I'm not clear on you battery. 40AH SLA?
Being in a similar situation, I will say a small wind turbine certainly will help in the winter. If there are trees, it will not do much except in the winter.
It won't need to be much of a turbine. The small battery can only accept so much power, so fast. Even a 1A windmill will make quite a difference.
Here, in winter, there is no wind power for 4-7 days, then too much for 1-3 days. The 1 to 3 days will bring the battery voltage up higher than it should be, even with a relatively small or tiny windmill.
I often bring my windmill in the house after the battery is full. Really. LOL. Keeps kids from messing with it.
I would recommend a HAWT to start with. There are not many successful low speed VAWTs. A windmill close to the house has less turbulence than many people would think. My best overall spot is 2 meters out from the corner of the house, so it can catch almost clean wind from most directions.
Might Google search the board (top right) for "box fan" to get started with some ideas. And their blades work fairly OK, and they are quiet.
"Fungus" has chronicled a tiny simple stepper windmill making a 1/2A. My luck isn't that good. But a half amp will do quite a bit for a small system.
G-