Ok, so before I get started, this is just a little food for thought and it's only my opinion but I have read a lot now about all these amazing benefits that having a curved sword imparts to its user. This got me thinking about whether or not the sword was designed like that deliberately and if it really affects the performance of the user. The katana and indeed its predeccessor, the tachi and all their variants had one signature visual component that stands out above all others. They all have a graceful curvature to them whether it is pronounced or very subtle it is there. As an aesthetic, it is hard to argue that it is not important as it reflects the history and the evolution of the Japanese sword, each progression and variation being very much like rings in a tree, all telling something about the era of their creation. As to the actual function of the curvature however, there are much cloudier discussions.
It has been suggested that the curvature of the blade aids in the slicing action of the sword or that it affects the balance in a way that is advantageous to the practitioner. It is also said that this slender curve makes nukitsuke or the action of drawing and cutting with the sword easier because it helps it to clear the opening of the saya with much less effort.
All this and many others offered up as explanation however seems to be fuelled mainly by conjecture by people in heated arguments or by subjective opinions formed by martial artists. There seems to be very little in the way of science to back up any of this, but this isnt to say that advantages in cutting arent conferred as a result of the curvature of the blade, simply that these subjectivity or emotionally driven discussions are inconclusive.
Practical tests have been done however and the results observed as best could be. When done with a variety of swords from different areas in different styles, against both hard and relatively soft targets, everything else being equal such as the quality of the steel and the quality of their construction, there have been no noticeable differences it would seem in the performance of any one of them.
What we know to be true however is that the Samurai formulated their martial arts around their needs at the time, evolving them as and when. If there are any advantages to the curvature of the sword when wielded by Samurai then I believe they evolved after the sword was placed in their hands and were a response to that curvature and the way that it changed the handling of the sword. In fact from an entirely materialistic point of view, the curvature was a result of the forging technique that produced the differentially hardened blades with hamon that are prized by many collectors and martial artists. We also know that a curved blade was possible before this forging technique was, but still there are no historic examples of curved non differentially hardened katana. It would seem that this confirms that the form of Iai followed the form of the sword and not the other way around.
So whether or not it really helps the cutting motion at all is still out there. I do not know the answer, but it does seem like the Japanese sword arts evolved to use it as effectively as possible in the same way that the sword arts of other countries like England or France evolved to use their more stout and straight or flexible and more needle like blades. What do you think?