Normal every day objects can be digitally represented through computer-aided design (CAD) models. Furthermore, these CAD models can be realistically sized, attributed, and imported into optical, mechanical, or radio-frequency (RF) models to help in calculations such as radar cross-section (RCS). When imported, some models can present many questions due to the complexity of the model. For instance, what RCS signature does an airplane’s wings have relative to the RCS generated by the airplane’s body? Does the size of the propeller, or the struts for the tires cause these components to act as antennae instead?

   To better understand the complete output of an RCS model, it is instructive to break (a) the CAD model down into (b) it’s constituent components, which can then be isolated into (c) shapes that can be easily understood.

An airplane simplified as a canonical shape

Mesh characterization

   One method used to track the fidelity and density of a mesh is by characterizing the number of elements per wavelength (EPW). In this case, the wavelength is the wavelength of the incident source expected to interact with the mesh, so EPW is relative to the radiation defined in the model. Although a higher mesh density results in higher EPW counts, it also affects the solution accuracy and can significantly increase simulation runtime. For multi-parameter models that include multiple frequencies, polarization states, etc., the overall execution time could be increased dramatically.

   Unsurprisingly, this too can be characterized, and limitations on the parameter set can be defined so each model runs at a known fidelity and will achieve completion in a reasonable known time. However, this trade study also means running multiple models and tracking their average execution time over a series of simulations. For instance, the EPW value of the mesh illustrated in the above figure (c) can be slowly increased to the create the following shape definitions. Although the model on the left (a) would certainly run much faster in an RCS simulation, it would lack the fidelity of model (c) on the right. Of course, the simulation runtime for model (c) would be greater, so it’s possible model (b) may be a good compromise of both execution time and RCS response fidelity. Models performed for this study used the CUBIT software from Sandia National Laboratories, and the CAD shapes were defined and modified in Blender.

Meshes in an EPW trade study

Canonical shapes

   It’s worth taking a moment to ask, “How do you know our RCS response is correct?” The answer to this is validate the model’s RCS response against known and accepted RCS profiles. For instance, there are a number of “3d bodies of revolution” that have been historically used to determine the accuracy of new and existing RCS software. The shape used in the previous examples is known as the “conesphere”, but other shapes include “ogive”, “double ogive”, spheres, “squat cylinders”, and “squat dihedrals”. 

   It’s also worth noting that the canonical nature of these shapes is not only meant for simulation — they are also canonically, well-defined shapes that can be used with empirical RCS measurements that further help to validate output from the simulations. Below are four shapes typically used to validate RCS calculations. From left to right, they are (a) the NASA almond, (b) ogive, (c) double ogive, and our beloved (d) conesphere.

An EPW trade study

   Implementing the conesphere model illustrated above, the RCS of each conesphere with increasing EPW values can be plotted using simulated bistatic RCS measurements. In the illustration below, a conesphere mesh is attributed with different EPW values; the resulting meshes are then fed into an RCS mesh and the bistatic RCS calculation is plotted on a polar plot. The “HH” on the polar plot illustrates that the simulated radiation is horizontally polarized, and the RCS signal  response is only collected for horizontally polarized radiation. As the mesh density increases, the RCS values are seen to converge. Like any other scientific application, which mesh is “good enough” is highly dependent on the application.

Convergence of the conesphere RCS

 Down the rabbit hole

   Keep in mind that all of this effort — the airplane body approximation, the EPW mesh density study, and the fidelity comparison with validated RCS responses from canonical shapes — are all based on one aspect of the airplane CAD model we started out with. Although, if validation is demonstrated for the conesphere, it stands to reason that the airplane model could be added into the simulation next, swapped out for the canonical conesphere shape.

   On the other hand, if a study were being performed on the RCS of standard airplane wings versus a more sophisticated swept-back wing model (or some other drastic aerodynamic body change), it may be beneficial to forego the airplane model altogether and concentrate specifically on the airplane wings and optimizing their design for high lift and low RCS signature.


   Radar cross-section modeling is a fascinating field, and has an even more interesting history. From stealth fighters to warships, RCS calculation has become a highly sought-after skillset and a detail that is widely applied across the aviation industry.

   In some cases, RCS doesn’t matter too much — commercial airliners, for example, do not care about minimizing their RCS because they have no fear of being spotted. In fact, their RCS pattern allows them to be spotted via RADAR and tracked for safety purposes throughout their flight. Other military jets, however, care deeply about their RCS footprint and take every precaution to minimize their visibility to RADAR.

   Luckily, RCS calculations are no longer secretive and have become fairly mainstream. Unlike in the late 1960s, RCS calculators are now available to academics and professionals alike through software such as ANSYS, Matlab, WIPL-D, and others.