The important part of the long answer is the charge controller - those batteries cost way too much to cook them out. And the controller maker will specify how much voltage your panels need to supply (more than 24 certainly) to provide a charge for several hours a day so you aren't wasting money on something that actually does very little.

I also hope you have a very secure location to store this rig at work because while a bike with a tow trailer is easy to disguise and awkward to move, as soon as you put a solar panel on it, it becomes a very obvious theft target and maybe a vandalism target. And since you want to charge at work, it has to be outside. And since for effective use the panel has to mostly face the sun but you don't want to drag it broadside through the air while riding, you will have to either work out a pivoting mount or angle the whole trailer to the general position of the sun when parked and have the panel flat on top. I personally would probably redesign so that at work the trailer pulled up along side the bike and was chained/locked to it to make a really awkward mass that had the panel bolted through the lid with blind bolts.

Yes, you have it right you need two 12V panels wired in series to give 24V to charge a 24 volt system.

But along with the 24V you also want some amperage, otherwise it takes forever to charge. Most of the little chargers are called trickle charges because they only have an amp or two.

If you had two 25 watt solar panels putting out 24V you have :

watts = volts * amps

50 watt = 24V * x amps

x = 2 amps

If your battery is say 50 amp hours of storage, then if you are putting in 2 amps it will take you 25 hours of sunlight to power it back up from a dead battery.

So the charge time depends on how many amps you are putting in there at 24V

A car battery charger typically charges at 10 amps at 12V, so 12 * 10 = 120 watts of power going in there

So if you go solar make sure to use a charge controller and a big enough panel to get close to 100 watts for any decent recharge time. The charge controller makes sure that the battery only gets voltage going one way and it least 24V. So if the sun went behind some clouds and the voltage dropped to 20V, the controller shuts off the current until the voltage equals 24V or more

A solar panel to charge a 12V battery has 36 cells in series. This allows for temperature of the panel up to 60°C, and the maximum required charge voltage. For a 24V battery, 2 panels in series. A 24V battery requires around 28-29V, but look up your battery data sheet to be certain. A specialized converter using electronics could charge a 24V battery with a 12V panel.

The system voltage is controlled by the battery unless the battery is faulty. The 2 panels in series could be 42 volts no load, but the battery pulls this down to whatever is required by the battery. This is because the panels are a current source, the current is determined by illumination, and attempts to draw more result in reduced voltage. Even a short circuited panel delivers approx. the same current with no voltage. The battery voltage varies from around 20V (really flat) to around 28V (really charged).

A 30W panel is around 1.75A, considering the optimum panel voltage for power is around 17V for 36 cells. This is small compared with what you are using. The battery wastes about 30% of the power, in chemical conversions. The time to charge it is 14h at the 10h rate, which is Ah/10. (i.e. ampere hours)

You did not give the AH rate from your 24V battery pack,therefore , unable to suggest a correct current rate solar panel. The solar panel open voltage rate at least 30V to charge a 24V cell. No harm to controller since the charging current is so small even bike is in running condition.

Charging voltage = 2*13.8 = 27.6V

Current regulated to AH rating divided by 10

Charging time = 10 hours

I have an electric bicycle that I travel to work by, pulling a modified child carrying trailer that holds two 12 volt deep cycle batteries in series to power the 24 volt bike motor. I'm thinking about adding a 50 watt solar panel (or larger depending on the room I can make available) to charge while I'm at work and to provide some extra juice while on my more distant travels.

Can I get a solar panel to charge them while they're connected the way they are: in series? Does charging work that way?

I've read that in order to charge the 24 volt battery setup (if the answer to the Q above is yes), the output from my solar panel would need to be a little more than 24 volts. Is this true? If so, how many volts?

Since the bike is supposed to be powered at 24 volts and I have an x-volt (x > 24v) solar panel connected to it, will this cause any damage to the controller or other components while running them?

Will it help supply power even while the motor is being run?

Thanks.