[Petrochemicals (OP)]

Stealth technology is coming apace, the banded buzzword phrase is "radar cross section". Claims of RCS being the size of a mobile phone, 25 cent piece or ball-bearing being very well, but how does this relate to actual detection. If someone throws a phone at you, you are likely to detect it.

How does apparent size at distance affect radar detection, for example if I throw a ball bearing into the sky 5km from a radar station is it going to be detected?

[alancalverd]

The return signal strength decreases with the inverse square of the total path distance (i.e. there and back). I doubt that you could distinguish a ball bearing from all the other noise and targets at 5 km without some very sophisticated moving target discrimination, and even that tends to depend on the target moving in one direction and very quickly - a tiny ballistic blob (a sphere is not a good reflector) at 5 km wouldn't show against clutter on most traffic control radars and probably wouldn't interest any military systems.

[vhfpmr]

The return signal strength decreases with the inverse square of the total path distance

Fourth power. Square law on the way out, and again on the way back.

If the target's smaller than the wavelength of the signal, the reflection strength also increases with the fourth power of the frequency, which is why radar systems prefer high frequency.

[Bored chemist]

If the target's smaller than the wavelength of the signal, the reflection strength also increases with the fourth power of the frequency, which is why radar systems prefer high frequency.

How does that work?
Where does the rest of the return signal go if you use a longer wavelength?

[evan_au]

Fourth power.

That extreme signal loss is further hampered by the fact that high frequencies travel in straight lines through the atmosphere, so low-flying planes or missiles are hidden by the curvature of the Earth. This is also not helped by that any rain absorbs high frequencies.

Commercial radar systems overcome this loss by mandating a transponder on commercial planes. When the transponder detects a specific signal from the radar (reduced by the inverse square law), they transmit a signal back to the radar (which is also attenuated by the inverse square law), so they don't suffer from an inverse-fourth law.
However, military radars cannot assume that an attacking force would be so helpful as to leave their transponders turned on, so they need extremely high power.

Australia, with a very long coastline, has deployed an "Over the Horizon" radar system which operates at much lower frequencies than modern radars, and can bounce off the ionosphere. It would be best for detecting large objects like ships, but with frequencies up to 30MHz, can also detect light aircraft.
https://en.wikipedia.org/wiki/Jindalee_Operational_Radar_Network

[alancalverd]

Yep, 4th power, of course. Brain in neutral. Hence very high transmitter power (megawatts) and a carefully shaped chirp pulse to squeeze that power into the narrowest possible spectrum, followed by a very tightly tuned and gated receiver to detect the picowatts of return signal against background noise. Plus some cunning circuitry to stop transmitter energy entering the receiver!

[evan_au]

Where does the rest of the return signal go if you use a longer wavelength?

Waves (including radar pulses, in this case) tend to go "around" objects that are smaller than half a wavelength - they just keep on going rather than being returned.
- A very small fraction does get returned (vhfpmr describes it as having a 4th power, but I've not seen that written anywhere else...)

Stealth planes use a couple of other tricks to avoid detection:
- The plane is shaped so that most of the reflected energy is returned in a different direction than towards the radar transmitter (it helps if you know the direction of the radars monitoring the area, so you can plan a course that avoids reflecting back to them)
- The plane has coatings that absorb radar energy, rather than reflect it. These absorbent materials are concentrated around the areas most likely to cause significant reflections, like engine intakes and sharp edges.

[Bored chemist]

The other advantage to short wavelengths is that you can use smaller dishes (or lenses- though that's unusual) for the same angular resolution.

Waves (including radar pulses, in this case) tend to go "around" objects that are smaller than half a wavelength - they just keep on going rather than being returned.

Sorry. I'd misread the post as saying the reflectance was frequency depended for sort wavelengths.

Once you have a wavelength  that's a fair bit smaller than the target, the wavelength doesn't directly affect the return signal strength.
So, unless  you are looking at drones or such, any wavelength les than a metre or so will be equivalent.
And they have been using much shorter wavelengths than that since WWII, so the effect is no longer driving any developments towards shorter wavelengths.

The idea of an array of small drones is interesting- in principle, you can use an array of them to cancel out reflections much like anti-reflection coatings on a lens.