Second-Trace Echo or Close Target?
An X-band radar on 9410 MHz with a 4-foot slotted-waveguide antenna mounted 40 m above the water is operating in a coastal area where a strong surface duct has formed. In short-pulse mode the set uses a 2000 Hz PRF. The operator sees a steady, weak echo at 11.0 nm on a bearing of 045°. The vessel's AIS display shows a large ship on that same bearing at 51.5 nm, and one other AIS contact at 6 nm on a different bearing. Sea state is calm, the presentation is north-up relative motion, the range scale is 12 nm, and gain, STC and FTC settings are normal. Nothing is visible optically or on AIS at 11 nm.
1. Compute the maximum unambiguous range at this PRF and explain the 11.0 nm echo.
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Run-out distance between pulses: R(max) = c / (2 × PRF) = 3.0×10⁸ / (2 × 2000) = 75,000 m = 75 km ≈ 40.5 nm.
The AIS target at 51.5 nm is beyond that. Its echo returns during the second sweep, so it is painted at 51.5 − 40.5 = 11.0 nm - exactly where the phantom echo appears, on exactly the right bearing. That is a second-trace echo.
Sanity check on plausibility: geometric radar horizon ≈ 4.12(√h₁ + √h₂) km with heights in metres = 4.12(√40 + √30) ≈ 4.12(6.32 + 5.48) = 48.6 km ≈ 26 nm. A 51.5 nm detection should not be possible in a standard atmosphere - it is only visible because the surface duct is trapping the X-band energy and bending it around the horizon. The duct is what makes the second-trace echo possible at all, and it is also a warning that all ranges on the display are suspect.
At 2000 Hz the set is fine for a 12 nm scale in a normal atmosphere; the ambiguity only bites when propagation is anomalous.
2. The operator switches to a 3000 Hz PRF "to sharpen the close-range picture." What happens, and what is the rule of thumb for choosing PRF?
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At 3000 Hz: R(max) = 3.0×10⁸ / 6000 = 50 km ≈ 27 nm.
The 51.5 nm target now folds to 51.5 − 27 = 24.5 nm, a different false position than before - and a genuine 30 nm contact would appear at 3 nm, which is far more dangerous. The picture gets sharper close in and simultaneously more lying further out.
Rule of thumb: never rely on an echo beyond roughly 80 % of the unambiguous range, i.e. about 32 nm at 2000 Hz and 21 nm at 3000 Hz, and always know the PRF of the selected pulse length. High PRF buys pulse-packing and close-range discrimination at the cost of unambiguous range; long-range scales should use the low-PRF, long-pulse setting. The operator should also note that a second-trace echo keeps the correct bearing and repeats identically, so bearing comparison alone will not expose it.
3. How would you confirm the diagnosis, and what else would you tell the watchkeeper while the duct persists?
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Confirmation:
- Drop to the 1000 Hz (long-pulse) setting: R(max) = 150 km ≈ 81 nm, and the 51.5 nm target should jump to its true range.
- Compare with AIS range and bearing for that specific contact.
- Check whether the echo moves when PRF changes but not when range scale changes - a real target at 11 nm stays at 11 nm.
- Note echo strength: second-trace returns are weak (double the path loss) and may only paint with high gain.
Advice to the watchkeeper while the duct lasts:
- Treat long-range echoes with suspicion on every PRF; cross-check all contacts against AIS and visual.
- Ducting also produces false clutter and sea-return-like noise at long range, and can make close-range targets appear on unusual bearings due to anomalous height errors.
- Keep the radar on low PRF for offshore work, and do not change pulse length/PRF without re-evaluating what is on the screen.
- Log the condition - anomalous propagation is a normal, recurring weather phenomenon in that area, and the next watch will see it too.