Re: What is the basic theory behind continues curvature

That's a good question.

The geometry of an aircraft greatly influences it's radar cross section.
Let's consider the radar cross section of different shapes:

1. Thin convex structures, like a toothpick
2. Flat surfaces with concave structures, like a bicycle reflector

If you trace out the rays of radar waves and their reflections, you will
quickly discover that thin convex shapes reflect much less than others.
There's nothing magical about thin convex structures, it just turns out that
flat surfaces with concave structures are really good reflectors.

If you look closely at the surface of a bicycle reflector, you will see
what looks like miniature pyramids arranged in a grid. These pyramids look
like the corners of a room where the walls and ceiling meet. It turns out
that this structure can ideally reflect all incoming waves back to the
source. This works with sound just as it would with light or radar waves.
It's easier to trace this out in two dimensions, but it works the same way
in three dimensions. It's also best to minimize surface area because larger
surfaces reflect more than smaller ones.

This observation suggests two things:

1. Minimize surface area
2. Avoid concave structures

Early stealth aircraft used obtuse angle so that any incoming radar wave
bounces off in a direction that is far away from the source. This isn't
perfect, but it's a lot better than a 90 degree corner. Corners can appear
in odd places. Commercial aircraft may not look concave, but consider the
wing roots. The attachements to the fuselage creates corners that are not
far from 90 degrees. This is the kind of structure that engineers try to
avoid when designing stealthy aircraft.

Newer stealth aircraft try to reduce corners further through the use of
smooth surfaces all around. This continuous curvature is even better than
obtuse angles used by older stealth aircraft.

The materials are also important. If the surface has a resistance of 377
Ohms, it will absorb most, if not all of the radar waves. This is because
the impedence of free space (air in this case) is about 377 Ohms. This is
like adding foam to the walls in a room, the foam will absorb much of the
sound and reduce echoes. Recording studios often carpet the walls to
achieve the same effect.

I hope that answers your question.