  Ice crystals settling through a turbulent cloud are rotated by turbulent
velocity gradients. In the same way, turbulence affects the orientation of
aggregates of organic matter settling in the ocean. In fact most solid
particles encountered in Nature are not spherical, and their orientation
affects their settling speed, as well as collision rates between particles.
Therefore it is important to understand the distribution of orientations of
non-spherical particles settling in turbulence. Here we study the angular
dynamics of small prolate spheroids settling in homogeneous isotropic
turbulence. We consider a limit of the problem where the fluid torque due to
convective inertia dominates, so that rods settle essentially horizontally.
Turbulence causes the orientation of the settling particles to fluctuate, and
we calculate their orientation distribution for prolate spheroids with
arbitrary aspect ratios for large settling number Sv (a dimensionless measure
of the settling speed), assuming small Stokes number St (a dimensionless
measure of particle inertia). This overdamped theory predicts that the
orientation distribution is very narrow at large Sv, with a variance
proportional to ${\rm Sv}^{-4}$. By considering the role of particle inertia,
we analyse the limitations of the overdamped theory, and determine its range of
applicability. Our predictions are in excellent agreement with numerical
simulations of simplified models of turbulent flows. Finally we contrast our
results with those of an alternative theory predicting that the orientation
variance scales as ${\rm Sv}^{-2}$ at large Sv.
