I see some things a little different...
I think you can - hockey stops. There's no denying the ski bends, just not enough tilt to grip and deflect... granted, it's a "corner case"...
Ah - not quite. That's the problem with physics and reality sometimes it's too idealized...
I had a quick back and forth on this with Jurj, the inventor of the shaped ski. While it (talking to some famous guy) doesn't validate the rest of my post, he's right that there is a maximum ski bend at a certain force applied on it (and resultant GRF), given the snow's deformation ability. When you reach that maximum, the ski won't bend anymore even if you double the force applied.
Let's have this thought experiment - glide on ice on a green run, with all your body weight on the ski. Getting deflection at 5 degrees tilt results in a larger radius than getting deflection at twice that tilt, ay 10 degrees, although your weight is the same. The force vectors change slightly since you're turning tighter, but not much. If my cousin (yeah, he's like that) decides to jump on my back in the middle of that turn, the turn radius won't change because the ski bend won't get bigger although the force just doubled in all directions (and the GRF with it, lest I sink into the snow). That's Jurj's point, and I think he's right.
Either case, same weight/pressure bent the ski twice as much just because I tilted it more. The lateral component was higher at 10 degrees, but it doesn't change the fact that I was applying the same tilt and weight to the ski.
And that gives you also the logic behind controlling the GRF with technique: it's a matter of the angles you're able to create at what point in the turn.
So... at normal speeds is this, let's say 30 mph or 50kmh: at linear speed X, some people are able to tilt the ski N degrees and get an R radius turn while others are able to tilt at N+n and get an R-r degree, with a bigger deflection force.
Let's have another thought experiment: one of them almost ran into me the other day, so this is fair: catching one of those morons that are tucking it straight down, with a lasso from the side of the run and deflect them into a turn. The turn radius is given by your distance to the moron and it's constant then, regardless of the tucker's mass and speed. If the speed is double, there will be a lot more centripetal force for the same radius and you'll need a stronger lasso. That's the basic theory behind it: at a given snow and max tilt angle A, the ski bend B resulting in the maximum radius R. At any speed above V, the ski won't bend anymore, because the snow doesn't give in anymore, but you have a bigger centripetal force to recon with, because V is higher. Or the skier is fatter... At the same time, if it's possible to have a bigger angle A++ it will allow a bigger ski bend thus a smaller radius, thus a higher maximum GRF. That's where technique comes in. That doesn't change the fact that if you go at it with twice that speed, the ski won't bend anymore, your body will just have to put up with higher turning force, the higher GRF. (of course, idealized assuming the ski has no lateral twist - which actually gives the skis their maximum force thus radius at an angle (a racing lasso is stronger but has it's limits too)...
The ski bend is not a result of the turning radius - it's the other way around: your ability to bend the ski dictates the radius...
cheers.
You cannot go straight down when the ski is bent a lot. Simply impossible.
I think you can - hockey stops. There's no denying the ski bends, just not enough tilt to grip and deflect... granted, it's a "corner case"...
GRF is dependent on weight, speed and turning radius, it has nothing to do with the ski or ski technique. Doesn't even matter if it's on snow. It is merely physics, what you're traveling on and with is not important. It doesn't matter whether you make a 12 meter radius turn with 4 meter offset at 50 km/h on a ski, a sled, a bycicle, a tractor, or whatever. As long as these items weigh and behave the same as a ski, the physics will be the same. You can do this on sand, rocks, grass whatever. Ergo, if you would be able to move yourself forward at 50 km/h and make a 12 meter radius 4 meter offset turn, the centripetal force and GRF would be exactly the same on any surface and on any item (if the weight is the same).
Ah - not quite. That's the problem with physics and reality sometimes it's too idealized...
I had a quick back and forth on this with Jurj, the inventor of the shaped ski. While it (talking to some famous guy) doesn't validate the rest of my post, he's right that there is a maximum ski bend at a certain force applied on it (and resultant GRF), given the snow's deformation ability. When you reach that maximum, the ski won't bend anymore even if you double the force applied.
Let's have this thought experiment - glide on ice on a green run, with all your body weight on the ski. Getting deflection at 5 degrees tilt results in a larger radius than getting deflection at twice that tilt, ay 10 degrees, although your weight is the same. The force vectors change slightly since you're turning tighter, but not much. If my cousin (yeah, he's like that) decides to jump on my back in the middle of that turn, the turn radius won't change because the ski bend won't get bigger although the force just doubled in all directions (and the GRF with it, lest I sink into the snow). That's Jurj's point, and I think he's right.
Either case, same weight/pressure bent the ski twice as much just because I tilted it more. The lateral component was higher at 10 degrees, but it doesn't change the fact that I was applying the same tilt and weight to the ski.
And that gives you also the logic behind controlling the GRF with technique: it's a matter of the angles you're able to create at what point in the turn.
So... at normal speeds is this, let's say 30 mph or 50kmh: at linear speed X, some people are able to tilt the ski N degrees and get an R radius turn while others are able to tilt at N+n and get an R-r degree, with a bigger deflection force.
Let's have another thought experiment: one of them almost ran into me the other day, so this is fair: catching one of those morons that are tucking it straight down, with a lasso from the side of the run and deflect them into a turn. The turn radius is given by your distance to the moron and it's constant then, regardless of the tucker's mass and speed. If the speed is double, there will be a lot more centripetal force for the same radius and you'll need a stronger lasso. That's the basic theory behind it: at a given snow and max tilt angle A, the ski bend B resulting in the maximum radius R. At any speed above V, the ski won't bend anymore, because the snow doesn't give in anymore, but you have a bigger centripetal force to recon with, because V is higher. Or the skier is fatter... At the same time, if it's possible to have a bigger angle A++ it will allow a bigger ski bend thus a smaller radius, thus a higher maximum GRF. That's where technique comes in. That doesn't change the fact that if you go at it with twice that speed, the ski won't bend anymore, your body will just have to put up with higher turning force, the higher GRF. (of course, idealized assuming the ski has no lateral twist - which actually gives the skis their maximum force thus radius at an angle (a racing lasso is stronger but has it's limits too)...
The ski bend is not a result of the turning radius - it's the other way around: your ability to bend the ski dictates the radius...
cheers.
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