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Scattering of EM waves from trees and
foliage as well as the propagation of EM waves in the presence of
forests plays an important role in many civil and military applications.
For example, in the usage of Foliage Penetrating Radar (FOPEN) for
detecting potential targets in the forest. If all the trees are modeled
as dielectric rods and plates, the CPU time needed for rigorous MoM
simulation is unacceptable for the real-life problems. However, the
approximate but still accurate modeling is possible using the WIPL-D Pro
EM solver.
Efficient MoM Modeling of Trees and Foliage
Computationally efficient modeling of trees and foliage can be done with
metallic wires (for branches) and metallic plates (for leaves) with
distributed loadings over them. The error is negligible for all branches
that have the radii
a<=λ/8, where
a is the radii and
λ is the wavelength at the
operating frequency. The branches that do not satisfy this condition
have to be modeled rigorously as the dielectric rods. With this approach
the number of unknowns needed for the simulation is reduced
approximately 100 times! Only ~100 unknowns are needed for the modeling
of a single tree, using presented approach.
Model of Tanks in Forest – Complex Scenery
The model of a tree with only metallic
wires and plates is valid up to approximately 150 MHz (considering that
the tree trunk has diameter less than about 2 ft / 60 cm). Over that
frequency, the tree trunk has to be modeled as the dielectric rod. On an
ordinary PC with 2 GB of RAM, the simulation of the whole forest with
100 randomly placed trees and additional objects inside takes only a few
hours.
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Models of Trees |
Detail of leaves and branches |
The presented approach opens the
possibility for a rapid full 3D EM simulation of complex sceneries
involving trees, foliage, and potential targets inside forests. Applying
this approach on the parallel computers and clusters allows simulations
of the whole landscapes and complex sceneries.
Case Study
Project: Calculating Radar cross-section (RCS) of a tank alone and the
same tank in the forest at 100 MHz. The forest has 50 trees, and the
tank is positioned in the middle of it. The total number of unknowns for
the project is 5196 (1604 for the tank and 3592 for the forest). The
number of monostatic directions is 721.
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Model of Tank |
Model of Tank In Forest |
RCS of Tank (yellow) and Tank in Forest
(blue)
Comments: The simulation of the
scenery took approximately 30 minutes on an ordinary PC (3.2 GHz Intel
Pentium 4 with 2 GB of RAM at 433 MHz.)
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