A parallel application of electromagnetic (EM) modeling of aircraft is electromagnetic shielding and coupling. My recent post on calculating radar cross-section (RCS) looked at simplifying an airplane CAD model to a more simple canonical geometry, and performing validation and EPW trade studies on the model. The simplifying process is shown again below using (a) a life-sized airplane computer-aided design (CAD) model, (b) the same CAD model with an applied mesh, and (c) the much more simplified aircraft body approximated as a conesphere.

An airplane simplified as a canonical shape

Aircraft RCS

   The previous discussion on RCS ended a bit prematurely; although we had demonstrated possession of a meshed airplane CAD model, the discussion only examined a bistatic RCS for the conesphere shape, and not the aircraft as a whole. The simulations, however, do not know the difference between a conesphere mesh and an aircraft mesh, so it is straight-forward to make the substitution of one geometry for another.

   The images below illustrate substituting the simple aircraft model for the conesphere model used earlier. The model (left) shows segmentation of the aircraft into its different components: a nosecone, wings, fuselage, tail, rudder, ailerons, and elevators. Put into the simulation, this model produces the bistatic RCS plot on the right. As indicated in the left image, RCS is calculated “in-plane” with the aircraft’s wings, circling the aircraft in the same plane.

Simulated RCS of an aircraft model

Surface currents

   Interestingly, by calculating the RCS of the aircraft, we also capture another aspect of the model: surface currents. By understanding the surface currents on (a simplified version of) the aircraft’s body, it is possible to predict at what angles and frequencies an aircraft may become susceptible to. While surface currents (and shielding from resonant currents!) may not be a big deal for civilian or commercial aircraft, they become a much higher concern when considering EM coupling onto the body of similarly shaped objects like missiles and other deadly ballistics.

Calculated surface currents on a simplified aircraft body

   But why are surface currents such a concert to such assets? The answer lies in the construction. Electromagnetic waves are similar to water in that every single opening in a structure will be penetrated, enabling radiation to enter the container. Unlike water, however, EM radiation can also excite resonant modes along different facets of the geometry, thereby causing sections of the container to re-radiate radiation similar to an antenna. In turn, the radiation itself becomes an issue because the energy radiated by the “antenna” can then couple onto electrical wires and circuit boards used to keep track of trajectory, detonation conditions, and other factors.

   The importance of understanding the surface currents becomes alarmingly obvious. If any of these factors were to be interrupted, corrupted, or disabled by stray electromagnetic radiation, things become involuntarily dangerous very quickly.

Multi-angle radiation

   In the polar RCS plots illustrated so far, the source and detector have all been rotated in one 2D plane around the 3d meshed object. In reality, radiation will be approaching the object from all sides at different angles. It stands to reason, then, that similar studies should be performed for multiple angles. In doing so, the polar line plots of RCS transform into a three-dimensional surface representing the bistatic RCS covering a wide variety of angles. Although limited by the two-dimensional surface of this screen, the illustration below attempts to show (left) a single RCS scan of the conesphere geometry alongside a (right) RCS “surface” created by calculating RCS of the conesphere across a large number of angles.

RCS surface

A missing parameter

   As the model grows more complex, so does the execution time and complexity of the results. Although the RCS “surface” illustrated above seems complicated, that surface was generated using only one frequency. With different frequencies, the RCS calculated at each angle of the conesphere also changes. Restricted by the 2D imagery of this screen, the evolution of the RCS surface as a function of frequency can be done by extending the RCS surface “slice” above into a video of the morphing RCS surface as a function of frequency. This type of morphing surface is shown below.


   As the RCS measurements become more physically accurate and the models grow in complexity, bookkeeping can become a nightmare, and the simulation’s execution time can become tediously long. However, there are factors in place to help mitigate some of these hurdles. For instance, calculation of an RCS surface as a function of angle (or the evolution of a surface as a function of frequency) are prime candidates for hyperthreading and parallelization across many cores. As discussed in the previous RCS article, lowering the mesh’s EPW count to a value that still maintains a high degree of model fidelity.