  A smooth fibration of $\mathbb{R}^3$ by oriented lines is given by a smooth
unit vector field $V$ on $\mathbb{R}^3$, for which all of the integral curves
are oriented lines. Such a fibration is called skew if no two fibers are
parallel, and it is called nondegenerate if $\nabla V$ vanishes only in the
direction of $V$. Nondegeneracy is a form of local skewness, though in fact any
nondegenerate fibration is globally skew. Nondegenerate and skew fibrations
have each been recently studied, from both geometric and topological
perspectives, in part due to their close relationship with great circle
fibrations of $S^3$.
  Any fibration of $\mathbb{R}^3$ by oriented lines induces a plane field on
$\mathbb{R}^3$, obtained by taking the orthogonal plane to the unique line
through each point. We show that the plane field induced by any nondegenerate
fibration is a tight contact structure. For contactness we require a new
characterization of nondegenerate fibrations, whereas the proof of tightness
employs a recent result of Etnyre, Komendarczyk, and Massot on tightness in
contact metric 3-manifolds.
  We conclude with some examples which highlight relationships among great
circle fibrations, nondegenerate fibrations, skew fibrations, and the contact
structures associated to fibrations.
