There are two important things to know about charging lead acid batteries.
- There is very very deep and arcane* magic involved, without the knowledge of you are doomed to miserable failure. (*But not necessarily dark).
- The magic has been very well investigated over 100+ years and there are exponents of the deep and arcane arts willing to share with you most (not all) of the secrets. If you are serious about your quest you should avail yourself of their expertise. If not, just take the red pill.
If you read what the masters say and follow it, your battery's life, and maybe your own as well, will be a long and successful one.
If you fail to diligently study the advice of the masters then you may get lucky. But, probably not.
Below I point you to the beginnings of your lead-acid journey, but as I do so I'll note:
Starting with "A Car Battery" [tm] is not the ideal way to meet your objectives. While it is possible to make a car battery last much longer than it would have without suitable care, it will not last anywhere near as long as batteries made for the task that you have in mind.
Car batteries may tend to contain stuff like antimony - because it makes them more resistant to physical abuse. Batteries that wish to live long and prosper (but that are less worried about mechanical abuse) may contain calcium because eg of its effect on self discharge rate .
It is unlikely that you will buy an off the shelf charger that really does what you want unless the sales pitch/blurb specs spell out that it does what you want in some detail. Most chargers are liable to do the basic charging thing and may be designed to "float" the battery. Any thought of equalization / topping cycles et al are usually far from their minds, as sales rather than performance are a priority.
Good does not have to be horrendously expensive (but can be). But, incredibly cheap is also usually "cheap and cheerful".
Here is a superb starting place:
How Lead Acid Batteries Work by Constantin Von Wentzell.
Note that his interest is "Marine Batteries" for use in his boat. The usage patterns of his application differ from yours.
His: fast charge, deep, often daily discharges, float when charged versus,
Yours: long term float with occasional deep discharges.(). Despite this he has much to say that is useful and valid.
If you read outside this page you will see that he started his investigations due to very bad advice given by a person whose positions in the industry would lead you to expect his advice to be good. But it isn't. ie "appeal to authority" is risky. Accept that an expert should know much, but also use your brain and consult multiple experts.
This site was referred to by a stack exchange member today - I has not seen it before [This is such a good page that it is plagiarized in many other places to help vend ads. If you see it elsewhere be sure not to buy the products advertised.)
Follow the arrows and read. Once suitably informed have a look at the next level up. He has links there to a number of other good resources.
THEN
All battery roads lead to Battery University.
They don't know everything, & not everything they say is correct - but you may never notice the flaws! :-). A good site. ( They note: "Sponsored by Cadex batteries".)
You should glance at their top level Learn about batteries page to get a feel for the scope of the site, and then leap into.
Charging lead acid .
DO note the subject menu on the left side of the page.
From the above page:
Charge in a well-ventilated area. Hydrogen gas generated during charging is explosive.
Choose the appropriate charge program for flooded, gel and AGM batteries. Check manufacturer’s specifications on recommended voltage thresholds.
Charge lead acid batteries after each use to prevent sulfation. Do not store on low charge.
The plates of flooded batteries must always be fully submerged in electrolyte. Fill battery with distilled or de-ionized water to cover the plates if low. Tap water may be acceptable in some regions. Never add electrolyte.
Fill water level to designated level after charging.
Overfilling when the battery is empty can cause acid spillage.
Formation of gas bubbles in a flooded lead acid indicates that the battery is reaching full state-of-charge (hydrogen on negative plate and oxygen on positive plate).
Reduce float charge if the ambient temperature is higher than 29°C (85°F).
Do not allow a lead acid to freeze. An empty battery freezes sooner than one that is fully charged. Never charge a frozen battery.
Do not charge at temperatures above 49°C (120°F).
OR
You could just buy a charger that claims to do all the things that these and other pages say a charger should do. But, you'd know a lot less :-).
Example of A plagiarising ad server ripping off this sites copyright material. And again more plagiarism and yet again.
Better: A site acting as if it is a search engine and accumulating related sites to try and sell ads - actually useful - Performs a service and no copyright infringement.
Best Answer
Your dumb charger is just providing a slightly regulated voltage. It works due to the combined resistances of the charger and battery limiting the current. As the battery voltage gets close to the charger, the voltage potential is less. So with a fixed resistance, the current drops.
I doubt that you can modify your current charger to push 38 A up to 14.4 V. This could only happen if the combined resistances and voltage difference allow sufficient current flow.
Most likely you will need a higher voltage source and then circuitry to make a constant current source to provide a fixed amperage. Shutting it off can be done with a simple comparator circuit. Put a 10k trimmer pot across the battery voltage and run it into a comparator along with voltage from a zener regulator. Then you just adjust the voltage divider from the pot till it trips at the correct battery voltage. Use that to turn off a high current MOSFET or something similar. (Might use the same MOSFET to control the constant current.)