Swords, Force, and Energy

[Steven Snyder]

I am not a science major, but I find the topic fascinating. I was raise in a nice redneck town in the South, which means they didn't focus on science but if there is ever a cattle stampede I will know what to do.

After finding this site I think I have learned a lot from the teachings of Mr. Wong and others who have such physics sites around. But now comes the test because I am being debated on another board by someone else on similar topics.

The topic is what causes the actual damage of a melee weapon, and how it is measured.

It is my argument that the nature of injuries from kinetic weapons is based on that tools ability to deliver energy to the target to break chemical bonds.

This energy has little to do with Force (F=ma), but Kinetic energy which should have the formula of (E=(0.5*m)*(v*v)). This formula seems to show that the energy you can deliver to a target is more dependant on the velocity of the weapon than the mass, technically a weapon that weights half as much but moves twice as fast should be capable of twice the energy of a heavier slower counterpart.
The cross-section of the weapon (how much of it actually comes into contact with the target) also bears some importance because the energy must be divided between the surface of the impact, meaning that a razor blade will cut deeper than a hammer simply because there is less surface area to distribute the energy and there is less material to displace.

My opponent believes that somehow Force is the cause of the damage, citing a reference to the Law of Conservation of Momentum.

Am I mistaken in my evaluation, I expect that I am a little off-base but I don't know how far off I am? Any help would be appreciated.

[Darth Wong]

Depends on what you're talking about. In some cases, you can use either force or KE. If you're trying to figure out the upper limit for work done on the target (ie- amount of damage), you can use thermodynamics and declare the impactor KE to be the upper limit, which it is.

If you're trying to figure out whether it will penetrate armour, you can use either; they should evaluate to roughly the same stress result.

And if you're talking about recoil and overall solid-body collision physics, then we must use momentum.

[Durandal]

The topic is what causes the actual damage of a melee weapon, and how it is measured.

Depends on what you mean by damage. If you're talking about a person, damage would be basically how much you can impair his vital operations. If you're measuring the ability to penetrate armor, you'd have different criteria.

It is my argument that the nature of injuries from kinetic weapons is based on that tools ability to deliver energy to the target to break chemical bonds.

That's a pretty sound argument.

This energy has little to do with Force (F=ma), but Kinetic energy which should have the formula of (E=(0.5*m)*(v*v)). This formula seems to show that the energy you can deliver to a target is more dependant on the velocity of the weapon than the mass, technically a weapon that weights half as much but moves twice as fast should be capable of twice the energy of a heavier slower counterpart.

Force plays a role in impact and penetrations as well. If you want to understand this better, consider that Newton never wrote the equation for force as

F = ma.

He wrote it as a differential equation,

F = m(dv/dt).

Acceleration is just the rate of change of velocity. You could have something with very little kinetic energy impact with comparably tremendous force, for example. Suppose I fire a bullet, and it's muzzle velocity is 200 m/s. Let's just say it weight 0.05 g. It'll have 2 kJ of kinetic energy, which is quite a fair amount. Now, let's say that, when the bullet hits the wall, it's head is compressed by about 0.02 m. That means that the total distance it took to stop was 0.02 m. We can figure out, based on this, the amount of time the bullet took to stop, and with our muzzle velocity, the total acceleration the bullet underwent.

Start with the equation

d = (1/2)a(t^2).

Solving for t and substituting a with (Delta-v/t), we obtain

t = 2d/Delta-v.

Plugging in 200 m/s for Delta-v and 0.02 m for d, we get a time of 0.0002 s. This means the acceleration the bullet underwent was 1 000 000 m/s^2 (about 100 000 g's), giving a force of 50 kN.

The cross-section of the weapon (how much of it actually comes into contact with the target) also bears some importance because the energy must be divided between the surface of the impact, meaning that a razor blade will cut deeper than a hammer simply because there is less surface area to distribute the energy and there is less material to displace.

In this case, force has plenty to do with it. The smaller the surface area of contact, the greater the pressure. That 50 kN is distributed over a very small area, making penetration power greater.

My opponent believes that somehow Force is the cause of the damage, citing a reference to the Law of Conservation of Momentum.

He's right, too ... but I'm not sure what conservation of momentum has to do with force. Force does not have to be conserved, but momentum does.

Where the damage comes from is more dependent upon the target than anything.

[Steven Snyder]

Depends on what you're talking about. In some cases, you can use either force or KE. If you're trying to figure out the upper limit for work done on the target (ie- amount of damage), you can use thermodynamics and declare the impactor KE to be the upper limit, which it is.

If you're trying to figure out whether it will penetrate armour, you can use either; they should evaluate to roughly the same stress result.

And if you're talking about recoil and overall solid-body collision physics, then we must use momentum.

I have a feeling I should probably stop by my local college and take a physics course at this point, but I do appreciate all your help in dealing with this.

To elaborate more, the debate is concerning the realitive weight vs velocity question of a sword.

Assume a regular 42 inch sword weighing 4 pounds and a counterpart that is equal to the normal blade in everything except that it only weighs half as much. Would the lighter blade be superior because a wielder could get twice as much velocity out of it?

From what I have gathered from the two posts, the amount of penetration is more dependant on Force (Newtons?) than KE. The upper limit on just how much damage (work) you can cause a target is based on the KE equation. I have been under the impression that all Force is really used for is setting an object in motion or stopping one.
I can almost see that you would need to apply force to an object to penetrate any armor it has because the armor may not be able to generate 'an equal and opposite' force to oppose the strike. And so once that has been overcome you can then use your KE figure to see if the strike can actually penetrate the armor by breaking chemical bonds. I understand how you figure out the amount of Netwons but I am clueless as to understanding stress limits of materials and what will buckle and what won't.

Thanks for not flaming me on the subject, I have little formal education in this subject but I am trying to pick it up.

[Darth Wong]

Assume a regular 42 inch sword weighing 4 pounds and a counterpart that is equal to the normal blade in everything except that it only weighs half as much. Would the lighter blade be superior because a wielder could get twice as much velocity out of it?

In terms of which one can damage the other? The superior sword is the one that's stronger. It's not a matter of KE or momentum; it's a matter of material properties.

In terms of which one is better in a fight, the lighter sword is better if it's just as strong, assuming all other things being equal, because the swordsman can thrust and parry with greater agility.

In terms of which one would be forced back in a clash, their momentum would be the same (twice the velocity and half the mass equals the same momentum), so neither would have an advantage.

From what I have gathered from the two posts, the amount of penetration is more dependant on Force (Newtons?) than KE.

The key variable is stress in the target, which is related to force ... which can be derived from KE.

The upper limit on just how much damage (work) you can cause a target is based on the KE equation.

Right.

I have been under the impression that all Force is really used for is setting an object in motion or stopping one.

Or deforming it.

I can almost see that you would need to apply force to an object to penetrate any armor it has because the armor may not be able to generate 'an equal and opposite' force to oppose the strike.

Let's put it this way: a hydraulic press generates force but almost no KE, yet a high-hardness spike on a hydraulic press will penetrate just about anything. Physical stress in the target is the key variable for determining whether you can damage it, but with an impactor that has no driving force behind it other than its own momentum, its KE determines the amount of damage it can do.

And so once that has been overcome you can then use your KE figure to see if the strike can actually penetrate the armor by breaking chemical bonds. I understand how you figure out the amount of Netwons but I am clueless as to understanding stress limits of materials and what will buckle and what won't.

There are limits to what you can understand without serious study; I hope you have some appreciation for the basics.

Thanks for not flaming me on the subject, I have little formal education in this subject but I am trying to pick it up.

Not a problem. A lot of people assume that this board seizes upon people who don't know much about science and abuses them ruthlessly, but it's the key ingredient of arrogance which brings out that reaction (ie- fuckwads who come here and spout a lot of scientifically ignorant nonsense as if they do know what they're talking about, or who introduce themselves by pointing out what they see as "errors" in our arguments based on their creationist beliefs). I see no reason to flame someone asking an honest question.

[Korvan]

Swords with different weights are often used with quite different styles, so it's hard to determine which is "better". For instance, with a broad sword, I could deliver an overhead vertical stroke that would be near impossible for someone with a rapier to parry, but during the relatively long setup and execution of the move, I could be run though several times.

The speed of a weapon is dependant on both its weight and the strength of the weilder, but the relationship is not strictly a linear one. Internal friction of muscles, the weight of a person's arm and other factors impose a "speed limit" on a strike, even with a weightless weapon.

However, for heavy weapons, techniques using gravity, body weight, and momentum can result in a final striking speed that is greater than the above empty handed "speed limit".

I've done a bit of thinking on this subject with the idea of putting together a reasonably accurate melee simulation. But the more work I do, the more I keep thinking how much easier it is to just roll a d20.

[Steven Snyder]

First of all to address Mr. Wong: The exact meaning of which blade would be better refers to what could cut through more organic material in an impact. Both blades being identical in all properties except one only has half the mass of the other.

What exactly did you mean by the statement, "I hope you have some appreciation for the basics."? I understood about everything except for that one seemingly minor point.

Swords with different weights are often used with quite different styles, so it's hard to determine which is "better". For instance, with a broad sword, I could deliver an overhead vertical stroke that would be near impossible for someone with a rapier to parry, but during the relatively long setup and execution of the move, I could be run though several times.

My objective wasn't to find out what would work better as a parrying weapon but what would cleave through organic material better.

The speed of a weapon is dependant on both its weight and the strength of the weilder, but the relationship is not strictly a linear one. Internal friction of muscles, the weight of a person's arm and other factors impose a "speed limit" on a strike, even with a weightless weapon.

I understand that there is a limit on the speed that an arm can achieve based on the rate that the host body can accelerate it and the limited distance the limb can traverse in a specific angle.

That speed limit is the maximum I see possible that a man could move an object such as a sword. In fact the additional mass of the sword will even further reduce the speed of the swing, and a more massive weapon will be proportionally slower.

However, for heavy weapons, techniques using gravity, body weight, and momentum can result in a final striking speed that is greater than the above empty handed "speed limit".

I am not fully versed on physics but I think that statement is a bit misleading. Yes over time you could get a weapon moving faster with assistance from gravity than you normally could, but it seems that your range of motion would minimize or completely eliminiate this effect. But mainly I feel that gravity wouldn't help you much is because of the relatively short amount of time it would have to accelerate a weapon. How long would it take a downward strike to hit once it is in a position to benefit from gravity? A quarter of a second? A tenth of a second?

Secondly as I understand gravity it is a constant force on all objects regardless of weight. Meaning that a heavy weapon would get the same gravity induced velocity increase as a light weapon because gravity accelerates them at an equal speed.

Now the downward swing would allow the blade to exert added force to the target in a manner similar to how Mr. Wong described the hydraulic press. But unless the weapon was extremely massive I don't see that being much of a deciding factor.

I could be wrong.

[Durandal]

First of all to address Mr. Wong: The exact meaning of which blade would be better refers to what could cut through more organic material in an impact. Both blades being identical in all properties except one only has half the mass of the other.

Well, this should be obvious. Assuming each blade is weilded with the same velocity, the more massive one will do more damage.

I am not fully versed on physics but I think that statement is a bit misleading. Yes over time you could get a weapon moving faster with assistance from gravity than you normally could, but it seems that your range of motion would minimize or completely eliminiate this effect. But mainly I feel that gravity wouldn't help you much is because of the relatively short amount of time it would have to accelerate a weapon. How long would it take a downward strike to hit once it is in a position to benefit from gravity? A quarter of a second? A tenth of a second?

It would actually be zero unless you allowed gravity to do all your work for you. Think about it. If you're holding a sword straight out in front of you, it isn't accelerating. This means that the force your arm is exerting on the sword is at least equal to and opposite in direction from gravity. So, swinging the sword while holding it rigidly will essentially negate gravity's acceleration unless you completely relax your arms and just let it fall.

Secondly as I understand gravity it is a constant force on all objects regardless of weight. Meaning that a heavy weapon would get the same gravity induced velocity increase as a light weapon because gravity accelerates them at an equal speed.

"Regardless of weight" is a bit redundant. Weight is the force of gravity acting on an object. But yes, all objects are accelerated at 9.8 m/s^2 independent of mass.

[SWPIGWANG]

In terms of which one is better in a fight, the lighter sword is better if it's just as strong, assuming all other things being equal, because the swordsman can thrust and parry with greater agility.

Another thing that one has to worry about is weight balance of the sword as it dramically effects the handling and damage effects of the sword. See below for examples.

In terms of which one would be forced back in a clash, their momentum would be the same (twice the velocity and half the mass equals the same momentum), so neither would have an advantage.

I don't think that one would be able to swing a sword half as heavy twice as fast. After all there are limits on how fast the arm can swing appearently and a heavy weapon, like a hammer, can hold more momentum. After all, the sword that is half as heavy requires twice the energy to get the same momentum and I'd think that if the momentum is limited by the amount of work that can be done by the muscle, rather than force, a heavy weapon would be superior. If it is a up down stoke the heavy weapon is indeed superior because it can convert more potential energy into KE and momentum using gravity and a sword twice as heavy would have gained 2 times the momentum from gravity.

Secondly as I understand gravity it is a constant force on all objects regardless of weight. Meaning that a heavy weapon would get the same gravity induced velocity increase as a light weapon because gravity accelerates them at an equal speed.

This is true, but the weight balance may play tricks as the acceleration of a rotational object means that the tip might accelerate at a rate far faster than g. For a evenly weighted stick, the acceleration is twice at the tip then at the center and the net result might be greater than g at lower angles. The formula is A = aL = ((LMGcosD/2)/(1/3ML^2))*L and I'm too lazy to work it out.


There is also the method of damage, like slashing, cutting, stabbing, hacking as well. A slashing katana that can cut a man in half might seem like the most powerful weapon, but it is ineffective against heavy plate armor compared to classical roman gladius or a heavy claymore as the former uses a beautiful cutting edge and the latter from either higher force concentration or raw momentum. There are also cases where weapons like rapiers can fine chinks in armor and hurt the man inside while bypassing armor. Damage is a complex thing highly dependent on what you are breaking and how the other guy is countering. Afterall, cracking the skull requires a whole different set of properties from poking holes in the torso, not to say steel, iron, leather, bamboo and wood the guy might wear.

Of couse when in doubt, just take out the uber heavy two handed anti-horse weapons and that should kill anyone stupid enough to be hit by it.

[The Dark]

I don't know that much about actual sword techniques, but I'll try to add my views here. According to a historian friend of mine, a baseball bat is the closest common item to a broadsword for weight and balance. I played baseball for three years (until I blew my left knee out in marching band ), and can say we always went with the lightest bat we could grab. We actually did tests in practice, and found that we could get slightly more distance out of a 19oz bat over my 34oz beast I used for building arm strength. We would use the heavy bat to warm up on-deck and then switch to the light bat for hitting, so we could get more velocity on the ball. This is used on sword schools also, where practice swords are designed to be heavier than combat swords. This leads to more developed muscle and faster swings.

As far as actual combat goes, a lot depends on the target. A light blade will usual be designed for penetration of unarmored areas (i.e. rapier). This blade won't do much damage outside of a small area, but it can easily penetrate through to internal organs and cause death by a number of different, rather gruesome organ failures. A broadsword, on the other hand, is a cutting weapon. It isn't likely to damage organs, but blood loss will be serious, and it was known to occasionally break bones in arms or legs when it hit. The two-handed longsword, counter-intuitively, was primarily a piercing weapon, as it was really too heavy to slash (recovery time was too high). It was faster than a broadsword, and its heavy mass behind the point could penetrate armor, and at times run through the person, though this was exceedingly rare (usually the target could partially deflect the blade, and "only" take a gash in the side or have an arm crippled).

Of course, against armor, various polearms or axe or hammer were best, as they could either pry the armor open, cut through it, or smash it into the body of the wearer. But you said organic matter, so my previous paragraph is my last word on that.