The best geometry for blades

[Vincent Le Chevalier]

1- When I said the angle is zero in straight blades I should had add that the edges had to be parallel to each other for that to be true; in a triangle shape blade the angle is not zero and we have a "guillotine" effect.

I think this effect can be safely neglected because the edge angle is ordinarily very small... At this level of detail you'd have to take into account the evolution of the cross-section of the blade as well; generally I believe the triangular blades have a cross-section that gets closer to a square as you go towards the tip. Sorry to add one more variable here

If the strike has a slicing motion that adds to the geometry of the blade, I would say it benefits more the straight blade since you only need to draw the sword in straight line and, with a curve sword, you should draw the sword following the curvature of the blade... Seems to me this a more awkward, difficult and unnatural way to strike.

It might seem so but that's not proof it is. The problem is that maths won't tell you which design is more natural or feels better to the user, at least not easily, because in order to do that you'd have to model the user. We delve into ergonomics here...

To add a slice to a straight blade you just have to maintain an angle at your wrist, so that the speed is not orthogonal to the edge. Waiting for the impact and then drawing the edge is not the most efficient way to do it, because after the impact you lack pressure at the cutting spot. The guillotine effect is more powerful: pressure is given by the mass and speed of the blade, slice is given by the angle of the blade.

That's why it is better to test geometries to use a straight katana vs a curved katana; this way the mass distribution would not be something to consider. But again, for cutting the whole thing straight blades will do just as good, though now I should add that the straight blade should be triangle-shaped to match the slicing effect of the curved katana. Mmm... Though the mass distribution might favor the katana since the triangle-shaple blade will be lighter the closer to the tip. Mass distribution is something I did not consider in the formulas... Oh my God

Heh See? That's why I gave up trying to find the optimal cutter
I haven't looked in detail but I suspect straight blades and curved blades are rarely balanced the same, they could have different mass distribution. So if you try comparing just the geometry, you don't get a meaningful result because one or both of the theoretical blades do not even actuallly exist

All swords are a work of compromise. I don't think you can win on all accounts, or there would have been a "best sword" design found very early in history, everywhere in the world. The mass distribution, for example, does not have to be optimized for pure power. It also conditions the handling of the sword, and you cannot really have a fast, light and agile sword that strikes with the power of an axe. The cross-section varies to ensure strength, stiffness, correct mass distribution and cutting power, but you cannot find the cross section that does it all perfectly. The curvature gives a natural "guillotine effect" but the thrust becomes less intuitive with a very curved blade...

Actually, I figure many swords are not optimized for pure raw cutting power, but for versatility, being able to wound sufficiently with many parts of the blade, and many techniques. Thus, one can generally find another design that does one aspect better than the sword. And yet, the sword is more useful overall

Even worse, users are not just robots that swing their swords always in the same way. Experienced practitionner will intuitively tune their techniques to match the weapon and get the most out of it, while remaining tactically viable (another thing that is somewhat hard to model mathematically).

In all that, the effect of curvature alone is a bit covered in the noise...

I'm sorry to bother you with all this stuff, but I think keeping the bigger picture in mind is important. I know it helped me when studying this stuff...

The next thing you should do, and this can be suprisingly difficult, is get your theory to face the real world: get a straight sword, a curved sword, cut as much as you can with them, and explain the differences (if any). Plenty of suprises can arise

Good luck! I hope you'll enjoy doing maths on swords as much as I do

[Francisco Urbano García]

The next thing you should do, and this can be suprisingly difficult, is get your theory to face the real world: get a straight sword, a curved sword, cut as much as you can with them, and explain the differences (if any). Plenty of suprises can arise

Good luck! I hope you'll enjoy doing maths on swords as much as I do

Yeah, I totally agree, the theory give you insights about what to test and what to expect but, at the end, you have to confront them with reality.

Nonetheless I have learned a lot in the process to get a math theory for the blades, and thanks to your comments about slicing-effect and weight distribution I realized there are more things to consider.... For instance, the balance of weight might give advantage to a katana vs a straight triangular-shaped blade for up-down cuts, but that weight might turn disadvantage if the cut is down-up... so again more things to consider in a cut!!! I should summarize all this thread in case I go "real" test.

Anyway, it was real fun, thank you Vincent for joining in

[Maxime Chouinard]

Actually, I figure many swords are not optimized for pure raw cutting power, but for versatility, being able to wound sufficiently with many parts of the blade, and many techniques. Thus, one can generally find another design that does one aspect better than the sword. And yet, the sword is more useful overall

I agree with you completely here. The sword is, most of the time, a polyvalent tool, and so must be a good performer in most situations. And so people came with designs that compromised in order to perform well.

[Stacy Clifford]

Actually, I figure many swords are not optimized for pure raw cutting power, but for versatility, being able to wound sufficiently with many parts of the blade, and many techniques. Thus, one can generally find another design that does one aspect better than the sword. And yet, the sword is more useful overall

I agree with you completely here. The sword is, most of the time, a polyvalent tool, and so must be a good performer in most situations. And so people came with designs that compromised in order to perform well.

I think one thing that doesn't get considered much in discussions like this is defensive capability. A strongly curved blade is a bit more difficult to make accurate parries with on the flat, partly because of the changing angles and partly because they tend to distribute more weight toward the end for better cutting, reducing their agility. If you have a very offensive style of swordsmanship or spend all your quality time on horseback running past people at 40 mph and don't need to parry a whole lot, that's probably OK with you. If your style has a more well-rounded defense and you face enemies who have time to make you use it, a straighter and more agile blade may make more sense. A sword's first job may be to cut things, but its second job is to keep you from getting cut, so a design that makes that easier to do also deserves some consideration and you can't leave it out of the compromise equation.

[Maxime Chouinard]

How is the changing angle such a problem? If your technique is correct there isn't supposed to be one. As for weight distribution, honestly I don't think it makes such a difference, again my personnal experience as shown me that timing and distance is much more important. So what is best? More training .

[Stacy Clifford]

How is the changing angle such a problem? If your technique is correct there isn't supposed to be one. As for weight distribution, honestly I don't think it makes such a difference, again my personnal experience as shown me that timing and distance is much more important. So what is best? More training .

With a lightly curved blade like a katana I don't think it makes much difference, but a more strongly curved blade like a shamshir it could. Of course if you parry correctly with the strong of the blade then it shouldn't matter a whole lot what type of blade you use, there I agree with you, but we're not always lucky enough to get the correct part of the blade out there in time. A straight blade is essentially a one-dimensional line, whereas a curve is two dimensions. In a parry that lands farther out along the blade, the extra dimension makes the leverage applied against your wrist and arm more complex, and thus more difficult to control than a simple straight line. Kyle Cook has a blade like that which I've played with a few times, and I can tell you for certain that it takes more muscular effort to turn the flat back and forth for multiple-direction parries than any straight blade I've handled with similar weight, even without anyone striking at you.

Weight distribution also makes a difference. On any single parry you can probably overcome and ignore it, but it does require extra exertion to move the end of the blade into line where you want it if it's more tip-heavy, and over the course of an extended fight that extra exertion adds up. I have two straight single hand wasters of about equal length and weight, but one is much more tapered than the other. The parallel-edged one is clearly harder to stop in mid-cut or force to reverse direction in order to defend, and it wears my arm out considerably faster than the more tapered blade. I love that parallel blade if all I'm doing is strikin because its forward momentum is easy to maintain, but I hate defending with it because it's so much harder to stop. I don't have a comparable set of curved blades to try it with, but the physics shouldn't be that much different.

Like you said, more training and more exercise always help, but if you have to defend yourself frequently with an object that requires greater energy to manipulate, it's going to result in more fatigue. Depending on the type of fight you expect to engage in, I think that is something that needs to be considered when choosing a blade.

[Maxime Chouinard]

I agree that a heavily curved blade might be different, I haven't done much work with those types so I really can't tell, although it never seems to have been a problem with 19th century sabre fencing, as much as I know about it.

I also agree that one should choose a blade that suits his physical capabilities, it is a common advice in most if not all styles.

[Stacy Clifford]

From what I know of 19th century sabre fencing, they mostly taught parrying with the edge, which is linear and acts more like the one-dimensional straight blade. The flat is where the leverage issue gets funky.

I also think the type of warfare a culture engages in affects preferred styles of blades. You don't see lots of stories about Mongols dueling with swords on foot, where more parrying is required. Having a good drive-by guillotine seems to have worked better for most horse cultures. Knights may have preferred to be on horseback, but they were expected to be all-around warriors and needed versatility.

[Benjamin Smith]

Thanks for the reply and discussion Francisco.