Note that this is a calculated radius. The intent of the paper was to compare a finite element analysis that took into account the groove made by the ski with the radii calculated by Howes law which didn't consider the groove. Howes law breaks down at higher edge angles as the calc-ed radius tends to zero - cos(90Deg)=0.
Unfortunately can't see any definition of hard/medium/soft snow. It links to ref #4 and that's not a downloadable paper without joining up to something or other.
The discussion in the paper is interesting.
Discussion
Dependence of the turn radius on edging angle, load on the binding, and snow properties
The edging angle had – as expected – the most substantial effect on the turn radius.
....
Different speed or different weight of an athlete causes an increase of the forces acting on the binding. For the ski-binding model implemented in our simulation we found a linear decrease of the turn radius with increasing force in the range between 1000 N and 2000 N. A heavier skier or a faster skier is thus able to carve a slightly tighter turn. However, for the ski studied here an increase in force by 100% caused a decrease in the turn radius by only between 1 and 1.5 m which corresponds to a relative change between 8% and 17%.
100% is a lot of Oreos!
Varying snow strength has a more complex impact on the turn radius. For edging angles below 40° softer snow lets the ski penetrate deeper into the snow causing the ski to bend more and therefore causes a smaller turn radius. At edging angles above 40° the groove that forms in the snow starts to substantially affect the turn radius preventing small turn radii. This effect is more pronounced for soft snow when a deep groove is created by the ski. For medium and hard snow types, when the ski’s penetration depth is smaller, the impact of this effect on the turn radius is also smaller.
One thing to think about in soft snow. An aim in carving is deflection across the hill. The more the centripetal force acts in the horizontal plane (from higher edge angle) the better. Bending the ski in the vertical plane, whilst useful for getting the ski out of the snow, isn't that useful for deflection across the hill.