Geometry of the Edged and Flexed Ski

Abstract

Refer to Fig. T4.1, which shows the outline of a conventional ski as seen from the top view. The contact length between the shovel and tail is labeled C. The tail width is T, the waist width is W, and the shovel width is S. We assume that the waist of the ski, where W is measured, is near the midpoint of the contact line. The sidecut, SC, is given by the relation SC = (S + T - 2W)/4. From the geometry illustrated in Fig. T4.1, we can write C ≈ δR _SC , and then expand the cosine function to use the first two terms only, as follows:

$$ \begin{array}{l}W = {F_N} + {F_{S,}} \\{F_N} = W\cos \alpha ,\quad {F_S} = W\sin \alpha \\\end{array} $$

((T3.1))

$$ \begin{array}{l}W = {F_N} + {F_{S,}} \\{F_N} = W\cos \alpha ,\quad {F_S} = W\sin \alpha \\\end{array} $$

((T3.1))

thus

$$ {R_{SC}} = \frac{{{C^2}}}{{8SC}} $$

.