Skier, curved motion on slope/ reaction force?

[Glenn G]

Hi folks,
I was thinking about an old physics olympiad question I read. Can't remember exactly but it was about minimising the reaction force of a skier as she took a curved path down a ski-slope. That got me thinking generally about what is going on with the reaction force in such a situation.
I got as far as some of my scribblings in the picture above (by first thinking about her just moving directly down the slope). I then realized my mechanics was not good enough to work out what was really going on.
Would really appreciate any input/help.
Glenn

 

[A.T.]

Can't remember exactly but it was about minimising the reaction force of a skier as she took a curved path down a ski-slope.

When you go perpendicular to the slope while turning downhill, you want gravity to provide all the centripetal force, to minimize the ground reaction.