Oh dear, there's none so blind as those that won't see. It is mathematical truth that parallel non-coincident curves have different radii. The theorems may not be as well known as Newton's laws of motion, but in denying them veeeight is being an idiot of equal proportions as last time. Even the source he cited in defence of his position doesn't support him. The graphs he hasn't shown are here, the ones showing that they are b) not parallel (the separation between tracks continually increases and decreases), c1) have different radii and d) have different edge angles. This is a relatively benign turn, requiring maximum edge angles of only 40 degrees, but there is still a difference of 5 degrees between the inner and outer.
But as I said in the previous post this is still the result of a model, and not what is necessarily happening in reality. And the argument is not that it is not possible to ski parallel tracks, but that you cannot do so with the skis doing IDENTICAL things. veeeight may well describe what appear to be parallel tracks, or think he's doing nothing different to the inner and outer ski, but he clearly is doing something different, even if it's only relatively small. As Sideshow Bob demonstrated, even the diagram he drew to demonstrate his point did exactly the opposite - to allow identical tracks through the body of the curve, you have to do something to get the inner ski diverging at the start of the turn. There was nothing wrong with the diagram, just veeeight's interpretation of it.
The really depressing thing is that once again a thread has been derailed by a largely irrelevant comment from veeeight half understanding a scientific point, and then refusing to accept that he's talking BS. I'm sure he's an excellent skier, probably a good instructor, but he's a pretty poor physicist and clearly an even worse mathematician. So rather than contribute something useful to the main discussion we have to go off on this ridiculous diversion. The only alternative seems to be to let his manifest untruths go unchallenged. This thread clearly has to be read in conjunction with http://snowheads.com/ski-forum/viewtopic.php?t=39016
So once again, here's what a guy who's been coaching to a high level for donkey's years thinks about it.
FastMan wrote:
Now, to the topic of 2 ski carving. In low edge angle turns it is quite doable to cleanly carve both the inside and outside ski. But when edge angles rise that possibility becomes more remote. To carve parallel skis, the inside ski needs to ride a higher edge angle, which means the inside ski needs to be tipped onto a higher edge. At high edge angles, good luck with that. Very hard to impossible to ski artificially bow legged at high edge angles.
So then, what really happens at high angles? A couple other options exist. First, a skier can keep the skis parallel, rotationally tension the inside leg, and power the inside ski through the turn so it stays in directional harmony with the carving/turn shape dictating outside ski. That rotational tension of the inside leg injects the inside ski steering necessary to keep it tracking the direction changing of the outside ski.
The other option is to employ a bit of a divergence of the inside ski at the start of the turn. Translation: manually turn the inside ski in the direction of the coming turn as you come out of the transition, so that the skis are no longer parallel, but resemble a reversed snowplow. From that point, both skis can carve the entire turn and the inside ski does not need to carve a sharper turn to stay with the outside ski.
jbob, carving on a hard surface? In which case adding pressure beyond that required to ensure then the ski is in contact with the surface along its full length will NOT change the turn radius - changing the edge angle will. And until you get to a race ski, that is not a huge amount of pressure; (how much do you apply when you bend the ski in a stiffness test? Significantly less than your own body weight. (Turns in soft snow are a different story - the bend is caused by pressure shifting snow differently along the length of the ski, but then you're not leaving pencil traces). So no "the engineers and math guys" would NOT have had the inner ski going straight.
Last edited by Poster: A snowHead on Thu 17-04-08 2:24; edited 1 time in total
Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
Masque wrote:
*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?
It's the radius the ski would turn with minimum edge angle (i.e. if you could hold a carve with it virtually flat). This is also the maximum possible radius the ski can carve without the edges skidding. Increase the edge angle (and pressure it into decamber so the edge stays in contact with the snow) and the turning radius reduces.
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?
GrahamN, I'm pretty sure that I cited that Physicsman's spreadsheet supported the notion that in reality for most of the time, the outside ski describes a tighter radius in that model, but conveniently, you chose to ignore that!
At the same time, you are choosing to be blinded by mathematics, and your model of concentric circles which clearly real life skiing doesn't subscibe to! Think about it! In skiing a series of GS turns, there is no constant radius as the edge angle is continually increasing and decreasing, thereby there is no one number for a constant radii.
Quote:
even the diagram he drew to demonstrate his point did exactly the opposite - to allow identical tracks through the body of the curve, you have to do something to get the inner ski diverging at the start of the turn. There was nothing wrong with the diagram, just veeeight's interpretation of it.
Again, you seem to be blinded by your stake in the ground! The 8 second diagram was drawn using copy and paste - so all the arcs are of identical radii - with different centres - disproving the notion that each subsequent inner arc has a tighter radius.
No one here has yet come up with a convincing counter (no pun intended) on how you are able to lay down pencil thin RR tracks at recreational speeds, without any rotational effort on the inside ski.
The assembled crowd in the bar tonight again are 100% positive that in that situation no rotational force comes into play, and that the tracks are not different. And that the whilst we have independent leg action, we are doing the same thing on both skis. So either all the racers, coaches and instructors here are delusional, or the maths and physics guys are wrong.
Quote:
And the argument is not that it is not possible to ski parallel tracks
So have you changed your tune now and accepted that the inner track identical to the outer track?
Quote:
you have to do something to get the inner ski diverging at the start of the turn.
You'd better get your money back from all your race training sessions, if that's what you're doing! I have yet to meet a current race coach who actively encourages scissoring at the start of the turn.
My second set of pictures (2 of Grandi, 1 of me, 1 of HH) show no scissoring/diverging whilst carving. I'm pretty sure that we know if we're introducing some rotational input or not.
Just because reality doesn't fit your mathematical model and understanding, there's no reason to presume that we are necessarily fudging it to produce clean RR tracks!
Take a snowboarder craving down a perfectly groomed piste, laying down near-sinusodial arcs.
Take a second snowboarder, laying down those arcs side by side, matching every peak and trough - laying down identical, but parallel arcs.
Are you going to tell me that if I overlaid those tracks, they won't match, because the second snowboarders tracks have a smaller radius inside the arcs?
Last edited by Well, the person's real but it's just a made up name, see? on Thu 17-04-08 6:44; edited 3 times in total
veeeight, The boarders are separate entities and have identical radii with the centre of rotation displaced by the distance between the tracks. A skier cannot do this as the skis are joined at the tip of the triangle formed by your feet and head, they have to share a turn centre point around which the skiers centre of mass can travel which means that they have to be doing different things ie. the inner ski is further along the turn and is at a slightly increased angle of attack. The tighter the turn and the lower the angulation, the greater the difference in angles needed between the skis. . .
If a simple "craving" boarder with very little ski time can understand this . . .
Anyway, snowHeads is much more fun if you do.
Anyway, snowHeads is much more fun if you do.
Masque, a skier CAN do this, as each ski is independent up to the hip socket in the pelvis, we can independently move each joint from the ankle up to the femur in each leg, and this is the skill required to make the skis do the same thing in high level skiing!
Last edited by Anyway, snowHeads is much more fun if you do. on Thu 17-04-08 6:51; edited 1 time in total
If I start out on a flatish slope and just edge my skis in one direction to ride the sidecut very gently, with no rotational input, my ski tracks will never converge. And yet I will produce thin identical RR tracks. Where's the "centre"? (Or rather can you see the path of the fictional centres of those arcs)? They look nothing like the static "centres" of those circles above!
Then you can post your own questions or snow reports...
Then you can post your own questions or snow reports...
veeeight, at low speed in a long turn and at a low angle of attack the skis will have almost no perceptible difference because they are far away from the centre of the turn they do not need a significant difference to track a seemingly parallel path.
As for being separated at the hips. . . now you are talking bollux. The hips are joints that CONNECT your feet to a single centre of mass, that mass is what describes an arc around the centre point of the turn. The skis are travelling in a parallel path around a single point and have different radii. To achieve that you will be making small adjustments of foot/knee.whatever to maintain those two tracks and all you've shown so far is a complete unawareness of bio-mechanical feedback because if you cannot feel yourself making adjustments to foot/toe/knee/hip/etc. in maintaining your path you have a greater problem than just geometry
After all it is free
After all it is free
Quote:
at low speed in a long turn and at a low angle of attack the skis will have almost no perceptible difference because they are far away from the centre of the turn they do not need a significant difference to track a seemingly parallel path.
Well, how about the set of photos on the previous page? All showing reasonably high edge angles?
Quote:
and all you've shown so far is a complete unawareness of bio-mechanical feedback because if you cannot feel yourself making adjustments to foot/toe/knee/hip/etc. in maintaining your path you have a greater problem than just geometry
Well that's me plus 25 racers, coaches and instructors here all fooked then.
I'm surprised that you can accept the concept of two snowboarders going down a piste side by side doing identical things, and the tracks are identical, and yet if I connect the snowboarders shoulders with a rigid bar (mimicing the pelvis) all of a sudden the one of the radius is different and one of them has to be scissoring and diverging their turns ............
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You'll get to see more forums and be part of the best ski club on the net.
Masque, bravo.
I can't answer your question about the geometry of skis as the maths is a bit too deep for me, and I find it doesn't translate to what goes on while on the hill either.
Masque wrote:
So is "Inner Ski Tip Lead" an essential part of carving parallel 'tram tracks' and all the angst above is just about tip-lead produced by other factors of body position and skiing confidence and in reality is NOT a problem in its own right but just a symptom of other skiing issues that when corrected will eliminate undesired poor foot position?
For me excessive tip lead can be a problem in it's own right, regardless of what the root cause is whether that be turning the hip in to the turn, deliberately adopting a body position which you think is 'right' or any other potential cause. I see some very good skiers who do a kind of foot shuffle at transition (and the associated movement of their hips), pushing their inside leg forwards and drawing their outside leg back. The range of this movement is in no way proportionate to the edge angles that they are creating by inclination or angulation. So the tip lead is not a result of what they are doing biomechanically, but a movement they have adopted for whatever reason. If this excessive tip lead leaves them in a weaker position for managing the forces that build up in the turn then they are compromising their potential performance by adopting a body movement which is unnecessary. It is a problem which can and should be fixed, although as I'm finding it is not easy to change movement patterns which have become ingrained.
Ski the Net with snowHeads
Ski the Net with snowHeads
veeeight, OFFS! You said "gently"!!!
Right The photos show a skier at speed and again FFS! look at the differing edge angles between the inner and outer ski in he photo you used above!
And yes if 25 people cannot understand BASIC mechanical geometry they are "fooked". Having two parts of a SINGLE mass in contact with a surface does not mean that they are independent of that mass, they are just doing different things. In this case to maintain parallel tracks they are at differing angles. It is you body's mass that goes around the turn. If you think that the two objects dangling below your crotch are separate from each other (in this context) then you are fooked. They are able, within a limited range of motion to articulate around your central mass and the only way to keep you going around that turn is for them to be connected to that mass
As for 'lead' it is exactly why a m/cycle inclined on a single track has the wheels slightly out of line with the front at a more acute angle to the rear as it is further along the path arc describing a similar cone shape to our skiing simile.
We ski in three dimensions NOT two, the centre of our rotation is not necessarily at the surface of the snow, at low speeds it is well above the surface lessening the difference in edging angles needed to create parallel tracks.
snowHeads are a friendly bunch.
snowHeads are a friendly bunch.
jbob wrote:
I have apply way more pressure to it than the inner one say 80/20. So given that my feet were not broken (I do tend to have a lead of about 10cm in practice) , and I had equal edge set on both skis, then the radius of the outer ski would be significantly smaller than the inner one due to the extra pressure. If the engineers and math guys were right it would have resulted in the inner ski tending to go straight on and the outer ski crossing over it and me ending up in hospital, I am pleased to say that this did not happen. I was not consciously at least, applying any pivot to the inner ski, they just run parallel.
Good example. I think the inner ski doesn't go straight on in practice because you are able to actively steer it to compensate for the different loaded ski radius. The active steering itself creates an additional torque on the ski, loading the tip creating the necessary turn radius. Like this perhaps:-
I think you have to consider combined vertical load AND steering torque when looking at the total ski loading. You might not consciously apply this steering torque, but I'm about 95% certain it must be happening. Otherwise how else is the inside ski going to bend into the tighter radius required to remain perfectly parallel.?
In the above photo I think my outside ski is being deflected almost entirely by vertical pressure and the inside ski mostly from steering torque. Hence my outside ski is more heavily loaded in the centre from the vertical load applied through my boot. The inside ski is more heavily loaded at the tip from my applied steering torque.
Last edited by snowHeads are a friendly bunch. on Thu 17-04-08 8:18; edited 2 times in total
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.
MasqueI'm surprised that you can accept the concept of two snowboarders going down a piste side by side doing identical things, and the tracks are identical, and yet if I connect the snowboarders shoulders with a rigid bar (mimicing the pelvis) all of a sudden everything changes, one of the radius is different and one of them has to be scissoring and diverging their turns ............
So if you're just off somewhere snowy come back and post a snow report of your own and we'll all love you very much
So if you're just off somewhere snowy come back and post a snow report of your own and we'll all love you very much
Quote:
Otherwise how else is the inside ski going to bend into the tighter radius required to remain perfectly parallel.?
<groan>
The inside ski does not ski a tighter radius!
(It only skis a theoretical tighter radius if you consider that it shares a common virtual fixed point - which in real life skiing it does not!)
And yes, it is possible to get the inside ski to track parallel with the outside ski in arc to arc turns without any rotary input at recreational speeds. Most skilled skiers on this forum can do it.
Last edited by So if you're just off somewhere snowy come back and post a snow report of your own and we'll all love you very much on Thu 17-04-08 8:08; edited 1 time in total
You know it makes sense.
You know it makes sense.
veeeight, WE CAN ALL SHOUT . . . if you connect them at the shoulder it's even easier to see the two boards at slightly different angles to the snow as they track around the carve. Once joined, the two boarders have a single mass to turn around a single focus. Two boarding objects have different turn centres.
Apples and Pears . . . you're talking bananas.
Otherwise you'll just go on seeing the one name:
Otherwise you'll just go on seeing the one name:
OK someone else can take over, this is getting circular (no pun intended).
I give up. I'm going back to the bar to tell them all that they are all wrong, the mathematicians say that what they are doing is impossible.
Poster: A snowHead
Poster: A snowHead
veeeight, I'm saying, you're probably not doing what you're saying. It's not just maths it's physics.
Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
veeeight wrote:
Quote:
Otherwise how else is the inside ski going to bend into the tighter radius required to remain perfectly parallel.?
<groan>
The inside ski does not ski a tighter radius!
(It only skis a theoretical tighter radius if you consider that it shares a common virtual fixed point - which in real life skiing it does not!)
And yes, it is possible to get the inside ski to track parallel with the outside ski in arc to arc turns without any rotary input at recreational speeds. Most skilled skiers on this forum can do it.
I think the mathematicians are being very harsh on you, but they do have an extremely strong point regarding the turn radius. But as Martin Bell has very eloquently put it, there are several ways we are able to achieve these parallel turns. Note I've editied my post above for clarity. Bear in mind you are a much better skier than myself (definitely!), but I'm a better mechanical engineer than you (almost certainly). If we all work together we can possibly learn something new?
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?
I think the one thing you're not grasping, veeeight, is that the hips/pelvis rotates throughout the turn. It does not stay exactly perpendicular to the fall line, nor does it stay perpendicular to the skis. I think you demonstrated what happens to the hips in a good post of yours on a different thread.
Now let's think about these hip angles. Imagine a turn from travelling left perpendicular to the fall line to right perpendicular to the fall line. You've turned through 180 degrees. Now where is your inside hip socket and your outside hip socket?
You want to talk about two independent snowboarders, how do the snowboarders do this 180 degree turn (with the same radius) if they start turning together? Can you draw a curve that turns through 180 degrees in one direction (doesn't have to be an arc of a circle) in your CAD package and then duplicate it (without enlarging it or rotating it) and put it next to the first without the curves converging and diverging? Want to put 100$ on it?
I think the mathematicians are being very harsh on you, but they do have an extremely strong point regarding the turn radius. But as Martin Bell has very eloquently put it, there are several ways we are able to achieve these parallel turns.
The turn radius thing really is the entire crux of the argument though. Until we accept that for parallel turns with skis and feet starting and ending together so there's no tip lead on either foot at start and end of the turn, there either has to be some divergence or the turn radius has to be different. Only when we accept the turn radius is different and the inside ski is tracking a tighter curve relative to the snow can we start thinking about the subtle points that Martin, FastMan, GrahamN and I have been talking about that make this ski track a tighter curve.
Anyway, snowHeads is much more fun if you do.
Anyway, snowHeads is much more fun if you do.
Masque, with the greatest of respect, you're in the same boat at GrahamN, where what I'm doing doesn't fit the theoretical model, therefore I must be doing something else (a fudge). The collection of people that I mentioned earlier, including myself have spent years refining our motor nerves pecisely so that we can feel and control our muscles to do exactly what we want them to do.
I don't think it's a case that we are doing something we say we're not. We're quite adamant about that.
The turn radius thing really is the entire crux of the argument though. Until we accept that for parallel turns with skis and feet starting and ending together so there's no tip lead on either foot at start and end of the turn, there either has to be some divergence or the turn radius has to be different. Only when we accept the turn radius is different and the inside ski is tracking a tighter curve relative to the snow can we start thinking about the subtle points that Martin, FastMan, GrahamN and I have been talking about that make this ski track a tighter curve.
Absolutely agree.
Then you can post your own questions or snow reports...
Then you can post your own questions or snow reports...
A fundemental question:
With high end skiing being outside ski dominant, in a clean arc to arc turn, how on earth can you make the inside ski bend into a tighter radius (if that's what you think it is) than the outside ski?
(with no rotary input, which, is 100% possible).
If the inside ski is skiing a smaller radius, then by it's very nature it will always be diverging.
These skiers are not showing symptoms of a diverging inner ski:
I don't think it's a case that we are doing something we say we're not. We're quite adamant about that.
It's simply that you don't fully understand the subtle physics of what you're doing. But that's hardly surprising as you are a skier, not a physicist
I wouldn't take that in any way as a criticism of your knowledge. In my sport (F1 motor racing) racing drivers have little in-depth knowledge regarding the physics of their car (even the like of Schumacher) but it doesn't stop them driving extremely fast. Engineers on the other hand understand the physics involved in far more detail, but can't drive anywhere near as quick. See my point here?
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.
Is there a way of deleting double posts? My connection is sooo slow?
Last edited by You'll get to see more forums and be part of the best ski club on the net. on Thu 17-04-08 9:13; edited 1 time in total
Ski the Net with snowHeads
Ski the Net with snowHeads
veeeight wrote:
If the inside ski is skiing a smaller radius, then by it's very nature it will always be diverging.
Look at this image.
Measure the distance apart the curves are - use your ruler perpendicular or normal to the curves at each point, to mimic no tip lead and feet parallel. The inside curve there has a tighter radius than the outside, agree? But shock horror, the curves are not diverging. They're always the same distance apart!
snowHeads are a friendly bunch.
snowHeads are a friendly bunch.
veeeight wrote:
A fundemental question:
With high end skiing being outside ski dominant, in a clean arc to arc turn, how on earth can you make the inside ski bend into a tighter radius (if that's what you think it is) than the outside ski?
(with no rotary input, which, is 100% possible).
I don't think you can without the "steering torque" input I tried to describe earlier. But on a long radius turn, this steering input would be tiny.
veeeight wrote:
If the inside ski is skiing a smaller radius, then by it's very nature it will always be diverging.
No, it will remain parallel to the outside ski (reminder about concentric circles again)
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.
Sideshow_Bob, And this is why one gets tip lead as the inside ski must travel faster.
Taking your image as ski tracks, and taking the top of the image as uphill, we can presume a turn to the left is being made. The Outside/right ski will be leading
as the previous turn finishes but then as the turn progresses, the left/inside ski will overtake it as it must travel the same distance in the same time....tip lead explained ?
So if you're just off somewhere snowy come back and post a snow report of your own and we'll all love you very much
So if you're just off somewhere snowy come back and post a snow report of your own and we'll all love you very much
veeeight wrote:
Masque, a skier CAN do this, as each ski is independent up to the hip socket in the pelvis, we can independently move each joint from the ankle up to the femur in each leg, and this is the skill required to make the skis do the same thing in high level skiing!
What makes you think both skis are doing EXACTLY the same thing? They will have different loads distributed differently along the length of the ski. I'll bet there's also (however small) steering torque inputs, especially on the inside ski. One thing is for sure, if we accept that they are neither diverging or converging, they MUST be following different radii, the tighter the turn the bigger the difference.
You know it makes sense.
You know it makes sense.
Conversely: It's more useful to think of ski tracks as segments of arcs (as your imaginary centre/s are moving alongside the arc, you are never skiing about a fixed point inside a circle):
All four lines are exactly identical. It would appear from the top diagram that the inner line has a smaller radius that the outer line.
But in the bottom picture I've nestled up the two lines close together, and as if by magic, with a little visual imagination, they overlap (well they should do as they are all identical). They are of the same radius.
Your left ski has an identical sidecut radius to your right ski. In a park and ride situation, wheren you just tip the ski over to the side, both skis are describing identical arcs - but because they are displaced by a certain distance apart, this gives rise to the illusion that the inside track is a smaller radius.
Otherwise you'll just go on seeing the one name:
Otherwise you'll just go on seeing the one name:
veeeight wrote:
Your left ski has an identical sidecut radius to your right ski. In a park and ride situation, wheren you just tip the ski over to the side, both skis are describing identical arcs - but because they are displaced by a certain distance apart, this gives rise to the illusion that the inside track is a smaller radius.
They will only describe identical arcs when loaded in precisely the same way i.e. same edge angle, same loading. In such a case the resultant lines left in the snow will NOT be mathematically parallel.
Poster: A snowHead
Poster: A snowHead
veeeight, Hmmmm, now that is a interesting. Think I will leave it at that before my brain starts to hurt. Thanks for the good natured chat, perhaps techy talk can work.....if people take the right attitude
Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
Frosty the Snowman, I thought that might get you thinking......
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?
veeeight wrote:
All four lines are exactly identical. It would appear from the top diagram that the inner line has a smaller radius that the outer line.
But in the bottom picture I've nestled up the two lines close together, and as if by magic, with a little visual imagination, they overlap (well they should do as they are all identical). They are of the same radius.
And yet again as in the first diagram, you're not starting or finishing with your skis level! Continue those curves through 180 degrees. Can you? Try it, please!
MB,
If people really want to use WC Racers as a model for technique we probably should be looking primarily at their practice runs rather than when they're going for broke in a real race. There's efficient skiing and then there's winning. Sometimes the 2 meet.
I had a lesson with BASI instructor last year who suggested that as WC racers epitomised all that was good and efficient in skiing, more and more instructors were following the principles that their (the racers) style of skiing was something to be copied, albeit it much slower speeds.
So......deep breath......it looks as though some tip lead is infact a necesary "evil" if one follows the principle that unequal pressure on each ski prevents RR tracks? There must be some extra ankle flex on the inside ski (though with the inside ski forward perhaps not quite as much as with no tip lead) and I suppose that the effect on the shovel end of the ski in terms of pressure/flex enables the uphill ski to pretty much track the outside ski.
Just to throw another grenade in. Surely most racers do not constantly have their skis apart at the same distance? During turn initiation, as the inside and outside skis change, one quite often sees the skis closer than at the apex of the arc when often the skis are further apart. Clearly, through the course of the arc, the RR tracks cannot be parellel......
Anyway, snowHeads is much more fun if you do.
Anyway, snowHeads is much more fun if you do.
veeeight wrote:
GrahamN, I'm pretty sure that I cited that Physicsman's spreadsheet supported the notion that in reality for most of the time, the outside ski describes a tighter radius in that model, but conveniently, you chose to ignore that!
Not at all. In the top graph above, the blue line is the outer ski for the first turn, the pink one the inside (in fraction 1.0-2.0 they're obviously other way around). The top graph above shows the outer ski increasing in edge angle relative to the inner, and so having a shorter radius, for about 1/4 of the turn. For the rest of the turn the outer ski has a longer radius.
Quote:
At the same time, you are choosing to be blinded by mathematics, and your model of concentric circles which clearly real life skiing doesn't subscibe to! Think about it! In skiing a series of GS turns, there is no constant radius as the edge angle is continually increasing and decreasing, thereby there is no one number for a constant radii.
None of the arguments you are so stubbornly refusing to accept require circles or a constant radius - I have referred to moving centres of curvature several times since that reference to the theory of parallel curves. Concentric circles are just a special case that are easier to understand, since you are clearly having difficulties understanding any of the arguments proving you're talking BS.
Quote:
Again, you seem to be blinded by your stake in the ground! The 8 second diagram was drawn using copy and paste - so all the arcs are of identical radii - with different centres - disproving the notion that each subsequent inner arc has a tighter radius.
Identical yes, but not parallel. Take lines from the centre of curvature of any point on one of those tracks and trace it to the neighbour and you will see a difference in the distance between the tracks. As Sideshow Bob pointed out, the necessary consequence (it would make no difference if you to 8 seconds or 8 hours) of those tracks is that the inner track starts turning before the outer.
Quote:
Take a snowboarder craving down a perfectly groomed piste, laying down near-sinusodial arcs.
Take a second snowboarder, laying down those arcs side by side, matching every peak and trough - laying down identical, but parallel arcs.
Are you going to tell me that if I overlaid those tracks, they won't match, because the second snowboarders tracks have a smaller radius inside the arcs?
No-one is arguing that you cannot lay down identical tracks (sorry Masque, the two snowboarders or the two skis are the same thing), it's just that those tracks are not then parallel. Look at a set of spooned 'S'es in powder. If done well they are identical, but they are furthest apart at the apex, and closest at the transition. It's very simple geometry. Take a curve (circles, parabolae, sinusoids, freehand, I don't really care, as long as it turns through something like 90 degress at some point). Pick a point (that is not an apex) and shift that curve perpendicular to its path at that point, i.e. as for hip separation. They will then be significantly closer at that apex, and will almost certainly cross. These two curves are identical, but clearly not parallel.
Quote:
Quote:
And the argument is not that it is not possible to ski parallel tracks
So have you changed your tune now and accepted that the inner track identical to the outer track?
No, I've never argued that you can't lay down identical tracks, it's just that they are not then parallel.
Quote:
Quote:
you have to do something to get the inner ski diverging at the start of the turn.
You'd better get your money back from all your race training sessions, if that's what you're doing! I have yet to meet a current race coach who actively encourages scissoring at the start of the turn.
So FastMan's talking BS?
At recreational levels it may well be that the deviations from equivalence are sufficiently small that they are not noticed. Back to the model again for an example: 18m ski, 20 foot lateral offset, 70 foot between gates, 12 inches between tracks at apex and transition. Track separation varies by only 3/4 of an inch, eacg angles up to 40 degrees at apex with a difference of only 2 degrees (although again the model may be showing its limitations here, as the skis are turning at greater than their sidecut radius for the majority of the turn). The problem is not with this, it's the extrapolation from this to manifestly false assertions.
Continue those curves through 180 degrees. Can you? Try it, please!
Firstly I am only using MS Word to sketch these, secondly, if you want them through 180 degrees, you are assuming that the imaginary centre is static, and we are skiing about an imaginary centre in a circle - which in the real world, we are not! This is where the model falls down!
Then you can post your own questions or snow reports...
Then you can post your own questions or snow reports...
veeeight wrote:
Conversely: It's more useful to think of ski tracks as segments of arcs (as your imaginary centre/s are moving alongside the arc, you are never skiing about a fixed point inside a circle):
All four lines are exactly identical. It would appear from the top diagram that the inner line has a smaller radius that the outer line.
But in the bottom picture I've nestled up the two lines close together, and as if by magic, with a little visual imagination, they overlap (well they should do as they are all identical). They are of the same radius.
Your left ski has an identical sidecut radius to your right ski. In a park and ride situation, wheren you just tip the ski over to the side, both skis are describing identical arcs - but because they are displaced by a certain distance apart, this gives rise to the illusion that the inside track is a smaller radius.
v8, presumably you can see that those curves aren't parallel.
After all it is free
After all it is free
So, we now have a split?
One party is now saying that the tracks are identical (but not necessarily parallel)
One party is now saying that the tracks are parallel (but not identical as they are of different radius)
One party agrees that two snowboarders is the same as two skis
One party agrees that two snowboarders is not the same as two skis
The original argument was that you needed scissoring to carve your turns. I said not.
Who is now saying what?
Last edited by After all it is free on Thu 17-04-08 9:55; edited 1 time in total
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You'll get to see more forums and be part of the best ski club on the net.
veeeight wrote:
Quote:
Continue those curves through 180 degrees. Can you? Try it, please!
Firstly I am only using MS Word to sketch these, secondly, if you want them through 180 degrees, you are assuming that the imaginary centre is static, and we are skiing about an imaginary centre in a circle - which in the real world, we are not! This is where the model falls down!
I don't care about where the centre is or even if it's a circle! Just draw a skier and tracks travelling straight across the piste heading right and then turning so he's straight across the piste heading left! It's pretty simple, and something I'm sure everyone has done at some point while skiing, even you maybe!
Use whatever line you want, but make sure it's the same curve being followed for both inside and outside ski with no enlargement. Can you do it?
Ski the Net with snowHeads
Ski the Net with snowHeads
veeeight wrote:
So, we now have a split?
I don't see one!
Quote:
One party is now saying that the tracks are identical (but not necessarily parallel)
That is the case with your diagram. You really need to understand what is meant by a parallel curve. GrahamN posted the link before. Think railway lines curving round to the right. Are these lines parallel to each other? If you took up the inside track and placed it atop the outside track, would they overlap exactly?
Quote:
One party is now saying that the tracks are parallel (but not identical as they are of different radius)
That is the case with my diagram of the arcs of concentric circles.
FAQ
Poster: A snowHead
boarder with very little ski time can understand this . . . 
