There are many factors that play a role regarding this issue so it is not easy to give a definite answer.
It is right to assess the daily energy usage first:
- Engel fridge about 25 Ah/d
- light about 5 Ah/d
This is a total of 30 Ah/d, without laptop and radio.
If you would only use the charging through the alternator every 4 days the size of the battery would have to be about a total of 4 d * 30 Ah/d = 120 Ah * 2 = 240 Ah.
The reason to double the size is that you could use typically only about half the capacity of a deep cycle battery. The battery shouldn't be discharged below 20 % state-of-charge and you typically can charge it with the alternator and standard regulator only to about 80 % with typical driving times. The extra 10 % headroom is compensation for an aging battery. So the system should be sized that you typically use only about 50 % of the installed battery capacity.
So if you are not able to install such a high capacity you can improve the situation by the following steps:
Improve alternator charging
The problem with alternator charging is that with very long wire runs the voltage drop is so high that the charge voltage is not high enough to get significant energy into the battery. The first step is to use thicker wires and better connectors. Doubling the wire thickness will half the voltage drop.
But this will still not be enough because the the typical alternator regulator doesn't have a charge voltage that is required to charge deep cylce batterys. The charge voltage at AGM/GEL deep cycle batteries should be about 14.3-14.4 V at 20° C, regulators use only about 14.0 V. For flooded batteries the charge voltage must be even higher to recharge batteries with a few hours of drive. So what you need is a regulator which higher charge voltage. But that is not so easys because you also have your starter battery of your vehicle and this still has to have the same charge voltage as before.
There are two solutions:
- You can either use a high voltage regulator and a split diode with voltage drop at the starter battery connector.
- Or you can use a voltage booster or DC/DC charger.
I prefer the second solution because you don't have to change anything in the vehicles electrical system. You just connect a device like the
Sterling Battery-to-Battery Charger to your vehicles starter battery and the battery in the trailer and everything is fine. Of course, you should upgrade the wire path so that it can sustain the amperage.
This all will shorten the charging time considerably. You should be able to recharge your battery within a few hours of time to nearly 100 %. This gives you an extra of about 20 % usable battery capacity. So you probably can reduce installed capacity to about 170 Ah.
Additional source: solar panel
Depending on weather, time of year and the area you are, the amount of energy you can collect by using a solar panel varies heavily. So there is really no easy answer to the question how large a panel should be. The other point is that you may not be able or may not wish to place your vehicle in the sun because it is just to hot there. Just think about placing your trailer with the Engel in the sun. As the environmental temperature rises the Engel uses more and more power. This may not be compensated by the higher energy production of the panel. So I think that a kind of removable panel may be of advantage. This way you can the panel into the sun and the trailer can stay in the shade.
Regarding the size of the panel there is a rule of dumb:
In summer in an area in the mid you get about 300 Wh/d per 100 W installed power on average. If you go south it goes up to about 400-500/d Wh, if you go north it drops to about 200 Wh/d. In winter this values drop considerably, especially in the north. You can improve the situation considerably, especially in the northern areas, if you track the sun. This would be a further advantage for a removable/movable panel.
So if we take the average of 300 Wh/d then a 100 W panel delivers about 25 Ah/d. So the effective daily use of battery capacity in the above example would drop to about 5 Ah. Of course, this doesn't mean that you can now reduce the battery capacity to 5 Ah/d * 4 * 2 = 40 Ah. You have to have some reserve for days with bad weather and you have to size everything for the worst case regarding the season and area you would like to camp. And you may also reduce the size of the solar panel to reduce cost. Battery capacity may be cheaper than the necessary solar wattage to compensate.
So take some numbers and run a calculation. Look at the costs for the battery and solar panel and find a combination that is comfortable to you. And please, give some extra reserve. I.e., the lifetime of the battery increases considerably if it is not discharged that deep.
Additional source: generator
A generator is very convinient because it delivers power as you need it. The generator itself and the fuel is cheap.
But it also has the disadvantage that it makes annoying noise and bad smell. Even if you don't bother, others staying in the same area may have a problem with it. It is also some kind of paradox that on one side someone seeks out for nice places in wonderful nature, with all kind of natural noises and smells, an on the other side than runs a noise and stinking generator just to recharge the battery. I always would try to find a solution that is less disturbing even if it costs a bit more. I would use the generator only in real emergency.
BTW, I run the high power and high energy electrical system in my truck only with the alternator. As I indent to be mainly in northern areas I have no solar panels installed. I have only a cheap small generator for emergency if something failes.