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Coilguns are one of the most widely used projectile launch systems using electromagnetic force. The ideal coilgun would propel a projectile with maximum velocity while also having a high power efficiency. The physics of coilguns is well understood; however, optimizing the coilgun design is much more difficult, as it requires the consideration of the parameters of every component of the system, such as the coil, projectile, and power supply. In this paper, electromagnetism, kinematics, and electrical circuit theory are employed to analytically describe the operations of a coilgun with permanent magnetic projectiles. These analytical equations are then implemented using mathematical programs. Coilguns with distinct design parameters and current profiles can be tested numerically to quickly find the optimal combinations to achieve the maximum velocity or power efficiency. The results are presented and measurements are utilized to verify the predictions. [ABSTRACT FROM AUTHOR]