Primary radar, range and resolution

What does a primary radar need from the aircraft?

An echo can be detected without a cooperative transponder.

Echo timing

Primary radar transmits energy and receives a reflected portion. The round-trip delay gives slant range: R = cΔt/2. Antenna direction provides bearing information. The target need not transmit a coded reply, but its reflecting properties, aspect, distance and screening affect whether the echo can be detected.

A 200 microsecond round-trip delay corresponds to about 29.98 km or 16.19 NM. A primary echo is not automatically an identified aircraft, and a two-dimensional surveillance radar does not obtain a complete altitude measurement from that echo alone.

Horizon and clutter

Terrain can screen a target, Earth curvature can put it below the beam, and returns from ground or weather can obscure it. Processing reduces unwanted echoes but has its own limitations. A missing primary target is not proof of empty airspace. The laboratory makes detection conditional rather than painting every geometric target as visible.

The same delay, a different interpretation

A primary radar receives an echo 200 microseconds after transmission. It computes about 29,979 m slant range. If the target is 25,000 m away horizontally and about 16,550 m above the radar, those components approximately satisfy the same slant range. The large synthetic altitude is chosen to make the geometry visible; a range measurement alone does not tell the radar which height is correct.

A target can also change its reflecting aspect during a turn, altering echo strength without a proportional change in distance. Reducing return strength in the experiment does not move the aircraft; selecting terrain masking removes detectability under the stated assumption. These independent changes explain why range, bearing, identity and detection confidence must not be compressed into a single claim that a target is “on radar”.

Why can two targets merge into one return?

Separate range resolution from angular resolution.

Two independent dimensions

For a simple uncompressed pulse, range resolution is approximately cτ/2, where τ is pulse duration. Shorter pulses separate closer targets in range. At 1 microsecond, the ideal range resolution is about 150 m. Real systems also use pulse compression and processing, so pulse duration alone is not a universal performance specification.

Angular separation depends on effective beamwidth and processing. A 1° beam spans about 0.87 NM at 50 NM range. Two targets at similar range inside that angular width can be hard to distinguish. Increasing range widens a fixed angular beam’s footprint.

Trade-offs and interpretation

Short pulse and narrow beam assumptions simplify the mechanism. Detection also depends on signal-to-noise ratio and target reflectivity; resolution is not the same as accuracy or probability of detection. The experiment reports the ideal separation threshold and labels merged targets instead of claiming an operational separation minimum.

Resolution, ambiguity and Doppler are different

For a simple pulse repetition frequency of 1,000 pulses per second, the interval between pulses is 1 ms. An echo that takes longer than this can be associated with the wrong pulse unless the system resolves the ambiguity. The simple unambiguous-range estimate is c/(2 PRF), about 149.9 km. This is separate from the 150 m ideal resolution of a 1 microsecond uncompressed pulse.

Doppler processing instead uses frequency change associated with radial motion. A target moving mainly across the line of sight can have little radial velocity despite high groundspeed. Different radar designs use these effects differently. Do not apply the simple pulse formula as a complete modern radar specification: coding, compression, coherent processing and ambiguity-resolution methods can change its useful performance.

Can you explain and apply the mechanism?

Four original questions. Work from the stated facts, then compare your reasoning with the explanation.