# Shape Optimization of an Integrated Mast for RCS Reduction of a Stealth Naval Vessel
## 3 Analysis Results  
According to the aforementioned rules in Section 2, we defined the threat frequencies of the L-, S- and X-band and the threat regions of 0\({}^{\circ}\) to 360\({}^{\circ}\) in the azimuth plane and 0\({}^{\circ}\) to 10\({}^{\circ}\) in the elevation plane, respectively. The cardinal points were also defined as \(\pm\)5\({}^{\circ}\) in the forward, starboard, port and stern regions in the azimuth plane. Figure 3 shows the geometry and dimension of the initial shape and optimized shape of the integrated mast, respectively. The length, width and height of the initial integrated mast were 10 m, 10 m and 12.5 m, respectively, and those of the optimized mast were 10.95 m, 10.95 m and 15.1 m, respectively. The details of the dimensions of the initial and optimized design are shown in Figure 3. The physical size of the optimized mast was a little larger than the initial integrated mast. We analyzed the RCS of the integrated mast using the asymptotic solver of CST Microwave Studio based on the SBR method, which included the diffraction fields at the edges [26]. We assumed that the integrated mast and the naval vessel were a PEC. The maximum number of reflections was set to five and the mesh consisted of curved triangles and the normal tolerance/degree was set to five. The simulation was carried out on a PC (Dual Intel Xeon CPU E5-2640 v4 at 2.40 GHz, 256 GB memory). The RCS was simulated in the azimuth plane and in the elevation plane at intervals of 1\({}^{\circ}\) in the L-, S- and X-band, respectively. The RCS results of the initial model and the optimized mast are illustrated in Figures 4 and 5 as three-dimensional RCS patterns, respectively. The scattering mechanism was mainly composed of specular reflections and edge diffractions. As shown in Figure 4, the RCS of the initial model had many spikes regardless of frequencies and polarizations. The major spikes of the initial model occurred at 0\({}^{\circ}\), 45\({}^{\circ}\), 90\({}^{\circ}\), 135\({}^{\circ}\), 180\({}^{\circ}\), 225\({}^{\circ}\), 270\({}^{\circ}\) and 315\({}^{\circ}\) in the azimuth plane for the elevation angles of 10\({}^{\circ}\) and 15\({}^{\circ}\) due to the side slope and the chamfered edges. However, as the spikes at 0\({}^{\circ}\), 45\({}^{\circ}\), 90\({}^{\circ}\), 135\({}^{\circ}\), 180\({}^{\circ}\), 225\({}^{\circ}\), 270\({}^{\circ}\) and 315\({}^{\circ}\) in the azimuth plane when the elevation angle was at 10\({}^{\circ}\) were in the threat regions, they had to be eliminated or minimized for stealth design. To eliminate or minimize the spikes, we reduced the chamfered edges at 45\({}^{\circ}\), 135\({}^{\circ}\), 225\({}^{\circ}\) and 315\({}^{\circ}\) in the azimuth plane and left only a minimum space for antenna installations. The side slope of the integrated mast was redesigned with the same slope as the superstructure to focus the spikes on the cardinal point. Moreover, the top radius and the height of the truncated cone were modified to reduce the RCS. The shape of the integrated mast was minutely changed in all parts and the overall size of the integrated mast was slightly increased. As shown in Figure 5, the RCS of the optimized model had four or eight major spikes in the azimuth plane when the elevation angle was at 15\({}^{\circ}\) regardless of frequencies and polarizations but the spikes were not in the threat regions. To compare both the results of the initial and the optimized shape, their RCS patterns in the azimuth plane for the elevation angles of 0\({}^{\circ}\) and 10\({}^{\circ}\) in the L-, S- and X-band were plotted and are shown in Figures 6-8, respectively. Note the results at the elevation angle of 0\({}^{\circ}\) in the L-, S- and X-band. Due to the impact of the scattering by the truncated cone on the top of the integrated mast, both the results for the initial mast and the  
Figure 3: Dimension of the integrated mast. (**a**) initial mast, (**b**) optimized mast.