I am having an incredibly difficult time trying to understand the idea of Broadness in terms of swords. I've read about Sword properties. So, looking at the 3 different blade shapes (lenticular, diamond, and hexagonal), I have some interpretations for broadness.

At first, I thought it was the length or width of your blade. Now I think it's the width of the actual edge, or the length from the flat of the sword to the end of the edge. Is that what determines broadness? Or is it the thickness of the blade?

If you have two blades with the same thickness, and you make one wider, you will be making the edge sharper. You will be required to make the angle of the triangle more acute. Is this how you determine the broadness? The ratio between the thickness to the wideness?

Breadth and width are essentially synonymous when it comes to sword blades. Unless specified otherwise, it's the measure across the blade from one edge to the other, or from the edge to the back on single-edged blades.

Thickness is measured from flat to flat, and length from one end to the other. The dimensions of a sword blade are easy to tell apart even without labels: since sword blades are by definition relatively long, flat pieces of metal, almost always the length is somewhere around ten times greater than the width, which is again ten times greater than the thickness, very roughly speaking - i.e. length is always far greater than width, and width is always far greater than thickness. :)

PS. Note that a blade's width almost always varies along its length; this is called profile taper. Usually when only one measurement for breadth is given, it's taken at the widest point, typically right at the base (but not always - some swords, like the famed Conyers falchion, actually have negative taper, i.e. they grow wider instead of narrower away from the hilt). Thickness also varies similarly, almost always growing thinner away from the hilt; this is called distal taper.

So, what makes the broader blade more capable of cutting? Is it due to factors associated with broadness (sharpness, mass, etc?). I just don't understand how making the blade wider effects its ability to cut with the edge. A thin blade that is just as sharp, heavy, and long would do the same as a broad blade, yeah? Except for that it might not be physical possible for a blade to be thinner while maintaining the same sharpness, weight, and length.

More mass equals more kinetic energy which in turn equals stronger blows (deeper cuts) and a more rigid defence against other weapons maybe?

A broader blade simply has more cross-sectional volume, and thus mass, than a narrower blade of the same thickness. An object's momentum equals its mass multiplied by its velocity, so a heavier blade moving at the same speed hits harder. Penetration into material is a product of momentum and impact area, and since both blades are equally thin and thus have equal impact area, the heavier blade with more momentum cuts deeper than the narrower, lighter blade.

Let's see if I can explain this.

There are three things that are relevant to cutting: sharpness, thickness, and mass.

Sharpness can be defined very simply as the intersection of two planes. Your ideal sharpness is when those planes intersect very acutely. You can be sharp with an obtuse angle, but the greater the angle of intersection of these planes is, the more effort it will take to cut with. Compare a cold chisel with a good kitchen knife, for example. The chisel has a very obtuse edge versus the knife, which is much finer. The more perfectly this angle is formed, the sharper it will be; a blunt edge is one where this angle has been worn away and the bevels do not intersect. To make it sharp, you remove material until they intersect again.

Thickness is not quite the same thing as mass. They can correlate, but not always.

A broader blade gives you:

a.) a thinner blade with the same amount of metal as a thicker blade, which then also gives you:

b.) the same mass as the thicker blade. The broad blade is, HOWEVER:

c.) Thinner, which means that you can hone a finer edge on the blade. A thick blade will have a steep bevel because you're going rapidly from the thick part of the blade to the edge. A thinner blade will have a more acute bevel.

Therefore, a large thin blade is *generally* going to be a better cutter than a thick, more robust blade of the same mass.

Does that help?

Think of a blade in mechanical terms: you have a moment of area along the cross-sectional profile of the blade (which will likely change along its length) and a rotational moment of inertia which will describe how the sword moves when swung. Both of these moments are linked through shared aspects of geometry and material properties. Although area is two-dimensional and therefore can have no volume (and thus no mass), the change in area (dA) along the length of the sword most certainly does! Let's do some simple figuring:

Rotational moment of inertia (MOI), commonly just called "moment of inertia," is the sum of masses times each mass's location squared from a designated point. You can find a more descriptive calculation here: https://en.wikipedia.org/wiki/Moment_of_inertia

The simplest way to practically relate this would be to take the rotational moment of the sword at its center of mass (point of balance) such that the edge is swinging as cutting (obvious, but clarity can't hurt), and then re-calculate the moment of inertia with respect to the sword being swung in hand via the parallel-axis theorem. You can see from the equation that the longer a sword is, the farther the mass is distributed along its length, and geometric distance is weighted more heavily than mass with regard to impact on the total MOI. This makes good sense, as a very long sword is difficult to control with one hand, and two hands with plenty of torque are needed to make such a sword both nimble and lethal.

For area moment of inertia, there is a link attached at the top of the linked Wiki page, and you can find calculations there. In brief, the wider an object is in one plane, the more resistive to flexure it is in that plane. This is easy to see in a sword blade: the flat flexes easily while the edged plane will not. Generally, to be stiffer in the flat plane, the sword must either be fullered or have more mass in the section. To be more resistive in the cut, the blade must be wider. This kind of describes why swords good at cutting and swords good at thrusting are designed the way they are, eh?

*****

As a simple measure, I often like to think of cutting power in terms of "local momentum." For instance, if you sliced the blade up into sections, each would have a mass and a rotational velocity, and momentum = mass x velocity. Cutting blades often have more even mass distribution throughout the blade while needing to be broader to resist flexure in the cut. So, such a blade bites deeper into a target when swung at speed, because the relevant "local momentums" are in effect against the target. Going back to the previous section, more even mass distributions generally move a cutting sword's center of mass out from the guard, and this coincidentally generally speaks of a higher moment of rotational inertia. Fun stuff![/i]

This has been so helpful.

I've known that the broader blades are better for striking, it's made sense to me, and I've accepted it as fact. And I've looked at pictures of blades described as broad.... but there was just something missing. A tiny piece that didn't fit, that you guys fixed for me, thank you.