Knowing how the mass loss of carbon-rich AGB stars depends on stellar parameters is crucial for stellar evolution modelling, as well as for the understanding of when and how circumstellar structures emerge around these stars, e.g., dust shells and so-called detached shells of expelled gas. The purpose of this paper is to explore the stellar parameter space using a numerical radiation hydrodynamic (RHD) model of carbon-star atmospheres, including a detailed description of dust formation and frequency-dependent radiative transfer, in order to determine how the mass loss of carbon stars changes with stellar parameters.