## 5 Simulation Method Uncertainties
### Solver Accuracy  
We worked with two different solvers, each used in a more and a less accurate configuration. It is important to understand what the reduction in accuracy is with the changes in configuration. Since it would not be computationally reasonable to perform full MoM simulations of the entire flight path, we instead selected a smaller number of points along the path. We then performed full simulations on these points. We began this by selecting nine uniformly spaced data points from the entire flight period to obtain broad coverage of the full flight. This initial choice meant that most of the points were from times where the aircraft was in level flight and side-on to the transmitter and receiver, so additional points were added where the aircraft was turning and therefore where the orientation of the aircraft relative to the transmitter and receiver was changing significantly. We used the region where the magnitude of the roll exceeded 18\({}^{\circ}\) as a computationally friendly proxy for this turn and selected 5 additional uniformly spaced data points from the region. One data point happened to exist in both data sets, leading to a total of 13 unique data points. These data points are shown on the flight track in Figure 10, and their yaw, pitch and roll values are shown in Figure 11.  
In most cases, the full MoM simulations converged after the second iteration, with the mesh for the second step typically having approximately 354,000 elements. However, the seventh, eighth and ninth example points required three iterations to converge (in all cases only just missing the default convergence criterion on the second iteration), with the final meshes each having approximately 460,000 elements. It is likely not a coincidence that these points occurred when the aircraft was banking, was pitched up, and had its tail to the transmitter and receiver, as opposed to the side-on illumination and near level flight of the other sample points, but we do not have enough data to be certain about which of these factors are significant, or how general this behavior is. When comparing each of the five simulated frequencies independently, the largest difference between the full and basic MoM simulations was 1.72 dB, the mean difference 0.44 dB and the median difference 0.31 dB. If the means of the RCSs across the five simulated frequencies are computed and then the differences of these mean values are taken, the resultant maximum, mean and median differences are 1.38 dB, 0.36 dB and 0.27 dB. Thereare not a sufficient number of data points here to draw truly general conclusions about the effect of the measurement geometry on the scale of the error in our basic MoM solver method, but for the purposes of our measured flight, the errors are small, particularly when compared with the 34 dB range of simulated RCS values. Figure 11: The 13 yaw, pitch and roll values used for the full MoM simulations (red dots) plotted on the full set of available values (blue lines), used for the SBR+ simulations: (**a**) yaw simulation points; (**b**) pitch simulation points; (**c**) roll simulation points. Figure 10: Points at which full MoM simulations have been performed. The impact of the errors can be seen in Figure 12, which shows the means of the five-frequency received-power values (\(P_{S}^{t}(t)\), Equation (7)) computed with both the basic (single iteration) and full (multi-iteration) MoM simulation methods. Similar comparisons between these full MoM simulation points and the full and basic SBR+ simulations yield mean errors of 3.2 and 5.8 dB, respectively. In both cases this is driven by a single extreme value for one data point, but in the basic SBR+ case, there are nevertheless three data points at which the error exceeds 10 dB. However, for the SBR+ simulations, we can obtain a more robust estimate of the error in the SBR+ method from comparisons with the basic MoM values at their 242 common simulation points, which yields slightly lower mean differences of 2.1 and 2.5 dB, respectively.