I am designing a model airplane that flies using solar cells on its wings. I have a 7.4 V, 2200 mAh battery I want to use for it in case it flies in a cloudy area and needs more power, but everywhere I look you need to use an expensive, bulky charger to charge it.
This is probably pretty basic but how can I charge it with a current from solar cells?
You need a proper charger to charge Li-po batteries safely, using the right algorithm; "just using a current" won't do and could damage the batteries.
For your purpose, you need a solar charge controller to match the solar panel to the battery, preferably an MPPT charger.
Such a charger doesn't have to be bulky. There are dedicated ICs and modules for exactly this purpose, like the LT3652 and the LTM8062; Adafruit has a ready-made one.
You can google around for other (pseudo-)MPPT solar battery charger ICs and modules that fit your specifications. You can make a charger with one of those that ticks all the boxes of a safe solar charger, but is still very small and light. It will also be fancy, but that can't be helped.
You should also add a cell-balancing BMS to your 2S battery pack, if it doesn't already have one. This also can be small and light.
If you can keep the voltage of each cell individually to less than or equal 4.1V (4.0V safer still) then you can charge with current from solar panels.
If solar panel max current into battery is never less than manufacturer's maximum charge current then you do not need a current limiter.
You could charge the 2S 7.4V battery directly from the solar cells BUT each cell must have a maximum voltage limiter.
HOWEVER using a "proper" LiIon charger need not be expensive or complicated or bulky. To design correctly you need to know the parameters that I mentioned in a comment. If you don't know these then even a 'simple' solution is undesignable.
Panel specification
Battery specification
Motor specification
With lithiums you need a battery management system. No other choice. If you don't want a BMS, use nickel metal hydride.
A BMS is a Battery Management System - it protects the battery from conditions which would damage it or set it on fire. However it is not burdensome, heavy or costly - it just requires a little knowledge you haven't acquired YET.
Look at any of the Youtube videos where people home-build lithium "power stations" out of piles of 18650 batteries. The BMS and balancer are the smallest parts. Cheapest too.
And here's Big Clive talking about basic 1-cell BMS's bought dirt cheap off eBay, and pointing out there's no earthly reason to dangerously hotshot them straight a supply such as a USB cord.
You certainly should buy a ready-made BMS and balancer, as you're in it to do your project... not re-invent the wheel.
Once you have the BMS in place to keep the battery from catching fire... I'm not overly concerned with the quality of your solar charge controller. Is the additional power possible with an proper charge controller (or better: MPPT) worth the weight? I leave such design decisions to you.
Short answer: It cannot be done safely or without damaging the battery. Why? because batteries have to go through a charge cycle with a constant current and then a constant voltage. This means you need a charger with a controller.
A solar cell cannot output a constant voltage on its own, this means a solar charge controller is needed.
The other problem is if you want to charge the battery fast, you will need to have a power supply that can source adequate current.
If you really want to charge a battery from solar cells you can look for a solar charge controller that is compatible with lithium ion batteries (and probably a 2S) configuration.
No you don't need a dedicated charger, but if you don't use one you will essentially have to build your own. A lipo charger needs to do the following things:
Limit the charge current to some value. Usually 1C, but for some batteries it can be up to 5C.
Limit the voltage to 4.2V per cell.
Manage each cell individually. It's not ok for instance to have one cell at 4.3V and the other at 4.1, even though the total is fine.
Here's an example of how you might do it (forgoing MPPT on the solar panels for simplicity):
Be careful, overcharging a lipo is a sure way to start a fire.
You need circuit for limiting current and voltage. It is not too large, massive and expensive. https://aliexpress.ru/wholesale?catId=0&initiative_id=SB_20221025042011&SearchText=lipo+charger+module&spm=a2g0o.productlist.1000002.0
Voltage of your battery 7.4 V. It means, you have serial connected cells. You need module for balancing voltage for avoiding exceeding maximum voltage on the individual cell.
You need BMS for two cells in series ( 2S ) and charger module.
