 ## Radar Cross Section Benchmark on Simple Shapes

#### Introduction

This document presents simulation results from CAPITOLE-RCS on simple shapes. The monostatic RCS is calculated and compared to measured data publish in the following article : A.C. Woo, H.T.G. Wang, M.J Schuh and M.L Sanders « Benchmark Radar Targets for the Validation of Computational Electromagnetics Programs » IEEE Antennas and Propagation Magazine, Vol. 35, No. 1, February 1993. Theses models are intended for validation and benchmarking of Electromagnetic Simulation softwares. All simulations with CAPITOLE-RCS software was made on a Windows 10 laptop with Intel core i7 CPU and 16 Gb of RAM memory

#### 1. NASA Metallic Almond

• Model :

The NASA almond is actually not a simple shape. It is defined by mathematical equations to form a surface with almond shape. This model is very intersting to study RCS because it highligts a large dynamic on RCS value. The mesh should be refined on the tip and the bottom to keep a good accuray on the results.

The total length is 0.25 m (9.936 inches)

• Simulation parameters :

The Monostatic RCS is computed at 3 frequencies : 1.19, 7 and 9.92 GHz

For both Vertical and Horizontal polarization

The RCS is plotted in dBm2 as function of azimuth angle from 0 to 180°. Zero degrees azimuth corresponds to incidence on the tip. The elevation angle is zero.

• Solver :

Method of Moment method was used with MSCBD solver and EFIE equations.

 1.19 GHz 7 GHz 9.92 GHz Mesh size Lambda/40 Lambda/15 Lambda/15 Number of unknowns 3 546 17 262 34 692 Total time 2 seconds 17 seconds 57 seconds

Figure 1 – NASA Almond mesh model

Figure 2 NASA Almond RCS @1.19GHz CAPITOLE-RCS vs measurement

#### 2. Metallic Simple Ogive

• Model :

The model was created from the analytic expression to  create a curve and revolved to create a surface. The total length is 0.254 m (10 inches)

• Simulation parameters :

The Monostatic RCS is computed at 2 frequencies : 1.18 and 9 GHz

For both Vertical and Horizontal polarization

The RCS is plotted in dBm2 as function of azimuth angle from 0 to 180°. Zero degrees azimuth corresponds to incidence on the tip. The elevation angle is zero.

• Solver :

Method of Moment method was used with MSCBD solver and EFIE equations.

 1.18 GHz 9 GHz Mesh size Lambda/50 Lambda/20 Number of unknowns 3 648 34 968 Total time 1 second 1 min 12 s

Figure 3 – Metallic Simple Ogive mesh model

Figure 3 – Metallic Simple Ogive RCS @1.18GHz CAPITOLE-RCS vs measurement

#### 3. Metallic Double Ogive

• Model :

The model was created from the analytic expression to  create a curve and revolved to create a surface.

The total length is 0.191 m (7.5 inches)

• Simulation parameters :

The Monostatic RCS is computed at 2 frequencies : 1.57 and 9 GHz

For both Vertical and Horizontal polarization

The RCS is plotted in dBm2 as function of azimuth angle from 0 to 180°. The elevation angle is zero.

• Solver :

Method of Moment method was used with MSCBD solver and EFIE equations.

 1.57 GHz 9 GHz Mesh size Lambda/40 Lambda/15 Number of unknowns 3 288 15 096 Total time 1 second 13 seconds

Figure 5 – Metallic Double Ogive mesh model

Figure 6 – Metallic Double Ogive RCS @1.57GHz CAPITOLE-RCS vs measurement

#### 4. Metallic Cone-Sphere

• Model :

The model was created from the analytic expression to  create a curve and revolved to create a surface.

The total length is 0.689 m (27.127 inches)

• Simulation parameters :

The Monostatic RCS is computed at 2 frequencies : 869 MHz and 9 GHz

For both Vertical and Horizontal polarization

The RCS is plotted in dBm2 as function of azimuth angle from -180 to 0°. -180 degrees azimuth corresponds to incidence on the tip. The elevation angle is zero.

• Solver :

Method of Moment method was used and EFIE equations.

MSCBD solver for 869 MHz case and MLACA for 9 GHz case.

The MLACA solver is more accurate for low level RCS, particularly for 9 GHz conesphere in HH polarization.

 869 MHz 9 GHz Mesh size Lambda/40 Lambda/20 Number of unknowns 8 664 227 793 Total time 12 seconds 3h 11min *on a 48 cores server

Figure 7 – Cone-Sphere mesh model

Figure 8 – Metallic Cone-Sphere RCS @869MHz CAPITOLE-RCS vs measurement

#### 5. Metallic Cone-Sphere with Gap

• Model :

The model was created from the analytic expression to  create a curve and revolved to create a surface.

The total length is 0.689 m (27.127 inches)

• Simulation parameters :

The Monostatic RCS is computed at 2 frequencies : 869 MHz and 9 GHz

For both Vertical and Horizontal polarization

The RCS is plotted in dBm2 as function of azimuth angle from -180 to 0°. -180° degrees azimuth corresponds to incidence on the tip. The elevation angle is zero.

• Solver :

Method of Moment method was used with MSCBD solver and EFIE equations.

 869 MHz 9 GHz Mesh size Lambda/40 Lambda/15 Number of unknowns 8 952 131 508 Total time 13 seconds 7 min 26 s

Figure 9 – Cone-Sphere with gap mesh model

Figure 9 – Metallic Cone-Sphere with gap RCS @869MHz CAPITOLE-RCS vs measurement