Side cut shape: is it catenary,circle, parabola, elipse ...?

[jonnyhifi]

OK: a topic that has been touched on before I know; but I can't as yet find a decent geometric argument:

To keep things simple: I am firstly wanting to consider how a ski performs on piste. (Clearly in deep poweder different factors come to dominate), which is 99% of my skiing.

I understand the effect of inclination of the ski, on decreasing the turn radius. Also I understand why a ski standardly starts with positive camber (so the tips and tails will essentially always be touching the slope, and the ski pressed into reverse camber when the ski is weighted).

So the million dollar question: what shape should the side cut be; if you want the arc that the ski makes in the snow to be circular, i.e. so you can set up perfect carved arcs ?

I'm not convinced by the blithe way that people talk about planes cutting cones and hence giving you conic sections; i.e. parabolas, maybe elipses etc..., as yes we have a plane (i.e. the piste) cutting --or intersecting-- an inclined something: but once the ski is in reverse camber, why should the shape of the edge of a ski be as if part of a cylinder, and indeed if it was, that would generate a conic section, not the other way round...?

Is it the case that actually the ski would always need to have had a different shape in design depending on the angle on inclination , and therefor any design shape is a compromise short of having a dynamically changeable side cut radius ski?

I should be able to think this through (I'll admit to having a maths degree.. a long time ago but heh I never was any good at geometry) but I am being lazy; anyway it's a physics/ engineering problem isn't it ?

I feel this should have something to do with differential geometry, gauusian curves etc....

Any geometrists out there ?

I know everyone always assumes curves must be conic sections, but there are many smooth curves that kind of look like that but aren't e.g. cateneries... etc...

so some technical terms to perhaps get the physics juices flowing (or indeed perhaps for search engines to find !)

conic sections, geodesics, Klothoids, parabolas, elipses, segments of circles, strakes, gaussian curvature, glissette roulette, hypocycloid, catacaustic, cardiod, etc etc.... when you start looking there are so many smart smooth curves that have ben defined, and examined, which should I make my skis follow?

I'm sure that the conventional pressure/ flex observation effecting the geometry makes life more awkward still; as the ski of course won't bend uniformly, but I think there must be an argument for the pressure distribution changing dynamically so the ski bends into whatever geometry guarantees touching the surfcae all along its length. If this is so, then getting the geometry right at design will even out the actual pressure "anomolies" along the edge of the ski in use. Also, this may explain why the geometries mentioned in the tech article, turn out to not acually be too important: it all goes bananary and sorts itself out however it was made: only the gross side cut really effects things. Similarly the reson why flex profiles seem so variable and there is no consensus: apart from gross stiffness issues as long as the ski can bend smoothly; and as a skier you will be able to bend it in use, the rest just doesn't matter: hence there is no real consensus between mass manufacturers on shape, or flex distribution: only on "stiff/soft" and "short radius/ long radius" geometry.

Any views guys and girls ?

Jonathan

[brianmwaters]

There are at least two papers online (that I haven't read yet) that talk about ski geometry, and they have an equation that gives you the turning radius based on edging angle and sidecut geometry. I'd imagine you could gain some insight by reading them.

The Effects of Sidecut Radius on the Dynamics of Alpine Skiing:
http://www.mta.ca/faculty/science/physi ... Skiing.pdf

The Ideal-Carving Equation and its Applications:
http://www.citebase.org/abstract?id=oai ... cs/0310086

Like I said, I haven't read them completely, but I get the feeling the second paper is a bit better.

- BW

[brianmwaters]

btw, couldn't you just do some fancy linear algebra and model it as a projection taking points in the plane of the ski to points in the plane of the ground, along a vector normal to the plane of the ski??

[bigKam]

The first paper points to the Lind and Sanders book, which is an interesting read from a technical point of view. It may help you get started. It'll be interesting to see how the rigorous analysis pans out. Keep us posted.

[yan0]

I've been turning many of these questions over recently and come up with nothing. I recently bought the Lind and Sanders book and jumped to the section about equipment. It does get into some detail, but it's not targeted at people designing skis, it's targeted at people who want to "sort of understand" what's going on. I like how they get into loading, I really dislike how they don't take mounting point, core thickness, or core width into account. I just downloaded the two pdf's on this feed - I haven't looked at them yet, but I will.

ANYwho- I'm operating on a few assumptions here, which may very well turn out to be wrong. For starters, I'm assuming that sidecut should be circular - afterall we want the ski to bend in a perfect arc, anything else will dump energy into pushing snow around and in turn lessen grip. If we do in fact want sidecut to be circular and we want the waist of the ski to fall under the center of the boot, we want the "slope" of the sidecut under the boot to be 0. In this configuration, the location of the waist of the ski along it's running length depends on the ratio of the tip width to the tail width. Experience tells us that we want a tail that's narrower than a tip, which shifts the waist of the ski towards the tail, which we see in every pair of skis on the mountain (... ... pretty much....). However, the ratio of tip to tail dimensions varies a great deal from ski to ski - does the waist location vary accordingly? What is more important to preserve, ratio of running length in front and in back of the waist or a circular sidecut radius? I'm sure the answer to this varies somewhat on what kind of a ski one is designing - a race ski designed to be used on firm snow/ice would put an emphasis on a circular sidecut whereas the design of a powder ski would focus more on a balanced feel.

I suppose the most frusturating thing is that there is no "right" answer - we can develop formulas that give us the "idealized" sidecut dimensions, but they are only "ideal" given various assumptions, whatever they may be. At most, they're a jumping off point. But it's nice to have one of those....
j

[endre]

I have been analysing ski shapes for a while, and as part of the analysis I read off the sidecut radius at several parts of the ski with this instrument:

It is an arcmeter made to measure radius in mm, it is very accurate (to about +/-10mm of a 20mR) and gives me the sidecut radius for each side and each part of the ski (over a 500 mm segment.)

The results were surprising. Most skis have a deviation of about +/-1-4mR from the right to the left side, in average the radius is pretty accurate, but it seems that all have a major problem with warping of the base material before layup. the two skis of a pair usually bends the same way.

When mass produced skis are as unprecise as this, I find it hard to believe that there is a noticable difference between radial, parabolic and elliptic sidecuts (which is microscopic).

[Dutchjibber]

That makes me wonder what the difference is for Worldcup race skis... Any chance you can get hold of a pair of those to use your fancy gear on?

Maybe it is a good idea to have a good look at WC race skis in general as they should be completely optimized for ferfect carving arcs...

[telexis]

The results were surprising. Most skis have a deviation of about +/-1-4mR from the right to the left side, in average the radius is pretty accurate, but it seems that all have a major problem with warping of the base material before layup. the two skis of a pair usually bends the same way.

It is funny because I just finished my first ski and I seen the same thing happening... On the picture below, my base is align with the rear of the ski but doesn't align with the front.



I am not so sure why... I cut the template on a LaserCamm and then use a router to cut the base. Up to that point the base was ok (I think)... then I remove the base from the template and glued the edges... then the base is wrapped! Anybody has an idea how that happens?

Hopefully I will be able to make better ski than big company! :-)

Alexis

[ben_mtl]

I noticed the same thing on my skis, it's not so bad but still it's a little different.
I think the problems comes from when I bonded the edges to the bases, I guess as the edge is not exactly the perfect shape before I bond it, I have to bend it when applying my spots of "super glue". That might explain the kind of "distortion" (+ maybe the base which wrap a bit even if I cut it just prior to bonding edges...)

I'm thinking of a system on the bottom mold which would set the edges to the correct position (a slight grove where base-edges are sitting while pressing)

Telexis -> do you have pics of your skis ?

[MontuckyMadman]

The big boys have simple molds to prevent this. The one shop I saw put a few drops of superglue on the base when they aligned it in the mold. Even after they glued the edges on with an exact template it still warped a-symmetrically. You have to clamp the base material down constantly until you are ready to press. I saw the base material warp before my eyes in seconds after I cut it on a CAD vacuum table by machine. Its plastic, ya know?

[SHIF]

... then I remove the base from the template and glued the edges... then the base is wrapped! ...Alexis

This thread is way off topic, so I'll add my two cents.
We all make asymmetrical skis our first few builds. The sintered base material is funny stuff and it takes special care to achieve success. This topic has been covered many times. Here is a good thread to consider:

http://www.skibuilders.com/phpBB2/viewt ... light=shif

Back to the original topic, I remember Volkl designs their skis for a circular sidecut to occur on a fully weighted ski edge. This arc is on a plane. The ski is flexed into it's dynamic shape, i.e. on edge and turning, and it’s edge exactly follows this theoretical arc. This was their marketing angle a few years ago, called “3-D Sidecut Technology”.

Others use variable radius sidecut shapes, probably to mimic the Volkl 3-D concept of considering the flexed ski. I bet, however, that a simple circular arc shape is more than adequate for our home-made skis. Plus it’s easy to make and looks very clean and accurate when sighting down the length of a ski, admiring the perfection.

Cheers,

-S