I just purchased a used Trek 520. Probably a 2003 model. It rides great, but I noticed that when I am in the lowest gear (large chainring/smallest cog) and stop pedaling quickly, the top part of the chain will droop and slap the chainstay. It is very brief and hard to actually see well until the bike is being looked at on the stand.
I have checked the length, using the Park Tool easy calculation (L = 2 (C) + F/4 + R/4 + 1) and the Shimano method. With the Park calculation, it says the chain is two links short. When I use the other Park Tool Method (putting the chain on "big" and "big" and add two lengths, it says the chain is two links short.)
chainstay 17.75 f=52 r=34 My chain is 57 links
So, I put the bike horizontal and pedaled fast, then stopped quickly while putting tension on the derailleur with my finger and pushing towards the back of the bike. There was no chain droop or slap.
I am wondering if there should be more derailleur tension and if there is any adjustment that could be done, like adjusting the postition etc. Can more spring tension be put on the derailleur?
It is a Deore LX.
Tell me how I should think about this and what the next step might be.
Most likely this has nothing to do with chain tension or length. It's probably the freehub body hanging up a bit, causing the cogs to want to keep turning while you're coasting. This will cause the symptom you describe.
Take the wheel to a mechanic and have the hub overhauled, including servicing or replacing the freehub body.