# Shape Optimization of an Integrated Mast for RCS Reduction of a Stealth Naval Vessel
## 3 Analysis Results
optimized mast had four spikes in the threat regions, which were at around 45\({}^{\circ}\), 135\({}^{\circ}\), 225\({}^{\circ}\) and 315\({}^{\circ}\), but they had relatively uniform values in the rest of the regions. Furthermore, the RCS (red and solid line) of the initial integrated mast was larger than that (blue and dashed line) of the optimized mast in the threat regions. At an elevation angle of 10\({}^{\circ}\), the RCS patterns of the initial integrated mast were also generally larger than those of the optimized mast and also had four spikes in the threat regions among the eight major spikes. On the other hand, the RCS spikes of the optimized mast were removed or minimized in the threat regions. In order to obtain the representative RCS values of the integrated mast, the geometric mean and the arithmetic mean were used. The geometric mean and the arithmetic mean were calculated based on all azimuth angles except for the cardinal points in a particular elevation angle and are listed in terms of the elevation angle in Tables 1 and 2, respectively. The geometric mean and the arithmetic mean of the optimized mast decreased by a maximum of 25.39 dBsm and 46.46 dBsm and by an average of 12.63 dBsm and 14.57 dBsm, respectively, compared with those of the initial mast. The representative RCS values of the optimized mast were improved overall. However, the geometric mean for the VV polarization at an elevation angle of 3\({}^{\circ}\) in the X-band and the arithmetic mean for HH polarization at an elevation angle of 0\({}^{\circ}\) in the S-band were degraded by 1.66 dBsm and 2.1 dBsm, respectively. It may seem that there were a few problems with the optimized mast but there were not. This was because, as mentioned in Section 2, the shape was limited due to the dozens of radars, sensors and antennas installed on the integrated mast, which might make it impossible to reduce the RCS for all incident angles in the spherical coordinate system. The geometric mean and the arithmetic mean also might have different results because the geometric mean had the dominant value for the large values and the arithmetic mean had the dominant value for the small values. Note the results in Figure 7a. The RCS (solid line) of the initial integrated mast had mostly larger values than those (dashed line) of the optimized mast but smaller values at azimuth angles of 45\({}^{\circ}\), 135\({}^{\circ}\), 225\({}^{\circ}\) and 315\({}^{\circ}\). Therefore, the arithmetic mean of the optimized mast was larger than that of the initial mast due to the RCS values at the elevation angles of 45\({}^{\circ}\), 135\({}^{\circ}\), 225\({}^{\circ}\) and 315\({}^{\circ}\). This was why the geometric mean and the arithmetic mean had different results as shown in Figure 7a. Figure 4: Three-dimensional radar cross section (RCS) pattern of the initial mast. (**a**) HH polarization in the L-band, (**b**) VV polarization in the L-band, (**c**) HH polarization in the S-band, (**d**) VV polarization in the S-band, (**e**) HH polarization in the X-band, (**f**) VV polarization in the X-band. (Unit: dBsm). Figure 5: Three-dimensional RCS pattern of the optimized mast. (**a**) HH polarization in the L-band, (**b**) VV polarization in the L-band, (**c**) HH polarization in the S-band, (**d**) VV polarization in the S-band, (**e**) HH polarization in the X-band, (**f**) VV polarization in the X-band. (Unit: dBsm). Figure 6: RCS pattern of the integrated mast in the azimuth plane in the L-band. (**a**) HH polarization at an elevation angle of 0\({}^{\circ}\), (**b**) VV polarization at an elevation angle of 0\({}^{\circ}\), (**c**) HH polarization at an elevation angle of 10\({}^{\circ}\), (**d**) VV polarization at an elevation angle of 10\({}^{\circ}\). Figure 8: RCS pattern of the integrated mast in the azimuth plane in the X-band.