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:
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