4. Radar Cross Section: How Targets Look to a Radar

4.1 What is RCS, exactly

We snuck $\sigma$ into the radar equation as the "radar cross section." It deserves its own section.

The strict definition: $\sigma$ is the area of an isotropically scattering target that would produce the actual measured echo power. It is not the physical area of the target. For a perfect spherical scatterer, $\sigma$ equals the geometric cross-section. For a flat plate facing the radar, $\sigma$ can be vastly larger than the plate's area, because the plate concentrates the reflection back toward the radar like a mirror. For a stealth aircraft, $\sigma$ can be dramatically smaller than the plane's physical size, because the surfaces are designed to scatter the energy in any direction except back toward the radar.

Some typical RCS numbers, in m²:

These are nominal at X-band (8 to 12 GHz). RCS is frequency dependent, aspect dependent, polarization dependent, and a pretty messy function of the target's geometry.

4.2 RCS regimes by wavelength

When the target is much smaller than the wavelength, called the Rayleigh regime, RCS scales as $\sigma \propto f^4$ (or $1/\lambda^4$). This is the same physics that makes the sky blue: small particles scatter short-wavelength light strongly. A bird's wings, a few centimeters across, look very different to a 1-meter-wavelength UHF radar (almost transparent) than to a 3-cm-wavelength X-band radar (a strong reflector).

When the target is comparable to the wavelength, the Mie regime, RCS oscillates wildly with frequency due to interference between paths around the target. This is unpleasant for radar designers because the same target can have very different signatures at slightly different frequencies.

When the target is much larger than the wavelength, the optical regime, RCS approaches the geometric optics result. A flat plate of area $A$ has $\sigma_{flat} = 4\pi A^2/\lambda^2$, huge, because the plate acts as a directional mirror. This is why a corner reflector (three orthogonal flat plates) used as a navigation aid on a small fishing boat lights up like a battleship to a marine radar.

4.3 Geometric features that boost RCS

Some shapes are radar-loud beyond their size.

Flat surfaces normal to the beam. A square meter of flat metal staring straight at the radar has an RCS far larger than 1 m² because of specular reflection.

Corner reflectors. Three mutually perpendicular flat surfaces send any incoming ray back in the direction it came from. RCS of a corner reflector with side length $a$ at wavelength $\lambda$ is $\sigma = 12\pi a^4/\lambda^2$. A 30-cm-side trihedral at X-band has $\sigma \approx 1500$ m². Trihedrals are deliberately placed on lifeboats, on ice floes for satellite radar calibration, and on sea-buoys.

Cavities and reentrant geometry. Open jet engine intakes, exposed antennas, and any cavity that bounces the radar wave around inside before letting it out tend to be radar-loud. A modern stealth aircraft hides its engine intakes behind ducted bends so the radar wave never sees the spinning compressor blades directly; the blades are otherwise rotating corner reflectors.

4.4 Stealth: the engineering of small RCS

The two primary techniques.

Shape. Faceted surfaces, designed so that no facet is normal to a likely radar look angle, scatter most of the incident energy in directions other than back to the source. The Lockheed F-117, the first operational stealth aircraft, was famously faceted because in 1975 nobody could yet compute the RCS of curved surfaces from Maxwell's equations on the available computers; the engineers used a code called ECHO 1 that only handled flat plates. The F-117 looked like an angular black diamond. Curved-surface stealth aircraft, like the B-2 and the F-22, came later when computational electromagnetics caught up.

Radar absorbing materials (RAM). Coatings and bulk materials that absorb incident radio energy and convert it to heat. The classic recipe is iron-ferrite particles dispersed in a polymer matrix, tuned to the target wavelength. Multilayer absorbers ("Salisbury screens" and "Jaumann absorbers") stack quarter-wavelength dielectrics to broadband-cancel reflection. The B-2 has a coating tens of microns thick over its entire surface; it has to be reapplied periodically and cannot get wet during certain phases of maintenance.

A stealth aircraft is not invisible. It has reduced RCS over the operating frequencies of its likely opponents. Long-wavelength radars (VHF and HF) tend to defeat shape-based stealth because the wavelength is so much larger than the surface features that the optical-regime mirror tricks fail; this is one reason Russia and China invested in long-wavelength counter-stealth radars. Multistatic and bistatic radars (multiple receivers separated from the transmitter) also help, because shape-based stealth is optimized for monostatic geometry.

Hardware-security tie-in. Stealth is fundamentally a side-channel reduction technique: the aircraft is the secret, the radar return is the leakage, and shaping plus RAM are the countermeasures. The same intellectual move appears in chip-level countermeasures against differential power analysis: "current-balanced" logic styles try to make 0-to-1 and 1-to-0 transitions look indistinguishable in the power trace, the same way stealth tries to make a fighter look indistinguishable from background clutter. The mathematics is dual.