Abstract. We present results from recent direct numerical simulations of heavy particle transport in homogeneous, isotropic, fully developed turbulence, with grid resolution up to 512 3 and R λ ≈ 185. By following the trajectories of millions of particles with different Stokes numbers, St ∈ [0.16 : 3.5], we are able to characterize in full detail the statistics of particle acceleration. We focus on the probability density function of the normalised acceleration a/arms and on the behaviour of their rootmean-squared acceleration arms as a function of both St and R λ . We explain our findings in terms of two concurrent mechanisms: particle clustering, very effective for small St, and filtering induced by finite particle response time, taking over at larger St.