A manifold is called formal if it has the same rational homotopy type
as the cohomology ring. We first consider the formality of a sphere bundle
over a formal manifold. In this case the formality is entirely determined by
the Bianchi-Massey tensor, which is a 4-tensor on a subspace of the
cohomology ring, introduced by Crowley and Nordstrom. As a special case, we
will see that if a manifold and its unit tangent bundle are both formal,
then the manifold has either Euler characteristic zero or rational
cohomology ring generated by one element. Finally we discuss the case of
a general base manifold, and give an obstruction to formality.