  We consider relative normalizations of ruled surfaces with non-vanishing
Gaussian curvature $K$ in the Euclidean space $\mathbb{R} ^{3}$, which are
characterized by the support functions $^{\left( \alpha \right) }q=\left \vert
K\right \vert ^{\alpha}$ for $\alpha \in \mathbb{R}$ (Manhart's relative
normalizations). All ruled surfaces for which the relative normals, the Pick
invariant or the Tchebychev vector field have some specific properties are
determined. We conclude the paper by the study of the affine normal image of a
non-conoidal ruled surface.
