  This paper studies various properties of the Pomeransky-Sen'kov
doubly-spinning black ring spacetime. I discuss the structure of the
ergoregion, and then go on to demonstrate the separability of the
Hamilton-Jacobi equation for null, zero energy geodesics, which exist in the
ergoregion. These geodesics are used to construct geometrically motivated
coordinates that cover the black hole horizon. Finally, I relate this weak form
of separability to the existence of a conformal Killing tensor in a particular
4-dimensional spacetime obtained by Kaluza-Klein reduction, and show that a
related conformal Killing-Yano tensor only exists in the singly-spinning case.
