Mathematica in Furtive Fighters and Squashed
Sidelobes
You've decided to paint red and
yellow flames on the side of your motorcycle. You want to blend the
colors along each flare according to a mathematical formula involving
hyperbolic trigonometric functions. Anything less than perfection would
render the whole paint job useless. What's the best approach?
Leading aerospace engineers faced a similar problem in applying a
surface coating to fighter aircraft. The critical feature in this case
is not
color but the electrical conductivity at the surface. This physical
property determines how an electromagnetic wave will scatter when it
hits the aircraft. But different parts of the aircraft have different
levels of
surface conductivity, and there's the catch--if there are sharp changes
in
conductivity from one area to another, the incoming wave scatters in a
way enemy radar can detect, thus giving away the fighter's position.
To avoid this problem, airframers would spray a conductive surface
coating of varying thickness onto the aircraft's surface, blending the
edges so that no sudden transitions occur in surface resistance.
Although the mathematical properties of the ideal blending pattern are
known--they're a direct consequence of the laws of
electrodynamics--applying the conductive coating properly still required
a
technician with a spray gun to create gradually blending areas exactly
the way an airbrush artist paints flames on a motorcycle.
At least, that's how they used to do it, until they added
Mathematica to
their process. Mathematica is no stranger to either higher math
or the creation of
sophisticated graphic images.
The process now goes like this. Engineers use Mathematica's
numerical
power to precisely define the ideal coating pattern for a given surface.
Next, using a very high resolution PostScript printer, technicians print
out a "phototool," an optical mask, from
Mathematica. The phototool
is then used in a photochemical etching process to place the conductive
coating exactly where it's needed and with exactly the right thickness.
For some fighter parts, the ideal coating varies along the surface
according to the hyperbolic cosine function. Because Mathematica
is as
familiar with hyperbolic trigonometric functions as it is with literally
hundreds of other special mathematical functions, it could handle the
task
easily. The tight integration among Mathematica's algebraic,
numeric, and
graphics capabilities makes the path from initial mathematical model to
final phototool a single, smooth development process.
The Boeing Company sees applications of this new surface coating
technology--called CART for "Computer-Aided Resistive Taper"--in
commercial products and is seeking to license it to
communications-related manufacturers. For example, a similar process
can prevent electromagnetic scattering within a parabolic antenna from
creating large sidelobes that degrade the antenna's performance.
Key features of Mathematica used:
| 
Any questions about topics on this page? Click here to get an individual response.
![[ja]](/common/images2003/lang_bottom_ja.gif)