Summation:

A carving ski has an effective steering angle. This steering angle is not the local steering angle underfoot, the local steering angle at the tip or the local steering angle at the tail. It is an average steering angle averaged over the whole ski. What's more, it is a force-weighted average. Integrating the pressure vector over the surface of the base results in the net normal force on the base. This force has a direction and the plane normal to that direction has a steering angle relative to the current direction of motion, the current momentum vector. Of course we, well most of us anyway, are not going to do vector calculus as we ski, but we aren't likely to be calculating sines and cosines anyway. So the question is so what?

Although we cannot calculate the direction of that force, we can certainly feel it. Understanding how it is related to the summation of the local pressures and areas and angles of the ski will help us understand our turns.

To begin with let's concentrate on components in the plane of the slope. (BTW Big E, your 1G sideways and 1 g down add up to the square root of 2, not 2, so even us old guys can pull 3 g turns with a fairly straight outside leg

). Let's also admit up front there will also be friction and that this friction will act to oppose any motion of the ski, but since we are using Ghosts super-duper secret whale-oil formula it's small enough not to worry about. We can add it in later if you like.

Let's also look at a near-perfect carving edge-locked turn on some eastern ice, the path cut by the tip will depend on tipping angle due to the sidecut interaction with the surface.

If we were in a park and ride turn with a constant radius, perfectly balanced over the middle of the ski. All the force is sideways towards the centre of the turn and we have effectively a zero steering angle, steady speed turn goin on. Only problem is we don't ski that way! We increase the tipping angle and decrease the radius on the way to the apex and then decrease the tipping angle and increase the radius after the apex. What is going on as we tip to tighten the turn? The front of the sk is closer to the apex than the tail. The front of the ski is cutting an ever-decreasing radius, and the tail is still in the groove a few feet behind it. The tip is bent to a sharper local steering angle than the tail is. The vector-calculus integration would tell you that the effective steering angle is now significantly higher than zero, but you don't need maths to tell you that you are being forced back. Starting a turn and increasing the radius of a turn will slow you down. The opposite happens when you exit the turn, you accelerate out of it because the effective steering angle is negative; the tail of the ski is pushing more than the tip, due to it being bent more. Moving your weight for and aft increases the effect.

Now consider a ski that is not quite perfectly carving, the tip is being pushed out of its groove a bit. the path isn't so strictly tied to the sidecut. We can load up the front severly and get it to bend A LOT. creating a much larger steering angle at the tip. The cost for doing this is a lot of deceleration, but it can still be done.

We could look at low angle skidded turns, but why bother. It is much more useful to spend our time looking for a ski with a stiff tail and soft tip so we can ski faster.

That is all.