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Re: Forces on a dockline while docking....
I think you might be over-thinking this. And I'm too lazy to do any math right now.
1st...I don't know why you need throttle at all when the wind is astern. I'd be in neutral with just enough way on to steer. ( approach a dock at the speed you're willing to hit it). Sounds like you do that already.
As for your neighbor: Suppose you missed his line handoff...or worse got your finger caught against the cleat. what does he do when you're not there?
Once you pick up your line, you can then put it in gear (idle) and it should tuck you into the finger dock and hold you there while you attach your other lines. Your normal docklines should be able to manage this nicely if they are properly sized to begin with. I'm sure they are ;-)