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Purpose Helical coil electromagnetic launchers (HEMLs) using motion-induced commutation strategy solve the problem of synchronization control perfectly. HEMLs can meet the requirements of multiple applications such as the electromagnetic catapult, electromagnetic mortar and high-velocity coilgun. The trade-off between the velocity and efficiency is an important basis for these different applications. To optimize such objectives before actual design, the purpose of this paper is to focus on the efficient and flexible calculation model and algorithm. A novel structure of HEML is proposed after the transient simulation by this algorithm, which can improve the energy conversion efficiency and suppress the muzzle arc without affecting the velocity too much.Design/methodology/approach The equivalent circuit model of the launcher is established and the governing equations are derived. A combination of the four-stage Runge–Kutta method and the trapezoidal quadrature formula are used to solve the governing equations.Findings With smaller number of turns in the coils of HEML, the velocity is larger and the efficiency is lower. The non-uniform HEML is an effective option to improve the energy conversion efficiency and to suppress the muzzle arc with almost the same muzzle velocity as the conventional HEML.Originality/value The paper presents a common model and a flexible fast numerical method which can be used in multi-objective optimization of HEMLs such as the genetic algorithm. A new structure of the non-uniform HEML is proposed to improve the energy conversion efficiency and to suppress the muzzle arc of the launcher. [ABSTRACT FROM AUTHOR]