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This paper presents the results of the optimisation of aerofoils designed for the blades of a vertical axis wind turbine. The aerofoils are symmetrical and have thickness values of 27%, 33% and 50\%, with respect to the chord length. The aerofoils are optimised using ADflow, an open-source RANS CFD solver developed for gradient-based design optimisation. We performed two sets of optimisations and validated the optimal designs from both sets, measuring their performance in the wind tunnel. We used the first wind tunnel campaign to quantify the performance degradation caused by surface roughness and tune the turbulence model accordingly. The following optimisation runs did include at least one operational point with higher surface roughness. The outcome of the optimisation is significant, as the new aerofoils provide much better performance in terms of aerodynamic efficiency, suitability of the position of the aerodynamic centre, and sectional area. Numerical and experimental data are consistent. The results highlight the importance of capturing the fundamental physics in CFD-based design optimisation to minimise the discrepancies between the numerical predictions and experimental results with the optimal designs. Finally, the performance improvement measured experimentally of the optimal aerofoils verifies the utility of CFD-based design optimisation.