but might 36v from a pair of panels damage the actuator circuitry?
So here's the deal. Lead-acid batteries look electrically like a voltage source/sink with a small series resistance, with the voltage level a function of state of charge. 2V/cell (there are 6 cells in series in a 12V battery) is nominal, and if I remember right, their open circuit voltage is something like 1.9V empty, 2.1V full. That covers 90% of their behavior.
Considering that, the "1W@18V" spec of the solar panel isn't going to be able to "win" against the battery, and the solar panel's voltage will be pulled down to battery voltage, delivering probably 0.055A (=1W/18V) at whatever the battery voltage is.
When a battery gets completely full, however, its series resistance goes up dramatically, and the voltage goes up, until there's enough voltage to start electrolysis of the fluid and you get H2 and O2 generation at the terminals and loss of the electrolyte. A lead-acid battery, depending on the type + manufacturer, has a certain recombination rate of H2 + O2 => electrolyte that it can handle; if you electrolyze at a higher current than that, it leads to permanent electrolyte loss (+hence capacity loss)
So there is a safe current that can be delivered to a lead-acid battery continuously, where its own self discharge due to electrolysis balances the charging current. It depends on the manufacture + construction. I wouldn't feel worried about a C/10 or C/20 rate of charge (where C = the current needed to discharge a battery in 1 hour). Garage door batteries are probably > 1Ah capacity so you should be safe with 55mA charging current.
HOWEVER -- I would probably put a (zener diode and resistor in series) in parallel with each battery, the zener diode being about 14V and resistor being maybe 10 ohms or so, so that it keeps the battery terminals from getting charged too far.
Also: if you can, wire each solar panel to each battery (and keep the diodes), rather than the pair of panels in series wired to the batteries in series -- i.e. try to connect the center taps. By doing so, you'll charge each battery independently. Otherwise, what can ruin battery life is if the battery voltages diverge -- the one with the higher voltage will tend to get overcharged, while the other one will tend to get overdischarged and not completely charged.
The car charger is most likely a small switched mode power supply.
This should be fine running from any voltage (assuming a 5v output) of say 7v up to 50v+ (check the chip to be sure of the upper limit).
I am currently working with the MAX5035 family of chips which run from 7.5VDC (or 15VDC for the 12V version) up to 74VDC to give 3.3V, 5V or 12V.
Best Answer
Inverter efficiencies are typically horrible. If you run the inverter at maximum power output, the efficiency is typically poor (95%) but of course you almost never run at full power, so the efficiency is horrible (75%), and sometimes you only take a trickle of power, so the efficiency is 0 to 50%.
If the system is correctly sized and designed for efficiency, then 95% transfer efficiency is achievable.
Any inversion has similar losses. DC/AC then AC/DC loses efficiency, but it's only twice as bad as a single DC/DC converter, so in a well designed matched system you're only losing an extra 5%.
The efficiency you get will depend on the design of the systems you use. Typical solar inverter systems are designed to maximize the utility to the home owner, that is how useful the system is. If you are willing to accept a system that is designed with only one thought in mind -- using the minimum number of solar panels -- then you can certainly buy a system that is more efficient. (The systems I work on are better than 1%)
Now that panel prices have dropped, it is almost always cheaper to buy more panels.
Having said that, if your purpose is to charge a car, not sell power, then it is reasonable to look around and see what kind of systems you can buy. A correctly matched DC/DC system will be more efficient than a standard (one size fits all) solar inverter system.