to what voltage can a Lead Acid battery be discharged without damaging it ?
A fully charged battery has 14.2 Volts
how can we achieve that with 13.8 volts of charging voltage ?
Full lead acid (6 cells) have 12,72V-12,73V at 25C, measured 24h after charging. This value is for good new batteries.
Voltage of 14,2V can be used for charging in starting phase of charging, considering that battery is empty and need charging. If you supply 14,2V to full battery you can do lots of bad things for battery.
For my thinking based on my expirience, best lead acid charger is float charge 13,5V-13,8V (depence from ambient temp) with current control up to C/10.
Its possible to charge fully lead acid 12V from 12V source, I use this several times and works nice, I charge battery from another battery, but this is not good concept for your needs, you need real nice charger. That circuit used charge pump and is very simple with few parts with efficiency of 80%. Using this you can recharge some battery of some dislocated and isolated alarm solar system just with carrying one fully charged lead acid battery.
See this :
Please, do not get me wrong I just post this to show this is possible. Better make some nice regular charger with uC control. If you need circuit just say.
You can make simple and good charger with nice and reliable linear adjustable voltage regulator LM338K 5A limiting current. Just get 18V trafo, also not wrong 22V or 24V, because regulator can achieve full dissipation and full current of 5A with 10V differences Vo-Vi (24V-13,8V=10,2V). Of course good heatsink is needed, use one from PC CPU heatsink (Athlon, Duron) together with cooler. Or you can use LM350 for 3A or LM317 for 1,5A. You can add to this some LCD panel with charging data, like voltage, amperage, delivered ampere/hour, and resistance of circuit (good to monitor internal resistance of lead acid battery):
to what voltage can a Lead Acid battery be discharged without damaging it ?
OCV (Open Connected Voltage) for starter lead acid batteries lower voltage level is 11,7V-11,9V for 6 cells together or 1,95V per cell. Voltage at load when fully discharged 10,5V. If you measure OCV 10,5V you kill your battery like rabbit.
When you deeply discharge your battery (300-500 times starter in best way - best manufacturer declaration!) starting charging current in first phase should be C/20. Starter lead acid is not designed to cycling its float batteries designed for discharging for max 30-40%.
Deep cycle lead acid battery is different story for all aspects, charging, discharging, cycling, voltage levels, pricing,....