The signal makes the trip twice — out to the target and back — so spreading loss applies twice, giving \(1/R^4\) instead of \(1/R^2\).
A measure of how much power a target scatters back, in square meters — but it is not physical size. It varies enormously with aspect (the direction the radar views the target from), shape, and coatings. The slides write it \(\sigma\); the equation sheet writes RCS.
\(P_R = P_T G^2 \sigma \lambda^2/[(4\pi)^3 R^4]\).
Because the same antenna both transmits and receives. The equation sheet prints it as \(G_T^2\).
\(R_{\max} = \sqrt[4]{P_T G^2 \sigma \lambda^2/[(4\pi)^3 P_{R,\min}]}\) — every term sits under a fourth root. \(P_{R,\min}\) is the radar's sensitivity, its minimum detectable signal.
Raise \(P_T\) by a factor of 16. That is the fourth root working against the designer.
Halves it. The target's lever is equally fourth-rooted — but it is one-time engineering rather than a continuing power bill, which is why stealth wins.
\((1/100)^{1/4} = 0.316\), so range drops to about a third. Modest on paper, but the defended area scales as \(R^2\) and so shrinks tenfold.
The angle is the aspect — where the radar is, as seen from the aircraft, with 0° at the nose and 180° at the tail. The radius is \(\sigma\) in square meters.
The low RCS level the target shows at every aspect between the narrow spikes. Use the fuzzball value unless the problem names an aspect that falls on a spike.
How far below the aircraft's horizon the radar sits, looking up at it. A plot is drawn for one frequency band and one depression angle, so pick the plot that matches the problem.
The RWR is a one-way problem (\(1/R^2\)); the radar is two-way (\(1/R^4\)). Which one detects first depends on the two sensitivities and on \(\sigma\) — compute both ranges.
Friis solved for \(R\), with the radar as the transmitter: \(R = \frac{\lambda}{4\pi}\sqrt{P_T G\,G_R/P_{R,\min}}\), using the RWR's own antenna gain \(G_R\) and sensitivity.
Because the radar has to transmit to do its job. Transmitting is what gives you away — the foundation of electronic support.