## 1 Introduction  
During ship manufacturing, many plates with complex curvatures must be formed for the main hull of a ship, which is a time-consuming process. During this process, the line heating method creates local contraction deformation in a plate via a localized heating source, of which width is significantly narrower in size than the plate length or width as this processing method is based on moving a handheld oxyacetylene gun over a processed plate. In addition, it is believed that a narrower flame is beneficial to the formation of plate shapes with small curvatures. This method is widely deployed. It is difficult to control the heat input when using a flame heat source. For line heating-based automated forming equipment, an electromagnetic induction heating has become a new heat source for the hot forming of ship hull plates because it is easy to control. [PERSON] [1,2] investigated the pattern of ship hull plates forming by line heating, discussed the heating line deployment principle and the heating criteria based on the theory of inherent strain, and verified and modified the path produced via induction heating. This work laid the foundation for the development of automated line heating forming equipment for ship hull plates. With the successful development of an automated system for ship hull plates forming by line heating [3], induction heating devices are gradually replacing manual oxyacetylene guns and are becoming a common heat source in line heating processing. Inductionheating generates an eddy flow in the target material via an induction current with a specific frequency and provides heating via eddy flow heat conversion. Induction heating equipment normally consists of an induction coil and an alternating current (AC) power source. Here, the size of an induction coil is directly related to the heating area. Therefore, the induction coil size should be an important influencing factor for a forming process that uses induction-based line heating. [PERSON] [4] investigated induction heating deformation with specific induction coil dimensions and provided a simplified equation for predicting transverse shrinkage and angular deformation. The equation contains heating parameters such as speed and power; however, the effect of the induction coil dimension is not addressed. [PERSON] [5] calculated an induction heating system in three dimensions and suggested that induction coil dimension parameters could be adjusted to achieve an optimal design for heat distribution; however, the relationship between the induction coil coverage area and the heating object deformation was not addressed. [PERSON] [6] designed an induction coil shape via an empirical design method and investigated the effect of the coil shape under static heating. In some papers pertaining to the effect of special heating shapes on thick plate deformation, the temperature field and plate performance after heating improvement [7; 8] and the relationship between the induction coil or temperature field and plate deformation were addressed to some extent. [PERSON] [9] studied the shape parameters of the inductor and compared the processing efficiency during plate bending based on numerical experiments. [PERSON] [10] studied the influence of coil shape and heating parameters on temperature field distributions during static heating. [PERSON] [11] studied the influence of the cross-section parameters of the inductor on the temperature field and determined the main influence parameters of the coil using the experimental design method. However, there is no direct conclusion about the effect of the relative dimensions of the induction coil and the processed plate. Additionally, discussions of the effects on forming efficiency with the different dimensional induction coil are scarce.