  In this paper we study the stationary horizons of the rotating black ring and
the supersymmetric black ring spacetimes in five dimensions. In the case of the
rotating black ring we use Weyl aligned null directions to algebraically
classify the Weyl tensor, and utilize an adapted Cartan algorithm in order to
produce Cartan invariants. For the supersymmetric black ring we employ the
discriminant approach and repeat the adapted Cartan algorithm. For both of
these metrics we are able to construct Cartan invariants that detect the
horizon alone, and which are easier to compute and analyse that scalar
polynomial curvature invariants.
