“Flying under the radar” is one of the few pieces of aviation slang that means exactly what it says. It is not a metaphor about avoiding attention. It is a statement about geometry, and the geometry is unforgiving in both directions.

Ask how far a military radar can see and you will get an answer in hundreds of kilometres. That answer is almost always wrong for the case that matters, because the number people quote is a power figure and the thing that usually stops a radar first is the curve of the Earth.

A radar set can be as powerful as you like. If the target is below the horizon, none of that power reaches it. And the horizon is much closer than most people expect.

The Earth gets in the way first

Radar is line-of-sight. A pulse leaves the antenna, travels in what is very nearly a straight line, hits something and comes back. The Earth, inconveniently, is not flat, so the straight line eventually leaves the surface behind and carries on into empty sky.

One complication makes it slightly better. The atmosphere is denser near the ground, and that density gradient bends a radio ray gently downward, so it follows the curve of the planet a little further than pure optics would allow. Rather than model the bending, engineers cheat elegantly: keep the ray straight and make the planet flatter. Recommendation ITU-R P.834-9 sets the standard effective Earth radius factor at k = 4/3 for heights below 1,000 metres, which turns a 6,371 km planet into an 8,495 km one.

Run the geometry on that inflated sphere and you get the rule of thumb every radar operator knows. The horizon distance in nautical miles is about 1.23 times the square root of the height in feet. Because both ends matter, you add the radar’s figure to the target’s: a radar at height H can see a target at height h out to roughly 1.23 times the sum of their square roots.

It is a rule of thumb and deserves to be called one. It assumes a standard atmosphere that the real one frequently ignores, it takes no account of terrain, and it says nothing about whether the return will be strong enough to detect once it gets there. What it does is set a hard ceiling. Beyond that line, transmitter power is irrelevant.

What the numbers actually look like

Put a ground radar antenna 100 feet up — a respectable mast — and point it at an aircraft flying at 100 feet. The sum is 1.23 times ten plus ten, which is about 25 nautical miles. Forty-six kilometres. At 500 knots, an aircraft crosses that from first possible detection to overhead in roughly three minutes.

Now let the same aircraft climb to 30,000 feet and change nothing else. The horizon becomes 1.23 times ten plus 173, which is about 225 nautical miles, or 417 km. The same radar, the same transmitter, the same everything: nine times the range, bought entirely with altitude.

That single comparison is the whole of low-level tactics. It is why strike packages went down to 200 feet in the Cold War, why the Panavia Tornado and the F-111 were built around terrain-following radar, and why the crews practised it obsessively. Descending is not about hiding in the noise. It is about physically putting the curvature of the Earth between yourself and the antenna.

Terrain makes it better still. The horizon formula assumes a smooth sphere; real ground has hills, ridges and valleys, and every one of them is an opaque wall to a radar beam. Flying a valley floor with a ridge between you and a known radar site is called terrain masking, and it is far more effective than the raw geometry suggests, because you are no longer waiting for the planet to curve — you have put a mountain in the way.

Which is why AWACS exists

If the horizon is set by height, and you cannot make the Earth flatter than 4/3, there is exactly one lever left: put the radar higher. Not on a taller mast — a mast tall enough to matter is not a mast, it is a mountain. Put it in an aeroplane.

Work the same arithmetic from 29,000 feet against a target at 100 feet and you get about 222 nautical miles, a little over 250 statute miles. The USAF fact sheet for the E-3 Sentry says the aircraft operates above 29,000 feet and that its radar detects low-flying targets at more than 250 miles. Those two numbers are not a coincidence. The quoted performance against a low target is, essentially, the radar horizon.

Saab’s GlobalEye makes the same argument in metric. The company publishes detection of low-flying threats beyond 400 km from a cruise around 35,000 feet. The horizon from 35,000 feet against a target at 100 feet works out near 450 km, so the advertised figure sits comfortably inside what the geometry permits rather than straining against it. Manufacturers of airborne early warning aircraft are, in effect, selling altitude.

There is a second problem that comes with looking down, and it is the one the Sentry’s fact sheet quietly boasts about solving: a radar pointed at the ground gets an enormous return from the ground. Separating a low-flying aircraft from that clutter took pulse-Doppler processing, which is a story in itself and one we have already told in how radar actually works. Geometry gets the beam to the target. Signal processing is what lets you believe the echo.

When the atmosphere misbehaves

The 4/3 factor is a standard, not a law. Real air departs from it constantly, and when it departs far enough the beam stops behaving.

ITU-R P.834-9 puts a number on the interesting case: when the vertical refractivity gradient at a given height falls below −157 N/km, the ray curves more sharply than the Earth does and becomes trapped in a duct. Warm air over a cool sea does this routinely. A radar caught in a duct can detect targets far past its nominal horizon, and can simultaneously go blind to targets above the duct that it would normally see easily.

Operators know this as anomalous propagation, and it is why a coastal radar occasionally paints shipping two hundred miles away on a summer evening and misses an aircraft at twenty. The geometry is not wrong; the atmosphere has temporarily changed the geometry.

The one radar that cheats

Everything above assumes the beam travels in a nearly straight line. There is a family of radars that refuses to accept this, and they look like nothing else in the business: over-the-horizon radar, which uses high frequencies and treats the ionosphere as a mirror.

Australia’s JORN does wide-area surveillance at ranges of 1,000 to 3,000 km, which is not an improvement on the radar horizon so much as a refusal to play by it. The price is severe: enormous antenna fields, coarse resolution, accuracy measured in kilometres rather than metres, and a dependence on ionospheric conditions that change with the time of day, the season and the solar cycle. It tells you something is out there. It does not give a fighter controller a firing solution.

The Soviet Union built the same idea at Chernobyl-2 and elsewhere, and the enormous Duga arrays are still standing. Shortwave listeners around the world knew the system by the repetitive tapping it put across the bands and nicknamed it the Russian Woodpecker, long before anybody in the West would say publicly what it was.

Why the phrase is literal

So the honest answer to “how far can radar detect an aircraft” is a question in return: how high is the aircraft, and how high is the antenna? Everything else — transmitter power, antenna gain, processing — only matters inside the line those two numbers draw.

That is why airborne early warning aircraft are among the most valuable assets any air force owns, and among the first things anyone plans to shoot at. It is why crews spent decades learning to fly at 200 feet in cloud and at night. And it is why “under the radar” is not a figure of speech at all. There is a line in the sky, it is drawn by the curve of the planet, and you can get beneath it.

Sources: Recommendation ITU-R P.834-9 on the effects of tropospheric refraction; the US Air Force E-3 Sentry fact sheet; Saab’s published GlobalEye figures; the Australian Defence Science and Technology Group on the Jindalee Operational Radar Network; Wikipedia (Radar horizon, Over-the-horizon radar).