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# Edging/Platform Mechanics

EDGING PLATFORM MECHANICS
I like to think of edging/platform mechanics in terms of the forces that are acting to cause the ski to rotate into the hill (positive edging forces) or away from the hill (negative edging forces). Some of these forces will be active forces while others will be resistive or reactive forces. In edge mechanics on hard pack snow and ice I consider the ski portion of the uphill edge under foot (the waist of the ski) as neutral since it is the proximate pivot point for rotation of the ski about its long axis. Depending on the perspective you choose you could look down the ski and see forces that tend to rotate it clockwise vs. forces that tend to rotate the ski counter clockwise.

It doesn’t really matter what terms one chooses to use to describe the forces so long as they end up being arranged so we know which ones are positive edging forces and which ones are negative edging forces.

We know that the forces acting on a skier are trying to pull them down in line with the slope and down towards the center of the earth. There are other forces as well. But we are really interested in the result of all the forces that pull the skier towards the snow. This force is not surprisingly called ‘the resultant force’.

In order to know what result the resultant force is going to produce in terms of edging/platform mechanics we need to know what other forces are acting on the ski. For the sake of simplicity let’s say that the force acting on the uphill edge underfoot is ‘neutral’ since this is the pivot point of the teeter-tooter.

On the uphill side of the pivot point the force from the edge of the sidecut of the ski will resist rotation of the sidecut edge into the hill by pushing back. So it is a negative force.

On the downhill side of the pivot some snow will resist rotation of the ski away from the hill depending on how soft the snow is. So this is a positive force. Since it is usually small compared to other forces we will ignore it.

The foot applies a force to the ski as a result of the external forces acting on the skier. Whether it is a negative or positive force depends on what side of the pivot point it is on. So the force applied by the weight of the skier on the ski can either be a positive or negative force.

A force applied under the ball of the foot could be a positive force or a negative force depending on foot position in the boot in relation to the ski and ski geometry. But a force applied under the heel will always be a negative force because it acts on the proximate center of the ski.

[ = limit of uphill sidecut, ] = the limit of downhill sidecut, (T = pivot point - uphill waist edge, ) = downhill waist edge, F = center of force applied by foot, S = center of force applied by snow

The examples below all relate to the outside ski of a turn. The software for posts prevents me from using spaces to show a scale so you will have to use your imagination until I can import some drawings.

Let’s assume the mechanics necessary to establish and maintain a platform exist. Here is what the forces would look like on the ski.

Example 1
[S- F+ (T ) ]Downhill >

If F is greater than S then the ski will rotate into the hill until F = S. If either force changes, then the other force must also change to maintain balance. Otherwise the unbalanced forces will cause the ski to rotate.

Now let’s assume force F is acting under the heel.

Example 2

[S- (T F- ) ]Downhill >

Now S and F are both negative so the ski will rotate away from the hill.

What if we increased the width of the waist of the ski as shown below.

Example 3

[S- (T F- ) ]Downhill >

Now F is on the downhill side of the pivot. So it is a negative force. The ski will rotate away from the hill.

At this point some will protest that I have overlooked the edging force that can be applied by the cuff of the boot. Actually I haven’t. I will address this in my next post.
I figured out a way to trick the software. The following examples relate the initial post and show somw scale in terms of ski geometry.

Example 1

[S-***F+*(T===============)********]

Example 2

[S-******(T=======F-=======)********]

Example 3

[S-******(T=====F-========================)********]
David M:
Quote:
 On the uphill side of the pivot point the force from the edge of the sidecut of the ski will resist rotation of the sidecut edge into the hill by pushing back. So it is a negative force. On the downhill side of the pivot some snow will resist rotation of the ski away from the hill depending on how soft the snow is. So this is a positive force. Since it is usually small compared to other forces we will ignore it.
This time you lost me. Are you taking about the uphill ski at the start of the turn (outside ski), or the uphill ski at the finish of the turn (inside ski), or both skis or each ski individually or the side by each effect?

I am not sure where this thread is going.

[ January 09, 2003, 04:50 AM: Message edited by: Pierre ]

Due to gravity.....straight downhill

I made the mistake of reading it first thing in the morning before I was caffeinated.
Actually, it is a direct feed for my classes today. Yesterday I did some of the stance and gait movement training indoors with my class and on snow. It was one of the best classes ever and perfect for the first of 10 lessons. One of the fellows said, "This brings everything together, doesn't it?" (Meaning the technology, the technique, tactics, and the human body.)

Bring it on, DM.

(He's talking about the outside ski, Pierre.)
David,

You really lost me too. And I don't even drink caffine in the morning. Maybe a picture will be worth a thousand words? Were those "graphics" supposed to be math or a picture?

One real question: What is the point/argument you are trying to make?

I did start to think about how the boot, as a lever, comes into play, as I can pressure my heel and the front of the ski at the same time using the lever. But I don't know if this relates to what you are trying to say.
Here are some pictures that should explain this. Picture one shows a cross section of a narrow waisted ski. "X" marks where the pressure from the skier interacts with the snow. In this picture, it is inside of the turn.
The second picture shows what happens when the ski is wider. The "X" is outside of the turn.

The third picture shows a view from the back of the boot, and shows what happens when the heel is weighted. The "X" is again outside of the turn.

Where that neutral spot is, between where the ski wants to flatten, and where it wants to fall over (the balance point?) would be greatly affected by the hieght of the lifters, bundings, boot board and footbed. I measured a pair of skis a few years ago, and the bottom of the sole of the boot was 2" above the bottom of the ski. And that doesn't include all of the stuff inside the boot. And obviously, the boot as a lever, will have an impact on this.

But back to my original question. Is there a point to your statement, or are you just making an observation?
Interesting, but unfortunatly, even as an abstract exercise, is only (semi)accurate for the factors considered as historical referance to old skis of minimal sidecut.

The modern shape skis we ski today have tip and tail widths that are signifigantly wider than the ski's waist. Half of that width differance extends to the inside of the edge at the waist creating a completly different relative leverage scenario than the the old ski had, which was even ommited from consideration in these formulations. This is a signifigant component negating the accuracy of any calculations that exclude this input data. These variables are further complicated when a shape ski is reverse cambered and those fat tip and tail leverage points are on a higher plane (up the leg shaft) than the foot applying the leverage. And I'm only scratching the surface of a long list of missing factors needed for any semblance of accuracy that would be of any relavent use.

Any calculation is only as accurate as the quality and completeness of the input data. FYI, snow is not a force unless it is moving in an avalanche, only the source of a frictional resistance overcome by force applied thru the ski. Sorry David, but overall this is garbage in, garbage out.

If we are discussing concepts, pictures help, discussion of relational factors helps. Inaccurate formulas resulting in false implications do not. They only imply false accuracy that really supports nothing, and can even detract from the credability of a valid premise. Which should be clarified up front so the exercise has focus and direction. (what, why, how, etc).

David, if you would really like to attempt a gonzo calculation using all the involved factors that should be considered to approach any relative sense of accuracy, let me know. I can help you with identifying a number of factors you do not appear to be aware of.

Just identifying them without any calc's might prove to be a far more enlightening exercise for us to undertake collectivly to expand our communities awareness of what factors are out there.

But lets say even if we did that calc, So what? How will calculating a (very abstract) number change the fact that we need only roll our feet with just enough intensity to ski in balance with your "resultant force" number? We back off or amp it up as needed to ackomplish our intent with our skis. This stuff is like anything else we teach, it needs identifiable direction toward a functional outcome for the conclusions. Else, what is the added value of the exercise to us, much less to the end customer? How will this help us ski better, or teach skiing better for our customers?

I think we all would like to have some idea up front of what we should be expecting to clarify with the time investment required to sift the substance from the meneusha in these abstract, and often miss-leading adventures in cyber-text.

End of rant. :

[ January 09, 2003, 11:51 AM: Message edited by: Arcmeister ]
Arc,

Good rant. As I was typing my response, I thought of about 15 factors, and there are probably quite a few more:

Just for grins:

length of ski
ski tip width
ski tail width
ski waist width
distance of CM to ski base
lateral position of CM
fore/aft position of CM
lateral Position of CG
fore/aft position of CG
firmness of snow
speed
lateral leverage of boot
fore/aft leverage
edge angle (oh yeah, the obvious one)
pitch of the hill
deflection (twisting out) of the tip
ditto for the tail
how many beers you had the night before
torsional flex
longitudinal flex
binding stack height
length of fib/tib
length of femur
width of foot across med heads
rigididy of footbed
density of snow
boot stiffness, fore/aft & lateral
lunar cycle (anti-grav tide effect)
wind direction and velocity
aero drag coefficient of skiwear
Weight of boot/binding/ski pkg shift of CoG

I'm glad my body is smart enough to simply balance and dance with the "resultant" of all this so my brain doesn't have to do the math.

Years back I heard a story about when K2 was using Boeing labs in Seattle to do high tech ski design testing, and the engineers would go out for beers after, the Boeing guys wanted to talk ski design problems because they had more complex and challenging factors involved than their simple everyday aero-space stuff. From those conversations K2 got into the piezo-lec-trick-lights dampining (which they sold to Head who is now using it).

[ January 09, 2003, 01:41 PM: Message edited by: Arcmeister ]
Rusty, ArcM & JohnH (as well as Si - in a post a couple of weeks ago re Ph.D. candidates which he has supervised) -

Excellent comments about a style of writing which masks oversimplification of important points, makes it almost impossible to determine what simplifying assumptions have been made, and in distinguishing between facts, assumptions and conclusions.

As with his previous posts, IMO, DavidM does make *some* good points, but, like others, my strong concern is that his style of presentation makes his analysis sound infallible and overly authoritative to people without technical backgrounds. I have heard this style sometimes referred to as "Speaking from the Mount", and it is extremely off-putting to large numbers of people, especially on the very egalitarian Internet.

I have not commented on any of his posts in the past because I know the huge ammt of time it would take to respond to individual points in a mixture of accurate and (possibly) inaccurate or poorly phrased statements. With other internet authors, I have done this in the past on various simple physics topics (eg, centrifugal force), and I just don't have the time right now to begin another similar exchange. On the other hand, I though it appropriate to at least add my agreement with the concerns others have raised.

Rusty - with respect to your question, "Where is this thread going?", after looking at his previous postings, about the only hypothesis I can come up with is that DavidM might be writing a book (or very long article) in this area and is testing out the sections on us, one at a time. At least this would explain why 10-20 paragraph discussions of various topics appear from out of the blue, and then are often concluded with a statement like, "more on this later".

More on this later

Tom / PM

[ January 09, 2003, 06:29 PM: Message edited by: PhysicsMan ]
Quote:
 Originally posted by Arcmeister: I'm glad my body is smart enough to simply balance and dance with the "resultant" of all this so my brain doesn't have to do the math.
Understanding it and doing it are so different. Understanding it doesn't mean you can do it and doing it isn't at all reliant on understanding it. I really just want to do it and making my brain hurt seems to interfere with that.
Today I was teaching a woman who most of you would call a good skier. I would say she skis at Level II. The first run, a warmup, she was having trouble holding an edge on the firm snow. On the ride up, we chatted about some of the stuff David M has been teaching about gait. Chiefly, on that ride we talked about the stance foot in walking. I asked her to recall how it feels to walk. How you touch down with the heel, which levers your foot forward and outside, which rolls the foot to land on the ball, which becomes a platform from which to swing the other foot for the next step.

Forget the formulas and the analysis: My experience and my body tell me that how we walk has a lot to do with how we ski, only the step is not a step but an exchange between the swing foot and the stance foot. In skiing, the instant I take pressure off my stance foot, it becomes the swing foot and naturally inverts, which lightly engages the outside edge. Simultaneously, my new outside foot follows the same adaptive process as when I walk: heel, outside, ball. I land on the ball, which presses the edge into the snow, the edge grabs hold, and deflects my ski into the turn, a direction which was initiated by the inversion of the inside foot to its outside edge. I continue turning as long as I keep the ball loaded, and I start a new turn when I unload it.

The movement analogy certainly worked for this student. The next run, she was engaging her edge throughout the turn, leaving one defined and one refined track. The run after that, she was releasing and landing smoothly and effecting the simplest exchange of stance/swing (that is, the chain was initiated by unloading the ball of the stance foot). The run after that she became aware of how the inside hip raises up to allow the foot to swing (invert) and initiate the direction change. The run after that we talked about skiing a slow line fast. I had her follow me. We were on a groomed almost-empty, wide, long, fairly consistent-pitched run. I made turns that ended on an uphill arc, requiring a bit of finesse and timing to release and catch smoothly.

Maybe it was this particular student. On the first chair ride, when I talked about the ball being the sweet spot of the foot, and the ski having a sweet spot, and getting the two matched up so that you feel like the ground is turning you and you're in balance against that force, she got this funny look on her face and said, "I've felt that! Just a few times, but I've felt that when the ground turns you! And I certainly didn't have it on that (warmup) run. But I remember how good it felt, and I'd love to learn a way of getting it all the time."

By the end of two hours, she was getting it most of the time, and KNEW it. And she also got a kick out of the uphill turns, especially the sense of hanging there until her skis hooked up again and then VROOOM she was back speeding on a curved trajectory again. Like a pinball.

Call it hooey if you want AFTER you try putting it into practice.

I will admit that the mechanics being discussed in this thread are a fog to me until I get more information, so I wasn't able to plug it in, yet. Nevertheless, I think we can make some hypotheses, like it's probably not a good idea to load the outside of the foot or the heel if you want to maintain balance and safety. I know this from my history as a biped. If I load the heel when I walk (say I've just painted my toenails) I hobble. I know if I load the outside of my foot by tipping onto it, I run the risk of turning my ankle and loading it, which is really, really painful.
DM, it makes sense to me. I've played with and felt what you are describing. I also understood which ski you were talking about. Presented in a simple way to them, others feel it too. understandng how to use our natural body movements in our skiing will never be folly to me, and all the variables in the world in our skis don't mean anything really if our body structure isn't working the way it was built to work. It will always be a strugle.

Keep going DM. [img]graemlins/thumbsup.gif[/img]

And folks, don't out smart yourselves. Look at what's right about what he's saying and not what's wrong with how he's presenting it. There's no one better than ski instructors at picking out faults instead of positives. And just like good skiing is no garantee of good teaching, good writing is no garauntee of good content, and poor writing is no garauntee of poor content. [img]tongue.gif[/img]
Sorry Ric B, but there are enough inconsistencies in David M's post to raise some questions.

Personally I have an issue with this emphasis on walking and using the ball of your foot. I don't think it translates all that well to skiing. Sure instructors may try to bridge that gap, and sometimes it works (witness nolo's great success with her student), but it often does not.

I still believe that using your shin (by flexing/relaxing your ankles) to control pressure on the boot tongue & ski shovel, is the most efficient way to get a reaction out of the ski. I realize that David insists that this compromises balance (since the foot tends to "float" a little when we press on the boot tongue), but it is hard to agree with that. The human body can balance on shins, knees and several other supporting bodyparts. People balance on a wire, where they DO NOT have the 3 point of contact that David describes. So I have to remain skeptical about this drive to equate skiing with walking. When you have 2 long levers attached to you feet, which must be turned from time to time, walking is a skill that will be completely inadequate. Any beginner will show you this. Balance is critical in skiing (no argument there), but balance alone will not turn a ski unless you are willing to "park-and-ride" your ski.

Maybe I am naive, or inexperienced in my skiing (my trip to Utah will certainly tell me where I stand with that), but to me the boot cuff is still the single most important tool to control my skis. The shape of the ski is still secondary to that, despite all the talk about skis turning themselves.

I prefer JohnH's approach, where control of the skis is achieved via ankle action, which translates into various degrees of pressure on the boot tongue. This has always worked far better for me than the pressure generated from the ball of the foot. I only offer a different perspective, that is all.

[ January 10, 2003, 07:08 AM: Message edited by: TomB ]
From a teaching point of view, I think that trying to dissect the forces and movements that occurr during a turn, to the degree that DavidM and others in this post have done, is going too far. For most skiers, even the most informed instructors, this is an unnecessary complication. I agree that understanding the physics, and biomechanics involved in skiing is important, and as an mechanical engineering student I find them quite interesting. However, I believe that teaching skiing using this type of mentality is the wrong approach. Using limited, and simplified explanations of the forces and movements, such as explaining stance and balance using COM and BOS (center of mass / base of support), and relating them to feelings that the skier will experience is a much better approach. Going out on a limb here, I believe that the only thing people have the ability to truly understand/experience are feelings. With that said, you should be spending your time contemplating how to help your students better experience the mechanics that you are describing, whether they are experienced instructors or beginners. The more you can help your student feel/experience, the more effective your teaching session will be.

just my \$0.02
Powderhoundin: I agree that understanding the physics, and biomechanics involved in skiing is important, and as an mechanical engineering student I find them quite interesting.

Going out on a limb here, I believe that the only thing people have the ability to truly understand/experience are feelings.
With that said, you should be spending your time contemplating how to help your students better experience the mechanics that you are describing, whether they are experienced instructors or beginners. The more you can help your student feel/experience, the more effective your teaching session will be.

DM: If you have read nolo and RicB's comments you should see that the concept of relating the mechanics of skiing to feelings is precisely my intent. I don't think nolo did anything with her student other than to make her aware of the feelings of something which she is intimately familiar with....walking. This aside, I don't see any need to bring any technical terms into the discussion with the student.

The reason I deem it necessary to dissect the technical aspects of the process is that there are all kinds of issues that can prevent one from using the mechanics that nolo conveyed to her student. When others in this forum protest that they can not relate to the mechanics of walking there is a very real possibility that some issue is preventing them from doing so. These people may be unable to get in touch with the feelings that are linked to the mechanics. When this happens it is unlikely that the problem can be resolved by guessing. Here is where the knowledge of the underlying tecnical issues comes into the picture. But even then, the student does not necessarily need to know the mechanics; only the cues to get in touch with the feelings.

When it comes to instruction based on feelings I can not imagine anything more practical than relating skiing to something we are designed to do namely walk. Once the connection has been made one can begin to feel the mechanics of skiing with every step they take.

MilesB, thanks for the drawings. You are on the right track here.
Powdogger,
I agree with your \$.02. You target "feelings", not sure if that is your cause or effect?. I target "intent" as the why, "move this or that" as the what/how/when, and referance the feeling or physical cue as an aid to recreate what they are learning.

This roundy-round we have going of late invokes reflection on the varied tunnels I dug in the past to "learn more" only to eventually discover that most of what I learned taught me that most of what I've learned is irrelivent to what I need to teach effectivly or ski efficiently, as alluded to in your point. The paradox is that the more I learn about skiing, the simpler it gets (by a lot!). What I cannot discount is the possibility that the path that got me to this point, and streaches beyond the horizon, was necessary to reach my present (temporary) perspective. I would not want to be without my laboriously accrued and/or satoried awareness of both what is relavent, and what is not. Could it be that this awareness is something that cannot be taught, only realized by discovery? Hmmmmm........

But I wonder if there's gotta be a better for most folks than all my previous meanderings. What else is the true measure of progress in the science of ski teaching? I think I continue to get better at providing direction for learners with a far easier path, and yet still guide side trips for those who yearn for deeper views. But sharing the short-cuts I've discovered is the only thing that gives them value. I'll keep pondering...

[ January 10, 2003, 10:16 AM: Message edited by: Arcmeister ]
Arc, extremely well spoken. While I have neither the experience or level of skill that you do I have experienced the very same type of progression in skiing (tennis as well). As I look back at my personal progessions I always wonder whether there was a more efficient path to be taken. Like you, I wonder whether the complexities which I have left behind were actually necessary. In coaching my kids or others (albeit as an amateur) I am highly motivated to try to help them find a more efficient path to "the simplicity of proficiency." I feel that my experiences are clearly helpful in doing so. It is this very issue which serves as the biggest motivation for both my interest in ski instruction and my own personal improvement.
Quote:
 Originally posted by Arcmeister: This roundy-round we have going of late invokes reflection on the varied tunnels I dug in the past to "learn more" only to eventually discover that most of what I learned taught me that most of what I've learned is irrelivent to what I need to teach effectivly or ski efficiently, as alluded to in your point. The paradox is that the more I learn about skiing, the simpler it gets (by a lot!).
Arcmeister - Grand Master of Ski Kune Do.

He took the best from each system and weeded out the garbage. [img]graemlins/thumbsup.gif[/img]
Warren, I also liked that same quote of Arcmeister's.

The fact of the matter, is that while what DavidM is doing might be way too technical and seemingly unnecessary, and really doesn't matter all that much to those of us reading it, the simple fact that these thoughts are going through his mind, and that he's gaining an understanding of all the complexities and variables, is, -in and of itself-, what he is learning from. I tend to think that there wasn't really a point to what he first posted (to us), but to him, he was clarifying the beginning of the thought process of other forces that interact with him when he skis, other than just balance, edge, pressure, rotary, and the "moves" that we commonly talk about here, such as crossover/under, rotary push off, flex/extend, etc.

He's learining from just throwing darts against a wall and listening to the conversation he sparked. So good for you David! Keep it up! [img]graemlins/thumbsup.gif[/img]
hey - this stuff helped me
Gave me a frame of reference for the hip thingy that was happening to me
& remember that when I posted a question about it during our season no-one here could help

I knew what it felt like & my instructor knew what was happening. We both felt it was linked to my foot problem - but WE HAVE NOT been able to get help. Bootfitters just don't have a clue - because I do not 'look' knock-kneed/bow-legged at ALL. A temporary shim on that foot helps - but is probably NOT the real answer & instructor is NOT keen to permantly shim me until we work out the problem
I fully understand what David is trying to illustrate. I show this all the time using a side slip/falling leaf exercise. Move F a little forward and the tips rotate down hill. Move F a little to the rear and the skis tails rotate down hill. He is also saying the wider the ski, the harder it is to do. I understand his simple words and his meaning but I do not understand his equations nor whether his is talking about both feet or just the outside foot.

He clearly is taking about just the outside foot for his equations but appears to be talking about both skis in his paragraphs and term definitions above the equations. I can accept either since is clearly doesn't matter to me which ski is pressured.
I understand his variables as he defines them but I do not recognize his equations for being a proper equation that can be deciphered. He appears to have single points such as S and F but also appears to have two dementional limits such as would be applicable to calculus but does not include this in his equation. There is no = signs so we would naturally assume multiplication of a limit times downhill>. downhill> is a term he has not defined. I clearly get no help from the diagrams at the bottom as the pictographs do not define the two dementional limits he is setting.
I understand what he is saying but for the life of me, I can't make sense of his equations.
My apologies to Pierre and others confused by my formulas. They were not intended to be formulas. I was trying to find a way to represent a cross section through the transverse aspect of the ski through the waist. I wanted to find a way to do this so members could play with the geometry and forces with a keyboard as a opposed to trying to import drawings.

[core sidewall
********* core
<iiiiii inside edge
oooooo> outside edge
W = force applied by foot
R = reaction force
Assume the inside edge at the waist [ is always the pivot for rotation into or away from the hill.

Using the above a ski is represented like this:

<iiiiii[********]oooooo>

Increase waist width:

<iiiii[*************]ooooo>

Increase sidecut:

<iiiiiiii[********]oooooooo>

Insert forces where they act and use + or - to show effect on rotation into or away from hill:

<RiiiWi[********]oooooo>

Does this make sense?
ummm no - no piccies
Sorry again. For some reason the posting software is deleting the repeated symbols. I will try and come up with a work around.
Square bracket is html code
try another symbol
Thanks dsski. Actually it was another symbol that was messing things up.

( = limit of sidecut )
[ = section through core sidewall at waist ]
ddddddd = inside portion of sidecut
ooooooo = outside portion of sidecut
******* = core section through waist

A schematic ski looks like this:
(ddddd[**********]ooooo)

Increase waist width:
(ddddd[*************]ooooo)

Increase sidecut:
(dddddddd[**********]oooooooo)

Show forces:
(R-ddW+d[**********]ooooo)
Note: Forces displace sidecut symbols.
Thanks dsski. Actually it was another symbol that was messing things up.

( = limit of sidecut )
[ = section through core sidewall at waist ]
ddddddd = inside portion of sidecut
ooooooo = outside portion of sidecut
******* = core section through waist

A schematic ski looks like this:
(ddddd[**********]ooooo)

Increase waist width:
(ddddd[*************]ooooo)

Increase sidecut:
(dddddddd[**********]oooooooo)

Show forces:
(R-ddW+d[**********]ooooo)
Note: Forces displace sidecut symbols.
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