  We study ribbons of vanishing Gaussian curvature, i.e., flat ribbons,
constructed along a curve in $\mathbb{R}^{3}$. In particular, we first
investigate to which extent the ruled structure determines a flat ribbon: in
other words, we ask whether for a given curve $\gamma$ and ruling angle (angle
between the ruling line and the curve's tangent) there exists a well-defined
flat ribbon. It turns out that the answer is positive only up to an initial
condition, expressed by a choice of normal vector at a point. We then study the
set of infinitely narrow flat ribbons along a fixed curve $\gamma$ in terms of
energy. By extending a well-known formula for the bending energy of the
rectifying developable, introduced in the literature by Sadowsky in 1930, we
obtain an upper bound for the ratio between the bending energies of two
solutions of the initial value problem. We finally draw further conclusions
under some additional assumptions on the ruling angle and the curve $\gamma$.
