I'm sure there's an ultrasonic transducer in there but I wonder how a 40w transducer (this is typical power for hand-held) can move such a giant blade around at 40khz. It does not seem physically plausible to me.
At this power level, there's no heating of the blade like the small blade tools you're describing. And firmware in the handle adjusts the operating frequency continuously to stay in resonance.
This all works because the ultrasonics aren't moving the blade like a reciprocating saw -- that would indeed require huge power. They're sending longitudinal shockwaves through the blade itself that cause the metal to expand and contract. Check out minute 2:30 in the video here to see that motion in action: https://youtu.be/cXjbSVt9XNM
Have you been able to find out how this is producing the cutting action? Like, is it the blade motion back & forth that's doing it or some other effect? (cutting and ultrasonics can both be surprising independently, so together...) Does the knife when powered have "sweet spots" that it helps to get a feel for? I imagine you learned a lot of interesting things during development of this.
Can you make a video of this doing any kind of bulk prep work, like dicing an onion or something? (Is there any reason this knife wouldn't be appropriate for that?)
The ultrasonic motion acts as an amplifier for physical sharpness. So, it's sharpest when it's got a geometrically great edge, but even as that edge dulls, it behaves sharper when on vs. off. This is reflected in BESS testing, and also in robotic cutting.
Moreover, a huge amount of the force required for cutting normal foods is actually a function of friction, not just bevel sharpness. So the reduced friction on the blade faces from ultrasonic motion remains just as effective even if the cutting edge is dull. In fact, commercial ultrasonic cutting machines don't use sharp blades at all!
Cut initiation is all about the cutting edge. In an ultrasonic blade, that edge oscillates and the tiny imperfections on the blade edge act like a saw to break the linking fibers in food. It's just like using a human-scale slicing motion, but at 40kHz, and with a microscopic stroke length.
Cleaving is mostly about friction. Cutting a block of cheddar is pretty much all cleaving, and a very sharp cutting edge doesn't provide much advantage. My blade vibrates along the blade face, so foods experience the coefficient of kinetic friction, not static friction. This reduces cutting forces, and does so in a way that's totally independent of the sharpness of the edge.
We experience different foods as more cut-initiation-centric or more friction-centric. Tomatoes are all about piercing the skin. Hard squash is a cleaving game. Bread is layers upon layers of initiating cuts in the bubbles of the crumb.
If you're interested, I published my testing on regular knives in the Quantified Knife Project by strapping 21 chef's knives to a robot arm and collecting data on cutting forces. The data are open-source on github, too. https://youtu.be/GUQy0Sdp8Hc