System of systems engineering (SoS) approaches are required for the architectural design of complex systems. In this paper, we propose an approach for the architectural design of SoS based on the mission profile modeling and analysis. The mission profile is decomposed to operations and the operations are mathematically modeled. This approach is applied to a case study of on-demand electric aviation system, for the evaluation of the different alternatives at the SoS mission level. Results show that using mathematical modeling and Multidisciplinary Design Analysis (MDA) facilitate the exploration of the different alternatives of SoS architectures. This helps SoS architects in making strategic decisions for the choice of best solutions in conceptual level.