 Poster: A snowHead
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| veeeight wrote: |
skimottaret, I think it's hard enough trying to bend the shovel of the inside ski to match the ouside ski already, nevermind trying to make it tighter!
I've seen high speed videos of some boot and foot work done here in Whistler, where the racer was wired up to pressure sensors all over his boots, and whilst he's carving razor sharp lines, parallel shins, it also shows on a seperate screen a dominant outside ski loading with almost nothing on his inside ski and boot cuff, and yet the inside ski is tracking parallel with the outside ski in a razor sharp track. |
See the last post I made, following on from a point of skimottaret
Having a more bent inside ski and a greater loading on the outside ski is not inconsistent.
Last edited by Poster: A snowHead on Sat 19-04-08 15:34; edited 1 time in total
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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, I'm with you. The inside ski isn't carving. It's being steered and the tracks are completely misleading.
Take two 10p pieces. I challenge anyone to get them to form "parallel" edges without being concentric.
So the inner track is a smaller radius. QED.
OK, so ski turn radius as I understand it is a function of edge angle and applied weight.
Presuming we are skiing properly with more weight on the outside ski than the inside (and you aren't playing with my patented inverted javelins) it's impossible to have a greater edge angle on the inside than the outside. The body isn't made that way.
Or you have more weight on the inside ski. Woops.
So the inside ski is being steered. End of story.
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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 just have, and when I get chance I'll upload it. Nothing special happens. Your feet are parallel, boots pointing in same direction, roughly a hip's width apart.
What do you think would happen?
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David Murdoch, that's exactly what GrahamN, LaundryMan and I have been saying, that there is a tighter effective radius for the inside ski, which either involves steering, a higher inside ski edge angle or slipping. Veeeight is the one disputing the inside ski has a tighter radius 
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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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David Murdoch, ahh another physicist joins the fray....
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veeeight, I'm with you. The inside ski isn't carving. It's being steered and the tracks are completely misleading.
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Im not sure that is what he is arguing...
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| skimottaret wrote: |
| Quote: |
a dominant outside ski loading with almost nothing on his inside ski and boot cuff, and yet the inside ski is tracking parallel with the outside ski in a razor sharp track.
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putting maths to one side doesnt that make you curious as to how this is happening? |
I do know how this is happenening! as do my assembled pub crowd experts. But it does start with the premis that the inside ski is not trying to prescribe a tighter radius. 
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skimottaret, sideshowbob, ahhh, sorry, oops. OK, so he's wrong in that there is no way that the inside ski is parallel and not 'scribing a smaller radius.
Last edited by Then you can post your own questions or snow reports... on Sat 19-04-08 15:47; edited 1 time in total
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Ok, is there anyone else besides Veeeight who still believes the inside ski is not turning tighter than the outside (and hence tracking a tighter radius curve), whether it's skidding, pivoting, carving or whatever?
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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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| Quote: |
As an instructor, would you encourage people to try and bend the inside ski into a tighter arc?
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veeeight,no, not as a general part of their skiing, but if that was a result of them carving a good set of tracks say coming into a gate late where the inside radius needs to be momentarily tighter that would be a good resultant as opposed to having to scissor.
I agree with you that you can sometimes have two seperate identical radii tracks as though laying one set of duplicate tracks over another. Others dispute this. This is cause our legs operate independtly. However this breaks down as the turns get bigger, try doing a 180 or 360 and it doesnt work anymore, the maths and shape of turn wont let you have the same radii.
If you are continue arguing about having the perfect parallel shins, perfect hips can create parallel curves you are wrong.
If you admit some small adjustments are happening during skiing to ensure the skier can make clean identical nearly parallel tracks we are on a similar wavelength. 
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| Sideshow_Bob wrote: |
| Ok, is there anyone else besides Veeeight who still believes the inside ski is not turning tighter than the outside (and hence tracking a tighter radius curve), whether it's skidding, pivoting, carving or whatever? |
Me. As convincing as all the maths is, I suspect that it's modeling the wrong thing or is missing an important element simply because the output we're getting (pencil thin tracks) indicates that the inside ski is not skidding, and the two inputs required to make it steer a tighter line without skid seem unlikely.
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snowHeads are a friendly bunch.
snowHeads are a friendly bunch.
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David, do you think the inside ski travels further, the same distance or shorter than the outside ski when we carve a 180 from pointing right across a slope to pointing left? What angle have both skis rotated through?
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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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david@mediacopy, wait till you see the next graph.,.. it'll blow your mind
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You know it makes sense.
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Chaps, I'm going skiing (and I'm definitely not going to try and get a tighter radius on my inside ski). You can talk amongst yourselves for a while.
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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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Yes I believe that you can have same radius arcs assuming different centres. But ARCS is the key word, not circles, not full sine waves not 360's that must converge during parallel movements.
Imagine a set of seperate but identical arc segment tht is two metres long and has a radius of 25 metres and is 20 cm apart, more like our experimental skiers model.
as a thought experiment imaging you have some giant cookie cutters, each with a set of arc segments each with slightly different sets of the same radii and you pick one up and stamp a pattern in the snow, stamp the next set at the end of the last set of tracks connecting the end of the last and so on. but you arent joining it up exactly cause you want to change direction a bit so used a cutter with a slightly different set of radii Sideshow_Bob, would argue you have a discontinuity at this point and he would be correct, i would argue that at the "join" if you make a subtle correction in radius, angulation etc. you can correct this small discontinuity and if we take the Reimann sum of these and integrate this set of movements we have a model that allows us to continuously trace a pattern down the hill with near as dammit same instantaneous radii....somewhat approximating what goes on in the real workd when we blend the elements of edge angle, bend etc while making turns with our two separate indepent legs
My education is long forgotten and this is probably new age cod "maths" but as a way to explain things makes sense to me at least.
Last edited by Otherwise you'll just go on seeing the one name: on Sat 19-04-08 16:52; edited 1 time in total
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Poster: A snowHead
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veeeight, I presume you can see that those aren't parallel tracks.
(In fact, they're pretty similar in form to the identical sine waves I posted here.)
There are lead changes too (assuming the geometer samples are simultaneous).
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Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
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Wow, this argument is beginning to go around in circles (concentric ones, of course  )!
I think the problem is that people are approaching from opposite directions.
V8 and skimottaret are making observations, and then trying to cobble together some kind of theory to fit them.
Sideshow Bob and GrahamN have put together a theory (starting from what is obviously very sound mathematical expertise) and are then trying to work out how the "real world" situation fits to that.
And so far there has been one succinct summary from the "other" place:
http://forums.epicski.com/showpost.php?p=897929&postcount=55
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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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Martin Bell, I agree with the epic summary and I'm sure sideshow bob and grahamN would. Will v8?...
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You need to Login to know who's really who.
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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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And on both turns, the radius of the inside ski is roughly 2.75m less, or tighter.
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Martin Bell, look again!
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| Quote: |
and skimottaret are making observations, and then trying to cobble together some kind of theory to fit them
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Martin Bell, with respect rubbish, dont put me in that box. i understand and agree with most of the maths, but as GrahamN and PM have stated the models are not perfect representations. I am trying to understand why the theory doesnt fit the reality of skiing and offer suggestions as to why. i have stated several times it is because we are making small subtle continuous changes. My cod maths "theory's" are just trying to get both parties to "see" the other side.
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| Sideshow_Bob wrote: |
| David, do you think the inside ski travels further, the same distance or shorter than the outside ski when we carve a 180 from pointing right across a slope to pointing left? What angle have both skis rotated through? |
I think that one of the problems is that the i/s & o/s skis are operating independently, and in the theoretical 180 degree carve you mention the i/s and o/s skis are going to be starting and finishing at different points ( i/s tip lead etc.) at least if the arc is one in a sequence of 180 carves. If it's not then a carve as described from a standing start pointing across the hill is going to be fairly tricky.
But to answer your question. If I think that the track is the same, then they must travel the same distance.
Thinking about this walking home from the pub last night (it's a long walk) I wondered if the 'parallel shins' image is a clue. Looking at the second image in the pic I posted earlier:
If the shins are parallel and the ski's are tilted at the same angle, the overlaid lines are never going to meet. Surly this means that each ski is tracking it's own radius. If the ski's have a common center (so that the i/s ski is going to track tighter) surly the lines will cross on such a way that the i/s ski is going to tilted more than the o/s one ?
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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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Sideshow_Bob, shorter distance. Maybe that's why cars have differentials?
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Is there an assumption that the tracks are 'perfect'?
I was wondering if someone were to measure the width of the groove in the snow of the best 'parallel' carved tracks you can make (using the hardest snowpack possible).
Then measure the thickness of a ski. Then measure the play that a ski has in that 'pure' carved turn groove (difficult since a dynamic ski is bent).
Then consider if the amount of play can account for the different turn radii that mathematically parallel curves would need to have.
This may indicate an actively steered inside ski (rather than a passively ridden but more loaded and hence bent ski).
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snowHeads are a friendly bunch.
snowHeads are a friendly bunch.
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| veeeight wrote: |
| Martin Bell, look again! |
V8, my bad  According to that table, the outside ski actually carved a tighter radius in both turns.
But the fundamental debate remains. The lines of crosses which you have put up are simply another way of observing a "real-life railroad turn".
It still doesn't explain how the skier managed to counter-act the fundamental laws of geometry, which state that the inside ski follows a tighter curve. (My money is still on divergence then convergence - based on the fact that there is clearly way more "daylight" between those lines of crosses in the turns than there is in the transitions. Plus the World Cup examples earlier.)
But this gap between theory and reality certainly remains a bit of a mystery.
(And skimottaret, apologies for lumping you in with the "non-mathematicians"!)
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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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What can I see from the data?
1/ Tracks which are not parallel i.e they clearly diverge - converge
2/ Tracks of different radii with the outside ski tracking a very slightly tighter line overall
3/ Quite a bit of changing tip lead
4/ There are discrepancies between the "geometer" sample points and the video analysis
These observations will fit the mathematical models, but not V8s main contradictory assertions i.e perfectly parallel tracks + both skis tracking identical curves + no tip lead
As a very experienced "data engineer" I'd love to hear more detail about how this data was measured. If it's all from video analysis, it's unlikely to be very precise. We use similar video analysis to study trajectories for our own and rival F1 cars for performance comparison. But when we compare the video derived data with our far more sophisticated on-board data, we see that the video analysis is pretty crude.
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You know it makes sense.
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It is worth restating the mathematical facts:
(1) It is not possible for curves on a 2d surface to be both identical and parallel (unless coincident)
(2) If the curves are parallel, the inner curve has a smaller radius.
veeeight's evidence does not contradict these mathematical truisms.
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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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It's perfectly clear from Veeeight's graph that the skis are diverging then converging, hence at the start of the turn the tips are further apart than the tails causing a slight scissoring position and at the end of the turn the tips are coming together, a slight snowplough-style position. This is similar to my analysis of the photos he posted of the world cup racers turning. This diverging and converging is something Veeeight rallied against several times and said was absolutely not necessary. Veeeight, do you agree that that graph shows the skis converging and diverging and the tracks are not parallel?
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Poster: A snowHead
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| david@mediacopy wrote: |
Thinking about this walking home from the pub last night (it's a long walk) I wondered if the 'parallel shins' image is a clue. Looking at the second image in the pic I posted earlier:
If the shins are parallel and the ski's are tilted at the same angle, the overlaid lines are never going to meet. Surly this means that each ski is tracking it's own radius. |
The photo there shows some tip divergence at the start of the turn. If you look at the direction the boots are pointing, you'll find that the inside boot is pointing down the hill more than the outside boot. It's a slight difference and the lines drawn in there make it difficult to pick up, but it's there. At the end of the turn there will be some convergence and a slight reverse snowplough. The tracks will not be parallel. At transition there will most likely be some slight almost unperceivable pivoting to get the skis from coming together to pointing apart again.
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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, do you have the entire paper avaiable? I'd be very interested in seeing how they calculated the 'turn radius' values quoted - are these minimum turn radius, average turn radius, turn radius outside the transition etc?
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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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| Sideshow_Bob wrote: |
| are these minimum turn radius, average turn radius, turn radius outside the transition etc? |
I was wondering that too, I assumed a simple average but it's not clear from the data provided. They are most definitely not constant radius.
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You need to Login to know who's really who.
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| Quote: |
They are most definitely not constant radius.
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this is a key point as i am still of the opinion that a skilled skier can make virutally identical tracks through small continuous changes with each independent ski and in order to this some momentary change in turn radius is required or we must have divergence as the maths say.
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(1) It is not possible for curves on a 2d surface to be both identical and parallel (unless coincident)
(2) If the curves are parallel, the inner curve has a smaller radius.
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absolutely true, but when we look at typical values of turn radius, ski bending, etc the "blur" is almost imperceptible as was proved by example. Unless you argue, wrongly as V8 is, that a skier has perfect alignment both one and two can IMO happily coexist during a typical, dynamic, ever changing turn.
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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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When you guys mention "divergence" , "convergence" and "parallel" do you mean the resulting tracks or the relative position of the ski's to each other ?
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GrahamN, would it be possible for you to do some more illustrative maths? Your calculations showing inner edge angle changes of 1 -2 degrees to allow for even tracking was most illuminating. In a similar vein could you work out the following to shed some more light on the practicality's. david@mediacopy, makes a good point about shin positions as in the real world the outer shin is typically angled more often than the inner.
Lets assume your same 25 metre turn radius example, but assuming both ski edges are at identical angles. What difference in radius would be required for inner and outer to track without divergence/convergence on a 2D plane?
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| Quote: |
but not V8s main contradictory assertions i.e perfectly parallel tracks + both skis tracking identical curves + no tip lead
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Lets not get carried away here with what you think I said.
This all started because person A said that scissoring and diverging are part of carving/skiing, and that the inside ski needed to carve a tighter radius.
Scissoring and Diverging are NOT part of carving/skiing, and the inside ski does NOT need to carve a tighter radius.
Did I ever say NO tip lead?
As for identical curves and/or parallel curves - well - we could go down that road further if you wish to continue, but now that we've established that you don't actually have to bend the inner ski into a tighter radius, we can move the discussion on usefully.
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| david@mediacopy wrote: |
| When you guys mention "divergence" , "convergence" and "parallel" do you mean the resulting tracks or the relative position of the ski's to each other ? |
Good point well brought up. Could be the source of some confusion between us. I look at skis, always skis, when I analyse skiers.
When I talk about scissoring, it's about the relative position of the skis to each other
When I talk about divergence, it's about the angle of each ski to the other. So zero divergence to me means that both skis are pointing the same direction.
David, As I rode up the chair yesterday morning on a bluebird hardpack day (we had a lovely artic front visit us) - I was able to see from overhead many many fantastic skiers and tracks left by good skiers (we have some of those here  ) - and quite observable, were two distinct sorts of tracks of interest to us:
1. Identical tracks, as shown by the mathematicians, where the distance between the tracks at the apex was slightly wider than the transition
2. Tracks where the distance at the apex and transisition were the same (clearly impossible as stated by maths/physics/engineering), and yet clean carved lines in the arcs.
As I got off the chair, trying to reconcile (2) - a thought did strike me that it might be possible to accept (2) - if you considered the turn in 3 distinct parts. After all, in the transisition, the skis are flat, and not really tracking (and in the data above, we have a long transition where the racer is lining up for the next gate).
On the second chair up, I actually watched a few racers and it started to fall into place. Some of the racers were utilising a well known tactic to give them a tactical advantage, and this could well give the clue as to why some of the tracks were narrower in the transition.
But I think, it would only be fair to consider the transition part of the turn as NOT edge locked (flat ski) - so maybe that opens some doors for some open minded people?
Last edited by After all it is free  on Sun 20-04-08 14:51; edited 2 times in total
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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 wrote: |
Laid down some tracks. Repeated. Walked up and inspected them.
Observations:
1. No skidding. Ultra thin pencil lines.
2. No inside ski divergence at the start of the turn (can't pivot)
3. Simultaneous edging movements on both skis. Same edge angles at the same time.
4. Was expecting track width to be wider at the apex than at transition (skiers holding a constant stance width) but couldn't measure any perceptible difference. Might be reasonable to expect this to change with even higher performance.
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Your very own observations (if actually correct) imply a tighter radius on the inside track. That's what the maths guys are telling you and it has nothing to do with ski technique, just analysis of your tracks as stated above. So anyway, please explain how all the above is possible without the inside ski tracking a tighter radius.
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| uktrailmonster wrote: |
| Your very own observations (if actually correct) imply a tighter radius on the inside track. That's what the maths guys are telling you and it has nothing to do with ski technique, just analysis of your tracks as stated above. So anyway, please explain how all the above is possible without the inside ski tracking a tighter radius. |
It implies nothing of the sort! I am perfectly comfortable as to how both skis can prescribe the same radius! I've never been in any doubt about that!
Look. If no one here (apart from David and maybe skimott, both of whom most probably have laid down clean carves) is prepared to accept that the inside ski does not track a tighter radius, then quite frankly, further progress of this discussion is pointless!
Last edited by Ski the Net with snowHeads on Sun 20-04-08 14:54; edited 1 time in total
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