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It is shown that if $\gamma: [a,b] \to S^2$ is $C^3$ with $\det(\gamma,\gamma', \gamma'') \neq 0$, and if $A \subseteq \mathbb{R}^3$ is a Borel set,then $\dim \pi_{\theta} (A) \geq \min\left\{ 2,\dim A, \frac{ \dim A}{2} +\frac{3}{4} \right\}$ for a.e. $\theta \in [a,b]$, where $\pi_{\theta}$ denotesprojection onto the orthogonal complement of $\gamma(\theta)$ and ``$\dim$''refers to Hausdorff dimension. This partially resolves a conjecture ofF\"assler and Orponen in the range $1< \dim A \leq 3/2$, which was previouslyknown only for non-great circles. For $3/2 < \dim A < 5/2$ this improves theknown lower bound for this problem.

Restricted families of projections onto planes: The general case of nonvanishing geodesic curvature