Parallel skiing revisited again, but this time by the master.

Ski Coaching
I have just received an email from John Shedden in response to our discussion on parallel skiing and whether or not it is possible. John has had a bit of a problem getting this post to load, so I have simply attached his commens in full to this post.
If YOU are having any similar difficulty please just email me at bobski@bobski.com
From John,
Could that be m(wsquared)     divided by r ?

We talk about circles for ease of conversation but What if the arcs are not circular but some other conic section?  Or even perhaps made up of several different sections of conic sections.
The arcs do have different "centres" if the legs are working independently of each other as each arc relates to each leg..or?

Perhaps  so called parallel skiing is vastly overrated as the only thing the skier has (more or less) complete control over is the INITIATION of the change of direction.  This is the focus of most peoples attention when learning and the rest of the 'turn' is subject to a variety of forces to which the skier will respond.  

Parallel 'starting' might be better named as simultaneous 'edge change' - (or as I might call it, simultaneous tilting. Bob ) - the initiation phase --followed by the reactive / steering phase - until the next initiation phase.

I can't speak for anyone else but when I steer my skis, even when I'm carving, I travel along curving 'pathways' which often change shape during a single 'arc' - if that isn't a contradiction in terms.

I supose what I'm saying is that we TALK about, "arcs" and "radii" etc because it makes conversation possible but theose words are just shorthand for more complex things going on . . we shouldn't believe everything we say!!


Very best regards,
John
This entry was posted by Bob Valentine Trueman on Monday, June 23. 2008 at 01:50. and is filed under Ski Coaching. You can leave a response, or trackback from your own blog. All new comments are subject to moderation before being displayed.

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  1. David says:
    #1 2008-06-23 06:20 (Reply)

    John's comment regarding "The arcs do have different "centres" if the legs are working independently of each other as each arc relates to each leg..or?" is interesting.

    I've recently been in 'discussion' as to whether 2 cleanly 'carved' ski tracks are the same or different radii.

    John's comment might hint that the radii are the same for both arcs.

  2. Bob says:
    #1.1 2008-06-26 02:59 (Reply)

    If the two arcs are segments of circles, I still don't see how they can do other than cross at some point, (and therefore cannot be parallel) UNLESS, the arc radii have the same centre (origination) point. Can you explain?

  3. David says:
    #1.1.1 2008-06-26 07:42 (Reply)

    >>Can you explain?

    Not me. I think we need to find someone in a ski manufacturers R&D department !

    But I'm curious as to the process that allows the inner ski to describe a 'clean' track if it's also describing a smaller radius arc than the outer ski, as the math suggest.

  4. Traci Elliott says:
    #1.1.2 2008-07-04 02:42 (Reply)

    ...you guys think too much and should get out and ski. :-) having said that - let's visit Bob's comment about two circles with a similar radii - do their arcs cross or not?

    play about with a geometry set -and watch where the circles cross - make the top of the page the top of the hill and the btm of the page the bottom of the hill - I suspect your arcs will cross but we are well into the next turn by then so it's irrelevent.

    video each other - and then when you are watching the footage - pause and draw on the TV screen where the center of mass is and then draw the arc of the ski - try to predict where the arc(s) will go - then play the video frame by frame and see if you are correct - pay special attention to the relationship between the center of mass and the arc of the ski -stationary?...or moving?....consistent radius? .....same "radius" for each foot?....take your time here and really absorb what is going on -

    Also - how are you describing "the actual radius" when talking about one ski vs another - surely you can't physically ski with the center of mass remaining static ( ie center of mass stuck to the page like the pointy end of the compass in a geometry set) - you'd be defying gravity think about this - we use these terms loosely to introduce and develop concepts - we are not trying to be mathematically accurate - we are trying to slide on snow.

    I like your aproach so far as it seems to be student centered in it's grassroots stages - but I think you have perhaps had a few bad ski lessons from bad instructors if you are so intent on trashing their efforts. If you attend a reputable ski school you'll find that, just like in any business - the good ones are out there if you look - and a "bad one" shouldn't ruin the reputation of the industry - he/she is likely just a crappy instructor.

    The physics of skiing need to be taken in context - skiing is an open sport - a physical sport and a psychological sport - "conceptually" - you can make a link but "actually" there are many uncontrollable variables that will frustrate the physics major as we are applying principles here not working in a controlled lab setting....
    ...still it's fun to explore these concepts if you are interested.....

    note that kids learn without this knowledge - relying instead on plenty of action and kinesthetic feedback.....

    good discusson gentlemen - just make sure you get out and ski as well - video each other and use the slow motion button on replay - draw on the TV screen ( with scrubbble markers) to help you explore your physics concepts.....
    ski you later!
    Traci :-)

  5. Bob Valentine Trueman says:
    #1.1.2.1 2008-07-04 04:29 (Reply)

    Hello Traci,

    Thank you for joining in. You say that you suspect my circular arcs will cross, but that this is irrelevant because a new arc will by then have begun.

    Well, they do cross, inevitably. Whether or not there would be then have been a direction change would depend on the kind of skiing being done at the time. However, the significance of the fact that they would cross, is that this fact establishes that the arcs are at not time parallel: which is the essence of this light-hearted discussion.

    CENTRE OF MASS

    Traci is correct in her assertions regarding the dynamic or kinaesthetic nature of the locus of the centre of mass. However, again, the discussion is about the relationship of each ski to the other. Whilst the centre of mass (actually a conceptual centre only, being an aggregate of many other centres) is frequently of interest, in this particular instance, in order to develop concepts around parallelism I feel it has no direct relevance to the discussion, though of course it is of very considerable relevance to skiing and how she is performed!

    MATHEMATICAL ACCURACY

    Traci asserts that we are not trying to be mathematically accurate. When we are skiing, that is true of course, but just at present, while mentally conceptualising the physical, that is actually precisely what we are attempting to work towards. And very interesting it is.

    SKIING
    I thank Traci for her admonition to do a bit of skiing - I must try it.

    Thank you for joining in Traci, you sound like a good and dedicated instructor - just the kind the sport needs, and has a shortage of. Perhaps we'll meet one day and you can show me how it's done.

    Bob Valentine Trueman.

  6. Tony York says:
    #2 2008-06-25 07:56 (Reply)

    Had a look at your blog again, & saw John Shedden's contribution. It makes a lot of sense to say it is all very complicated, & probably changes quite a lot during a single arc. However, there is one thing he is confused about, and that is the use of angular velocity. For a mass m moving in a circle radius r at speed v, the centripetal force is m x(v squared)/r. This is presumably what John was thinking of when he queried the formula. When using angular (not linear) velocity, w, the centripetal force is m x(w squared)x r, as in my original contribution.

    Tony York


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