So your 40kw outboard
drives you at 20km/h and you 1/2 kw motor drives you at 7km/h- amazing.
My home solar system is 5kw and makes an average of 20kw perday. On the hottest day (>38 degrees C) it makes 30 kw.
You need 1kh per hour for say 5 hours. Your battery will give you at best 2.4 kw because lead acids drop below cut out voltage when half charged and there is a risk of damaging the battery if you try to drain more.
You need 2.6kw to be generated in the 5 hours that you are trolling. Given typical weather
conditions etc this might mean that you might need more than a 1kw solar system to guarantee that you always have enough charge when you need it. You must generate the charge as you are trollin; any charging
before or after trolling is merely topping up the batteries
for the next time. This assumes that it is a perfectly sunny day, no, clouds, the panels
pointing in exactly the right direction at all times and no shading by sails
etc. Even so I don't think that this might be enough.
There is no such thing as a calm day. When you then put your dinghy
in a 5 km/h heading breeze your 500w will be largely consumed countering this and so you will need to use more energy and so generate more power. If the tide is running against you, then more energy (if it's running with you, less) . If I am on open waters and floating, my GPS
says I'm doing 1-2 knots on a "calm" day. That's current
and breeze so light that you don't notice and not necessarily taking you in the direction you want to go.
I would suggest that you do some detailed calculations on the cost/benefits of your project
. We did this for the home system and found that the cost of batteries
was greater than the savings made. This is not including the cost of panels
and the risk of damage to them. Electricity storage
has a very long way to go.