TITLE: Examples of sphere bundles
QUESTION [10 upvotes]: For certain values of $k$ it is known that $\mbox{Diff}(S^k)$ is not homotopy equivalent to $O(k+1)$. So there are sphere bundles that do not arise from vector bundles.
Since I've never (knowingly) come across such a sphere bundle I'm interested in seeing some enlightening examples of sphere bundles which do not come from vector bundles.
Thank you for any contribution.

REPLY [5 votes]: As far as I know the only explicitly-described such bundles are in Hatcher's paper:

Hatcher.  Concordance spaces, higher simple-homotopy theory, and applications.  Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ, Stanford Calif 1976), Part 1, pp. 321. 

I think in Igusa's Higher Franz Reidemeister Torsion book there might also be these examples, although I don't have the book at home with me so I can't check.  But that seems likely as Igusa has also developed these examples.