Mathematica in Furtive Fighters and Squashed Sidelobes
Mathematica Facilitates Precision Coating Technology
September 14, 1998--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--until recently, applying the
conductive coating properly still required a technician,
gradually blending areas with a spray gun exactly the way an airbrush artist does when
painting flames on a motorcycle.
At least, that's how airframers used to do it until they added Mathematica
to their process. Mathematica, the world's only fully integrated technical
computing system, 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 define precisely 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. This phototool is then used in a
photochemical etching process to place the conductive coating exactly where it's needed
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 handles 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.
"Any number of programs can generate PostScript graphics, and some of
these are even acceptable for CARTs," said Matthew M. Thomas, Technology
and Define Processes, The Boeing Company. "But few of them offer the ease
of use Mathematica offers, and none of them offers the mathematical
sophistication Mathematica offers. Ease of use is why we use Mathematica
with CARTs today. Mathematical sophistication is why we'll use
Mathematica with CARTs in the future."
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.
To highlight CART technology, Boeing will share a booth with Wolfram
Research, makers of Mathematica, during Wescon/IC Expo 98, North
America's largest technology expo for OEM electronics professionals,
from September 15 to 17 in Anaheim, California.