  Let $\gamma: I \to S^2$ be a $C^2$ curve with $\det(\gamma, \gamma',
\gamma'')$ nonvanishing, and for each $\theta \in I$ let $\rho_{\theta}$ be
orthogonal projection onto the span of $\gamma(\theta)$. It is shown that if $A
\subseteq \mathbb{R}^3$ is a Borel set of Hausdorff dimension strictly greater
than 1, then $\rho_{\theta}(A)$ has positive length for a.e. $\theta \in I$.
This answers a question raised by K\"aenm\"aki, Orponen and Venieri.
