I believe we should started a new thread, but OK.
First of all I have to apologise for choosing wrong words, I said I can not find the right expression, I have degree in physics, not in English, sorry.
Yes, I have read claims as: Increased GJ -> Less ski twist (true), Increased GJ -> Larger penetration at ski ends (not measured, suspected), Increased GJ -> Larger side force thus less skidding (wrong), Increased GJ -> Smaller turn radius (true).
Your interpretation was Increased GJ -> Less ski twist -> Larger penetration at ski ends -> Larger side force thus less skidding -> Smaller turn radius.
So again: skidding is geometry problem not edge grip problem. If the geometry of the turn and ski edge don't fit, there is no theory to ski without skidding.
In above experiment there is a general error in interpretation of results:
- CG of the load is not projecting inside ski boot area all the time, at the end of the run it si projected in front of toe piece
- because of above M(x) for less torsionally stiff ski will make the torque (thanks for correcting me) rotating the ski out of the turn more than torsionally stiffer ski.
I stand by my general point that the experiment you describe isn't adequate to demonstrate what you claim. And insisting people who are skeptical try it for themselves doesn't address the problem, because what people are going to doubt isn't that you got the results you did, but rather that the results of such an experiment say anything about how a ski actually skis.
You are just confirming my point. What I am saying that edge grip has nothing to do with ski performance, I am sorry if I do not have ability to put it more clearly.
The question is, if (we both are) true, then where is the difference? My answer is M(x)
"Skiing is movement of skier on curved path in space consisting of translation and rotation (1)"
This definition is incomplete, since it leaves out flexing and bending. I.e., there are also (slow) vibrational degrees of freedom.
The scope of modelling physical systems is that first you determine the system, in this case the system is skier+skis+boots+...googles, and the system interacts with snow slope. Fist step is to observe the system in time frame of interest - several turns = 10-20s. In this scope there is only translation and rotation. Internal vibrations can and should be neglected. One can determine rough constrains out of simple model. On this basis you go to time scope of 1s or less and explore behaviour of the system in this scope.
This kind of modelling was successfully used in development of skis for years
"Edge grip is force perpendicular to the length of the ski (4)"
I disagree with this -- if you're standing flat on the ski, there's reaction force from the snow perpendicular to it. Yet there is no edge grip. I think edge grip is the sum of the lateral components (those parallel to the snow surface) of the snow reaction force along the length of the ski that are perpendicular to the length of the ski at each point.
See above, simplification used in rough model, final equation is taking all that into account M(x) where x is position on the ski edge (curved in euclidian space of ski slope)
"But we all feel the difference in ski performance. The answer is in our perception of edge grip. During skiing the ski and the skier rotates. How fast the ski rotates at given CG position, angulation and load is perceived as edge grip."
This is a very confusing statement. It needs to be explained much more clearly for someone to understand what you really mean. By load do you mean static load? And if you change the angulation but keep everything else the same, what happens to the perception of edge grip? None of this is clear. In any case, to the extent I can make sense of your statement, I don't agree with it, because I can choose to rotate the ski in a skidded turn at the same rate as it would rotate in high-g carved turn, yet there will be far less edge grip in the former case. More importantly, I think there's a much more straightforward way of explaining what accounts for our perception of edge grip: it's the same as what I gave above for measured edge grip. I.e., our perception of edge grip arises from how much lateral force we're resisting during a turn. And no, I am not, as you accuse, confusing feelings and measurements. I have to ask: Do you yourself know what edge grip feels like in a carving ski, i.e., do you have any video showing you personally have the experience of carving -- and I don't mean just riding the sidecut, I mean really loading the ski so it visibly bends, and resisting the forces that are generated?
As I explained at the begining, I am maybe not proficient enough in English, but I try my best. It is not my fault to make English so dominant that we are forced to deform it at our best knowledge :-)
I can not make shorter and more precise explanation as I did.
- load = dynamic load at given moment
- You can not change angulation without changing turn radius and therefore load - skiing is done in equilibrium of all dynamic forces, if not, skier makes a nice fall
- skidded turn the same as high-g carved turn - yes at the same radius, but not at the same speed and the same load and the same ski edge angulation
our perception of edge grip arises from how much lateral force we're resisting during a turn.
Yes, this is the feeling or perception that I oppose. That is why I have defined edge grip as measurable quantity, not perception and upgraded to how your perception could be presented in some kind of physical property of the apparatus - the ski
"M – momentum of the external forces acting on the skier"
This is very confusing. I think you might be trying to define a torque, which is a moment of force. "Momentum" and "moment" are two completely different things. In your defense, I suspect this may be a problem with your English rather than your physics.
You are right, Torque, sorry
I'm not saying you don't know what you're talking about. I'm not making a personal comment about you. Rather, I'm saying the presentation on your webpage gives the impression you are completely confused about physics, and that you also don't understand skiing, and that's going to hurt your marketing. It seems what you have is very innovative, and I'd hate to see it fail because of a bad presentation. Regarding the physics, I'd urge you to partner with a professional physicist, explain to him or her what you're trying to say, and have that person re-express it a way that makes sense to other physical scientists and engineers. [And out-of-place statements like "Because speed is much lower than speed of light, we can forget about Einstein" aren't helping you either, because it comes off like someone trying to sound like a physicist without being one.]
As professional physicist I confess I have limited ability to explain complicated problems in simple way, I will hire a marketing guy to sell you dry stick of dead fish as sushi.
I will try to rewrite the page, wish me luck :-)