daSlider: "...The notion of the zero angle of attack is also absurd..."
No it isn't. In RR track turns, every point on your edge passes over the same patch of snow. Take a snapshot of this from above (or draw a diagram) and you will see that at each point along the curved edge, the angle between the edge and the groove in the snow that the edge is leaving is zero. This is the definition of angle of attack. In a skid, or even if the designed shape of the reverse-cambered edge doesn't exactly fit the hill, there will be a substantially non-zero angle of attack either somewhere, or all along the edge.
Your next sentence about the common efficiency of yachts, birds, and jets is exactly why I proposed (in the 1st post of the turkey - whipped cream thread) a definition of carving based on minimum width / minimum drag. Have you forgotten this?
-------------------Martin Bell: "... I've just realised, you have the opportunity to go and collect some real world data: Bryce Mtn is not too far from your location in the DC suburbs! Go up there sometime and try out some grass skis - you'll find, you cannot skid or pivot those things. The only way to turn them is with pure tipping movements, exactly as you would when carving on snow. ..."
You know, I had exactly the same idea. Until you (or someone) posted that link to Bryce, I had completely forgotten that grass skiing was available just a few hours away. It sounds like a hoot & I'll give it a try first chance I get out that way.
Since you have experience on grass skis, let me ask you a question. Can you use them (either the treaded or wheeled versions) on pavement? If so, do they still feel like they are carving, ie, no rotary is needed/possible?
-------------------Martin Bell: "... I therefore conclude that I probably spent most of my earlier life carving very long turns on (in?) snow that was slightly less than infinitely hard, on skis that had almost (but not quite) no sidecut! ..."
Don't forget that in a long radius turn at high speeds there is lots of vibration going on, so there are plenty of events where part of the ski has left the snow and can come back down in a slightly different groove. In other words, an overall curved path of a given average radius can be composed of a series of slightly disjointed smaller arcs, each of longer than average radius. This happened a lot in the "old days", especiallly in SL.
-------------------Martin Bell: "... So, you scientists out there, would this be calculation correct? If the ski with 19mm sidecut depth were to be edged at 45 degrees (pretty serious edge angle), the ski center would actually have to travel 26.9mm to regain contact with the snow (19 divided by the sine of 45 deg). ..."
Right answer (for this one case), wrong formula. I didn't dig out my notes, but I'm pretty sure it would be 19 divided by the cosine (not sine) of the edging angle. In the case of 45 degrees, both sine and cosine are the same, but in the case of small edging angles, your formula would predict huge displacements because the sine of small angles is small.
-------------------Rusty Guy: "... If you ever want to get the guy started ask Bob B about spatulas ... I have an old credit card. Along one of the long edges of the rectangle I have taken a pair of scissors and cut a half moon shape. ..."
Well, since BobB isn't around, don't keep us guessing - what did you think?
BTW, I also made myself up one of those cards. I find that it doesn't work too well for me on my leg (too soft for the demo to be compelling), but it does work well on hard surfaces. I was going to mention it as well, but assumed everyone in on this conversation already had played around with one and already knew the basics.
------------------RickB: "... Many times I've had students say they thought the force of the turn would drive them into a tree lets say as they skied by. This is a real fear of people I teach. They feel like there is something that is going to make them go flying in the direction their outside leg shaft is pointing if they were to release their turn or skis. But this doesn't happen when we release the turn. If we release the turning forces we will go straight, if we reduce the turning forces we lengthen the arc. ..."
RickB, that's an interesting insight. I have had students say that they felt like they were going to "slide out" (especially on hardpack), but they didn't say in which direction, and I didn't think to ask. Unfortunately, most of my students are going so slow that sliding downhill is the only direction they are worried about.
After your last post, I now think I do have a better idea why you felt the forces were illusory. Thanks.
Tom / PM