Nonlinear scaling study of a railgun

Scaling method has been used widely in railgun technology. But nonlinear problem is seldom studied because of the complexity and uncertainty. In order to employ the scaling method better, the paper brings the nonlinear drag model to the solid armature railgun circuit. Several drag functions were compared including drag model associated with velocity (VDM), drag model associated with current (CDM), and drag force associated with integrated factors (IDM). Scaling relationships of these drag models were discussed. And then, a novel experiment was constructed to compare the drag models at low velocity. Further simulations at high velocity are also studied. At last, the nonlinear scaling method was verified by an example at high velocity. It shows that VDM is far from satisfactory at high velocity. The scaling conditions of VDM are too strict to use in practice. CDM is workable only in high velocity condition which satisfies conditions of linear scaling method (LSM) in nature. But it is worthless when the velocity is less than about 0.5 km/s. Although a bit complex, IDM is very accurate at any condition. Coefficient α in IDM should be taken considering different test conditions. Scaling relationships of IDM could not be derived at low velocity due to nonlinearity. While at high velocity, IDM could be simplified to CDM and realize LSM. Further research indicates that IDM could use the scaling method directly and realize approximate LSM at high velocity. Due to the work range of the solid armature is usually 1~2km/s, nonlinear scaling method could be used in a railgun with IDM. What should be noted is that the velocity scaling factor must be controlled above about one quarter to avoid the nonlinear field. A detailed analysis of the experiments and simulations will be presented in this paper.