[ under construction ] 



Basics of Forces 

  • Every action force has an equal and opposite reactive force. 

Newton's Third Law. 

  • The skier's center of mass can be moved from side-to-side only by applying force with something against the snow. 

(Normally that something must be either the tip of the pole or the side of the ski.  Pushing down on the base of one ski can help only a little, and even that little is possible only if the skier's center of mass is not currently directly over that ski). 

Since Force requires Work (see below), this implies that moving the skier's body weight from side to side always requires Work. 

  • Acceleration equals Force divided by Mass 

This implies that 

 - - the quicker you want to get all or part of your body go get moving, the more force it takes. 

 - - the more of your body you want to get started moving in some direction, the more force it takes. 

 - - when the skier's body is moving forward at constant speed

 - - the more parts of a skier's body which remain more close to constant forward motion, the less force needed for acceleration. 

  • De-acceleration is a kind of acceleration 

So also if the skier wants to slow something down -- something which is not otherwise slowing down due to some natural force like friction or air resistance -- then the skier must apply a force. 

To move the body from side to side requires the skier to apply a force to start the body moving toward the other ski (acceleration).  And then another force to slow and stop the body (de-acceleration) from moving on past the other ski.  Since it requires two forces, it doubles the Work (see below).  But since these sideways forces are not pushing the skier forward, this double work is a wasted, another source of inefficiency.  

To move the body weight up and down requires the skier to apply a force to start the body moving upward (acceleration).  And then another force to slow and stop (de-acceleration) the body's downward motion from gravity -- into stable position over the ski -- rather than crashing down into the snow (in which case the snow and ground supply the force to stop the downward motion).  Since it requires two forces, it doubles the Work (see below, and also Double Cost of Extra Down-Force).  But since these vertical forces are not pushing the skier forward, this double work is a wasted, another source of inefficiency. 

  • The ski cannot feel where the skier's upper body is. 

The ski can only feel the forces as they come through the binding. 

Therefore it is possible to temporarily "fool" the ski into feeling the skier's body-weight as over the center of the grip zone. 

This implies: 

 - - It is possible to start the kick early, even while the hip is behind the ankle, even while the toe is far in front of the skier's center of mass.  This is important for both advanced classic stride (see below under Work, and the Striding Smooth and Long "secret") and advanced hill bound for climbing up a steep hill



  • Friction is proportional to downward Force (other things being equal) 

Very important for getting more grip friction for Classic stride. 

  • With a ski on snow, friction is greater when the distribution of the down-force pressure is uneven 

If the entire weight of the skier is all on one ski, the best glide is with the ski riding flat with no edging forces applied. 

But the best glide is with the skier's weight evenly distributed between the two skis (and each ski riding flat on the snow with no edging forces). 

The ski will have more friction for grip if edging force is applied and one edge is digging into the snow.  This is true even if the ski is not angled away from the direction of motion.  (So it is possible to get some of the "herringbone" effect, even without the herringbone angle). 

  • Friction to prevent movement from starting is different from friction during motion 

The first kind is called static friction, and the second kind is dynamic friction.  The magic of grip wax for Classic skis is that it has higher static friction and lower dynamic friction -- so that can glide as well as grip. 

Power and Work 

Therefore the skier can get more effective work out of each stroke either by pushing more intensely or by pushing through a longer ground-contact distance. 

The only Force that counts for effectively moving the skier forward is the component of force in the forward (or backward) direction -- not any up or down component. 


 - - Early start to leg-push helps. 

 - - Full finish to leg-push helps 

 - - Lower body position can help (lengthen snow-contact distance) 


 - - it only helps to lengthen leg-stroke to in ways that permit applying additional force.  (e.g. rotating the hips about the vertical axis can lengthen the leg-stroke, but those vertical-rotator muscles are not very effective at applying force).  

  • Power equals Cadence times Work-per-stroke 

[ to be added ] 

(Nothing about glide.) 


 - - not wasting Time matters 

 - - Cadence matters 


  • Higher peak force puts disproportionately greater stress on a muscle 


Ski Design 

  • Camber -- the more the weight and down-force of the skier are focused on the center of the wax pocket, the greater proportion of snow-pressure will go through the grip zone of the ski base. 
  • Side-cut (or "carve") 

[ to be added ] Easier Turning versus Classic-stride Grip 

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More Complicated stuff

Sustainable Speed 

This gets more complicated. 

[ to be added

(Nothing in there about glide.) 

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Double cost of extra down-force 

[ to be added

(combines reactive force with gravity) 


Double Cost of Extra Down-Force 

Dead spots in the stroke cycle

[ to be added


Is more Glide good? 


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