Although the concept of determining angular velocity out of the readings of multiple, displaced accelerometers is not new, apparently it has not yet matured into practical technologies. A new generation of low-cost MEMS accelerometers, which is expected to breakthrough in the next years, may enable gyro-free navigation in small platforms such as UAVs, ground vehicles and small planes. In this work we analyze a Gyro-Free Inertial Navigation System (GF-INS) employing four triads of accelerometers in a Distributed Redundant IMU configuration (DRIMU). We investigate the statistical properties of the angular velocity estimator by means of simulations and we speculate on the noise level requirements for the accelerometers that would allow a gyro-free navigation system to match the performances of a conventional IMU. Furthermore, we investigate the performance of using the gyro-free angular velocities estimator in combination with GNSS for navigation in a classical error-state EKF.