To clarify my comments about SL vs powder skis: these skis are at opposite ends of the spectrum and have completely different intended uses. However, for any ski working in a given set of conditions trying to make a turn of a given size, having a smaller turn radius reduces the required stiffness to hold an edge. I'm not going to derive this, but essentially it's similar to why it's easier to carve on a modern shaped ski than an old straight ski. Two skis could have otherwise identical construction and be trying to do the exact same thing, but simply building one with a smaller turn radius means that to make a carved turn of a given turn radius, the edge angle required is smaller, thus the skis can deflect more and still maintain the turn.
I think you misunderstood me. Torsional stiffness definitely matters more for a SL ski than a powder ski. But this is entirely due to the usage. In slalom racing you want maximum edge grip in the most difficult conditions. In powder skiing, that's not the priority. I was trying to point out that a SL ski can still have better edge grip than a powder ski despite a greater torsional deflection due to things like the effects of a narrower width and a tighter turn radius. I haven't seen enough powder skis to make a generalization about if they would typically deflect more or less than a slalom ski, but I'm sure that a powder ski with anything close to a "race" construction would deflect less than a SL ski with a similar construction.
The torque T is proportional to the width of the ski. The area moment of inertia J is proportional to the width squared. The angle of twist phi = (TL)/(JG). L is the distance from the fixed point to the deformed cross-section considered. G is the shear modulus, a property of the materials. Thus wider skis should deflect less than narrower skis for a given torsional load.
Yes, it was sloppy to say that stiffer = less vibrations. Vibrations are definitely a lot more complex than that. I'm also happy to see you using the term damping instead of dampening. However, I still think that that's a reasonable heuristic if we assume resonances are avoided, etc. If I had to blindly guess between two otherwise similar skis which one had better vibration characteristics, I'd guess that the stiffer one would perform better. This is actually true with all of the skis that I've personally ever handled. Of course I've heard that for example, Atomic's D2 skis are softer yet damp vibrations better than otherwise comparable skis, due to their unique construction. I haven't had a chance to inspect any D2 skis in person and don't know how true this is one way or the other. My point is just that all else equal, stiffer generally tends to handle vibrations better, even though it's possible to do clever things. And by stiffest you can bend, I meant the stiffest skis you can properly ski, not just bend for one ideal turn or some nonsensical notion.
Higher frequency, smaller amplitude vibrations are desirable for a few reasons. The larger the amplitude, the harder it is to maintain properly pressured contact between the edge and the snow. Also, higher frequency vibrations are more readily absorbed and damped by most materials. You have made the assumption that damping is independent of frequency. Thus stiffer improves the transfer function dynamics over most Poincare sections from the Hamiltonian phase space of the system. In practice, the skis never have a chance to damp completely to a motionless state because they are constantly being perturbed, so trying to make the decay faster isn't very effective. Keeping the response amplitude small is a better goal.
I did not suggest to look only at G. Moreover, you can't just take the material G value, you need to determine the effective G from the composite structure (and if you want to do some engineering with this you really need the full blown orthotropic stiffness matrix). Rather, I wanted to point out that you need to look at more parameters than just phi before you can make claims about which ski will have better edge grip. G is just something I'd personally try to get from the test as a fun thing to do, but that's no where near enough to make the claims you made in your marketing video. Adding 5mm to each end of the torque arm does not properly account for the effects of a greater width. It should be 50mm longer on each end (100mm total, very roughly). This is a moot point however since as I talked about above, a torsion test won't tell you what you're trying to figure out. I really do think that the idea of a ski with legitimate use of carbon fiber and not just stringers or veneer could work great, but the video test is not grounds to have even the slightest cogency for the hypothesis of it having better edge grip than a slalom ski.