  We give an upper bound of a Hamiltonian displacement energy of a unit disk
cotangent bundle $D^*M$ in a cotangent bundle $T^*M$, when the base manifold
$M$ is an open Riemannian manifold. Our main result is that the displacement
energy is not greater than $C r(M)$, where $r(M)$ is the inner radius of $M$,
and $C$ is a dimensional constant. As an immediate application, we study
symplectic embedding problems of unit disk cotangent bundles. Moreover,
combined with results in symplectic geometry, our main result shows the
existence of short periodic billiard trajectories and short geodesic loops.
