If you stand twice as far from a lamp, four times less light falls on you. A radar echo has to travel that path twice — out to the target and back — and so becomes weaker very rapidly with distance.
In practiceThat is why the radar warning receiver (RWR) in a combat aircraft usually hears an enemy radar well before that radar can see the aircraft (Radar Warning Receiver (RWR)). The signal to the RWR only has to travel one way. The pilot therefore knows there is a radar before the radar knows there is an aircraft.
Energy leaving an antenna spreads out over an ever larger spherical surface. Because the area of a sphere grows with R², the power density decreases with the square of the distance — the inverse square law:
For radar it is worse. The signal has to travel out and back, and the target behaves like a new (weak) transmitter. On the way out 1/R² applies, on the way back another 1/R². The received echo power therefore decreases with the fourth power of the distance:
The consequences are far-reaching:
- Range is expensive: 2× more range requires 16× more power (or a correspondingly better antenna/receiver). That is why long-range radars are large and power-hungry.
- Detection range scales weakly with everything: Rmax ∝ ⁴√(Pt · G² · σ). Doubling the power yields only ~19% more range.
- The jammer has the advantage: the jamming signal only has to travel one way (1/R²), the radar echo out and back (1/R⁴). At long range the jammer therefore almost always beats the echo; only when the target comes closer than the burn-through range does the echo become stronger than the jamming.
A radar detects a target with an RCS of 10 m² at 200 km. The same target with stealth measures (RCS 0.001 m², a factor of 10,000 smaller) is only seen at 200 / ⁴√10,000 = 200 / 10 = 20 km.