  An analytical formula that accurately accounts for the Lorentz contraction of
the excluded volume of two relativistic hadrons with hard-core repulsion is
worked out. Using the obtained expression we heuristically derive the equation
of state of Boltzmann particles with relativistic excluded volumes in terms of
system pressure and its surface and curvature tension coefficients. The
behavior of effective excluded volumes of lightest baryons and mesons is
studied at very high temperatures (particle number densities) and for very
large values of degeneracy factors. Several parameterizations of the obtained
equation of state demonstrate a universal asymptotics of the effective excluded
volume at high particle number densities. It is peculiar, that the found
maximal packing fraction $\eta \simeq 0.75$ of Lorentz contracted particles is
very close to the dense packing limit of classical hard spheres of same radius
$\eta_{exc} \approx 0.74$. We show that the developed equation of state is the
grand canonical formulation of the morphological thermodynamics approach
applied to Lorentz contracted rigid spheres.
