Geepers, ever since I told you your mogul dude is in the back seat, you've been harassing me at every chance. I'm sorry it upset you so much, but I've had enough of it, and I'm not going to stand for it any more. This is the me too era after all. The writing is on the wall, you're just not getting it, and I suspect if anyone else wrote it, you'd get it. So, back the duck up, buckle up for a ride, here we go, 100 pages and a thread lock. You're not getting the last word.
Your analysis has nothing to do with the side cut of the ski - the object going around the turn could have any side cut (including a straight edge) and your calc would pop out the same number.
Quite the opposite, it has everything to do with the sidecut. Because of the platform angle limitations, it's impossible to get enough lean to carve 16 meter turns with a 5 degree edge angle for some speeds. Is that really a surprise? Sharp turns give lots of CF. CF takes lots of lean. You can't lean past a 90 degree platform angle. If you think you can carve sharp turns with low edge angles, then it's hopeless talking to you. So, now what's the only carving solution if we can't carve sharp turns with low edge angles? It's carving large circles with low edge angles. And that's where the sidecut comes into play. The ski is not designed to carve large circles. Rsc is the largest circle that the sidecut is designed to scribe approximately. Go back and read that physics of skiing section on carving with 0 degree edge angle and see the radius that the ski is designed to follow. For larger circles the tip will not follow the tail even approximately around a circle. Don't get hung up on the zero angle though too much. You could just take the limit as the angle goes to zero, and the equations work out nicely describing a smooth transition from forward motion to edge locked carving, which is a feature by the way, not a limitation.
1. Platform angle of 90 degree. We're not stuck at 90 degrees to the ski base. We can counter balance so that (using Ron Lemaster's definition) the platform angle is less than 90 degrees. That means the groove in the snow (the banked track our ski is going around) is steeper than the inclination angle of our CoM so there's some Fg keeping the ski in the track.
1. We're stuck with not being able to exceed 90 degrees. Going less than 90 doesn't fix the problem of not being able to carve 16 m turns with low edge angles, because you must have more lean not less. A platform angle less than 90 degrees represents less effective lean, a platform angle greater than 90 degrees represents more effective lean.
2. We have 2 skis and we can actively distribute weight between them so we can control our balance when Fg does not equal CF.
2. Two skis do not change the fact that you must have lean to counteract CF. Neither ski will have enough lean to carve sharp turns with low edge angles. Both skis are designed to carve only sharp turns edge locked.
3. Every single part of a ski has to fit a precise geometric shape to the manometer for the ski to carve. We are not skiing on uniformly smooth pitches of infinite hardness. (It only feels like it at times...)
3. Carving a circle when the ski is shaped like an ellipse would be an approximation. Carving a 200 meter turn, when the ski is designed for a maximum of 16 meters is not an approximation.
Long and short is we can and do make a variety of radius turns on fixed side cut skis without skidding.
The Physics of Skiing book has a different section for soft snow carving. I haven't digested that yet. These equations are for hard snow, and they are absolutely true. You can turn at the top of the turn, but it starts out predominantly skidding, and then becomes less and less until you are edge locked carving a ~16 meter turn based on the sidecut of the ski. The only fallacy is your own perception of what you are doing on skis.
