 Poster: A snowHead
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| veeeight wrote: |
| 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. |
If we're talking about pencil thin tracks with no skidding, the skis will be in perfect alignment with the tracks. Only the amount of tip lead will make any difference to the skis relative position compared to that of the tracks.
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Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
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| veeeight wrote: |
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! |
Well you can't have perfect parallel RR tracks AND your inside ski tracking the same radius as the outer. You can have either perfect RR tracks, in which case you need to get your head around the geometry and explain how the inside ski can track the required tighter line, or you can accept that the tracks diverge and converge to meet your criteria that the inside ski does not track a tighter radius. So which is it to be? I'm happy to discuss either scenario, because I think they can both be done in theory.
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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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skimottaret, just to keep the maths a bit simpler, I'll illustrate a particular example: where the skier has built up some speed and executes a turn on level ground, by getting his skis on edge at an angle (A) to the surface. The key force is the reaction (R) acting perpendicular (as it must) through the plane of the ski. Balancing forces vertically, the vertical component of R (given by R.cos(A)) must equal the skier's weight (mass (m) times acceleration due to gravity (g))
R.cos(A) = m.g ... Equation (1)
The force required to keep a body moving in a circle is given by F = (m.v**2)/r where v is the velocity and r the radius and ** is used as the the symbol for 'raise to the power' (i.e. square, in this case). This force is provided by the horizontal component of the reaction (R.sin(A))
R.sin(A) = (m.v**2)/r ... Equation (2)
Dividing Equation (2) by Equation (1), we get some convenient cancellations, thus:
sin(A)/cos(A) = (v**2)/r.g
The sine of an angle divided by the cosine of an angle is its tangent, so this simplifies to:
tan(A) = (v**2)/r.g ... Equation (3)
So, if we take a velocity of 10 m/s and approximate g to 10 m/s**2, tan A for a 25m turn is 10/25 = 0.4: which gives A of 21.8 deg approximately.
Assuming that 25m is for the outside ski, what of the inside ski? If they travel at the same linear speed (which implies the inner ski leading), since r is smaller, then tan(A) and hence A is greater. If the radius is 40cm smaller then A becomes 22.1 approximately.
What if there is no lead/lag? The outside ski is travelling at a faster linear speed than the inside ski to keep up. It's slightly easier to consider this case angular velocity w (measured in radians/second) - which, in this case, will be equal for both skis - than linear velocity. They are linked by w = v/r. Substituting this into Equation (3), we get:
tan(A) = (r.w**2)/g
Since r will be smaller for the inside ski, then tan(A) and hence (A) will also be smaller. (I must admit to finding that counter-intuitive; maybe grahamN or sideshow bob will spot a flaw in the logic.) Anyway, according to that, A will be 21.5 deg approximately.
Last edited by Well, the person's real but it's just a made up name, see? on Sun 20-04-08 15:01; edited 1 time in total
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veeeight, i concurr in that i dont believe that the inside ski MUST have to have a tighter radius. I think they can be identical, but crucially I think you can do this because something else is allowing it (different edges angles, ski bent at shovel etc). Where we differ is your assertion that you can do this with identical edge angles and no tip lead lag. YOu have softened your stance in that tip lead lag is allowable and i am waiting for Grahams calcs (if he fancies doing them) to see if that alone can eliminate or reduce to near nothing convergence...
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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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You'll need to Register first of course.
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veeeight, can you comment on the fact that those graphed measurements you came up with show divergence/convergence (as well as lead/lag)?
Last edited by You'll need to Register first of course. on Sun 20-04-08 16:09; edited 2 times in total
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Veeeight, that's one of the diagrams I drew earlier. Start the feet level pointing straight down the fall line, no tip lead either foot, instant rocking, same weight/ski distortion/edge angle/ski turn radius and the skis will cross at the 90 degree point. Take that diagram, the curves are identical and can overlap exactly. What's wrong with it? Please enlighten me?
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laundryman, Yes I can!
Last edited by After all it is free  on Sun 20-04-08 15:44; 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.
You'll get to see more forums and be part of the best ski club on the net.
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Sideshow_Bob, Nothing is wrong with it!
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veeeight,
| Quote: |
| Two soft skis, side by side , on a green slope, loaded with the same weight, and tipped to the same angle by a mechanical device, will produce identical radii. |
Said radii, if scribed, will not be parallel.
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snowHeads are a friendly bunch.
snowHeads are a friendly bunch.
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| PJSki wrote: |
veeeight,
| Quote: |
| Two soft skis, side by side , on a green slope, loaded with the same weight, and tipped to the same angle by a mechanical device, will produce identical radii. |
Said radii, if scribed, will not be parallel. |
PJSki, In that exact scenario above, I agree. However that's not how we ski...............
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And love to help out and answer questions and of course, read each other's snow reports.
And love to help out and answer questions and of course, read each other's snow reports.
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veeeight, so you still say that your skis scribe the same radii and that the tracks remain truly parallel? Or are you saying that the inner ski is rotating rather than scribing an arc?
Last edited by And love to help out and answer questions and of course, read each other's snow reports. on Sun 20-04-08 16:03; edited 1 time in total
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| veeeight wrote: |
| 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! |
Hey, I was probably laying down clean carves, live on TV around the world, when you were in nappies! And I am sure all the other contributors in this debate can lay down picture-perfect railroad tracks in their sleep.
I repeat, ad nauseam, this discussion has nothing to do with what can be observed and performed in a real life situation. It is about the fundamental laws of geometry (which cannot be changed by anyone, no matter how many friends in a bar agree with him) and how skiers somehow circumvent them.
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 Sun 20-04-08 16:04; edited 1 time in total
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You know it makes sense.
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| veeeight wrote: |
| Scissoring and Diverging are NOT part of carving/skiing, |
How can you say that, when the graph which you yourself put up, clearly shows the skis getting wider (diverging) into the turns and getting narrower (converging) out of the turns????? (None are as blind as those who will not see... - but this is "doublethink" worthy of 1984.)
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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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Martin Bell,
| Quote: |
| Hey, I was probably laying down clean carves, live on TV around the world, when you were in nappies! |
I bet his poop didn't smell though. 
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Poster: A snowHead
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A question for the mathematicians: are veeeight's responses converging with your statements and questions at any point, or do they remain - as seems apparent to this non-mathematician - mostly parallel* to them?
*I use this word loosely.
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Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
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| I wrote: |
| veeeight, can you comment on the fact that those graphed measurements you came up with show divergence/convergence (as well as lead/lag)? |
That's great economy of expression. Three one-syllable words to show that you're rude, arrogant, conceited and wrong.
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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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You need to Login to know who's really who.
You need to Login to know who's really who.
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Hurtle, the basic, governing rules of geometry are not to be denied.
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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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Hurtle, the thing is (someone else pointed it out earlier), it is v8 - not the mathematicians - who is making a definite, singular statement: that two curved lines can be both identical in form and parallel (I paraphrase him slightly). The mathematicians are stating (with reference to an accepted proof) that that cannot be; but that you can get pretty damned close in an infinite number of ways. If he could just accept that, everything would be hunky-dory; but instead he attempts to lead us down blind alleys.
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You'll need to Register first of course.
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PJSki, laundryman, yep, even I've managed to hoist those propositions on board! I was trying to make a very feeble joke. Sorry. 
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laundryman, I noticed, but cannot blame you at all.
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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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| Martin Bell wrote: |
| veeeight wrote: |
| Scissoring and Diverging are NOT part of carving/skiing, |
How can you say that, when the graph which you yourself put up, clearly shows the skis getting wider (diverging) into the turns and getting narrower (converging) out of the turns????? (None are as blind as those who will not see... - but this is "doublethink" worthy of 1984.) |
Ah! crossing of wires here. My references to diverging are about the skis, not the tracks.
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| Quote: |
| Ah! crossing of wires here. My references to diverging are about the skis, not the tracks. |
Nice try, but it won't wash. 
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snowHeads are a friendly bunch.
snowHeads are a friendly bunch.
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And love to help out and answer questions and of course, read each other's snow reports.
And love to help out and answer questions and of course, read each other's snow reports.
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veeeight, well, as you know, I'd be the last to suggest that the theory is more important than the practice, so have a good ski. Whilst I shall be sorry to miss out on your 'path to enlightenment', my money is on the mathematicians and the engineers for the theory, and on the skiers referred to by Martin Bell in his post of 16.20 for the practice.
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Hurtle, your money was also onthe mathematicians and engineers that the inside ski tracks an tighter radius, when true life real skiing measurements showed that the opposite was true....
(or did I imagine that?)
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You know it makes sense.
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Martin Bell, you know better than to justify with photos such as those............ intent or outcome?
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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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| PJSki wrote: |
| Quote: |
| Ah! crossing of wires here. My references to diverging are about the skis, not the tracks. |
Nice try, but it won't wash. |
I think you'll find that from page 1 of this discussion my references to scissoring/diverging are about the skis.
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Poster: A snowHead
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veeeight, except that the inside ski does (Must) track a tighter radius. End of that story. And it isn't carving a tighter one either. End of that story too.
I also posit that my inner ski, typically is scribing a tighter radius because I am steering it with almost no weight on it.
Take two dimes. The only time that their circumferences are parallel is when they're concentric.
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Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
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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, for every photo you produce with scissoring, I will be able to match with parallel skis, you know that! You're breaking your own guidelines about using WC photomontages to prove a point! You also know that it's not a 'mistake', when going balls to the wall, are racers really concerned with producing tidy clean lines.....?
Last edited by Well, the person's real but it's just a made up name, see? on Sun 20-04-08 17:32; edited 1 time in total
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You need to Login to know who's really who.
You need to Login to know who's really who.
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| PJSki wrote: |
Martin Bell,
| Quote: |
| Hey, I was probably laying down clean carves, live on TV around the world, when you were in nappies! |
I bet his poop didn't smell though. |
Well, I don't want this to turn into a V8-bashing session.
Let me go on record as saying V8 is obviously an excellent skier and instructor, who has contributed much to this forum and has doubtless been of great help to many skiers in Whistler.
He has always demonstrated an extensive knowledge of ski technique. In this case, I just think he is not quite getting his head around the geometric/mathematical paradox of this debate, which is purely theoretical.
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Anyway, snowHeads is much more fun if you do.
Anyway, snowHeads is much more fun if you do.
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veeeight,
| Quote: |
did I imagine that?
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You did. It appeared to me that the mathematicians and engineers convincingly demonstrated an already proven theory. Meanwhile your 'true life real skiing measurements' have nowhere shown that the opposite is true. However, even your opponents agree that the difference can - as shown, inter alia, by GrahamN at 1848 on p9 of this thread - be almost infinitesimally small. Thus (to repeat) what you actually see in your ideal tracks is illusory, although your perception is capable of approximating very closely to the geometric reality.
Whether it is adviseable to adopt the skiing techniques of Bode Miller is, of course, a wholly different topic!
Forgive me for intruding on a technical argument. I have no technical knowledge of either the theory or the practice, but I plead the fact that it is customary for lawyers to weigh up the arguments of specialists in this way. Thank you for indulging me.
Last edited by Anyway, snowHeads is much more fun if you do. on Sun 20-04-08 17:34; edited 1 time in total
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You'll need to Register first of course.
You'll need to Register first of course.
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| veeeight wrote: |
| Martin Bell, for every photo you produce with scissoring, I will be able to match with parallel skis, you know that! You also know that it's not a 'mistake', when going balls to the wall, are racers really concerned with producing tidy clean lines.....? |
But you yourself produced a graph with clearly observable scissoring - which you have not yet explained.
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| Hurtle wrote: |
| Meanwhile your 'true life real skiing measurements' have nowhere shown that the opposite is true. |
No, go and read the results carefully again. They show that the outside ski tracks a smaller radius than the inside ski.
Last edited by Then you can post your own questions or snow reports... on Sun 20-04-08 17:36; edited 1 time in total
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| Martin Bell wrote: |
| veeeight wrote: |
| Martin Bell, for every photo you produce with scissoring, I will be able to match with parallel skis, you know that! You also know that it's not a 'mistake', when going balls to the wall, are racers really concerned with producing tidy clean lines.....? |
But you yourself produced a graph with clearly observable scissoring - which you have not yet explained. |
Scissoring...... as defined on page 1 - refers to the angles of each ski to the other, I have never referred to scissoring as varying track widths. I have also likened scissoring = diverging skis many many times in this thread, never about the track width.
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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, All I've seen is you getting confused, and wobbling from one set of assertions to another. You are just wrong on so many different levels it's hard to know where to begin, though some have tried.
Just taking one of your statements at random:
| Quote: |
| the overwhelming concensus was inside and outside track had the same radius, different centres (your hip sockets). Don't forget that the two centres (your hip sockets) are moving with the arc, as opposed to a fixed point on the snow. |
A centre of rotation can only be at the centre of rotation by definition. In the case of two perfectly carved skis, the centres will be at two fixed points in the snow. And not the hip sockets as you incorrectly state. The hip sockets are actually scribing their own concentric arc to that of the ski they are linked to.
Last edited by You'll get to see more forums and be part of the best ski club on the net. on Sun 20-04-08 17:47; edited 1 time in total
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| Martin Bell wrote: |
Well, I don't want this to turn into a V8-bashing session.
Let me go on record as saying V8 is obviously an excellent skier and instructor, who has contributed much to this forum and has doubtless been of great help to many skiers in Whistler. |
Awwwww, shucks And I've never thought of you as a dinosaur neither, Martin! I have lots to learn about having cohones of steel at warp speeds!
And just so it doesn't appear that I'm backing out of this interesting saga, over the next few days I have to coach some racers and examine some wannabe instructors (should I pass the mathematicians I wonder). So my presence here will be sadly missed by some, I'm sure.
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FAQ
Some people have a nasty habit of putting words in my mouth 
).
