4 Questions

 Ghost, if you are going straight down the hill, you are not on an edged ski, its N/A

If you are turning, at the instant you are at the fall line, you have steering angle.  Otherwise the ski would not continue to turn.

Its not zero.

But regardless, zero or non-zero, the rear of a carving ski is not negative steering angle because the ski is not brushing at all.....its slicing.  Every point along the ski has the same local steering angle.

It's NA to a carving ski as well.

You are assuming falsely that the conclusion is true to try and prove a premis.

Forget what you think know, and just look at the facts of the premis.  Ski points down. You are moving down.  Steering angle is zero.  The steering angle is not defined by whether or not you are turning.  It is defined by what the direction of motion is and what angle the edge is pointing in.

The edge only matters if you're using it Ghost.  If you're running straight you are on flat skis.

I think you're just debating to debate at this point.

Get LeMaster's newest book, "ultimate Skiing" read it and get back to me.  he covers this topic in more detail than his previous book.  At this point I'm going to have to say we disagree and I don't particularly think you know what you're talking about, but you don't seem to get it and I'm tired of trying.  Good luck.

None are so blind as those who will not see. 
I think you don't know what you're talking about.  And the fact that you cannot find anything wrong with my argument proves it.
I guess there's only one way to settle this.

 Ghost, 

At one point in the arc the body moving to the left side of the trail, and the next it is moving to the right.  At some point, it's moving directly downhill.

Same comment with the skis.

What does that have to do with steering angle? 

Steering angle measured underfoot at the time the body is moving directly downhill when the ski directly underfoot is pointing directly down hill is zero.  This is an example of local steering angle that I'm hoping some people will be able to see, and finally admit the truth that is staring them in the face.

Just to show you that I am not just arguing.  I have been convinced that local steering angle as defined by LeMaster is actually applicable to a carving ski.  At the front of the ski the steering angle actually does act against the direction of motion doing negative work on the skier and slowing him down.  At the rear of the ski the negative angle does work on the skier speeding him up, and under foot, no work is done on the skier, as the force in the skier's direction of motion is zero. (sine of zero is zero).

Then what causes the steering angle to become non-zero again?

Ski shape causes the local steering angle to be non-zero at tip and tial. Rotating a decambered ski about it's long axis also increases steering angle at tip and tail. 

OK, but it is the local steering angles at tip/tail that turn the ski. It is the steering angle underfoot that turns the skier.

I'm not certain that for every turn I make, the direction that the skis are pointing and the direction that the CM is moving ever becomes parallel. 

Now we are getting somewhere.

The sine and cosine of the local steering angle indicates how much of the pressure acting on that part of the ski is directed towards turning and how much is directed towards slowing down/speeding up the skier. At the point under an arcing ski where the edge lines up with our current direction of motion, that is to say at a local steering angle of zero degrees, sine of the steering angle = 0 and cosine of the steering angle =1 means all of the pressure acting on that part of the edge goes to turning and none goes to stopping. Should you suddenly throw them sideways, at 90 degrees, sine 90 =1 and cosine 90 = 0 means it all goes to stopping and none goes to steering.

Nice dissections Ghost! 

At each moment in a carved turn the skier's current momentum can be isolated and drawn with a directional arrow. 

Each microscopic, point along the carving ski's engaged edge has its own Local Steering Angle - relative to the just-mentioned direction of our skier's current momentum. (If measured against that particular point's own direction of momentum, then the Steering Angle would approach Zero instead)

At points near the tail of the ski, those Local Steering Angles just happen to point in a "negative" direction relative to our skier's overall direction of current momentum (assuming we've assign a 'Positive Value' to the Local Steering Angles near the Tip)

.ma

 That's all well and good, Ghost, but these local angles only serve to turn the ski, not the skier. So when you write that these local steering angles contribute to turning the skier, you have to take into consideration the stiffness of the ski to judge their entire effect.

Lemaster throws them out entirely.  You're saying they actually matter.

The difficulty I have in making them matter is that the connection between the local steering angles at the tip and tail have to go through a flexible ski and a flexible boot/ankle system before they can actually deflect me.  Lemaster goes so far as to say the tips and tails don't turn the skier.  Only the steering angle that is created underfoot does that.

Look at it this way... if the local steering angles at tip and tail were substantial contributors, then the longer ski would turn more when carving and the snowblade would turn less.  The opposite is true.

 Even further to that, since the tips and tails do little to actually turn the skier, I will argue also that the local steering angle of the tip and tail are not really related to the direction the CoM is moving (for the same reason, the tip and tail are too uncoupled from the CoM).  Rather the direction the ski tip or tail is sliding and the steering angle thus formed.  The deflection caused on that particular part of the ski. Whether or not that deflection actually has a significant effect on moving the skier is dependent on numerous factors.  How far away from the center of the ski obviously determines some of this.  How about this for a wrench in your works...if the deflection from the tip or tail are not in the same direction as the mid section of the ski, might they impart a torque force on the skier mass?  Might they actually be capable of being more effective in that way then in simply pushing the CoM as the mid section of the ski does?  Its not on or off, all or nothing either.....

1)  What are the pros and cons of being countered while steering?  

Pros:  Counter is useful in a tuck, because it naturally puts the weight/pressure over the front of the outside ski (because of where your hands are.)   If you don't have the strength or are tiring, counter allows you to rest by resisting the buildup of forces (from change of direction) skeletally, rather than muscularly.  Counter naturally leads to a position from which you can unwind to pivot for the next turn.

Cons:  Counter leads to a "static" kind of skiing, and creates a large risk of promoting excessive inside tip lead, which leads to a host of problems.  (I have a lot of experience with the lab work that backs up that latter observation...)

2)  What are the pros and cons of staying square while steering?

Pros:  It's a more fluid, less static skiing, more two-footed and faster (in my experience, playing with it at a clinic while timed) more natural in taking advantage of a more natural gait dynamics-driven approach.  Less vulnerable to promoting excessive inside tip lead.

Cons:  It doesn't have the limited advantages of counter, listed above.

3)  When is "skiing into counter" a good option, and when is it not?

I don't know.  Seems reasonable, when carrying a tuck through the flats at the bottom of a race course, when you're tired and the counter/tuck thing is working for you.  Runs the risk of a static, less balanced, less "flow" kind of skiing, but that's less of an issue when you're setting up for a big unwind/pivot move to make the next gate.

Topic 4 is beyond me.

SfDean.

Post #284

 Right.  Good!  So....let's take it even further.  

In an arc'd turn we can say that we have minimized that rotational torque and maximized the turning effect on the actual skier.  If that is the case, then in an arc'd turn, the tip and tail would need to neutralize each other.   If there was negative steering angle on the tail, then they would not neutralize each other at all, they would collude together to create a pinwheel effect.  They must both be positive and they need to be similar in value also in order to eliminate that rotational torque.

In a side slip you have also eliminated the rotational torque by ensuring that both the tip and the tail cause approximately the same amount of summed up steering angle to occur on each side of the boot(front and back).  Steering angle is very large in that case, in fact its so large, with reduced edging, that its not steering the skier at all, its only producing a lot of skid.  But the point is, that there is large steering angle in the front, large steering angle in the back, and the delta between them is going to be something very close to zero.  Its not the sum, its the delta, that indicates the rotational torque.

Now then take the arcing case, We have reduced the rotational torque in this case also, but we have reduced the overall steering angle of the ski to as close to zero as we're going to get while making a turn. Whether its zero, or very very close to zero, it mattereth not in the discussion about whether there is ever any negative steering angle.  The front half of the ski and the back half of the ski need to have a very small delta between them in terms of their local steering angles.  If the front half is positive, the back half needs to be positive also.  Otherwise there will be more rotational torque.

I'll buy that for a dollar!