On the developable ruled surfaces of low smoothness

The classical description of the structure of developable surfaces of torse type is formally possible only starting with $C^3$-smoothness. We consider developable surfaces of class $C^2$ and show that the directions of their generators at the boundary points of a surface belong to the tangent cone of the boundary curve. In analytical terms we give a necessary and sufficient condition for $C^1$-smooth surfaces with locally Euclidean metric to belong to the class of the so-called normal developable surfaces introduced by Burago and Shefel'.