Since you are asking about duration of power to run fan what you want is a way to compare and calculate power storage (battery), solar production (panel) and device draw in one common denominator. I would suggest amp hours.
- list devices that you will need to power.
- add how many amps they draw.
- estimate number of hours each device will be used per day.
- multiply amps time hours for each device to find amp hours.
The total of all those devices amp hours is how many amp hours you need each day to be off grid.
Look at battery amp hours ratings.
Deep cycle battery is storing the power, these batteries have a rating for amp hours. Roughly how many hours battery can deliver 1 amp. Not exact because actual load makes a difference (high load draws down faster) but a standard.
Say your battery has a 100 amp hour rating. You should not discharge it below 50% to avoid damage that will reduce battery life. So you have 50 amp hours you can use to run your devices.
amp hour output.
Solar panels are typically specified by watts BUT they also have an amp output. approx amp ratings for 100 watt might be 5.2 and a 50 watt might be 2.7 amp.
The panel amp output is equivalent to saying in full sun for one hour this panel will replace its rated amp output amp hours in the battery.
E.G 5.2 amp hours in the case of our example 100 watt panel.
Then as a ball park figure solar panel
will provide its full amps for 4 hrs. of the day and half the amp rating for 2 hrs. in the morning and evening.
So a 100 watt panel that produces 5.2 amps would roughly provide 4 hrs. x 5.2 and 4 hrs. x 2.6 amps so it would feed 31.2 amp hours back into the battery per day.
Ideal situation is solar that can provide enough amps to totally replace the amps you draw from the battery in a day, with a little surplus amp production. BUT even if your panel falls short of daily needs you can draw down the battery as long as you don't draw it below 50%.
E.G if you use 20 amp hours daily and your only able to add 10 amp hours from solar it would take 5 days for that deficit to equal 50 amp hour drop in battery charge.
You could camp for 5 days without plugging in if your battery was 100 amp hour battery and you had a 10 amp hour a day deficit. Even though your solar was "undersized" however you would have less wiggle room for overcast or rainy days when you could not get the 10 amps from you solar panel
Most devices will have an amp rating on them but it can be calculated from voltage (12) and watts of the device using ohms law to provide amps. Fantastic fan I think would be about .45 amps per hour so less than 5 amp hours in 10 hours of running.
Devices such as laptop that you charge from an AC inverter will draw more amps from battery than the laptop charger specifies due to the inverter having some inefficiency in the conversion from 12 volt DC of battery to 110 volt AC. Not enough to matter in general unless you are cutting it close in your capacity. Don't forget camera battery, mine the charger does not draw much but takes a long time to charge.
If you go with portable panel consider dimensions of location where you will store it in the camper or tow vehicle. One member (Carol) set up bungee cords to strap her panel to a closet wall out of the way, this of course means the panel had to fit in that location.