  We study unit horizontal bundles associated with Riemannian submersions.
First we investigate metric properties of an arbitrary unit horizontal bundle
equipped with a Riemannian metric of the Cheeger-Gromoll type. Next we examine
it from the Gromov-Hausdorff convergence theory point of view, and we state a
collapse theorem for unit horizontal bundles associated with a sequence of
warped Riemannian submersions.
