I think this is it. Knock yourself out:
If you are interested in the physics, there was an attempt at a white paper made and a link to it is posted on this forum somewhere during the last year. The consensus I think was generally that the people writing the paper knew a lot about physics and little about actual skiing. Their understanding of skiing was somewhat limited and implied they were not high end skiers. So their analysis was a bit flawed in that way.
Part of the whole point I was trying to make earlier is that while it may be somewhat intriguing for certain types of people to break down skiing into physics models....most of the time they are doing it either blatantly inaccurately or using some hypothetical simplified situation that is not a clear picture that will help anyone's skiing. There were some books written in the 70's that pretty much nailed the "how skiing works", and they don't require an engineering degree to understand.
That being said, its summer time and if you get off on calculus, then why the hell not. Enjoy yourself.
Calculus is The Secret (TM). It can be bludgeoned into handling the singularities that tend to arise when some quantity under consideration (often a component of acceleration or velocity) passes through zero as it changes sign.
It suffers from the problem that many mathematical models consist of systems of partial differential equations that are too complex to have closed form solutions, even with many simplifying assumptions. If one was to develop such a model for skiing, the problems alluded to by others in this thread occur:
1. If it's complex enough to have more than a distant relationship to reality, even a numerical solution could be difficult.
2. If it's simple enough to have a closed form solution, it doesn't represent reality closely enough to be useful to anybody.
If number 1 occurs, the geeks will apply for a research grant to buy time on a massively parallel computer somewhere.
If number 2 occurs, a bunch of ski geeks on Epicski will complain that too much stuff got left out and the mathematical model really should look more like #1 if you want to accomplish anything.
We might also note that any model is further complicated by an enormous array of human variables which are difficult to quantify. Psiman shows one thing, but psiman with a nervous system shows something else. Individual perception and reaction will cause any skier, even a skilled one, to vary considerably from any model we might develop.
That, of course, is why we ski.
Friction and enhanced drag
2. Terminal velocity is now just under 60mph, and is approached after about seven turns.
3. Once terminal velocity is approached, you get to spend about as much time slowing down as you do speeding up.Linear acceleration is still greatest in magnitude when moving downhill and smallest at transition. The peaks in speed, however, occur slightly after turning away from straight downhill, and the speed minima occur slightly after each transition point.
4. Maybe there’s someone with a frame that can sustain the ~3.8 g’s at ~56 mph, but I’m sure I would have had to break out of the carve long before that point.
There’s a lot of information in these plots that I’m sure I haven’t processed yet, and many more variations that could be tried.