 Poster: A snowHead
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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: |
If the outside lane starter ran faster then they would finish equal after a 90 degree turn  |
And who ran further? The outer lane. And who turned a tighter turn? The inside lane! They've both turned through 90 degrees, but the inside lane did it in a shorter distance. Tighter corner!
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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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uktrailmonster, only if you are theoretically measuring the inside and outside runner from a common centre.
This bit is important:
However - if you tied each runner to a bit of rope of the same length (ignoring the potential of getting tangled up) - and gave them two different, moving centres (eg: asked a further two runners inside the running track to keep up with the track runners keeping the rope taught) this is skiing.......... 
Last edited by Well, the person's real but it's just a made up name, see? on Fri 18-04-08 16:55; edited 2 times in total
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i tried to put a line under this, but head above the parapit just for fun... 
I believe a skilled skier can make virtually identical left and right tracks that can be near as dammit overlaid, hence i believe the radii can be the same. You can do this because the skis have different centres of radius roughly a hips width apart, and, crucially the skis act independantly, each leg/ski making subtle continuous corrections with differences in tip lead, edge angle, edge engagement, ski bend etc. during the dynamics of cleanly carving a turn. We are tallking about inches and 2 degrees of variation, certainly possible.
The purest, mathematical view that these curves arent strictly parallel is correct in the academic sense, but i have seen tracks as above and we are debating skiing here not candidates for the Field Medal.
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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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| skimottaret wrote: |
| You can do this because the skis have different centres of radius roughly a hips width apart |
The hips also rotate through the turn though! If the hips stayed pointing directly down the fall line and the feet on a line directly across the fall line you could indeed have two separate centres separated by hip width, but then you'd have increasing problems when you came to making turns further out of the fall line. Your skis would start to converge pretty rapidly, and I don't think it's really possible to have the hips directly down the fall line while the skis were skiing parallel to the fall line.
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Sideshow_Bob, sure they do, i did say "hip width" as that would be typical. but i think the position of hip socket is somewhat irrelevent as it isnt the important centre of radius. it is the point under the foot where the skis transcribe the arc that we should focus on. That point is affected by all the factors listed, and it couldnt give a hoot where the hips are... 
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Ok, the wider the stance and the tighter the overall turn, and with the hips rotating with the turn (but not necessarily staying parallel to the skis), the more difference there is between inside and outside turn radius, and the tighter the inside ski has to turn relative to the outside. For carved slalom turns where the turn radius of the centre of mass is often only twice or three times the ski length, there's a more significant difference.
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| Martin Bell wrote: |
| veeeight wrote: |
| laundryman, fair point. But they do insist in trying to best fit their 2D paper models into real life 3D skiing, |
Good point, V8. This is where theory and reality diverge (to use a currently popular term  ). Physicsman would be the first to admit that his model assumes an infinitely hard surface and does not allow for any extra ski flex due to snow compression and differing fore-aft loading.
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And every time the model has been cited it's been included with the caveats that it's a restricted model, and it's been used for illustration of typical types of differences that would arise from certain tracks (approximating to a sinusoid). And even more important, the model is not asserting anything about HOW those turns are generated - e.g. the issue of forces, whether the skis could actually hold the angles required, speed around the tracks etc., is in the area of dynamics that PM was at pains to point out was not being modelled. But HOW the skis are made to follow certain tracks is a different question to WHAT the skis did to follow those tracks. Being aware of what the assumptions are in a model and its limitations is the essence of scientific analysis - and failure to do that is a hallmark of cod science. Again the whole crux of this argument is that it's V8 who is actually asserting a model that is provably incorrect (parallel tracks and equal curvature), not that PM's model is exact.
So we have an experimental result that the tracks are indeed parallel - although it would be nice to know what the error bars on the measurement are - 1mm, 10mm, 20mm? Good. What was the width of the tracks BTW, and what was the error in that measurement? We also have an estimate that different edge angles of the order of a degree or two would be enough to achieve the variation in curvature required to make those tracks through perfect carving for those tracks. This could be refined if we had more information on the size of the tracks and the ski sidecut, but it's not going to be radically different.
And for the umpteenth time, whether something is a circle or an ellipse or some general nondescript curve makes no difference to the argument - it's just that circles are much easier to visualise and draw. The theory of parallel curves is well understood (sorry, I overstated the case last time around, it's only just over 300 years since Leibnitz did it in 1692, following Huygens in 1673). It would be laborious but entirely possible to draw parallel curves with a sinusoidal midline, then move them so that they overlay and they will not be identical. It may also be possible to produce graphs of radius of curvature as skis described such a path. Would that demonstration satisfy V8 that his model is rubbish?
So we're left ith the assertion that the skis are angled identically. Note here that it's V8's model that they're identical angles - no measurement errors/tolerance allowed. So who's trying to fit artificial models to reality? The required 1 degree for a pure carve would result in about 1cm difference in separation at the knees (my knees are about 54cm from my soles, then there's boots and bindings). But do the boots have that little play in them that this is where it all comes from? As MB alludes, we've previously had reported how boots may be blown out to allow more play and ankle rolling . Are we really being asked to believe that V8 knows that his knees, joints, boots are angled at this level of accuracy (i.e. to equal angles, not whateve angle is required to keep the skis pointing in the desired direction), when holding a 40-50 degree edge angle. Could/can you Martin Bell?
Does the inner ski have to bend more to carve a parallel track? Absolutely, if tracks are parallel then the inner ski will have to turn tighter than the outer. FastMan also wrote as much. If the track is not carved, then not necessarily.
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| veeeight wrote: |
uktrailmonster, only if you are theoretically measuring the inside and outside runner from a common centre.
This bit is important:
However - if you tied each runner to a bit of rope of the same length (ignoring the potential of getting tangled up) - and gave them two different, moving centres (eg: asked a further two runners inside the running track to keep up with the track runners keeping the rope taught) this is skiing.......... |
Ok I give up, you just don't get this at all and refuse to either accept or understand the basic geometry of parallel curved tracks. If you think the inside rail of a railway track has the same radius as the outer, just a different centre point, then you are deluding yourself.
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| GrahamN wrote: |
| The theory of parallel curves is well understood |
Not in V8's bar it's not!
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snowHeads are a friendly bunch.
snowHeads are a friendly bunch.
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GrahamN, well said and with a more pragmatic "engineers" view of the maths involved I must say  .... I agree with the above but am slightly fuzzy about the last sentences as i think there is a general misunderstanding about the term "parallel" tracks. Using a rigorous definition you are correct that inner ski must bend more to carve a true parallel track. This seems to be a bee in V8's bonnet.
But if we assume independent leg action, tip lead/lag etc. along with different centre points of radii can we not have tracks that are "identical" with the same radii, but not neccesarily parallel?
Im not arguing but trying to see if you feel the "experimental" model can work in this case, I think one source of confusion may be that some here are assuming two separate centres of radii and others assume a single point. I am in the two centres camp but am now doubting whether that is relevent in the 25 metre rad typical turn...
your thoughts?
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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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| skimottaret wrote: |
But if we assume independent leg action, tip lead/lag etc. along with different centre points of radii can we not have tracks that are "identical" with the same radii, but not neccesarily parallel?
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Yes of course, but they absolutely CANNOT be parallel. It doesn't matter how these tracks are created. You can draw them in the snow with a giant pair of compasses or ski them or whatever you like.
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| skimottaret wrote: |
Im not arguing but trying to see if you feel the "experimental" model can work in this case, I think one source of confusion may be that some here are assuming two separate centres of radii and others assume a single point. I am in the two centres camp but am now doubting whether that is relevent in the 25 metre rad typical turn...
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If perfectly parallel then it MUST be a single centre, even if that centre itself is moving. I think it's possible to ski either single point or twin points, it just depends if you want the tracks to be parallel or diverging / converging.
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You know it makes sense.
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| skimottaret wrote: |
| GrahamN, well said and with a more pragmatic "engineers" view of the maths involved I must say .... |
Well actually, it's exactly the same view of the maths I've espoused all along. One of the most irritating things about this argument is the repeated accusations of "absolutism" levelled by V8 at us, when a) it's his view that's the absolutist one
| 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 b) him repeatedly ascribing to us views we have time and again told him are not true (fixed centre, only circles etc) - the "straw man" style of argument. The only absolutism from our side has been in demonstrating (time and time again, but he still can't see it) that his model is not possible and self-contradictory. At no point has anyone said anything along the lines of "such and such a curve requires a 47.8 degree edge angle and that if you did it with a 45.2 angle you're deluding yourself because the model says something different". PM's model describes a possible solution to running a course (I think with the objective of making the with the smoothest possible direction changes, but I forget now), and allowed for non parallel, non-identical tracks, but has only ever been used as an illustration.
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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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This bit is important:
Two runners running around a running track that turns through 90 degrees.
Each runner is tied by a rope of identical length - to two further runners inside the running track.
All the runners are asked to keep "level" with each other (so, that would entail the outside runner running faster), and the two innermost runners are asked to keep the rope taught at all times.
Is this Possible? Yes or No?
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Poster: A snowHead
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| uktrailmonster wrote: |
| skimottaret wrote: |
But if we assume independent leg action, tip lead/lag etc. along with different centre points of radii can we not have tracks that are "identical" with the same radii, but not neccesarily parallel?
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Yes of course, but they absolutely CANNOT be parallel. It doesn't matter how these tracks are created. You can draw them in the snow with a giant pair of compasses or ski them or whatever you like. |
The experiemntal observation is that they ARE parallel - in which case the inner track is tighter than the outer at any given angle (e.g. with respect to the fall-line). The question is then whether allowing fore-aft separation between the feet allows the skis to have a more nearly equal curvature by actually sitting at different points along that path. This would need to be considered individually for each different path but we could consider a few general points. It's obviously not possible if the paths are circular, as the radii are constant. For a curve that has a tightening radius, as for example approaching the apex of a curve (say around a gate) you could envisage one ski being moved forward so it's further into the tightening radius curve than the other. The problem is that the ski that needs tightening up is the outer one, so you would have to be entering the fall-line with outer tip lead. You have a problem right at the apex as there will be no point onthe outer track that turns as tightly as the inner track. Past the apex you may be able to get the parallel tracks with equal curvature at each point, but how far advanced the inner ski would have to be I don't know without some hefty calculations. So in general the answer is "in theory possibly - except for somewhere near the apex - but it's nothing a skier would ever do".
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Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
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| v8 wrote: |
All the runners are asked to keep "level" with each other (so, that would entail the outside runner running faster), and the two innermost runners are asked to keep the rope taught at all times.
Is this Possible? Yes or No?
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I'm sorry - I so want to say this: only if there is a school teacher there 
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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 wrote: |
All the runners are asked to keep "level" with each other (so, that would entail the outside runner running faster), and the two innermost runners are asked to keep the rope taught at all times.
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Define "level". What are the inner runners doing? Running in their own lanes, standing still, something else?
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The inner runners (in the grass area of the arena) are running alongside the outermost two runners (who are in their lanes).
The inner runners priority is to keep each of their ropes taught.
So, when viewed from above, the two outermost runners are in their lanes, the two innermost runners are on the central grass area, running alonside the track at the general speed of the two outer runners, keeping their ropes taught.
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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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Sorry, just seen your earlier statement of the question. Yes it is possible, but the inner runners are having to turn through a tighter radius. Have you ever heard 200m runners moan about being drawn on the inside track? Have you seen the angle thay have to lean into the bend to manage the forces as they run that bend? That's because of the tighter radius on the inside of the bend. The grass-runners are running pretty slowly though. I don't really see where you're going with this though, as it's just the concentric circles problem that you've taken such a dislike to up to now.
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| Quote: |
but the inner runners are having to turn through a tighter radius.
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Uvavu! 
Please please please please visualise this (the following) carefully!!
Lets just take ONE runner in lane 6, tied to a piece of rope 15m long, attached to another runner inside the track on the grass area. They both run forward, keeping the rope taught.
Take the same runner, put him/her now in lane 5, repeat experiment.
1. What radius is the runner running with respect to his buddy (in the grass area) when he was in lane 5?
2. What radius is the runner running with respect to his buddy (in the grass area) when he was in lane 6?
Last edited by You'll need to Register first of course. on Fri 18-04-08 20:07; edited 2 times in total
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Serves me right for responding. You're making even less sense now than before. You're obviously never going to take my word for anything, or anything I quote for you, so go and ask a runner whether they'd prefer the inside our outside track of a bend. And remember that sideways acceleration is v*v/r.
Meanwhile, I have a couple of pairs of skis that need sharpening.
Last edited by Then you can post your own questions or snow reports... on Fri 18-04-08 20:06; edited 1 time in total
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It's a simple question! (or 2).
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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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veeeight, jesus, I wouldn't want to be your maths teacher. That would be a frustrating job!
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Actually it's not, since you've specified the grass runners positions very badly. If what you are asking could be equivalently framed as two runners in say lanes 6&8, then then repeat in say lanes 1 and 3, then they are running at a radius difference of 2 lane width in each case. But the radius of lane 8 is going to be much larger than when he's running in lane 3 - a difference of 5 lane widths.
Skis are getting lonely.
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snowHeads are a friendly bunch.
snowHeads are a friendly bunch.
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GrahamN, I don't understand what psuedo geometrical theory he's trying to prove either. If the runner stays in lane, he's following the radius of that lane. His mate can keep the rope tight by running around him in circles if he likes, but he has no relevance to the fixed radius of the lane. I think he's trying to visualise a moving centre, very badly!
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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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Well, if you guys could put aside any preconceptions and just visualise and answer the following question(s) lets see where that goes.
+++++++++++++++++
Lets just take ONE runner in lane 6, tied to a piece of rope 15m long, attached to another runner inside the track on the grass area. They both run forward, keeping the rope taught.
Take the same runner, put him/her now in lane 5, repeat experiment.
1. What radius is the runner running with respect to his buddy (in the grass area) when he was in lane 5?
2. What radius is the runner running with respect to his buddy (in the grass area) when he was in lane 6?
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uktrailmonster, you could be right. Would tie in with the rubbish previously about turning centres being the hip sockets - which as a number of us have said (including Martin Bell) have nothing to do with it. I certainly did radii and centres of curvature by 1st year A-level, if not before.
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You know it makes sense.
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| veeeight wrote: |
Well, if you guys could put aside any preconceptions and just visualise and answer the following question(s) lets see where that goes.
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You're asking professional mathematicians, physicists and engineers to put aside their "preconceptions" which are in fact basic geometrical theories proven hundreds of years ago.
I can see what you're trying to prove here, but you won't be able to because it's wrong! That's why nobody is buying it, especially not those of us who understand the geometry. It has nothing to do with skiing and in fact there are no skiers involved in your own current thought experiment.
But forget that for a minute, because it's going nowhere. Let's say you are right afterall and both ski tracks are totally identical. Why is that such an important concept to force on us, because I've honestly forgotten!?
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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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| Quote: |
Let's say you are right afterall and both ski tracks are totally identical. Why is that such an important concept to force on us, because I've honestly forgotten!?
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Because the inside ski is NOT tracking a tighter radius than the outside ski. It is laying down an identical track to that of the outside ski.
The inside ski is only conceptually tracking a tighter radius than the outside ski IF you mathmatically relate them to a common (static or moving) centre. But, in reality, both skis couldn't care less about what radii the other one is tracking. The two runners in lanes 5 & 6 show that relative to their respective buddies in the grass area, the piece of string is always 15 metres long.
In skiing this is important, because if you ski thinking that the inside ski has to bend more to track a tighter radius, then your skiing is going to fall apart. It only has to track the same (radius for want of a better word) as the outside ski.
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Poster: A snowHead
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| veeeight wrote: |
| ally tracking a tighter radius than the outside ski IF you mathmatically relate them to a common (static or moving) centre. But, in reality, both skis couldn't care less about what radii the other one is tracking. The two runners in lanes 5 & 6 show that relative to their respective buddies in the grass area, the piece of string is always 15 metres long. |
The 15m is the difference in radius between the buddy and the runner, just like 1m would be the difference in radius of turn between the turn the runner in lane 5 is making and the runner in lane 6. Do you agree the guy in lane 5 is making a tighter turn as he runs than the guy in lane 6?
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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: |
| The two runners in lanes 5 & 6 show that relative to their respective buddies in the grass area, the piece of string is always 15 metres long. |
Ah, now I see what you're getting at...and that shows the fallacy in your whole argument, and that you have no understanding of the concept of centre of curvature. The buddy in the grass in NOT at the centre of curvature of the outer runner, as he is moving at the same time. (And before you get excited about that, this is completely different from the centre of curvature moving, tracing out the evolute curve, for a non circular path). Yes the difference in curvature for the runner and his buddy is 15m in each case, but the buddy is running through a different radius curve in the two cases. If this is a 400m track, the buddy for the runner in lane 5 will themselves be running around an arc of about 7m radius (assuming a 1.5m track width), and about a 8.5 m radius when the runner is in lane 6. The radius of curvature for lane 5 is about 22m and that for lane 6 is about 23.5m.
Go talk to some runners if you don't want to believe mathematicians, scientists....
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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 wrote: |
| Because the inside ski is NOT tracking a tighter radius than the outside ski. It is laying down an identical track to that of the outside ski. |
That could be true - in which case the skis are not following parallel paths. Or they could be nearly identical and nearly parallel.
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Okay, I had a play with Visio earlier to try to draw some diagrams to explain stuff
On the left here's a turn similar to the one Veeeight posted earlier. The two curves overlap each other exactly, and have been formed by taking a copy of one curve and shifting it left by a small amount. Same radius turn for both feet. Looks ok doesn't it? But wait, the feet and skis are actually diverging then converging. Want proof? Let's continue the turn for longer, as happens on the right. Look what happens - the skis actually overlap! That's the problem with an identical curve. They're only separated in one fixed direction!
Here's what would happen if we started down the fall line with our feet level, hip width apart and tips in line, and rocked both skis onto the same radius of turn. This is the same as thinking about two snowboarders level who start the exact same curve together:
Now, what would happen if we drew a curve where the two lines were parallel. This means they trace the same evolute, and can be thought of in skiing as keeping the tracks the same distance apart as we rotate through the curve. On the left is a J-turn. Skis same distance apart throughout the turn, agree? On the right is what happens when we take the inside ski and outside ski tracks and put them on top of each other. Look what's happened, the inside ski (blue) is definitely turning more sharply.
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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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Now for the interesting ones. What if we did keep the skis parallel and pointing in the same direction yet the two tracks could be overlaid atop each other? Well, here's a curve demonstrating some turns where the inside and outside tracks would exactly overlap each other. I've drawn some 'boots' representing where both boots would be at varying times throughout the turns. I've also drawn a line through the boots, highlighting where they're pointing and to show the skis/boots are parallel everywhere - pointing in the same direction. This line is not the ski - the ski would be bent onto the curve. It's rather an arrow pointing where the boot is pointing.
Look what happens. The tracks definitely converge and diverge. They're getting closer and then further apart. There's also a lot of tip lead, outside tip lead at the start of the curve and inside tip at the end. The feet can only be parallel if they're in a line directly across the fall line at all times. This would make it very difficult when we make turns at greater angles across the fall line, and as demonstrated above, impossible if we want to turn up the hill.
Hey, I thought we wanted our feet to be close together and have no tip lead? That's one of the ideas we want, right? What happens if we take the same curves and draw it so our inside and outside boots are level as our hips rotate through the turns:
But what's happening now? The feet are no longer parallel. They're scissoring at the start of the turn, and then coming back together at the end of the turn. Does this make the skier fall over? No - the left and right tracks are identical. How can that be when the feet are pointing apart? Simple, the feet are at different points along each track.
I think we'll all agree neither of these pictures mirror skiing reality, so it's pretty clear that the curves cannot overlap for anything other than really shallow short turns.
Last edited by Anyway, snowHeads is much more fun if you do. on Fri 18-04-08 22:52; edited 1 time in total
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You'll need to Register first of course.
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Now, do I think the skier scissors so much as in the lower picture? No, I don't. This is only a demonstration of what would happen if both curves were identical. I hope the separation issue will clearly show that they're NOT identical, and I only drew the pictures to highlight what would happen if they were identical as VeeEight claims. Just to stress this is not how I think people ski. It's to highlight that the curves aren't identical.
Now how do I think people ski? I think that both curves are not identical. The inside ski will track a tighter radius. There's a combination of a bit of divergence and a bit of steering to help get the inside ski tracking this tighter turn, be it through greater shovel-flex, or pressuring different points of the ski to bend it more. Does the skier tip the inside ski onto a higher edge angle to make it turn tighter? He could, but it's pretty difficult as he'd have to be skiing slightly bow-legged, and the tighter the turn relative to the width of the stance, the greater the difference in angle. I don't see many pictures of racers with a more angled inside leg than outside, so I think there's more of the steering/loading/slight divergence going on. As I said before I'm in pretty much complete agreement with FastMan.
Last edited by You'll need to Register first of course. on Fri 18-04-08 22:35; edited 1 time in total
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Oh dear oh dear.
(Laundryman you could be onto something though).
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| laundryman wrote: |
| Or they could be nearly identical and nearly parallel. |
I think you're right there for the vast majority of turns. There's definitely a combination of a tighter arcing inside ski and some divergence/convergence of the tracks in most turns.
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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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Sideshow_Bob, thanks for that (fuller explanation of curves similar to what I posted three pages back). Unfortunately we're all quite clearly wasting our time with this bozo, who obviously has no intention of actually reading anything any of us say.
| veeeight wrote: |
| (Laundryman you could be onto something though). |
...and that is exactly the point we've been trying to get into your skull for the last 8 pages.
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| GrahamN wrote: |
| Sideshow_Bob, thanks for that (fuller explanation of curves similar to what I posted three pages back). Unfortunately we're all quite clearly wasting our time |
It's more to hopefully show the other more open-minded but undecided people still reading (are there any) that there are problems with identical/exactly-overlapping tracks, and that there is actually a tighter arc being skied by the inside ski.
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FAQ
