Generally speaking evry ship has a detection range, that depends on the weather conditions and the crew status (green, average elite etc). In GWX if you pass anything between 5-10Km from a DD (without radar) in a night and at decks awash there is no way you can be detected. That way you can actually sneak inside the convoy and position your boat whenever you want. The visibility of your crew and the enemy's depends heavily on the weather conditions, but as a rule of thumb you can see at least a couple of Kms further than they can, as your siluette in the sea is too small.
Fog conditions are a bit more tricky. Usually heavy fog means visibility of about 300-500m, which means that as soon as you see them they see you. Medium fog is about 1-2Km (at night) so you're still slightly into the darger zone. In those conditions you have to be ready to submerge as soon as possible (plus under water you have better 'visibility' due to the hydrophones)
Light Fog is almost like no fog so as long as you keep within the 5-8Km distance you're OK. In clear nights you can still follow the same pattern but you have to be a bit more careful as your wakes are more visible.
Another issue you have to be careful with is your speed. If you travel at high speed (10 knts and above) you raise quite a bit of wake and you make a lot of noise, so you can actually be picked up by the escorts before they have visual contact with you.
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