Hi: Im working on a project where I have a 4000 mAh lithium ion battery that I am trying to rig a solar trickle charger for.
You can trickle charge a lithium ion battery (in other words, charge it very slowly), but you must respect the voltage limits, and you must not charge it above 4.2 V. Safely charging lithium ion cells or batteries
always requires electronic charge control between the supply and the battery being charged. You cannot simply connect them to an unregulated power supply, solar or otherwise.
I was planning on using a cheapie USB solar charger intended for cell phone use, but when I wired it up, found that it was only putting out about 1.6v.
Then the charger appears to be broken. Cell phone chargers need to supply about 5 V so that the charging circuitry inside the phone can regulate it down. Are you putting it in bright enough sunlight?
(Note that if you are not charging a phone, you will need to provide your own charge control circuit that otherwise would be provided by the phone.)
Normally you charge these batteries at about 4.3v or so. What happens when you pump 1.6v into a 3.7v battery that normally charges at 4.3v?
You cannot "pump 1.6 V into a 3.7 V battery". This sentence is physically and grammatically in error.
Anything good? Anything particularly bad? If the latter, how does this charger manage to charge cell phones that nominally take 5v in?
The charger doesn't manage to charge any phones if it only generates 1.6 V. It is broken or it never worked.