Tsubamegaeshi brings to mind one of the classic ideas of "fictional swordmanship" that you see depicted in movies, anime, stories and other types of entertainment: the "floating target", as I call it.
This is where you cut a target so well that either the cut piece seems to be just floating in the air, for a brief moment, simply "hops" up and lands back exactly where it was cut from, or in the most amazing fashion (usually more fantasy than reality) simply sits there as if your sword simply passed througth the target. You can see it most evidently in some cutting sequences like Tsubamegaesh - the Swallow cut.
In the movies and anime, it's made to seem like when a great swordsman cuts through a target, it will never move at all and sit perfect as before, but either it falls off a few seconds later , or the swordsperson will tip it over to prove that they actually cut it. Perhaps that is possible, but in terms of physics it seems unlikely, unless you have a extreme thin sword (in terms of nanometers, a thousand times thinner than any real sword).
Tsubamegaesh focuses on the kiriage rising cut. However, the other cuts like Kesagiri and Suihei can also "leave a piece standing". I've seen it happen for all of these, however, it is fairly rare. One way, is when the cut actually goes wrong; when you look at the cut on the target, your sword actually turned a little bit, so it's not a straight line but a curve. This curve makes the target sit more easily when it should be sliding off. Another way is when the target becomes sloppy or frayed which means the base of the cut piece has spread out and it makes it easier for the cut piece to "sit down" on the target.
With the "perfect kesa" as people have described it, you cut through the target, and it sits in place. Extreme acceleration and a very, very sharp sword may make this possible (see other requirements below). One perfect kesagiri is a whole lot more impressive over all the other fancy complicated cuts, but it only counts if that is what you were planning to cut, rather than getting it by accident. I've seen this perfect cut happen a few times, but most often by accident. If you can do a perfect kesa 90% of the time you intend to try... now that is true skill.
In Tsubamegaesh, when the kiriage rising cut is fast enough, the target is cut, but it moves vertically up off the target, because of the direction of the cut. A good tsubamegaesh will go through the target so fast, that the diagonal vertical force from the cut equals the same force from the weight of the piece. They almost negate each other so the target seems to move only a little bit, usually upwards. It's a matter of physics and the forces applied.
What you need to get this to happen:
- speed - be very fast, and the sword passes through the target in the shortest amount of time
- acceleration - make sure you snap your cut; this puts in the additional acceleration into the motion of the sword
- angle (tachisuji) - the right diagonal angle is around 40-45 degrees from the vertical; too steep and it falls too quickly; too flat and it tends to fly off the target
- angle (hasuji) - the edge must be lined up to get the maximum effect of the wedge of the sword (cross section); if you get the angle off, then there is a slight bit of the side of the sword that pushes the cut-piece off the target like a flat bat rather than going through it.
All this is obviously just instinct, trial and error since you are not going to be measuring any of these. The faster generally the better. But getting the right angle is a hard thing to determine that only comes from experience.
Experience here means analyzing the cut immediately or shortly after you have done it. You think about where your tip was when you started and when you struck the target; where you hands were relative to the edge; where your body was; how twisted/turned your torso was; where your tip ended and the final angle of your sword. All this in an instant. :)
Okay, so its not that easy to analyze it, but that's where your sensei comes in to describe what they see, and also where videos of your cutting is. (FYI: I'll try to show more slow-motion videos so you can see more closely). However, no matter how many times you tell yourself that you should do something a different way, the only way to tell is to actually do it.
I should mention a few weeks ago, Andrew Cameron got very close to the "perfect kiriage". He cut the target near the very top, and it hopped straight up, and would have landed exactly back on top of the target. Andrew was really trying tsubamegaesh (which he pulled off nicely), but nonetheless, the kiriage was very good. It is in this video, in his second cut
on the target.
The speed factor is one reason I like encouraging tsubamegaesh. In trying to get the cut, the student learns to perform a kesagiri quite well, otherwise it just doesn't work. So it's an all or nothing effort that requires them to keep improving.
So enjoy the cut, and keep aiming for betterment.