The magnetic properties of arrays of nanoparticles are determined by the interplay between the individual particle properties and the dipolar interactions between them. Here we present a study of arrays of elliptical Fe(001) particles of thickness 10-50 nm. The aspect ratios of the ellipses are 1:3, their short axes a = 50, 100, or 150 nm, and the periodicity of the rectangular arrays is either two or four times the corresponding axes of the ellipses. Magnetic measurements together with numerical and micromagnetic calculations yield a consistent picture of the arrays, comprising single-domain nanoparticles. We show that the magnetization reversal, occurring in the range 100-400 mT for fields applied along the long axis, is mainly determined by the properties of the corresponding single Fe ellipses. The interaction fields of the order of tens of mT can be tuned by the array configurations. For the actual arrays the interactions promote switching. For film thicknesses below the Bloch wall width parameter of Fe, l(w) = 22 nm, magnetization reversal occurs without formation of domain walls or vortices. Within this range arrays may be tuned to obtain a well-defined switching field. Two general conclusions are drawn from the calculations: the character of the interaction, whether it promotes or delays magnetization reversal, is determined by the aspect ratio of the array grid, and the interaction strength saturates as the size of the array increases.