[Mack the Knife]

Yes, patience is the key. Fighting is normally suicidal (I don't even bother taking a snap-shot, as you do) and outrunning them is impossible. You only shoot yourself in the foot by trying to pick up some speed, as your engine noise becomes audible.

I'm still new to the game myself, so I'm not sure how well modeled some things are. For instance, if you hear depth charges going off behind you, you might be able to accelerate for 10-20 seconds because the noise of the explosions masks your engine noise (in fact, I think most hydrophone operators simply removed their headsets when depthcharges went over the side, because the noise of the explosions could damage their ears).

Also, ships have an area behind them, called their "baffles", in which their own engines render them deaf. It's a kind of blind spot. So when you hear a DD pass directly over you, you can accelerate for a few seconds (unless there are multiple ships around, of course, as the other ones might hear you).

Don't forget that while changing depth is useful to avoid depth charges, it can make noise as the pressure on your hull eases or increases (known as "hull popping" - that groaning sound you hear when you're diving and surfacing).

Zig-zag, accelerate in short bursts when you can, and wait. And wait. And wait. Prayer is optional.