Savonius wind turbines are drag-type vertical axis wind turbines. Their blades experience less drag while moving against the wind flow and more drag while moving in the wind direction. The drag difference rotates Savonius wind turbines and produces electrical power. Savonius wind turbines can catch wind from any direction. No yaw motion mechanism is needed for them to be pointed in the wind direction. Savonius wind turbines have simple structures and are convenient to install and maintain. They can operate on low wind speed and have good starting characteristics. Compared with horizontal axis wind turbines and lift-type vertical axis wind turbines such as Darrieus and Giromill wind turbines, Savonius wind turbines have relatively low power conversion efficiency. This is because of their drag-type nature which generates positive and negative torque on their advancing and returning blades, respectively. Savonius wind turbines are suitable for locations where power conversion efficiency can be compromised for the sake of low cost and high reliability. One major drawback from Savonius wind turbines is the negative static torque which lowers their self-starting ability. Although the negative static torque of Savonius wind turbines can be mitigated by adding additional components such as curtains, nozzles and ducts to them, these additional components make them complex and lose omnidirectional performance. In this paper, Savonius wind turbines are designed based on their geometric parameters to remove their negative static torque and improve their performance. Savonius wind turbines with different numbers of blades and other geometric parameters are designed, analyzed and simulated.