# Application Note 1: Modeling Radar Signature Of Real-Sized Aircraft Using EM.Tempo

## Introduction

In this application note, we will demonstrate how EM.Tempo can be used to compute the bistatic radar cross-section (RCS) of a large-scale target such as the Dassault Mirage III type fighter aircraft at an operating frequency of 850 MHz. A high-fidelity mesh of a structure like this involves tens or hundreds of millions of cells. As the operating frequency is increased, so does the size of the computational problem. Throughout the article, we will discuss some of challenges encountered when working with electrically large models. You can learn more about the basic procedure for setting up an FDTD RCS simulation in "EM.Tempo Tutorial Lesson 2: Analyzing Scattering From A Sphere".

## Computational Environment

The Mirage III CAD model has an approximate length of 15m, a wingspan of 8m, and an approximate height of 4.5m. Expressed in free-space wavelengths at 850 MHz, the approximate dimensions of the aircraft model are 42.5 λ0 x 22.66 λ0 x 12.75 λ0. Thus, for the purposes of EM.Tempo, we need to solve a region of about 12,279 cubic wavelengths. For problems of this size, a very large CPU memory is needed, and a high-performance, multi-core CPU is desirable to reduce the simulation time.

Amazon Web Services allows one to acquire high-performance compute instances on demand, and pay on a per-use basis. To be able to log into an Amazon instance via Remote Desktop Protocol (RDP), the EM.Cube license must allow terminal services. For the purpose of this project, we used a c4.4xlarge instance running Windows Server 2012. This instance has 30 GB of RAM memory, and 16 virtual CPU cores. The CPU for this instance is an Intel Xeon E5-2666 v3 (Haswell) processor.

## Importing the CAD Model & Simulation Setup

The CAD model used for this simulation was obtained from GrabCAD, an online repository of user-contributed CAD files and models. The imported CAD model has the "IGES" file format. After being imported to CubeCAD, the Mirage model is initially moved to a new perfect electric conductor (PEC) material group in EM.Tempo.

• The complete CAD model of Mirage aircraft imported to EM.Tempo's project workspace.

For the present simulation, we model the entirety of the aircraft, except for the cockpit, as PEC. For the cockpit, we use EM.Cube's material database to select one of the several glass of types with εr = 6.3 and σ = 0.017 S/m.

• Selecting glass as cockpit material for the Mirage model.

Imported large CAD models oftentimes require additional healing or welding of the geometric structure. For example, there might be small cracks or gaps between different surfaces. EM.Tempo's mesh generator is very robust with regard to small model inaccuracies or errors, and can resolve and cure most of the invisible or hardly visible structural defects using a control parameter called the absolute minimum grid spacing.

Since we are computing the radar cross section of a target, we need to introduce a plane wave source. For this example, we will specify an obliquely incident TMz plane wave source with θ = 135°, φ = 0°:

$\hat{k} = \frac{\sqrt{2}}{2} \hat{x} - \frac{\sqrt{2}}{2} \hat{z}$

We also introduce an RCS observable with a very fine angular resolution along both the elevation and azimuth directions: Δθ = Δφ = 1°. Although increasing the angular resolution of the far fields will significantly increase the simulation time, it is certainly needed for this project as the RCS of electrically large structures tend to have very narrow peaks and nulls.

We also define two field sensors: one with a horizontal plane underneath the aircraft, and another with a vertical plane along the length of the aircraft passing through its center line. The near fields are not the prime observable for this project, but they may add useful insight into the simulation without adding too much overhead to the simulation.

## Mesh Generation & Setting the FDTD Solver Parameters

To generate the FDTD Yee mesh of this structure, we use the "Fast Run/Low Memory Settings" preset. This will set the minimum mesh density at 15 cells per λeff, and permits grid adaptation only where necessary. This preset provides slightly less accuracy than the "High Precision Mesh Settings" preset, but it results in a smaller mesh size, and therefore a shorter run time. At 850 MHz, the resulting FDTD mesh contains about 270 million cells.

• The details of the FDTD mesh near the cockpit region of the aircraft.

For this simulation, we use most of the default simulation engine settings except for "Thread Factor". The thread factor setting essentially tells the FDTD engine how many CPU threads to use during EM.Tempo's time-marching loop. For a given system, some experimentation may be needed to determine the best number of threads to use. In many cases, using half of the available hardware concurrency works well. This comes from the fact that many modern processors often have two cores per memory port. In other words, for many problems, the FDTD solver cannot load and store data from CPU memory quickly enough to use all the available threads or hardware concurrency. The extra threads remain idle waiting for the data, and a performance hit is incurred due to the increased thread context switching. EM.Cube will attempt use a version of the FDTD engine optimized for use with Intel's AVX instruction set, which provides a significant performance boost. If AVX is unavailable, a less optimal version of the engine will be used alternatively.

After the sources, observables, and mesh are set up, the simulation is ready to be run. The complete simulation, including mesh generation, time-stepping, and far field calculations took 350 minutes on the above-mentioned Amazon instance. The far field computation requires a significant portion of the total simulation time.

## Examining the Simulation Results

After the simulation is complete, the 3D simulation data associated with the project observables can be visualized from EM.Tempo's navigation tree. The near-field distribution maps are shown in the figures below. The standing wave field patterns are visibly seen around the aircraft.

 Electric field distribution in the horizontal sensor plane underneath the aircraft. Electric field distribution in the vertical sensor plane passing through the center line of the aircraft.

The figure below shows the total 3D bistatic RCS pattern of the aircraft:

 The 3D total RCS pattern of the Mirage model at 850 MHz in dBsm. The aircraft structure is shown in the freeze state.

The figures below show the Cartesian graphs of the bistatic RCS pattern of the aircraft in the three principal coordinate planes:

 The Cartesian graph of the XY-cut RCS of the aircraft in m2. The Cartesian graph of the YZ-cut RCS of the aircraft in m2. The Cartesian graph of the ZX-cut RCS of the aircraft in m2.

The figures below show the polar graphs of the bistatic RCS pattern of the aircraft in the three principal coordinate planes:

 The polar graph of the XY-cut RCS of the aircraft in dBsm. The polar graph of the YZ-cut RCS of the aircraft in dBsm. The polar graph of the ZX-cut RCS of the aircraft in dBsm.