Snow Compaction and Work


One thing that slows a skier down is the compaction of the snow beneath a skier. Snow is mostly air and this allows a great degree of compaction. On packed trails, this compaction is negligible and contributes only slightly to the friction of the snow on the skis.

This diagram shows a skier who travels l distance on unpacked snow and sinks in h into the snow.

image from the Physics of Skiing

Logically, the distance the skier sinks in, h, is proportional to the skiers weight, FN. Work is defined as a force applied over a distance.

The work needed to propel the skier l distance through the snow is the same as the work done be the skiers weight along the height, h.

the force used to move the skier is defined as FFORWARD then

FN*h= FFORWARD*l

With different types of snow, a skier with the same weight will sink in different distances. For the reason, the coefficient of compressional friction, uc, is defined as:

uc=(FN)/(FFORWARD)=(h)/(l)

Frictional Force is defined as f=u*FN

So the friction from compression, fc, can be defined as

fc=(h)/(l)*FN

An example of the conversion of Potential Energy, PE, to Kinetic Energy, KE, and then work done by friction to transfere this Kinetic Energy from the skier is:

image from here

This assumes there is no friction until the skier reaches the ungroomed section. The formula that describes the energy in this equation is:

PEinitial + KEinitial = PEfinal + KEfinal - fc *distance