The current study systematically analyzes the impact of solidity (sigma) and number of blades (n) on the aerodynamic performance of 2-, 3- and 4-bladed Darrieus H-type vertical axis wind turbines (VAWTs). Solidity varies within the wide range of 0.09-0.36. A large number of operational parameters, i.e., tip speed ratio (lambda), Reynolds number (Re), turbulence intensity and reduced frequency (K) are investigated to provide a deeper insight into the impact of sigma and n on the dynamic loads on blades, the turbine performance and the wake. High-fidelity unsteady Reynolds-averaged Navier-Stokes (URANS) simulations, extensively validated with experiments, are employed. The results show that the turbine optimal tip speed ratio (lambda(opt)) is invariant to a newly-introduced parameter 'sigma lambda(3)', regardless of the turbine geometrical and operational characteristics. In addition, a new correlation is derived to estimate lambda(opt) as a function of sigma, which can also be employed to predict the optimal sigma for a turbine with a given lambda. It is also found that: (i) for constant-speed urban VAWTs, which due to the low mean wind speed in the urban environment, frequently operate at moderate to high lambda, a relatively-low sigma is optimal; (ii) an optimal VAWT is a moderately-high-solidity variable-speed rotor maintaining a relatively-low lambda, where due to the large blade chord length the resulting Re and K are favorably high; (iii) within the turbine optimal operational range, turbine power coefficient (C-P) is almost independent of n. The present findings support the optimal aerodynamic design of small-to large-scale VAWTs. (C) 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).