Ski Coaching

There is some discussion as to whether or not skis CAN be skied truly parallel, whilst making arcs.

IF they can, then the circles, the segments of which are being described in the snow by the skis, MUST be concentric. If those circles are not concentric then the skis can only be parallel at one infinitessimally small point. At two points on the circles they describe, the lines they are drawing will cross. This means the lines are approaching and diverging from one another. Clearly then, they are not parallel. The skis would then cross, as would the skier's legs and the result is not pleasant to contemplate.

If you wish to test this you can, very simply and without complex physics being involved. The skis can only describe circles of either the same or different radii.

Example 1: Same radius. If the two circles being described are the same radius, then either they will be concentric or not. If concentric there will only be one line drawn in the snow and since there are two skis that is not possible. So - if the radii of the two circles are the same, then the circles must be centred on different points.

Their circumferences cannot then be parallel. All you need in order to prove this to yourself is to take a set of compasses, (or in their absence a circular saucer or even a coffee cup), and draw two circles of matching radius, centred on two different, albeit nearby points. You will see that the circles cross one another twice. Therefore their circumferences are not parallel.

Example 2: Now consider two circles of slightly different radii. The only circumstance in which their circumferences can be parallel is if they are concentric.

IF ( and it may be big "IF" ) truly parallel arcs can be described by two skis acting simultaneously, then whatever the physical influences at work are, the inner ski must be reacting differently to the outer ski. Skis can only bend, tilt (with or without torsional distortion), or pivot.

Bending and tilting combined can lead to "carving". Pivoting leads to skidding, as does torsional distortion.

I have no idea whether true, absolutely exact parallel skiing is possible, but it seems  clear to me, that if it is, it can only be done with arcs which are part of concentric circles.

So - either it is possible and the inner and outer skis are being separately influenced by the external forces; or the external forces are equalised between the two skis, and while "parallel" skiing may APPEAR to be happening, that is a mistaken perception resulting from not being able to watch and measure sufficient of the circumference of the circles being described.

Bob Trueman