My first thought was, if you are not prepared to leave a harbour in thick fog with radar why have you got radar in the first place?
I guess we all have to learn to trust our instruments, it is true that they break down, but in 14 years of radar usage the only time mine has broken is when the mast has been stepped (grrrr).
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I wonder what the skippers of the Thames Sailing Barges (Engineless, no radio, no radar, no plotters, no GPS, no Sea Me) would have made of this thread.
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Well according to Jim Uglow's book they didn't go out if the wind was set against them or if it was foggy and they still died a lot.
Have no radar but using my shallow draft I have coasted from one harbour to the next in 200yds vis by keeping the shoreline in sight with the swell highlighting offlying rocks awash. Without the hand held GPS I'd have gone a lot slower if at all. If my insurance broker is reading this they didn't cover that trip.
I have left in fog repeatedly. Always with radar, which is also on in reduced visibility (less than 1 mile) to practise. I have crossed Hoek of Holland harbour entrance in 50m vis., along with others without radar. Now that would be scary!
I have sailed along Pierres Noires and Raz de Sein in F3 with 100m visibility, with the current going, SOG 12 kts. I wasn't skipper then did the navigation. We always passed within 15 metres of a buoy.
Would I do this without radar skippering my own boat? NEVER. I'd drop anchor in a safe location and wait or never leave harbour.