Poster: A snowHead
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OK, there is no cheating here.
I drew ONE arc. Copy and pasted it 3 more times, so I ended up with 4 arcs. So all 4 arcs are identical.
Displaced one arc to the other to give me 2 tracks, then mirrored the remaining 2, and joined them up.
Looks like I can overlay one over the other exactly.
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Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
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veeeight wrote: |
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Ok they're identical but not parallel, but let's not get hung up on that technicality!
What they do show is that if you did ski identical arcs like this then you would also have a massive amount of inside tip lead to deal with. Look at the start and end points of your curves! The only way to lay these (non-parallel) lines down without the tip lead is to ski the inside ski slower through the turn than the outside. Not sure if/how this can be done?
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Well, the person's real but it's just a made up name, see?
Well, the person's real but it's just a made up name, see?
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Quote: |
Ok they're identical but not parallel, but let's not get hung up on that technicality!
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Well it seems that this is the crux of the issue for some!
But for now do we have concensus that the inner track is of identical radius to the outer track ?
Last edited by Well, the person's real but it's just a made up name, see? on Thu 17-04-08 10:19; edited 1 time in total
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veeeight wrote: |
OK, there is no cheating here.
I drew ONE arc. Copy and pasted it 3 more times, so I ended up with 4 arcs. So all 4 arcs are identical.
Displaced one arc to the other to give me 2 tracks, then mirrored the remaining 2, and joined them up.
Looks like I can overlay one over the other exactly.[/img] |
Draw where your feet are at the start of that arc. Draw where your feet are in the middle of each apex. Draw where your feet are at the end. You have outside tip lead at the start, and inside tip lead at the end.
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Anyway, snowHeads is much more fun if you do.
Anyway, snowHeads is much more fun if you do.
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veeeight, Take 2 marker pens. Hold them firmly together parallel to each other. Now "ski" them however you like across your page. Their tracks will be parallel, but not identical! The inside pen in each turn will describe a smaller radius. Give that a go
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Everyone is now getting hung up on tip lead on my mickey mouse diagram. I could have quite easily have erased the ends to make it level!
BUT - here's the important nugget of information in real life skiing.
In order to produce those lines in the snow - yes, there is an element of fore-aft manipulation going on. The ankle joint is opened/closed (depending which foot), the knee joint bent and straightened, and the hip is rotated and opened constantly throughout the turn.
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veeeight wrote: |
But for now do we have concensus that the inner track is of identical radius to the outer track ? |
Yep, same radius, different centre. But how are you going to deal with the enormous resulting inside tip lead if your skis are both travelling at the same speed???
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You'll get to see more forums and be part of the best ski club on the net.
You'll get to see more forums and be part of the best ski club on the net.
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uktrailmonster, marker pens don't have identical sidecuts!
The point is that both skis do, and will describe identical arcs, not arcs of differing radii.
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Just to demonstrate that it really doesn't matter what the curve is, here are a pair of identical, displaced sine waves - which are clearly not parallel (click to enlarge):
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snowHeads are a friendly bunch.
snowHeads are a friendly bunch.
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Quote: |
But how are you going to deal with the enormous resulting inside tip lead if your skis are both travelling at the same speed???
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Skillful skiing
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And love to help out and answer questions and of course, read each other's snow reports.
And love to help out and answer questions and of course, read each other's snow reports.
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Quote: |
Just to demonstrate that it really doesn't matter what the curve is, here are a pair of identical, displaced sine waves - which are clearly not parallel
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And this could well explain why good skiers, that hold a constant ski width, will often have slightly narrower tracks at the transistion than apex (as both skis have the same radius).
Perhaps parallel skiing is a misnomer
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veeeight wrote: |
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Ok they're identical but not parallel, but let's not get hung up on that technicality!
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Well it seems that this is the crux of the issue for some! |
Absolutely. This all started with your assertion that it was possible to ski parallel tracks by doing the same thing to both skis. This whole argument is getting you to recognise that that is impossible - you can ski parallel fine, or in certain circumstances identical, but not both. Your graphs are not sufficient to show the problem with identical tracks though. So here are some to help you. All 4 lines are identical, random curves drawn in Paint, and no fixed centres of curvature. The pair on the left show them starting at identical times (the offset is -approximately - perpendicular to the track at its start), i.e. with no inner or outer tip lead. The problem with carving these tracks should be obvious. The pair on the right are the same tracks, but with the offset chosen to not cause the tracks to cross. They are identical, but clerly not parallel (look at the separation at the apices and the transitions). And the inner ski starts its first turn way before the outer.
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You know it makes sense.
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veeeight wrote: |
Everyone is now getting hung up on tip lead on my mickey mouse diagram. I could have quite easily have erased the ends to make it level!
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You can start with the tips together at the beginning of the turn if you like, but your identical length lines represent distance, time and speed. Erasing the end points to re-align them results in one arc now being shorter than the other. So what does that imply? Tip lead again!!!!
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Otherwise you'll just go on seeing the one name:
Otherwise you'll just go on seeing the one name:
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Well, actually, my main beef was the assertion that you needed to scissor/diverge your inner ski to ski clean tracks, as the inner track had a smaller radius.
In real life skiing - I do not need to scissor/diverge my inner ski to ski clean tracks, and no, the inner track does not have a smaller radius than the outer track.
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Poster: A snowHead
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veeeight wrote: |
And this could well explain why good skiers, that hold a constant ski width, will often have slightly narrower tracks at the transistion than apex (as both skis have the same radius). |
...which is something I've said at least twice in this discussion (even gave you a formula for how the tracks would diverge when keeping constant leg separation), but you carried on banging on about having parallel tracks.
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Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
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veeeight wrote: |
Everyone is now getting hung up on tip lead on my mickey mouse diagram. I could have quite easily have erased the ends to make it level! |
Yes, please do so! Please make the ends level. Now when you've done that, draw a line perpendicular to the point at the start of the turn. What's happening? These lines diverge. The skis are diverging. Scissoring! This is what happens if you want to keep the same radius of turn and the feet level and the same width apart - one turn has to start earlier.
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Well, the person's real but it's just a made up name, see?
Well, the person's real but it's just a made up name, see?
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veeeight, I think you are subtly coming round to the point of view of the mathematicians, scientists and engineers.
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In order to produce those lines in the snow - yes, there is an element of fore-aft manipulation going on. The ankle joint is opened/closed (depending which foot), the knee joint bent and straightened, and the hip is rotated and opened constantly throughout the turn. |
In instructing such people on how to produce fast/efficient/elegant/whatever turns, I think you should concentrate on such manipulations, rather that resorting to cod geometry or mechanics.
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Are we back to one of these arguments where two (or more) people are arguing different things, but trying to make them appear the same, so they can make the argument, without advancing the discussion?
I see five topics (at least) being "discussed":
1. Tip lead.
My definition: Is one ski ahead of the other at a paritcular point in a turn? If so, that is tip lead.
Should the distance be more or less? Should the distance vary through the turn? If so, how much and when?
2. Individual ski turning radius.
Do skis carve fixed radius arcs, or parabolas? Are they concentric or excentric? Are they congruent?
3. Parallel skis
Is the ideal to keep skis parallel? Can/should the gap between them vary during a turn, and it still be considered parallel?
4. Fixed distance between skis.
If the distance is fixed, how are the other topics varying? Is "fixed distance" the holy grail?
5. Identical turns.
Is this where the skis travel the same distance? If so, is this over part of a turn, one turn, 2 turns, or what?
I'd throw in another one - What is a turn?
Is it, e.g. from going across to the left to going across to the right, or is that only half a turn? Is a complete turn from going across to the left, turning to the right, then turning back to the left again? (or could it be though of as fall line to fall line turning - start going straight down the fall line, and the turn finishes when you are next going straight down the fall line)
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Anyway, snowHeads is much more fun if you do.
Anyway, snowHeads is much more fun if you do.
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GrahamN, it is possible to have a constant width parallel tracks skiing arc to arc, it obviously involves another input from the skier, but I can promise you that it is not due to any rotational movements of the inner ski!
I still think you're falling into the trap of trying to fit a real life dynamic skiing into a mathematical model, all the curves and lines produced above are based on fixed point/s of arcs, circles, parabolas etc., whilst on the real hill this point is ever changing, thus enabling us to ski and leave tracks that the mathematical models here can't describe.
eg: I'll ski some perfectly identical AND parallel RR ski tracks, with both skis at the same/matching edge angles at all times, and with no rotary fudging (and so will the rest of the crowd in the bar, who are, by now, quite annoyed at being told that what they are doing is impossible).
To be perfectly honest, my main focus in the debate has been about debunking the need to scissor/diverge in order to ski RR tracks, and to debunk the tighter inside ski radius. Your point about not being 100% parallel went by me, and I didn't really pick up on that point earlier. My apologies. But I'll still come down and show you perfectly parallel J turns/bananna turns if you like.......
Last edited by Anyway, snowHeads is much more fun if you do. on Thu 17-04-08 11:05; edited 3 times in total
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Masque, Good to see you back in the fray, I was LMAO thinking about you after this thread went ultra geeky
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*here's a question for you. A ski's stated turn radius, is it the side-cut dimension with the ski at rest or when the ski is dynamically stressed to maximum deflection?
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I was told by Phil S. that if you RR carve a turn holding a 10 degree edge angle to the surface you will make a sidecut radius turn. This was demoed without any big pressure build up and was meant to be on edges only. I will let the mathematics guys prove or disprove that statement, but his turns seemed to correlate....
With regards to tip lead being a bad thing, I should have named the thread "excessive" tip lead... Some tip lead is part of skiing and how much depends on angulation and other factors as discussed.
What i have been seeing which i still feel is a bad habit, or, a symptom of other problems are large visible gaps between boots when viewed from the side. IMO too much and a weak position unless one is really angulating into the hill as we have seen on the WC photo sequences. The average rec skier doesnt achieve those angles and shouldnt have as much tip lead.
Your point about boot flex is very valid and one made by COMPREX early on.. The impact of less inner ski pressure on boot flex hasnt been hasnt been discussed enough IMO.[/b]
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If you think you are skiing with identical 50/50 load on your skis the entire time (the only way both skis can be doing exactly the same thing), you are either mistaken or can achieve superhuman body positions to compensate for lateral load transfer.
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No way am I 50:50 (except for a brief moment in the transisiton, which is sometimes 0:0). When I said both skis doing exactly the same thing, I should have been more specific and said both skis with identical matching edge angles. Almost certainly not identical loads.
Anyway. I'm off out skiing to apparently unconciously steer my inner ski, scissor, diverge, and ski some converging ski tracks.
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You'll get to see more forums and be part of the best ski club on the net.
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veeeight wrote: |
all the curves and lines produced above are based on fixed point/s of arcs, circles, parabolas etc., whilst on the real hill this point is ever changing, thus enabling us to ski and leave tracks that the mathematical models here can't describe. |
Complete crap. I have no idea what the functional form of those lines I drew above have (OK they're probably Bezier curves, but I don't know or care what those actually are - Sideshow Bob probably does - and I certainly have no idea what values would describe them). I've lost count of the times I've told you that nothing I've said requires any fixed point - it's a general conclusion based on simple geometry, certainly known for 400 years and probably by the ancient Greeks too. No amount of dynamic this that or the other can change that - although doing that may change your original premise, in which case it's a different argument. Why do you not listen to the answers given to your unfounded assertions? Oh yes, silly me it's because you're a "ski instructor", and therefore the found of ALL knowledge? I can only assume you're invoking these diversionary arguments because you can't admit to having lost on your original point (which is a common MO of yours - invoke some jargon to divert/impress the punters to make you look knowledgeable, particularly if on shaky ground, only this time, as on the force/pressure thing, you've been caught out).
You still haven't said why FastMan, who I'm pretty sure has been doing this a lot longer than you (and who does appear to understand the mechanics of skiing too), should disagree with you.
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veeeight wrote: |
eg: I'll ski some perfectly identical AND parallel RR ski tracks, with both skis at the same/matching edge angles at all times, and with no rotary fudging (and so will the rest of the crowd in the bar, who are, by now, quite annoyed at being told that what they are doing is impossible).
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I'm going to stick my neck out and have a pop at this claim
Firstly, there is no such thing as identical AND parallel tracks. They simply do not exist. But as we agreed, it's a technical point regarding maths rather than skiing. Let's just say they kind of look identical and sort of parallel.
Secondly, however good you think you are, there's no way you are able to physically achieve identical edge angles and, most importantly, identical ski loads at all times. And even if you could and both skis carved an identical path, you would just end up with your skis crossing anyway as shown in [b]GrahamN's[/n] sketches.
Thirdly, you might not be consciously applying "rotary fudges" as you put it, but I doubt there is no torque input at all, especially on a short radius turn.
What you are really describing above I think is a rough approximation of how you want the end product to appear. Which is absolutely fine, but the underlying physics I feel are beyond your field of expertise. Please don't take that the wrong way. I can't ski as well as you but I'm confident I understand the physics and maths better
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snowHeads are a friendly bunch.
snowHeads are a friendly bunch.
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skimottaret wrote: |
I see a lot of "old school" skiers that scissor a lot and have a very pronounced inner tip lead. They think they are countering well and getting their shoulders square to the fall line but are really just twisting at the waist and not separating the upper/lower body, and, typically have a straight, stiff outer leg with a large inner ski lead of 20-30 cms.
What drills do you use to eliminate this problem? |
to go back to the original question, it would appear that one thing you should avoid is using terms like "parallel" or "radius" loosely when there are mathematicians or engineers in your class
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And love to help out and answer questions and of course, read each other's snow reports.
And love to help out and answer questions and of course, read each other's snow reports.
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veeeight wrote: |
No way am I 50:50 (except for a brief moment in the transisiton, which is sometimes 0:0). When I said both skis doing exactly the same thing, I should have been more specific and said both skis with identical matching edge angles. Almost certainly not identical loads.
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Ah a small breakthrough! If you acknowledge that your skis do have different loads on them during the turn, then that means they deflect differently and will therefore not carve the same path all by themselves. Worse than that, the more heavily loaded outside ski will naturally want to track a tighter arc than the inside ski. So you really have to compensate for this effect by diverging, steering, or using different edge angles. It's all very subtle and I'm sure you can make it appear invisible to the naked eye when demoing your RR tracks, but it won't go away.
I was looking at Martin Bell's photo links from a few pages back and they show all these effects, simply exaggerated by extreme racers.
On a practical note, you seem very anti-inside ski steering (correct me if I'm wrong). Warren Smith on the other hand spends a fair proportion of his DVDs training us to "power steer" our inside skis. What are your thoughts on this from an instructors perspective? Forget the physics discussion for a minute, I'm interested in your view as a ski instructor and I promise it's not a trick question to prove a theoretical point.
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Quote: |
to go back to the original question, it would appear that one thing you should avoid is using terms like "parallel" or "radius" loosely when there are mathematicians or engineers in your class
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yes indeed, funny enough during my basi course during our mock teaching sessions i got hit with a group of different "learner types" and one was a scientist, this thread would have come in handy then!
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You know it makes sense.
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uktrailmonster, i think that pressure/ flex of the skis is where the practicality of making near parallel carved tracks in snow diverges from the maths here.
i think it is down to slight loading of the inner ski's shovel and bending the ski around the turn when carving RR tracks. Shovels are very flexible and when i think back on doing drills where we had to make medium radius turns attempting to turn using solely only one of the three fundamental elements (rotation, pressure or edge)
During "pure" edge turns as you would do in a RR turn when trying to let the skis run wide and getting them to turn soley with the edges the shovels engage and do flex under pressure from the reaction with the surface and they then transcribe almost parallel curves. without some other influence i kinda agree with the maths that perfect parallel curves without tip lead arent possible.
Whether this something else is light pressure that comes from a rotary torque from the leg, slight ankle flex, or femur steering it comes from somewhere...
I am sure i will get shot down in flames by the maths guys but this point was alluded to by Martin and Comprex and wasnt discussed enough IMO
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Otherwise you'll just go on seeing the one name:
Otherwise you'll just go on seeing the one name:
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Sorry, uktrailmonster, but you should really softpedal on the pressure stuff. In a carved turn the important things are a) sidecut b) edge angle and c) have just enough pressure to get the edge on the ground. Any more pressure and all you're doing is pushing yourself further away from the ski. Different story with soft snow turns, or tighter than edge-carved turns, or (AIUI, hardly/never skied them) straight skis - which is I guess when you did pretty much all your racing?
Back to the sort of parallel/sort of identical thing. I reiterate just an example from PhysicsMan's model. In the "recreational" turn example, the tracks varied in separation by less than an inch and the edge angles differed by less than 2 degrees, at angles of greater than 35 degrees. The difference in angle at the start of the turn is less than a degree. I'd actually be interested in seeing how the skis diverge and converge during the path - maybe I'll see if I can modify the spreadsheet. I agree that anyone who thinks they are skiing to an accuracy of better than this is deluding themselves. There is no, and has never been, any argument that the differences may be small, but the argument is with veeeight's cod maths extrapolations from getting the wrong end of this stick. And if the guys in the bar are getting annoyed, I'm sure it's with the reported rather than the real argument - they're clearly not doing anything impossible, but they're not necessarily doing what they claim they're doing (which of course depends on what those claims are).
Back to the definitions of a few words. If curves are parallel, then they have:
1a) a constant spacing between them, measured perpendicular to the curves at that point;
1b) coincident centres of curvature, and hence radii of curvature that differ by that constant spacing
2) If the separation between two curves is increasing then they are diverging, and if that separation is decreasing then they are converging.
So given that veeeight has conceeded that the separation in tracks will often be narrower at transition then apex, he has to conceed also that there is divergence/convergence along the path - it's inherent in their definitions.
skimottaret, no flames from me, as I raised this very point back in my first post (on page 3) - and (possibly unwisely) made a comment in passing that veeeight's maths was balls. So apologies to the forum for kicking this off (along with Sideshow Bob) - but you can't let manifestly false assertions stand unchallenged.
Last edited by Otherwise you'll just go on seeing the one name: on Thu 17-04-08 12:51; edited 1 time in total
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Poster: A snowHead
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skimottaret, I'm thinking the same as you, hence my earlier post with the pic below, which was prompted by Martin B's posts. I think it shows the inside shovel bending quite a lot, without making any particular effort to force it. Thinking more about it, this shovel flex could come from rotary torque or maybe just simple forward loading of the tip from ankle flex. Probably a bit of both although I do try to be quite active steering with my inside ski (rightly or wrongly, hence my question, but that's how I was taught anyway)
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Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
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BTW we have a fully paid up mathematician here (Sideshow Bob), two ex-scientists (laundryman and me) and an engineer (uktrailmonster), arguing on one side of a maths point, with resources from a professor of Physics and an unequivocal citation from a long time coach. An an ex-WC racer thinks there's something in it (look at his last post on this thread). So who's the "armchair expert"?
Last edited by Obviously A snowHead isn't a real person on Thu 17-04-08 13:24; edited 1 time in total
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Well, the person's real but it's just a made up name, see?
Well, the person's real but it's just a made up name, see?
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I think I mentioned earlier in this debate that ankle flex may well have in input on the shovel flex, though possibly less so with extended tip lead. Could be (for recreational skiers) that over extended tip lead could manifest itself as divergence?
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Quote: |
Sorry, uktrailmonster, but you should really softpedal on the pressure stuff. In a carved turn the important things are a) sidecut b) edge angle and c) have just enough pressure to get the edge on the ground. Any more pressure and all you're doing is pushing yourself further away from the ski. Different story with soft snow turns, or tighter than edge-carved turns, or (AIUI, hardly/never skied them) straight skis - which is I guess when you did pretty much all your racing?
Back to the sort of parallel/sort of identical thing. I reiterate just an example from PhysicsMan's model. In the "recreational" turn example, the tracks varied in separation by less than an inch and the edge angles differed by less than 2 degrees, at angles of greater than 35 degrees. The difference in angle at the start of the turn is less than a degree. I'd actually be interested in seeing how the skis diverge and converge during the path - maybe I'll see if I can modify the spreadsheet. I agree that anyone who thinks they are skiing to an accuracy of better than this is deluding themselves.
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Graham, I havent been following the maths closely so forgive me if i get this wrong... My gut feel initially was that the differences between the models and real life were fairly small and secondary effects are what is keeping the skis parallel when making carved/surved tracks. Your analysis of the model showing a typ rec skier is out by a matter of only degress and inches during a "normal" turn seems to support that.
i dont think you can say the pressure is inconsequential on turn shape. Bend a pair a skis by hand and you will really change its shape quite easily. THe impact of pressuring a ski on the curve it transcribes in the snow to me seems to override the small influences when looking at a static ski model like physicmans and in my gut would easily account for the differences...
discuss or destroy this off the cuff hypothesis
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Anyway, snowHeads is much more fun if you do.
Anyway, snowHeads is much more fun if you do.
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GrahamN wrote: |
Sorry, uktrailmonster, but you should really softpedal on the pressure stuff. In a carved turn the important things are a) sidecut b) edge angle and c) have just enough pressure to get the edge on the ground. Any more pressure and all you're doing is pushing yourself further away from the ski. Different story with soft snow turns, or tighter than edge-carved turns, or (AIUI, hardly/never skied them) straight skis - which is I guess when you did pretty much all your racing?
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I think you slightly misunderstood my point. I wasn't really referring to a "pressure turn" in which you are actively pushing against the ski to bend it. I was referring to the "natural" load build up that is inevitable (it even feels good) in any turn due to lateral acceleration. The same force that loads up your car wheels unevenly when cornering. I was trying to explain that any difference in load between the 2 skis will bend them into different shapes and significantly alter their turn radius, obviously dependent on the stiffness of the ski. Look at the photo I posted. I'm not making any effort to push myself against anything, but my skis are still pretty bent out of shape from the loading.
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GrahamN, I am an ex engineer (lowly Msc though ) and an instructor i have to say i am tending towards V8's point of view. His arguements may have technical flaws but in practice i think make sense.
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skimottaret wrote: |
i dont think you can say the pressure is inconsequential on turn shape. Bend a pair a skis by hand and you will really change its shape quite easily. THe impact of pressuring a ski on the curve it transcribes in the snow to me seems to override the small influences when looking at a static ski model like physicmans and in my gut would easily account for the differences...
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Think you've hit the nail on the head there. We all know it's easy to adjust turn radius by subtle changes in pressure. The only complication being that the lightly loaded inside ski naturally wants to travel in a wider arc than the heavily loaded outer, therefore requiring a bit of correction from another source i.e steering, forward tip loading or whatever.
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You'll get to see more forums and be part of the best ski club on the net.
You'll get to see more forums and be part of the best ski club on the net.
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skimottaret wrote: |
I dont think you can say the pressure is inconsequential on turn shape. Bend a pair a skis by hand and you will really change its shape quite easily. THe impact of pressuring a ski on the curve it transcribes in the snow to me seems to override the small influences when looking at a static ski model like physicmans and in my gut would easily account for the differences...
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, and uktrailmonster The second sentence is the crux of my point on this, along with the example you gave of Phil S and the 10 degree carve. Bending in free space (up to a point) is pretty easy. But try this at home. Put that ski on edge onto a thin carpet and push on it lightly it so it grips onto the snow along its length. Now put your whole weight on it. Does the bend change? Very little. Any change would be due to the surface not being perfectly hard - pushing the centre of the ski deeper into the snow/carpet than the tips. What that's effectively doing then is pushing the snow under the ski out of the way and sort of changing the angle of the slope (it's lower down at the centre than the tips) - i.e. you could also see it as increasing the effective edge angle (but don't if that's going to confuse things) - but it's causing a wider track as it's actually no longer a pure carve. Of course if we look at it in fine detail there's probably no such thing as a pure carve, as the ski always has to cut a track for itself in the snow. Sharp edges and an icy piste are a pretty close approximation though.
But how did skiers carve on straight skis? Was it actually a carve, or a refined form of pressure turn? Any insight uktrailmonster?
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