How does a swords width affect its cutting?

Let's examine the various factors that influence the cutting ability of swords- just for general education.

The main factors involved in cutting are (in no particular order) Velocity, sectional density, Momentum at the Point of Impact (MPOI,) edge geometry, cross section and sharpness. All of these things inter-relate in a sword's cutting ability.

Energy is important to cutting ability and power. Energy is governed by mass and velocity- with velocity being the most important of these two. Contrary to firearms and impact weapons when attempting to cut through a target you want to transfer as little energy to the target as possible. *The more energy you start with, the more you can afford to expend displacing material as you cut through.* With two swords of the same weight, one would expect the faster sword to have more energy and cut better- right? NO, because there is a lot more to it than that.

Other factors enter into it as well- the ratio of mass to cross section is called sectional density. As an example- if we take a rapier and a viking sword that both weigh 2-1/2 pounds that are both an average of .1 inches thick at the point of impact, the rapiers POI can theoretically be moving faster than the viking sword's as the POI is farther from the point of rotation. However, the rapier will not cut nearly as well- and part of the reason is sectional density. The rapier is the same thickness at the POI, and may even have very nearly identical edge geometry. Being broader at the POI the Viking sword has a much higher sectional density- IOW there is more mass piled up behind the cutting edge, so it has greater momentum (and more energy) at the POI. Even if it transfers energy at the same rate as the rapier it's drawing from a deeper well, so to speak. The rapier cannot be moved enough faster than the viking sword to offset this advantage. Well, not by a human, at any rate...

Swords with a thin cross section at the POI experience less resistance to the cut because they have to displace less material. If they also have good Sectional Density they have a deeper well of energy to displace material. Similarly edge geometery comes into play- a steep angle at the cutting edge means that the sword has to displace material faster which 'bleeds off' energy more quickly as well- so a sword with 'bad' edge geometry will cut less well than a sword with 'good' edge geometry even if all other factors are equal. On the other hand if the edge geometry is too fine, while the sword cuts superbly it is easier to damage the edge. As in all things it's a balancing act- between cutting ability and durability.

So- Katanas are pretty thick at the POI and have pretty good edge geometry but aren't very wide- they have a lower sectional density than Viking style swords too. So why do they often cut just as well? Because of a mistake in our assumptions, actually. If the cross section of a Katana is thicker and it's width when measured straight accross the POI are lower than the broad bladed Norse sword the assuption is correct- but this is not the way that a Katana's sectional density should be measured. True, if you pretend the Katana is a viking sword and use it identically, it won't cut as well. Used properly however, the Katana's edge is drawn through the cut at an angle- the the Katanas cross section should be measured at an angle from the POI. If for example the Katana is drawn through the cut at a 45 degree angle it 'stretches' the width of the Katana. The Kat's Sectional Density should be measured across that 45 degree angle. If the Kat has a nominal width of 1 inch at the POI, measured across the 45 degree angle it has a width closer to 1.4 inches- consequently more mass is involved, and this raises the effective sectional density at the point of impact. Within limits the shallower the angle of impact at the POI, the greater the sword's effective sectional density. Striking with the edge at 90 degrees to the target it loses this- hence cuts less well.

Broad, flat-bladed swords are design for optimal cutting when the blade impacts the target at 90 degrees (roughly.) Katanas are designed to for optimal cutting when the edge is moving at an angle to the point of impact. Both methods work for same reason.

What's left? Right, sharpness. All other things being equal, sharp things cut better than dull things. A dull edge transfers energy to the target faster, resulting in a shallower cut. 'Nuff said.

I hope that you were all paying attention, as there will be a short quiz next period.