pitching a baseball. If 50 m/s is a standard speed for a physically gifted pitcher, a sword or mace swung by a strong warrior should be similar to that. The sword might be 3 lbs at most and it also benefits from the fact that it's swung in an arc. So, 50 m/s is a conservative estimate for a physically strong warrior (before he gets tired). They've done tests with men swinging swords as hard as they can and it will not penetrate the plate armor. But a bullet will.

Take the 3 lb sword and calculate its kinetic energy. The weight of the arm should factor in as well. Say that's 5 lbs, a conservative estimate for a beefy man wearing metal armor. Then calculate kinetic energy using the 50 m/s conservative estimate for a full power swing and you have about 4.5 KJ.

At 600 m/s (fast for a handgun) and a bullet mass of 20 g, you have 3.6 KJ.

But apparently breastplates *could* stop some early arquebus guns and firearms. It might come down to KE after all. This is material science and it is complicated. For example how with kevlar fibers around the area of impact stretch thus negating some of the energy of the bullet.

While researching this I learned that swords supposedly *could* still do damage to the person underneath just without penetrating the armor. Hardness also seems to come into play here. For example at some point if the hardness of the armor is high enough, like tank armor versus a lead musket ball, the energy will go into deforming the projectile and not the armor. I think that's right. I want my numbers to be sort of reasonable and the materials science aspect of military physics is a challenge.
 

FactChecker

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I think that you should be more specific about your definition of the problem. Is it a steel plate or kevlar? What is the area of contact of the sword? etc.
 
Okay, the consensus appears to be that even old wheelock muskets would penetrate late medieval plate armor. Those might have only 1.5 KJ of energy and the ammunition was round and not in any way pointy. Steel armor got thicker and at the same time covered less of the body until it would need to be so thick it was abandoned.

The sword in my example has way more KE than any musket and it's even focused into a smaller area. Swords would still cause bruising and broken bones but somehow the metal would stop the edge. I don't really know what's going on here and I certainly can't quantify it. Well, I sort of did quantify it in my game manual, but I don't know if my numbers are good since they are based on examples from the Internet and my own estimates.
 

Steelwolf

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Swords are actually more like a narrow mace when dealing with nearly any kind of armor. Most of those swords did not have a sharp razor edge like we would tend to think, the edge that took the least damage to the sword and still did the damage to the enemy was closer to the shape of a cold chisel.

Note, I was a swordmaker myself and built medieval armor for historical reproduction groups, and working with the SCA where armor is a specific for of safety equipment. So I actually have a LOT of experience in this area. I worked under the name of Steelwolf Armourie, but since am disabled am no longer able to DO such work, but I can most certainly advise on this subject, which comes up frequently, in actuality.

Most of the cutting idea for swords is the later period Japanese Katana, Persian Samshir and the Euro-American Saber and those were designed for gun era with no to cloth armor. Katana was built to cut bamboo and silk armor.

All the swords before them sere either long crushing weapons or a shorter thrusting weapon. The underarm thrust likely to do more lethal damage with a bronze sword than trying to do a slash and slash just cuts surface material, a thrust goes to the vitals. The sword is still not able to go nearly as fast as the bullet (even blackpowder musket is faster), and so is not able to attain the same kinetic energy

For a bit more Real Life experience about such, check with whatever local Society for Creative Anachronism in your area, they can show you a whole lot more about what combat with swords in armor is all about, by putting you IN armor and using safety-styled weapons of solid rattan. That and working with a local Black Powder/Mountain Men to see what those firearms were like the actual speed and power that they have, range etc. since the earlier blackpowder musket was a serious game changer for the military. If you are writing the data and experience will last you forever,

You will be able to get some real world info on what it really feels like, how restricted you are in swinging your own weapon with the armor on etc. There is a LOT more to it as the armor wearing types tended to train and run and live and work in their armor or heavy clothing, training with sword workouts etc. It was a brutal and typically short lifestyle.
 
Swords are actually more like a narrow mace when dealing with nearly any kind of armor. Most of those swords did not have a sharp razor edge like we would tend to think, the edge that took the least damage to the sword and still did the damage to the enemy was closer to the shape of a cold chisel.

Note, I was a swordmaker myself and built medieval armor for historical reproduction groups, and working with the SCA where armor is a specific for of safety equipment. So I actually have a LOT of experience in this area. I worked under the name of Steelwolf Armourie, but since am disabled am no longer able to DO such work, but I can most certainly advise on this subject, which comes up frequently, in actuality.

Most of the cutting idea for swords is the later period Japanese Katana, Persian Samshir and the Euro-American Saber and those were designed for gun era with no to cloth armor. Katana was built to cut bamboo and silk armor.

All the swords before them sere either long crushing weapons or a shorter thrusting weapon. The underarm thrust likely to do more lethal damage with a bronze sword than trying to do a slash and slash just cuts surface material, a thrust goes to the vitals. The sword is still not able to go nearly as fast as the bullet (even blackpowder musket is faster), and so is not able to attain the same kinetic energy

For a bit more Real Life experience about such, check with whatever local Society for Creative Anachronism in your area, they can show you a whole lot more about what combat with swords in armor is all about, by putting you IN armor and using safety-styled weapons of solid rattan. That and working with a local Black Powder/Mountain Men to see what those firearms were like the actual speed and power that they have, range etc. since the earlier blackpowder musket was a serious game changer for the military. If you are writing the data and experience will last you forever,

You will be able to get some real world info on what it really feels like, how restricted you are in swinging your own weapon with the armor on etc. There is a LOT more to it as the armor wearing types tended to train and run and live and work in their armor or heavy clothing, training with sword workouts etc. It was a brutal and typically short lifestyle.
I think part of the answer is clearly that plate armor only absorbs *some* of the energy from a heavy sword swing so it doesn't get permanently deformed very much by the attack. The idea about the collision duration affecting this might have been partly right. The faster bullet doesn't temporarily deform the flexible plate or have much of its energy conducted away by the metal like the sword impact does. I think. Maybe.
 

Steelwolf

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Yes, there is a fair amount of padding underneath that steel too, and the heat and weight of the armor etc. The bullet is hitting so fast that it often penetrates without doing it's full damage, which is why the larger slower rounds do more impact than a fast smaller caliber round, even though the energy is higher on the faster round, the time of contact has a lot to do with the shock cone of damage that will radiate from the impact.

One of the ideas with European armor and fighting was to crush the armor to the point it could not move limbs, and thus incapacitate the warrior. This is how some were captured rather than killed. But maces were nice since if you just crushed the armor around the enemy's shoulder or break their neck with a good smack to the helm. The Spanish Badelier of the 15th century was a large, almost cutlass looking blade, but it was heavy, two-handed and made to Crush armor, even though it looked like a nice slicer, it was a heavy 'war bar' with an edge.

The major purpose of armor is not to stop all attacks, but to deflect the majority, and keep the weight low enough to give the mobility to stay out of the way of the direct hits. Economic status always had a lot to do with what the family could afford to put their warrior in to as well. There are so many facets to this that perhaps I should start writing up an insights article as I have been teaching this sort of stuff, hands on or online, for 30+ years now. I have taught people how to hammer out armor, make tools, make knives, swords and axes (all of which are differing physics and balance/tuning to be 'Real') I taught myself how to make mokume gana and worked with white-smithing (gold, silver etc) and gem setting.

Also built a Great Helm for a gent, but it was Too Great a helm for him to actually wear and use, even though I had built it to the man's direct size and dimensions demanded and of the 12 ga steel he wanted (which the other armorers looked at me with wonder at hammering a full helm out of 1/8 in steel) but it was too much, would pull him off his feet, even though it gave him all the protection he could want, he could not Move with it. So, I took it as a learning experience (after a little bit of explanation that we are building safety equipment for a full contact sport, so us armor's have to know better than the fighters what they really need.

That was at a very dry event, no open fires allowed. and that night it poured rain, got cold etc, and nobody had prepared for that since it was high summer and bad fire season. Well, I got under my big canvas Norse A-Frame stype pavillion, and looked at fire pit, and helmet, fire pit, helmet...took a piece of 18 ga and bent corners to form a lid, and then used the huge pinecones and small branches all over, very dry, and cleared proper circle, put the huge helm upside down in the firepit and started a nice blaze, covered it with the 18 ga so it was not an open flame, open grillwork on the face, and the edges of the top, but it was a safe-contained fire (I was Navy Firefighter and so am super cautious about such) But ever since then I have kept the Helm Fires Burning!
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That is on top of a 55 gal drum, for scale. 1/4 in bar for horizontals. I did later cut slots in the sides for even venting, but before that I took a battle-stype pick to the sides of it, to see the damage for myself. Part of why I KNOW this stuff is because I DID it, this helm is from over 30 years ago, but close to that age.
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The lower is the Spanish Badelier, nasty piece of work, that. And above that was a 10 day run of work for me and an apprentice, Elena, who was learning the machining and setup side of the business, I was teaching her how to build swords right along with me and was doing well, and then my health came apart rapidly.

Edit: All of the work was done to tool quality unless otherwise asked, such as some props for conventions etc, or specific fencing type of gear. All fully hardened and tempered, heavy tang construction with permanent construction. No pommel screwing off, etc. But being disabled, the best I can do is to teach others about it and to help folks understand some of the realities behind it all.
 
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the higher velocity, lower weight object should have the advantage in penetrating. It would cause a much higher initial acceleration of the target and a greater initial force.
High velocity with the same energy actually means less impulse. The mentioned 4.5kJ 'full swing' of a sword would have far (!!!) more impulse than a 20g bullet with the same energy. Actually this counter-intuitive thing is what makes gun recoil still bearable compared to, for example: a staff hit. This is also the magic behind the various kind of maces. To break an armor you need energy, concentrated on a tiny surface: but to give a big shock needs 'only' impulse (and at the end you would also get a more or less intact armor, what meant a significant wealth that time when all this was still relevant).
 
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FactChecker

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Sorry, I should have been more clear. For the armor to stop a faster object, it would have to withstand higher accelerations at the point of impact and a higher force there.
 

Dr. Courtney

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Armor failures are due to the applied strain (force per unit area) exceeding the threshold of the material for failure. The force that an impacting object can apply is limited by the relation of kinetic energy to force in the work-energy theorem. The gist is that the force is dE/dx, where E is the kinetic energy and x is the linear dimension in which the impactor is moving.

If the kinetic energy of the impactors are the same, the fast impactor has the advantage in penetration because there is less time for the armor to move during impact and also less time for the armor and impactor to deform during impact. Motion and deformation essentially increase the stopping distance over which the interaction occurs. Increasing the stopping distance of an interaction always decreases the average force (which is simply E/d, where d is the stopping distance), and usually also decreases the peak force.

Another variable is that most materials have failure thresholds that depend on the rate of applied strain. Failure thresholds for ballistic events (faster than 300 m/s) are much different for impacts in the range of motor vehicle speeds which may also be different from impacts more in the range of speeds generated in most sporting stuff (balls, racquets, swords, bats, etc.)

In general, it is very difficult to reduce armor failures to a simple formula, because the armor and impactor are both moving and deforming during the impact. Ab initio approaches for predicting velocities where a given armor will fail are very complicated and usually wrong. Even once a method is tweaked to work with one given type of armor and impactor, it is likely to be much less accurate when used with a different armor and impactor.
 
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