  We compute the gravitational wave energy $E_{\rm rad}$ radiated in head-on
collisions of equal-mass, nonspinning black holes in up to $D=8$ dimensional
asymptotically flat spacetimes for boost velocities $v$ up to about $90\,\%$ of
the speed of light. We identify two main regimes: Weak radiation at velocities
up to about $40\,\%$ of the speed of light, and exponential growth of $E_{\rm
rad}$ with $v$ at larger velocities. Extrapolation to the speed of light
predicts a limit of $12.9\,\%$ $(10.1,~7.7,~5.5,~4.5)\,\%$. of the total mass
that is lost in gravitational waves in $D=4$ $(5,\,6,\,7,\,8)$ spacetime
dimensions. In agreement with perturbative calculations, we observe that the
radiation is minimal for small but finite velocities, rather than for
collisions starting from rest. Our computations support the identification of
regimes with super Planckian curvature outside the black-hole horizons reported
by Okawa, Nakao, and Shibata [Phys.~Rev.~D {\bf 83} 121501(R) (2011)].
